SDC) surface can be divided into four categories: random scattering, aggregation, multiple deformations and flow slipping. Sprayed droplets with diameters of 0.56 mm and 0.8 mm exhibit more frequent random scattering than do other droplets. However, this behaviour is unfavourable for cooling the dairy cow body. By analysing the dimensionless parameter B, we find that sprayed droplets with a diameter of 1.1 mm, which have a higher frequency of aggregation, is not conducive for cooling the dairy cow body. However, multiple deformations can contribute to the cooling process of a SDC. By analysing the relationship between We and γ, we can find the range of We and γ in which the behaviour of random scattering and multiple deformations may appear more frequently. The results show that sprayed droplets with diameters of 0.8 mm–1.0 mm exhibit multiple deformations more frequently, which is beneficial for the cooling process of a SDC.Exploring the behaviour of sprayed water droplets on dairy cow hair during the spraying process is of great significance to improve the effects of this process on cooling a dairy cow’s body. In this paper, we use a high-speed camera to examine the sprayed droplets of different diameters and then analyse the experimental results. The results show that the movements of sprayed droplets on the simulated dairy cow ( The mechanism of spray cooling is the heat evaporation of droplets on the cow surface. During the evaporation process, the droplets must exhibit certain movement phenomena. Through analysis, we can obtain the relationship between the droplets’ movement and their sizes and then study the movement characteristics of sprayed droplets and the mechanism of spray evaporation.Spray cooling is an important method for alleviating the heat stress of dairy cows7. Researchers have studied the spreading movement of a single droplet through experimental phenomena and numerical simulations10. Rioboo11et al. studied the relationship between the spreading regulation and the droplet size, striking velocity, and wall material when droplets hit different dry solid walls by an experimental method. Shen12 pointed out the contact time of impact water droplets on superhydrophobic surfaces directly reflects the extent of thermal and energy conversions between the water droplet and the surface. Yahua Liu13 show how superhydrophobic surfaces patterned with lattices of submillimetre-scale posts decorated with nano-textures can generate a counter-intuitive bouncing regime. Gauthier Anaïs14 propose a quantitative analysis of the reduction of contact time and thus to understand how and why macrotextures can control the dynamical properties of bouncing drops. Patricia15 found that variations in temperature do not influence the wettability and mobility of the water droplets. Patricia found that variations in temperature do not influence the wettability. There’s a complete bouncing when a droplet impacting on a superhydrophobic surface, and the impacting process usually consists of spreading and retracting stages16. Negeed17 used high-speed camera record droplet behavior in collision with hot surfaces, and used empirical relationships described the characteristics of droplets impinging on heated hydrophilic surfaces. Haibao Hu18et al. also used a high-speed camera to study the freezing process when water droplets hit a smooth wall at a low temperature. Yunchao SONG21et al. used the numerical simulation method to realize the numerical solution of the spreading movement when droplets hit a wall. In addition, they analysed the dimensionless parameters in the moving process.To date, much work has been conducted on the crushing characteristics of a droplet hitting a wallThe studies mentioned above mainly investigated a hydrophobic solid wall for single droplets. However, there are very few studies of sprayed droplets on a water-infiltrated cow hair surface using either experimental collection or numerical simulation. This paper considers the effect of water droplets in the spray cooling process. The statistical average method is adopted because the observation of a single droplet is limited in production and application. By using a high-speed photographing system, we collect records of the spray process over a given period of time and then observe, describe and analyse the video to explore the movement of sprayed droplets and the relationship between the movement and the characteristics of water droplets. This can also provide a theoretical basis for further study on the morphology of water droplets on cow surface and the heat transfer mechanism between the body and the surrounding environment.22 and group members tested different Japanese pool standard fan-shaped nozzles. According to the spray pressure, they finally chose the 9030, 9060, 9080, 90100, and 90120 model nozzles. The shapes of the nozzles are shown in Fig. The experiment was conducted in the Laboratory of Water Resources and Civil Engineering, China Agricultural University. Shuai Hong22. The material of the SDC skin is silicone with dairy cow hair to ensure the accuracy of the surface characteristics of dairy cow. The installation height of the nozzle was 2.2 m, which was 70 cm above the SDC back with reference to a domestic dairy farm. The spray pressures were 0.15 MPa, 0.20 MPa and 0.25 MPa. A precise pressure gauge was used to collect data. The neck area is the sensitive part on the cow for easing the heat stress23, so this test mainly shot the neck area using the high-speed camera.The 1:1 SDC model was used as the research object shown in picture 1 (c), and the SDC has a heating tungsten wire  to guarantee the surface temperature. And because the cows are warm-blooded animals, the body temperature of the dairy cow model was kept at 39 °C by the heating tungsten wire during the spraying experiment, while ambient temperature is 35 °CVRI Phantom high-speed camera. The final shooting parameters are as follows: resolution: 1280 × 800, exposure time: 398.8 μs, recording time for a single picture in one video: 526.32 μs, number of pictures: 5500, total length of one video: 2.9 ± 0.1 s .The video of sprayed droplets on the SDC surface was recorded by a United States V halogen lamp was used as a light source to assist the shooting with the high-speed camera. Because of the high speed of heat production, the single working time of halogen lamp is controlled within 1 minute, with an interval of 2–3 minutes to guarantee the lighting effect and life expectancy. The final placement of the experimental instruments is shown in Fig. A 220 MPa, according to the pressure gauge, and then waited for 10 s to acquire a stable water droplet. Subsequently, we opened the halogen lamp, adjusted the focal length, and made the image appear on the previously set location. We then clicked the button that controlled the high-speed camera on the computer to start shooting. After the ending single appeared, we turned off the halogen lamp and the water valve, saved the recorded video, and finished the shooting process. We continued to shoot the spray water with the same nozzle under pressures of 0.20 MPa and 0.25 MPa respectively. Then, we changed the nozzle, repeated the operation above, and saved the spray videos of different nozzles with different pressures.After all pieces of equipment were installed, we opened the water valve and adjusted it to acquire a pressure of 0.15 B, ratio of droplet radius γ and Weber number We for analysis. B is a parameter that describes the relative motion of two droplets, and We is a common parameter that affects the motion of droplets25. By analysing the relationship between We and γ, we can study the relationship between the droplets’ movements on the cow surface and their average particle sizes. The dimensionless parameter B is expressed as follows:R1 and R2 are the radius of two moving droplets, respectively, measured in m; and b is the space parameter of droplets, which is the projection length of the centre line of the collision droplets in the direction of their relative velocity vector, as shown in Fig. The experimental analysis included analysing the experimental videos and the relationship between the average droplet sizes and the characteristic parameters. We choose the dimensionless parameter r1 is the initial mean radius of the sprayed water droplet, r2 is the radius of the water droplet at the initial time when a certain droplet behaviour appears, and ρ is the density of water, kg/m3. v is the relative velocity of two droplets, and m/s. σ is the coefficient of surface tension, N/m.The average Weber number of the droplet is the ratio of the inertial force to their surface tension and is commonly expressed as26 shown in Table The characteristics of experimental water droplets arer1 is the initial mean radius of the sprayed water droplets and r2 is the radius of the water droplets at the initial time when a certain droplet behaviour appears.The droplet radius ratio γ isr1 of the sprayed water droplet is specified in Section 3.2.1. We use the SDC body as a reference to determine the parameter r2. The actual SDC diameter is d, and the diameter of the SDC in the high-speed photographic image is d0. The actual diameter of the water droplet is D (D = 2r2), and the diameter of the droplet in the high-speed photographic image is D0. Then, d, d0 and D0 can be measured by a Vernier caliper and the image size of the high-speed photograph. The Vernier caliper is an industrial caliper with a range of 150 mm and a precision of 20 μm to meet the test requirement. The scale conversion equation is as follows:The initial average particle size r2 = D/2.Then, the actual size of the water droplet can be expressed as By analysing the experimental videos, the behaviour of water droplets on the SDC surface can be divided into four categories: random scattering, fusion aggregation, multiple deformation and flow slipping.After the spray droplets drip on the SDC surface, some water droplets will gather with subsequent ones to form a new droplet that has a certain size and shape. A variable number of these new droplets scatter randomly and do not continue to gather with surrounding water droplets or slide along the surface of the SDC. These droplets semi-statically stay at the place where they are formed, as Fig. Setting the first picture as the initial time , we can see that the dropped water shows no difference but only shows a slight location change in the next 0.21 s, even though the spraying process is continuing. We call this behaviour “random scattering”.Because of the influence of shaking, the gathered droplets will aggregate again with the surrounding droplets. With the help of subsequent water droplets, the gathered droplets will also aggregate with the droplets at a distance, as shown in Fig. The pictures show the process of droplet aggregation within 0.053 s. From the pictures, we can find that at 0 s, the marked two water droplets do not contact and that a gap exists between them. After a certain period of time, at 0.016 s, the two water droplets begin to contact, and there exists a trend of mutual integration. At 0.021 s, the two water droplets are slightly gentle in the process of aggregation, which is due to the vibration offset between the water droplets, but this vibration offset does not appear in each aggregation process. Although the combination of two water droplets appears to be gentle at the last moment, this does not affect the tendency for them to gather. At 0.053 second, the two water droplets eventually fully converge together’ that is, the fusion process is completed.Multiple deformations mean that the shapes of the gathered droplets are influenced by the continuously dripping water. Multiple deformations are the most abundant spray water droplet behaviour and are irregular and unpredictable. For convenience, multiple deformations can be re-classified as broken deformation and non-crushing deformation according to whether the water droplets are broken. Non-crushing deformation includes spherical surges and vortex surges, and broken deformation includes segmental broken and exploded broken.Spherical surgeSpherical surge is when the shape of the droplet is spherical when a surge occurs. It is characterized by the observation that only a small amount of water droplets is splashed out and the original body is not broken, as shown in Fig. It can be seen from the pictures that at 0 s, the spherical surge behaviour is revealed. The water droplets are no longer smoothly spherical, protrusions appear on the top, and the body begins to contract. At 0.03 s, the water droplets change more sharply than at the previous time. Shrinkage and protrusion are more obvious, but the locations are different, which is the irregular deformation behaviour that is observed when surge occurs. At 0.07 s, small water droplets in the outer layer of the original body begin to split out due to the violent surge and further development. At 0.11 s, as the surge continues, some of the separated small water droplets of the original body are splashed out; the others are re-involved in the following surge process.Vortex surgeVortex surge is when the shape of the droplet is a swirl when surge occurs. It is characterized by the observation that the middle of the droplets is depressed and other parts are tilted, thus forming a vortex with a certain thickness that is short and unstable, as shown in Fig. It can be seen from the pictures above that the top surrounding parts of the water droplets are raised and that the middle parts are drum-shaped. The tilt gradually becomes thicker as the surge continues, and the “scroll” tends to be reduced.The vortex surge and spherical surge both belong to the type of non-crushing deformation and have the relevant characteristics. However, the two behaviour are relative, not antagonistic, and there is no clear boundary between these behaviour. Spherical surge can appear solely, it can appear after the vortex surge, and these two behaviour can even appear alternately.Broken deformation: Broken deformation can be divided into segmental broken and exploded broken. The main feature is that the original water droplets appear in different degrees.Segmental brokenSegmental broken refers to water droplets that have been dropped on the ox hair and gathered to form a certain size of the spray water droplets under the influence of subsequent water droplets, thus making the original water droplets break partly. It can also be called a broken edge. This is shown in Fig. It can be seen from the figure that at 0 s, the original body (the fragmented water droplets) gathers to form a droplet with a single shape and size. At 0.01 s, due to the subsequent water droplets, the original right side of the edge breaks out, and small water droplets splash, but the left part remains intact.Exploded brokenNon-crushing deformation: Non-crushing surge refers mainly to the surge behaviour in which the shapes of the gathered water droplets continue to change under the influence of subsequent water droplets. It is characterized by the observation that only a small amount of the water droplets of the original body (the surging water droplets) is splashed out and the original body itself is not broken throughout the changing process.Exploded broken refers to when the water droplets which have been dripping on the ox hair gather to form a droplet with a certain size, thus making the original droplet break to a significant degree under the influence of subsequent water droplets. The whole process is short and violent, as shown in Fig. From the pictures above, we can find that at 0 s, the spray water droplets that have been dripped and gathered present a common form. At 0.008 s, the water droplets begin to break, and when the water droplets break, the middle part depresses, while the surrounding part shows different degrees of protrusion. At 0.0095 s, the degree of crushing increases, and the middle depression part increases and deepens further. The surrounding part of the protrusion rises to almost the maximum height, and only one thin layer of water remains for all of the water droplets. At 0.011 s, the surrounding protrusions become shorter and tend to fall, and the surrounding water film becomes thicker than before owing to this tendency. At 0.013 s, the protruding part of the broken water droplets continue to become thicker and shorter than the previous stage, while the middle depression part becomes wider; at this point, the water droplets are already spreading. At 0.016 s, the surrounding part of the protruding part has fallen. The original body has spread on the surface of the hair, and only one circle of water droplets is left discontinuously. At this point, the broken process is over, and the whole process lasts for 0.016 second, which shows the short duration of the broken process.27. However, the difference in the contents, the environment and the form of the experiment contribute to some of the discrepancies in the behaviour, which requires further experiment and study. The exploded broken of the experiment already shows that the behaviour of sprayed water droplets have many similarities to that observed by SONG Yunchao and other researchers. For example, a thin layer of water forms when Rioboo11 observed the droplet impact process.The exploded broken is similar to the crown of a single droplet hitting a specific wallSegmental broken and exploded broken are relative but not opposing, and no definite boundaries exist between them. They both have characteristics of broken deformation, such as transience, which leads to the different broken degrees of the original body.Flow slipping, as the name implies, refers to when the water droplets overcome friction to flow and slip along the irregular path after they are gathered. However, there is a slight difference between the droplets flowing on the ox hair and those flowing on the floor. At the very beginning, the water droplets will not flow alone due to their small sizes and friction; only when they are gathered to a certain extent can they flow. When flow occurs, it tends to form a small stream of water or a separate water droplet rather than a continuous or a regular stream. From the video, the flow behaviour is less common than the other three types of behaviour.28 tested the sizes of sprayed water droplets and acquired statistics under different working pressures, as shown in the following Table To discuss the behaviour of sprayed water droplets more intuitively, we classify the average particle size of the water droplets in the experiment. Shuai HongT. The number of all the motion phenomena of the spray water droplets occur is recorded as N, and the number of any one motion phenomenon is recorded as n; thus, the frequency (p = n/N) of the movement of water droplets is obtained.In the analysis procedure, the average particle sizes of the sprayed droplets of different nozzles are divided and analysed. For the spray videos with the same particle size, the video will start playing randomly. Within a fixed observation period The frequencies of all behaviour under different particle sizes are analysed, and we can obtain the graph below:From the Fig. B to analyse the average particle sizes and the fusion aggregation behaviour of the sprayed water droplets, and use We and γ to study the characteristics and regulations of random scattering and multiple deformations of sprayed droplets. The flow slipping behaviour is not discussed because of its short residence time and weak characteristic.We use the dimensionless parameter B changes significantly due to the random movements of the sprayed droplets. Figure b” of their centre line “a” in the normal direction of their relative velocity vector. The dimensionless parameter B1 < B2 because b1 < b2. The characteristic of dimensionless parameter B is that when B = 0, the two droplets move along the central line; when B = 1, the two droplets move tangentially at the contact point. Picture 11 shows that when B1 < B2, the tendency of two droplets gathering together is much higher than that at the moment t2, which shows the randomness and uncertainty of the gathering movement of two droplets.When fusion aggregation occurs, the dimensionless parameter We and the ratio of two droplets’ radii γ have a certain relationship, as shown in the graph below:For the random scattering and multiple deformations, statistical analysis finds that the dimensionless parameter γ mainly concentrates in the region of 0 to 20, and We changes in the range of 100 to 1000; that is, when the inertial force is not obvious, the surface tension can still maintain the morphology of water droplets moving on the surface, in which case the sprayed droplets tend to exhibit random scattering.Figure γ mainly concentrates in the region of 5 to 30, while We changes in the region of 500 to 3000. When γ is constant, We increases as the sizes of droplets increase, which indicates that the hitting impact is more obvious because of the large kinetic energy of large particle sizes. Thus the inertial force plays a dominant role respect to the surface tension, and the surface tension cannot maintain a “stable form” of the water droplets on the surface, which results in multiple deformations are more likely to occur.Figure 29. Water droplets must form an effective water film (just infiltrating the ox hair) to facilitate heat evaporation while not flowing off the dairy cow surface (not conducive to heat transfer) when the droplets infiltrate the dairy cow. Therefore, it is very important to explore the movements and morphological changes of sprayed droplets on the surface of a dairy cow’s body.In this experiment, we use a high-speed camera to acquire the moving behaviour of water droplets and study the moving characteristics from a microscopic point of view. The best effect of spray cooling is to infiltrate the dairy cow surface without water droplets dripping off and without spraying the breastAccording to Fig. B between two sprayed droplets is decisive when fusion gathering occurs. If B is too small (close to 0), the two droplets tend to move along the centre line to gather into a larger droplet, which hinders the heat transfer of the dairy cow body and is adverse to evaporation. If B is too large (close to 1), the two water droplets tend to move tangentially, and there is no obvious aggregation behaviour. The two droplets can still have multiple deformations in the following spraying process and can thus contribute to the spray cooling. As shown in Fig. The dimensionless parameter We and γ when random scattering and multiple deformations occur, based on which we analyse the interaction between the inertia force and the surface tension and their relationship with the ratio of the droplet radius. Further study shows that as We increases, the inertia force gradually dominates, which makes the multiple deformations occur more frequently. To conclude, droplets of 0.8 mm to 1.0 mm have a higher frequency of multiple deformations, thus contributing to the spray cooling. The project team also has relevant papers studying the heat transfer of droplets with radius of 0.8 mm to 1.0 mm.Figures According to the experimental results, the movements of spray droplets can be divided into four categories: random scattering, fusion aggregation, multiple deformations and flow slipping. Multiple deformations can be divided into non-broken deformations and broken deformations.According to the results, droplets of 0.56 mm and 0.80 mm may exhibit random scattering more frequently, but this is adverse to spray cooling. And the droplets of 1.10 mm of high frequency of fusion aggregation are also unfavourable for spray cooling considering the waste of water. So we do not recommend the use of droplets of these sizes.B, we can conclude that fusion aggregation is unfavourable for spray cooling and that multiple deformations contribute to the spray cooling. Considering the waste of water and the high frequency of fusion aggregation, droplets of 1.1 mm are not recommended.By analysing the dimensionless parameter We and γ, we can conclude that when random scattering occurs, γ mainly concentrates in the range of 0 to 20, while We is in the range of 100 to 1000. When multiple deformations occur, γ mainly concentrates in the region of 5 to 30, while We changes in the range of 500 to 3000. Droplets with radius of 0.8 mm to 1.00 is conductive to spray cooling which have a higher frequency of exhibiting multiple deformations.By analysing the relationship between


The cold‐chain information has characterized by the loss and dispersion according to the different collecting methods. The description for the quality decay factors of aquatic products can be defined as the multidimensional information. A series of nodes with multidimensional information are assembled to be hierarchies aiming at describing the environment conditions and locations in the supply chain. Each of the single hierarchy levels constitutes a sequence of node information in a network, which is applied as internal information analysis. The cross‐layer information structure is defined as “bridge” information which is able to record the information transmissions among every hierarchy from the point of view of the whole chain. The study has established a novel structured modeling to describe the cold chain of aquatic products based on a network‐hierarchy framework. An organized and sustainable transmission process can be built and recorded by the multidimensional attributes for the whole course of cold chain of aquatic products. In addition, seamless connections among every hierarchy are attainable by the environmental information records continuously to monitor the quality of aquatic products. The quality assessments and shelf life predictions are estimated properly as the risk control in order to monitor and trace the safety of aquatic products under the supply chain perspective. Basic node information is indicated by multidimensional structure information consisting of those three categories. The multidimensional node information is featured by multi‐attribute parameters of aquatic products in the cold chain. Combining with three categories of basic information, multidimensional node information is established for the depth information description of the cold chain.Through establishing a creative basic node of information transmission, the cold chain of aquatic products is analyzed and evaluated in the ground of multidimensional node information, such as nodes of the supply chain, specific manufacturing and processing information, and environmental information of aquatic products. In this way, intensive information of aquatic products is developed and perfected with the multidimensional basic nodes for full‐dimensional information description of the cold chain. Meta‐information is defined as basic node description which is the smallest unit of node information description in processing. Definition of full‐dimensional attributed node information is mainly relied on processing information of aquatic products. It is processing meta‐information based on time series or procedures with parameters to describe multidimensional information of the cold chain in all aspects.3.2In the view of extensive scope of aquatic product information in the cold chain, meta‐information is divided into two types: the internal hierarchical information and the bridging information. The node information in the internal hierarchy is applied as information description of one stage in the cold chain. A bunch of meta‐information on the same layer is assembled together to be a network structure for describing aquatic products, such as processing stage, storage stage, transportation stage, and distribution stage. Regarding multidimensional attributes, the internal meta‐information on each layer elaborates full‐dimensional information of aquatic products on an independent stage of the cold chain. Information structure of the stages is composed of a network structure with node information on the same stage to describe the information transmission of the supply chain.From the perspective of supply chain, the cold chain of aquatic products was analyzed, and there was a kind of relatively special type of information. An interhierarchy information occurs in the circulation in different factories or by different suppliers. Thus, there are two types of interhierarchy information including location diversion and supplier diversion. Furthermore, it is the crucial link to connect the upper hierarchy and lower hierarchy. The upper hierarchical information only can be transmitted consecutively if interhierarchy information is connected seamlessly. Or else, deficient information of the cold chain is the definite consequence.In this research, the link of node information is defined as “bridge” node information which connects each hierarchical partition and transmission of aquatic products in the cold chain. The “bridge” information is a combination of two types of node information connected from the ending node of the upper hierarchy to the beginning node of lower hierarchy. Each single hierarchy exists independently and orderly. Specifically, the definition of hierarchy can be variety of location diversion, supplier diversion, and logistics diversion. Additionally, special hierarchy information is defined based on node information attributes, such as periodical attributes or operator attributes, as the specific information analysis and assessments. The hierarchical 3D network information modeling is built up to connect network information on the same hierarchy and transmit information among every hierarchy through bridge nodes. This method is able to cover information recording of the cold chain extensively and completely.Figure 3.3In the modern world, during the course of production in logistics, many of the modeling methodologies are applied, such as the control theory, Lagrange relaxation methodology, SCOR modeling methodology, and other advanced modeling methodologies. In this study, the structured model, especially like the colored Petri network, is more superior in risk control, validity analysis, and data tracking during the entire process of the cold chain. Compared with other modeling methodologies, the Petri network is more practical in analyzing structures and behaviors of the cold chain. Moreover, the colored Petri network is advanced enough to be inserted with multidimensional data, such as time, procedures, and any other environmental factors, which is exactly what we are working on.N =  structured network (net) are as follows:P∩T = Φ presents the location and the variation which are totally two different elements;P∪T ≠ Φ presents at least one element existing in the network;F = (P × T) ∪ (T × P) presents unidirectional connection between the location and the variation and prevents any direct connections among the same type of elements.The basic definition of the Petri network: The necessary and sufficient conditions of triple The colored Petri network uses colorful symbols for more vivid illustrations. Sometimes, a set of colors is added or transferred. Even an I/O function is transferred for more specific explanation.For example:P,T;F) broadly oriented network is the base net of Σ. is the nonempty finite set located on p with or without colors.As to t ∈ T, C (t) is the nonempty finite set transferred to t with or without colors.As to I− and I+ are negative and positive functions for P × T and T × PM0 is an initial symbol for Σ.In the colored Petri network, different colors are presenting different multidimensional information, such as green nodes for processing information of aquatic products, purple nodes for circulation information of the cold chain, and blue nodes for environment information. Therefore, the multidimensional information fusion and risk information management of the cold chain have been accomplished ultimately.4Based on the ergodic process of aquatic products, the multi‐attribute parameters are supervised by the thorough records, which is equipped with hierarchical network information modeling of the entire cold chain. The description of information transmission contributes to extract more complete information of aquatic products in storage during the cold chain. Various independent functions of analysis and assessments are implemented regarding the information extracted from the cold chain as follows: safety assessments, validity estimation, information tracking, real‐time monitoring, and risk warning of aquatic products in the cold chain.In the matter of multi‐attribute parameters, the clustering of multidimensional information attributes are extracted from the parameter sets. According to the research, there are three types of clustering by extracting attributes of multidimensional information as follows: behavior information clustering, environmental information clustering, and quality information clustering. Behavior information clustering concentrates on extracting multidimensional node information containing operational attribute parameters. Briefly, a set of operating information description is interpreted as multidimensional attribute information which is extracted from the circulation in the cold chain with time series. So it can be applied to analyze the operating safety and the chain management of aquatic products. Furthermore, it is also capable of collecting information in real time. Environment information clustering concentrates on extracting multidimensional node information containing the full‐dimensional environmental attribute parameters. The set of environmental information description is associated with attributes of full‐dimensional environmental media, including temperature, moisture, and ergodic time, which is extracted from the circulation of the cold chain with time series. Therefore, the congregation of full‐dimensional environmental data is considered as a risk warning to quality safety of aquatic products and environmental monitoring in the cold chain. Quality information clustering is the integrated analysis on the ground of behavior transinformation and environmental transinformation.The three types of clustering information are applied for the evaluation, management, and decision support of aquatic products in the cold chain. Safety conditions of the cold chain are analyzed on the basis of factors which have significant impacts on the quality safety of aquatic products. The conditional information is divided into two types: the safety conditions of operating protocols and the safety conditions of product quality in the cold chain. According to the decision‐making objects of operating protocols and quality assessments, the decision‐making of safety conditions is made based on information analysis extracted from the network hierarchical modeling.The decision‐making objects taken as one of critical conditions are so decisive for the quality safety of aquatic products in the cold chain. The decision‐making process contains three elements including the decision‐making objects, methods, and results. Nevertheless, the three elements are distinguishable according to different decisions as it is illustrated in Table Referring to the decision‐making modeling, the result is demonstrating the outputs of operating protocols or quality assessments of aquatic products. Decision‐making objects mean the conditions of operating safety and states of product quality for each batch of aquatic products in the circulation of the cold chain. Decision‐making process is conducted by the decision‐making methods. Besides, further discussion is made on the specific decision‐making process related to the operating procedures and the quality assessment of the product.4.1The evaluation of operating safety is defined as safety analysis and safety assessments of aquatic products during the processing practices in the cold chain from the view of operating managements. There are two main protocols commonly applied as follows: Hazard Analysis and Critical Control Point (HACCP) and Good Manufacturing Practice (GMP). In this research, regarding the criterion of qualified operating procedures and the limited time requirements, the operating safety is analyzed and evaluated by extracting the complete environmental information clustering and behavior information clustering from the hierarchical network modeling.The operating instructions or any quick response strategies are executed without delay only if the decision‐making information is made based on information description of quality safety analysis which is deduced from the decision support modeling.Based on the analysis of environmental temperature fluctuations, shelf life quality of aquatic products can be analyzed by the Baranyi model to evaluate aquatic product quality and analyze the overall safety level of cold‐chain aquatic products. This study mainly considers the influence of temperature on the shelf life quality of aquatic products.The Baranyi model was used to fit the curve of bacterial growth and proliferation, and the square root was used to describe the effect of temperature on growth kinetics of bacteria. The model was improved to fit the growth status of microorganisms under fluctuating temperature. Temperature fluctuation experiment was designed for verification.4.1.1T—storage time, d; N0—the initial number of microorganisms, l g CFU/g; Nmax—maximum value of the general number of microorganisms during storage, l g CFU/g; μmax—maximum specific growth rate of microorganisms, d−1; ν—h0, parameters, constants.The Baranyi equation was used to fit the relationship between the number of microorganisms and time variation; thus, the initial bacterial colonies, period of delay, specific growth rate, and maximum bacterial concentration  as follows:4.1.2Dynamic prediction of pseudomonas growth under fluctuating temperature:t = dt1 + dt2 + … + dti,dti  is the short time interval under an assumed constant temperature and N(ti) is the bacterial number at dti. N0 is the initial number of microorganisms when t = 0, and Nmax is the maximum number of microorganisms when they increase to the steady period. The influence of temperature on the growth state of microorganisms can be represented by the square root model, that is, μi=b(T−Tmin), where μi is the maximum specific growth rate at dti. Using the above method, shelf life of aquatic products can be accurately estimated.When Regarding the above modelings, the quality assessments are provided as a consolidated foundation of analysis and definition for the quality safety of aquatic products under various temperatures in the cold chain. All of information at each stage is applied to confirm the fluctuated temperature environments, which is necessary to select one of the proper assessment modelings for analyses and evaluations of the quality safety. Those modelings are also supportive to make correct decisions and quick response strategies based on the quality safety states of aquatic products.5In this research, the cold chain of tilapia is considered as an experimental object during cultivation, processing, storage, and transportation. Multidimensional node information of tilapia is involved in quality safety assessments and decision‐making strategies of risk warning in the cold chain. The Petri net, which is a simulation tool, is applied to establish a “network‐hierarchy” modeling for information transmission in the cold chain. In the 3D network‐hierarchy modeling, the circulation status of each node is elaborated through describing processing and environment information based on the attribute value of multidimensional nodes. Figure EP13, FP1), “GH” , and “IJ” , which are the crucial connections between the processing stage and the transportation stage, represent that tilapia have been delivered to the next stage. The nodes of bridge are considered as key nodes of information flows, which are extracted from the information communion center as it is required. Tangible information flows are consolidated to be a hierarchical modeling that the entire cold chain of aquatic products is visualized. Applying with this framework, all of data referring to the cold chain is stored in a multidimensional database.Referring to the tilapia, there is a complex network structure on every hierarchy of modeling to describe the transmission process of multidimensional information including the cultivation stage, the processing stage, the storage stage, and the transportation stage. The nodes of bridges “E F G H I J” are defined as links between two separate layers to establish a 3D transmission structure of multihierarchical information. The impressive framework of the structure represents the transmission and behaviors powerfully. Meanwhile, the analysis of the cold chain is accomplished completely and efficiently. As it is shown in Figure 1 to m11 with the multidimensional information description. The content of a token T is defined as C(mx:my) for the description of information transmission mode to record the association with input and output nodes. The captured tilapia are ready to be processed as long as the temperature sensors are launched by the modeling. In this stage, three levels of tilapia are transferred to the main network with information flows. Therefore, the information tracing is available at the transparent processing stage with more details.Before entering the processing stage, information description of tilapia is shown in Table At the processing stage, the information is shown in Table The data of intensive temperature monitoring is uploaded to the processing center by sensors for different batches of tilapia Table . RegulatAs it is shown in Tables The process of tilapia in the cold chain is taken as an example to analyze the validity of the modeling methodology which is researched on verification of the quality safety. The analysis of the entire temperature data as the most critical information is shown in Figure In this research, temperature data is shown in Tables 1 to m26 in Table Based on the above model, operating safety accidents generally occur at the processing stage. Time span of processing tilapia is a significant parameter to indicate the operating safety which is evaluated by extracting attributes notes of time from mmi) is “true.” Providing that Enabled (mi) is false, the quality analysis of aquatic products has to be implemented instead of triggering the next events; then, the processing time is over 40 min. Time–temperature data in the processing stage is revealed. The highest temperature for tilapia is 7.8°C while the lowest is 2.4°C at the processing stage in the cold chain. Time–temperature data is acquired from sensors every 30–s as it is estimated. There are 174 pieces of data records. The processing time within 29 min is approved to be safe according to the decision‐making modeling of quality assessments in the cold chain.The processing is considered to be safe enough to trigger the next events within 40 min only if the decisive variable quantity Enabled . Environmental temperature equipped with the Labuza modeling is practicing on quality assessments and shelf life estimations frequently. The related values of quality assessments become dimensionless parameters, while the quality decay occurs eventually.Quality control and shelf life estimations mostly depend on the time ranging from the processing stage, the storage stage to the consumption stage. Temperature control in the primary period of processing and transportation is extremely important for the quality safety of aquatic products in the cold chain. Thus, temperature fluctuations take an incredible impact on product quality of tilapia, especially in the processing stage and the transportation stage as the intensive and violent temperature fluctuations occur. Temperature in the storage stage is almost stable, although temperature in the transportation stage is fluctuated massively. Experimental data is calculated through TTT protocol and shelf life estimation modeling to verify enhancement of decay ratio of tilapia as time goes. Apparently, continuous temperature reduction is launched as decision‐making response strategies. Mathematically, the quality of tilapia is declined along with changes of environmental temperatures during the cold chain. The quality of tilapia is separated into five intervals, in which better quality interval range is 0.8–1 with relevant time 6 days and worse quality interval range is 0–0.2 with relevant time 24 days. The forth interval (0.2–0.4) is chosen to be a reference value of safe quality of tilapia with expiration date 18 days according to the quality assessment modeling. More specifically, expiration date 18 days is the outcome of quality decay estimation based on the Labuza modeling with the experimental time‐temperature data. In the extensive experiment of tilapia, expiration date 17.13 days almost equals the 18 days, which is calculated based on necessary data, such as actual circulating time 12.33 days in the cold chain and expiration date 4.8 days under the 1.5°C environmental temperature.6In this research, multidimensional information is collected to describe transmission information of the cold chain. It is a solution to aggregate analysis of information management with inadequate environmental information and quality information. The hierarchical network modeling is established through the analysis of transmission information for full‐dimensional information collections and seamless information records. A diversified and profound information collection and information transmission of the entire cold chain is conducted by multidimensional information in the network modeling. The wide and complete information description and information modeling are created based on the information transmission in the cold chain. Information of tilapia is studied intensively with the multidimensional information consisting of the processing stage, the storage stage, and the transportation stage from the hierarchical network modeling. The information is recorded and transmitted in the entire cold chain to compose the behavior information clustering, the environmental information clustering, and the quality information clustering, respectively. Then, operating safety and quality assessments are analyzed and evaluated by the methodology. Conclusively, the network‐hierarchy modeling with multidimensional information tends to conclude comprehensive analysis of environmental information and quality information, which ensures that the quality of aquatic products is evaluated precisely and accurately during the entire circulation of the cold chain. This model is available in effective information managements of aquatic products to provide significant references for decision‐making strategies which guarantee the safety of the cold chain. From the aspect of aquatic product management, information integration and in‐depth analysis of the whole process of cold‐chain aquatic products can be performed from the aspect of multidimensional information using this model from a single operation or independent temperature record. The overall management level of aquatic products can be improved, and risks of aquatic products can be managed and identified with early warnings. Thus, the safety of aquatic product cold chain can be enhanced.The authors declare that they do not have any conflict of interest.This study did not involve any human or animal testing. This study was approved by the Institutional Review Board of Ludong University.Written informed consent was obtained from all study participants.


To enhance the understanding of the current increase in life expectancy and decreasing gender gap in life expectancy.We obtained data on underlying cause of death from the National Board of Health and Welfare in Sweden for 1997 and 2014 and used Arriaga’s method to decompose life expectancy by age group and 24 causes of death.Decreased mortality from ischemic heart disease had the largest impact on the increased life expectancy of both men and women and on the decreased gender gap in life expectancy. Increased mortality from Alzheimer’s disease negatively influenced overall life expectancy, but because of higher female mortality, it also served to decrease the gender gap in life expectancy. The impact of other causes of death, particularly smoking-related causes, decreased in men but increased in women, also reducing the gap in life expectancy.This study shows that a focus on overall changes in life expectancies may hide important differences in age- and cause-specific mortality. It also emphasizes the importance of addressing modifiable lifestyle factors to reduce avoidable mortality. The gender gap in life expectancy is a well-known and well-explored pattern. Women in Sweden have had, on average, a 3-year higher life expectancy at birth than men since the 1750s HMD . The femInformation on underlying causes of death was collected from the Swedish National Cause of Death Register for 1997 and 2014 (National Board of Health and Welfare We restricted our analysis of underlying cause of death to eight main chapters and 15 sub-chapters of the ICD-10 (Table Age-standardized mortality rates were obtained from the National Cause of Death Register. Confidence intervals were calculated with the method used by Chiang . Number Between 1997 and 2014, age-standardized all-cause mortality decreased by 26% in men and 16% in women (Table Table Table Between 1997 and 2014, the gender gap in life expectancy decreased by 1.55 years. Figure Analysis of the impact of age-specific mortality on the gender gap in 1997 showed that mortality in people 65 years or older had the greatest impact on the overall gender gap. By 2014, a clear shift had occurred. Mortality in people 85 years or older had the greatest impact on the overall gender gap, although the gender gap also diminished in this age group.In this study, we assessed the impact of age- and cause-specific mortality on the increasing life expectancy among men and women, and on the decreasing gender gap in life expectancy, between years 1997 and 2014. We found that lower mortality in men 60–84 years explained most of the increase in men’s life expectancy, and that lower mortality in women 70–84 years explained most of the increase in women’s life expectancy. The decreasing gender gap was primarily the result of a more rapid mortality decline from circulatory diseases among men than women, especially in those 70–74 years.These results should be viewed in light of a number of limitations. First, everyone 85 years or older were collapsed in a single age group, since the official data used set this boundary for the oldest age group, and a large proportion of all deaths happened in this group. During the study period, the number and proportion of deaths occurring in this age group increased, as did the mean age of death HMD . Hence, We chose the study period specifically to facilitate comparisons of the causes of death. Sweden shifted from the ICD-9 to the ICD-10 in 1997, so by selecting 1997 as the initial study year, we minimized potential classification errors that could have arisen from a shift in coding the underlying cause of death. Another strength of the study is that we focused on main chapters from the ICD-10 and included a limited number of sub-chapters. Because coding errors increase with increasing level of diagnostic detail (Lahti and Penttilä With regard to age-specific mortality, a previous study that addressed cohort differences in mortality found that in cohorts born in and after 1880, the gender gap in life expectancy was mainly the result of higher mortality among men aged 50–70 years (Beltrán-Sánchez et al. Our results on cause-specific mortality are in line with what others have found; namely, that most of the increased life expectancy and most of the decreased gender gap in life expectancy is the result of reduced mortality from circulatory diseases. Our results show that decreased mortality from circulatory diseases accounted for 70% of the reduced gender gap, and that ischemic heart disease explained the vast majority of this decrease. We know that lifestyle has a profound impact on the occurrence of circulatory disease and of cardiovascular disease (Kones and Rumana The results also showed a rise in mortality from certain causes of death, which diminished the increases in life expectancy by a total of − 0.3 years in men and − 0.8 years in women. This was especially evident for unspecified dementia, Alzheimer’s disease and mortality from falls. Yet, some of the observed increases in cause-specific mortality should be interpreted with caution. Most of the observed mortality increases from these causes of death occurred in the oldest age groups. On the one hand, there are more inaccuracies on the death certificates of the oldest age groups (Lahti and Penttilä Researchers have consistently pointed towards the different evolution of smoking behavior among men and women as an important explanation for the decreasing gender gap in life expectancy Hemström , 2005. H


Kinetic studies of biological macromolecules increasingly use microfluidic mixers to initiate and monitor reaction progress. A motivation for using microfluidic mixers is to reduce sample consumption and decrease mixing time to microseconds. Some applications, such as small-angle x-ray scattering, also require large (>10 micron) sampling areas to ensure high signal-to-noise ratios and to minimize parasitic scattering. Chaotic to marginally turbulent mixers are well suited for these applications because this class of mixers provides a good middle ground between existing laminar and turbulent mixers. In this study, we model various chaotic to marginally turbulent mixing concepts such as flow turning, flow splitting, and vortex generation using computational fluid dynamics for optimization of mixing efficiency and observation volume. Design iterations show flow turning to be the best candidate for chaotic/marginally turbulent mixing. A qualitative experimental test is performed on the finalized design with mixing of 10 M urea and water to validate the flow turning unsteady mixing concept as a viable option for RNA and protein folding studies. A comparison of direct numerical simulations (DNS) and turbulence models suggests that the applicability of turbulence models to these flow regimes may be limited. The approach achieves microsecond mixing times with sample consumption of as little as femtomoles [The advent of microfluidics has popularized hydrodynamic focusing  to initimtomoles . Chaoticmtomoles  to add smtomoles ,5 of themtomoles . Chaoticmtomoles  and T-mimtomoles .These mixing approaches use different physics to achieve mixing. Laminar mixers rely on molecular diffusion to perform mixing. Chaotic mixers add flow velocity transverse to the flow direction to increase fluid parcel movement thereby increasing mixing. Turbulent mixers use significant disorder in the fluid itself to rapidly transport fluid parcels within the fluid to do mixing.The choice of microfluidic mixer to use for initiating kinetics is influenced by the spectroscopic technique used for probing the reaction of interest. The observation volume is significantly different for chaotic/turbulent mixers compared to laminar mixers and this in turn also affects signal-to-noise and sample concentrations. The hydrodynamic focusing aspect (0.1 to 1 μm in width) of laminar mixers requires the use of highly focused beams and high concentrations  . Specifically, we model various chaotic/marginally turbulent mixing concepts such as flow turning, flow splitting, and vortex generation using urea solution mixed with buffer, which is modelled as water mixing with water. Additionally, one of the limitations in computer-aided design of mixers operating at the onset of turbulence or chaotic regimes is that the applicability of turbulence models, which are intended for fully turbulent flows at high Reynolds numbers, is not clear. We address this outstanding question by performing simulations of mixing using various turbulence models and comparing the results with direct numerical simulations, which is model independent. The comparison allows us to critically evaluate the applicability of various turbulence models for use in mixer design in these flow regimes.This work uses an open source computational fluid dynamics (CFD) tool so other research groups can emulate the methodology. The parallel CFD solver twoLiquidMixingFoam from the OpenFoam  softwareThe mixing process was modelled as one stream of water (containing unfolded protein and urea) mixing with two other streams of water (buffer). Experimentally, the concentration of urea solution is typicAn assumption in our simulations is that the protein, buffer reagents and other small molecules added to the solutions do not perturb the mixing process in a measurable way. We present several lines of reasoning to justify this assumption. Experimentally , proteinAs such, it is necessary to model the fluids being mixed  rather than the relatively low concentrations of biological macromolecules and potassium phosphate (or other buffers) in the buffer that do not affect the fluid properties significantly. As discussed further below in our treatment of bounded scalar transport, the Schmidt number provides the means to model different solutions for the protein . This study only considers urea solution as the protein inlet solution. Furthermore, this study does not consider nanoscale particles and entities changing the fluid properties described in studies related to nanofiber fabrication by bubble electrospinning ,24.This class of mixers operate with a 1:10 protein (or RNA) solution to buffer solution dilution ratio and at a total flow rate of 3 mL/min at the exit. A diffuser is used to expand the mixied urea solution flow from a channel width of 30 microns to 70 microns so as to provide a larger observation area  and in order to slow the fluid down in the measurement section to increase the longest observable time. The operating conditions of the first concept are shown in TwoLiquidMixingFoam allows different levels of turbulence modelling to be performed to account for the unsteadiness and small scale unsteady chaotic 3D fluid motion. It can solve for the mean flow using Reynolds Averaged Navier-Stokes (RANS) equations, or use a large eddy simulation (LES) subgrid scale model, or use no model at all and perform direct numerical simulation (DNS). This work evaluates the RANS and DNS options. LES will perform between these two options. A RANS model requires the least computational resources  but incuU is the velocity.Conservation of mass for incompressible flow is given by the following equation, where p is the pressure and ν is the visocity.The mean-momentum equation is given by the following equation, where uiuj〉 yielding the RANS equation. Using the turbulent viscosity hypothesis [νT is the turbulent viscosity and k is the turbulent kinetic energy.The above equation describes the momentum equation for Navier-Stokes with the addition of the Reynolds Stress Tensor 〈pothesis , the Reyk and turbulent viscosity νT are modelled using two additional partial differential equations (the k − ω SST model). For incompressible flow the turbulent kinetic energy term in For RANS computations, the values of turbulent kinetic energy For the DNS simulations the Reynolds Stress Tensor becomes zero because all the flow time scales and spatial scales are accurately computed .k − ω Shear Stress Transport [k − ε in the free steam and k − ω in the boundary layer capturing some of the positives of both models while mitigating some of the negatives of each model. The detailed reasoning behind selecting this particular model from a design perspective is discussed in the Discussion section. The SST model equations to solve for k and νT in For this work the primary model used is the ransport  (SST) turansport  to behavF1 and F2 are blending functions to blend the wall solution and free stream solution for νT. Pk is turbulence production term. S is the strain-rate tensor. α1, β*, β, σk, σω, σω2 are tuning constants for the turbulence model. The blending functions and tuning constants for this model are defined in reference 27. The other two-equation models have a very similar form that also requires solving one or two advection-diffusion-reaction partial differential equations like Eqs In summary, α = 1) entering from the central inlet as it mixes into the other two streams of water which are buffer (and marked α = 0) coming from the two side inlets. Mixing is computed by calculating the transport of the normalized urea concentration variable, α. The transport equation for α is given by the following equation [TwoLiquidMixingFoam simulates the mixing between two miscible incompressible liquids by modelling the transport of one liquid phase into the other liquid phase. The fluids are assumed to be isothermal  and modeequation .Sc of urea in water is 950 [ν/Sc quantifies the diffusion of urea into the buffer solution (large Sc means the regular molecular diffusion is very slow). The turbulent viscosity νT in νT term. ν is the viscosity of water. Hence, it is assumed that urea solution has the viscosity of water and the buffer has the viscosity of water.The Schmidt number r is 950 . The difTurbulence in these small sized mixers is fairly weak and only marginally turbulent. The nature of the turbulence under these conditions is not well understood and so the turbulent mixing may not be well captured by the existing turbulence models.α variable is bounded between 0 and 1 where 1 is the maximum level of urea at the inlet and 0 indicates only the presence of buffer solution and no urea. Any value between 0 and 1 indicates how much of the urea containing fluid has mixed with buffer solution. For the inflow conditions in this mixer , a perfectly mixed flow will have α = 0.1.The Bernoulli’s Equation is used in the design process before any computations to determine the dimension of the throat of the mixer after the three inlets meet as shown in Athroat to be about 10% larger than predicted by Aexit is the area at the exit of the mixer. Qexit is the total flow rate through the mixer which is also the flow rate at the exit of the mixer. ρ is the density of the fluid. At the throat, the conditions for Bernoulli’s Equation to hold are not perfectly satisfied, but the 10% margin added to Athroat is expected to compensate for this.We recommend setting The NSF supercomputer Stampede at the Texas Advanced Computing Center was used for all simulations. For RANS simulations, all concepts shown in All of the design concepts were tested using the k-ω SST turbulent model and one of the designs  was testα (urea concentration levels) are presented that are traverse to the direction of flow (and at the diffuser exit location) on the right of Horizontal cross-sections of the velocity magnitude (speed) and α  is used to determine to what extent the urea containing fluid is transported into the buffer solution. What is sought is the most evenly spread profile. Since this is a 1:10 ratio dilution mixer, a fully mixed situation will have a uniform value of 0.1 throughout the entire mixer. From To analyze the mixing, The velocity magnitude information shows a similar trend for all the mixers: fast fluid in the core of the mixer and slower flow near the mixer walls. Friction causes the fluid to be stationary on the walls. However, each mixer is showing differences in the specific patterns of the velocity magnitude. This is caused by differences in the large scale secondary motions within each mixer. Certain motions are better at fully mixing the fluids but it is impossible to guess which ones are most effective without simulating the mixing. Asymmetry in the velocity profiles in The pressure plots shown in The concepts in α) at the end of the diffuser. However, it is necessary to understand the limits of the tools used to predict mixing and the detailed physics of the mixing process for this class of dilution mixers, as discussed below.Simulations using several different RANS models and comparisons with DNS provides an opportunity to critically examine the applicability of the RANS models to non-laminar mixers operating at the onset of turbulence. These points are discussed using the mixing concept shown in k and turbulent viscosity νT. This in turn influences the velocity and pressure fields as well as the transport of α. Turbulence models are based on various assumptions and as a result there is a wide variety to choose from. The impact that the turbulence model has on the final results for the reference design in k − ω SST [k − ε [k − ε [The Reynolds stress tensor, given in  − ω SST , RealizaT [k − ε , and theε [k − ε  models.νT, the velocity, and α using different turbulence models are shown in νT, is a measure of where the turbulence model is active (adding turbulent viscosity to the RANS equations) and also an indication of where turbulent mixing is likely to occur.The predictions for turbulent viscosity, νT, it is apparent that only Spalart-Allmaras and k − ω SST model are active and modelling turbulence in the flow as seen in k − ε and the Launder-Sharma k − ε are not active and are not adding any significant amounts of turbulent viscosity to the flow .From the plots of turbulent viscosity, the flow . The k −k − ω SST .α profile with the lowest maximum value is predicted by the k − ω SST turbulence model as shown in k − ε and Launder-Sharma low Reynolds number k − ε,  and the Kolmogorov length scale. For a urea solution with a Schmidt number of 950, the Batchelor scale is 30 times smaller than the smallest scales of turbulence determined by the Kolmogorov scales. This means that the DNS can resolve the fluid flow causing the larger scale mixing in this problem, but cannot resolve the smallest scales for the urea. For this problem, these small scales are not important to resolve.So, the smallest scale of transport of the scalar α would require 50 billion cells. Fortunately, it is not necessary to resolve these scales for this problem. The scalar transport of α simply tracks the velocity field and does not affect the development of the velocity field. The scalar field is not coupled with the velocity and pressure solvers.RANS simulations of the mixer require only 2 million computational cells. Velocity resolved DNS (the results presented herein) requires 50 million cells. To resolve all the scales of the The DNS simulation produces fully unsteady results. To compare to the RANS results and experiments we need to find the average flow behavior (averaged over time). This average is constructed from six instants of the DNS that were separated by a long time (separated by one device flow-through time). Ideally, more averaging samples should have been used, but limitations on computing resources prevented this, and the results are reasonably indicative even with this small averaging sample.k − ω SST turbulence model and (b) the averaged DNS. Comparing α profiles at the end of the diffuser for the DNS. Comparing these results to those predicted by the four tested RANS turbulence models shown in α profile predicted by DNS. It is interesting that the Realizable k − ε perhaps comes the closest to the DNS because it is essentially a low-mesh-resolution DNS. This indicates that using no model at all is almost as good as using a model for this type of flow. Note, however, that the absence of turbulent viscosity affects the mixing model’s ability to predict the fully mixed state (at 0.9 mm downstream) as shown in k − ω SST model may still be the better RANS model even though its predictions do not exactly match up with the DNS.α1. We expect that with more samples for averaging, the profile for α1 will approach a uniform value of 0.1.Results at the fully mixed point (approximately 0.9 mm from where the three inlets meet) are shown in α1 = 0.1 at any instant in time. This indicates that experimentalists should be careful about their interpretations if they are measuring highly non-linear responses. The average response may not be proportional to the instantaneous physics that is occurring locally in space and time. In However, when looking at the instantaneous snapshot , the resk − ω SST turbulence model and RANS simulation to design the mixer because it gives an easy to interpret profile of α. If a high resolution study is possible, we recommend perfoming DNS with temporal averaging using the mesh requirement dictated by the velocity and not by the passive scalar. The high cost of the DNS is not just from the larger mesh that is required, but also from the long simulation times needed to obtain sufficient averages.For quick design, we recommend using the The mathematics behind laminar diffusion based mixing is well understood and can be done by hand without the need for computers to determine mixing times and appropriate widths for the focused solution. But incorporating more fluid physics such as chaos, turbulence, and cavitation into the mixing process requires the use of computers to design mixers in a rapid fashion to reduce the number of physical iterations and thereby the cost of mixer development. The need to add higher order fluid physics is to increase the disorder in the dilution fluid thereby reducing the mixing times and possibly reducing the bias the dilution fluid induces on the biological macromolecule. This paper presents a computational approach to facilitate the design of mixer with higher order physics.k − ω SST turbulence model can be used for early design iterations. DNS simulations reveal a stark difference between the average and instantaneous urea concentration profiles. This property of mixers relying on fluid physics other than diffusion is important to consider when interfacing with spectroscopic techniques sensitive to instantaneous concentration and interparticle distances, such as SAXS. DNS with temporal averaging is recommended as the design tool of choice for cases where details and high resolution are required.A mixer design in which turbulence is generated prior to merging of the flow with urea is presented and shown to provide mixing in 125 microseconds at modest flow rates. This flow turning concept was able to induce the most chaos/turbuelnce into the buffer fluid compared to other designs allowing it to perform best. Though narrower channels would allow higher velocities which in turn would generate even more chaos/turbulence allowing faster mixing, narrow channels are prone to clogging and 25 μm is the lower limit before clogging becomes an issue. Comparison of our results with an experiment and DNS show that RANS simulations using the


Spiroplasmas are bacteria that do not possess flagella and their motility is linked to kink propagation coupled to changes in the cell body helicity. While the motility of bacteria with flagellar motion has been studied extensively, less work has been devoted to the motility of spiroplasmas. We first show that the motility of such bacteria has large variability from individual to individual as well as large fluctuations in time. The Brownian motion of such bacteria both in orientation and translation is also highlighted. We propose a simple model to disentangle the different components of this motility by examining trajectories of single bacteria in different viscosity solvents. The mean velocity of the bacteria turns out to depend on the viscosity of the medium as it increases with viscosity. Further, the temporal fluctuations of the bacteria motility turn out to be very strong with a direct link to tumbling events particular to this bacteria. This gene loss is considered to be associated to their parasitic lifestyle and the remaining genes to represent the minimal set essential for their survival, multiplication, protection and pathogenicity in the host3. Spiroplasmas mostly infect arthropods (insects and crustaceans) and plants, and many species are pathogenic to their host. A better understanding of the virulence mechanisms of these pathogens is at present required in order to better counteract infections such as the citrus stubborn disease4, May disease5, tremor disease6, or human infections8.Spiroplasmas are micro-organisms of the class Mollicutes which are considered as minimal bacteria. These Mollicutes have undergone drastic genomic reductions through evolution11. While swimming in liquid media is associated with the presence of flagella in most bacteria13, spiroplasmas do not possess any flagellar structure and their motility includes bending, flexing, and change of helical sense propagating along the cell body (kink propagation)14. This type of locomotion appears to be well adapted for bacterial propagation in viscous media such as those colonized by spiroplasmas . In support of this assumption, the swimming speed of spiroplasmas was shown to increase with viscosity in the early 1980s15. The motility of these bacteria is actually linked to the generation of two temporally distinct ‘kinks’ travelling down the length of the bacterium17. The first kink triggers a change of spiroplasma helicity, e.g. a transformation of a right-handed into a left-handed helical structure. This change of helicity is associated with a change in orientation. The second kink restores the initial helicity and orientation. Upon the passage of the pair of kinks, the bacterium moves forward in the direction of its longitudinal axis16. Spiroplasma movements are thought to rely on structural changes of an internal contractible cytoskeleton20, and on the structural network formed by the bacterial homologs of actin MreB proteins21. The cellular and molecular organization of this internal cytoskeleton acting as a linear bacterial motor was resolved for both Spiroplasma melliferum and S. citri20.Spiroplasmas are helical and motileS. citri strains, more or less affected in their motility, were hampered by the lack of quantification of the remaining motility capacities in these mutants22. More generally, studies to correlate motility and pathogenicity, or to understand the role of motility in spiroplasma biology, suffer from a lack of a simple method allowing the quantitative measurement of spiroplasma motility. It has to be mentioned that several studies reported the measurement of a mean swimming speed of spiroplasmas15. These studies bring important clues and significantly help understanding spiroplasma motility mechanisms and the dependence on the viscosity of the medium. Although the latter methods give important quantitative data, to our knowledge, no method described so far took into account the Brownian motion, which is necessarily critical for the displacement of bacteria with low Reynolds number. The variability in motility from bacteria to bacteria and versus time has not been addressed quantitatively either.Unravelling spiroplasma motility mechanisms may help in identifying potential drug targets to more specifically and more efficiently fight against these pathogens. However, to date, the relationship between motility and pathogenicity is unclear. Comparative studies of the pathogenicity of different S. citri was chosen as a model in this study as it is a pathogen of economic importance and can easily be cultivated in vitro. In addition, motility-deficient variants have been constructed or isolated for this species26. Our study and results should therefore be of interest to examine the potential correlation between motility and pathogenicity, and to identify drugs affecting spiroplasma fitness. A spiroplasma can roughly be represented schematically as a linear object with an internal motor ensuring a propagation speed along its axis and thus allowing a linear propagation of the bacterium. Nevertheless, the swimmer’s own movement in liquids competes with its Brownian diffusion27. On the basis of experiments conducted in media with different viscosities, we first study the effect of this parameter on spiroplasma paths. We demonstrate the change of average statistical properties of displacement and orientation of a spiroplasma population upon increase of the medium viscosity. A Langevin model of Brownian motion coupled to an internal motor is shown to be in agreement with experimental data. Our approach allowed us to analyze bacterial displacement, determine the mean speed of a single bacterium along with its variability from individual to individual as well as its temporal changes. Finally, a study of individual paths allows us to link the linear propagation velocity to the kink generation frequency, obtain the distributions of the velocity of the bacteria and identify the origin of the temporal fluctuations of their motility.The present study aims at presenting a reliable method to accurately quantify spiroplasma motility in liquid media of different viscosities. S. citri GII-3 wild type has been isolated from the leafhopper vector Circulifer haematoceps captured in Morocco28. Bacteria are grown in SP4 medium29, in which fresh yeast extract was omitted, at a temperature of 32 °C. During the exponential growth phase of the bacteria, one volume of the culture is diluted with one volume of Methyl-Cellulose (MC) dissolved in SP4. Here, Methyl-Cellulose (from Sigma (M7027), Mol. Weight 14000 g/mol) was used to adjust the viscosity of the solutions. This was added in different proportions of 0, 0.25, 0.5, 0.75 and 1% by weight. The viscosities of the corresponding solutions were η = 1.2, 1.9, 2.9, 3.9 and 5.5 × 10−3 Pa.s. respectively. The viscosities were measured by using a capillary viscometer. Complementary measurements using the Brownian diffusion of micron sized particles (Polystyrene particles of 1.1 μm in diameter from Sigma) to obtain their mean square displacement, their diffusion constant, and thus the viscosity of the solution using the Stokes Einstein relation were also carried out. These measurements turn out to be close to those using the capillary viscometer. Further, measurements using a cone-plate rheometer (Anton-paar) confirm these measurements and indicate that the viscosity of such solutions is roughly constant versus shear rate in the range 10 to 2000 s−1 suggesting that the solutions used are Newtonian. The elastic constants of these solutions are at least 5 orders of magnitude below their storage modulii again suggesting that the solutions are not viscoelastic.μm, and observed under an Eclipse Ni (Nikon) microscope working in reflection and equipped with a dark-field condenser. The Nikon oil immersion microscope objective was a 60x with a N. A. of 0.80. Bacteria motion is recorded with a camera Nikon Digital Sight DS-Qi1Mc (1280 × 1024 pixels) at a frame rate of 10 frames per second (fps), leading to a time between frames μm/pixel.Bacteria solutions were prepared between two sealed microscope slides, with a liquid thickness of 15 t was obtained as the center of mass of the scattered light intensity from the bacterium  of the bacterium is obtained from the orientation of the long axis of the scattered light intensity. In all cases, in absence and in presence of a kink, as in Fig. The orientation l and its width b can be estimated. The value of b was found to be roughly b = 0.6 μm. The length of the bacteria varies between 2 and 6 μm; Fig. From microscopy images, the length of the bacterium Escherichia coli can run and tumble leading to large fluctuations in their instantaneous velocity12. Little is known about such an effect in Spiroplasma swimming. We will come back to this point below.This section examines the variation of the motility of the bacteria versus solution viscosity as well as its variability from bacterium to bacterium. In fact, the motility of the considered bacteria may have large temporal fluctuations. It is well known that bacteria such as The influence of the viscosity on the motility can be appreciated in Fig. In order to carry out a quantitative analysis of the motility of such bacteria, we first propose an analysis based on the direction dependence of the velocity of the bacteria. The velocity of the center of mass of the bacterium V2(t) because it is difficult to resolve the orientation of the bacteria, i.e. the direction of the vector l = 3.5 μm) in a solution of 1% MC. This velocity is maximum near The bacteria are followed over long periods of time and an average value over time of the square of their velocity in a direction defined by the angle Vm(t) of a single bacterium in the direction of the long axis u(t) is the fluctuating component with a mean of zero. The velocity t, can be obtained as: E. coli for example30 but ellipsoids turn out to be reasonable in our case. These coefficients for an ellipsoid in a medium of constant viscosity η read31:kB is the Boltzmann constant, l/b.In order to analyze these effects in detail, we propose a simple model for the mobility of these bacteria. We assume that the bacteria have a motor velocity which has a well defined mean value and fluctuations around this mean value. Further, and because of their size, the bacteria are subject to Brownian motion. In principle, and if we note the motor velocity Let us assume that in the orthogonal direction the velocity is set only by the Brownian motion and in the longitudinal direction it is set both by the motor velocity and the Brownian motion, one can then write:α is similar for the three considered bacteria which is as expected from our model. However, the value of β differs from bacterium to bacterium. Since the translational Brownian motion is similar for the three bacteria, their velocities must be different. What is therefore important in this figure is that the difference between the two directions is not the same for the three considered bacteria signaling an inherent variability of the motor velocity from one bacterium to the next.Figure β, for the lowest viscosity solution (0% MC) is given predominantly by the value of α is given by the value of β is much higher than κ which is independent of the viscosity.Another important point is that such curves are very sensitive to the viscosity of the medium. In Fig. α increase as the viscosity decreases as expected if the sole contribution is Brownian motion. This can be tested directly from the variation of α versus solution viscosity shown in Fig. α confirms that the bacteria are diffusing in a background with a viscosity similar to that of the solution as measured using a capillary viscometer or a rheometer excluding effects related to Non Newtonian aspects of the solution or possible entanglement.From Fig. β/α increases as the viscosity of the solution increases indicating an increase of the motor velocity. This ratio can actually be used to extract the motor velocity (more precisely l/b with the expressions for β/α for the lowest viscosity solution. All these estimates turn out to be in agreement with each other.The second observation is that the ratio u(t). We will come back to estimating The values of the extracted motor velocities are shown in Fig. To summarize these observations, the viscosity of the solution plays an important role in the persistent motion of the bacteria which is more important in the direction parallel to the bacteria’s long axis. Further, Brownian translational motion is present under all conditions and is strong enough to almost mask the motor velocity for the low viscosity solutions. The motor velocity of the bacterium seems independent of length and increases with the viscosity. This velocity has an inherent variability both from bacterium to bacterium and possible temporal variability.While the above analysis allows to obtain the aggregate value of the mean velocity and the possible fluctuations around this mean value, we now propose a simple model of the motility of these bacteria. This model will allow us to obtain the mean velocities l, a minor axis of length b and are assumed to possess rotational symmetry around the long axis. We assume that the bacteria are subjected to translational (center of mass) and rotational (of the long axis) Brownian motion along with a persistent mobility along the long axis with velocity Vm(t). In the absence of inertia and assuming two dimensional motion, the equations of motion read:θ the orientation, t is time. The terms δThe bacteria are modeled as rigid ellipsoids with a major axis of length Dθ stands for the angular diffusion coefficient and is given by31:As indicated above, the brackets 27, which amounts to neglecting the fluctuating component u(t):The equations of motion, eqs u(t), if delta correlated in time, will only act as an additional noise similarly to While the assumption of constant motor velocity is not justified, we will use it here to obtain estimates of the average value (over time) of this motor velocity for each individual bacteria. This will allow us to obtain the variability of the mean motor velocity from bacterium to bacterium and estimate the temporal fluctuations from a comparison with the velocities obtained in the analysis presented in the previous section. Note that the effects of the presence of temporal fluctuations, i.e. MSAD(t) obtained by tracking individual bacteria and calculated from the temporal fluctuations of the orientation angle θ, are shown, for a 1% MC solution, in Fig. MSAD(t) is for a single bacterium. While all of them show overall linear behavior characteristic of Brownian dynamics, the value of the angular diffusion coefficient varies considerably from one bacterium to the next. This is due to the variability in the length of the tracked bacteria (eq. Dθ obtained from MSAD(t) for different lengths and different concentrations of MC. Each value of Dθ is obtained from 10 trajectories of bacteria with comparable lengths. The measured variation of Dθ is in good agreement with the expected dependence of the angular diffusion coefficient as a function of length and viscosity as given by equation 32.The simplest quantity to analyze is the angular mean square displacement. The angular mean square displacements eria eq. . In Fig.MSD(t) is more complex. Both the characteristic velocity and the diffusion constants play a role. This functional form has two characteristic time scales: tT corresponds to the scale for which the contribution of motor velocity and Brownian motion are comparable while tθ is the correlation time of angular fluctuations. The MSD(t) has three different regimes:for MSD(t) shows ballistic like behavior: for for The functional form of MSD(t) using equation tT and tθ in Fig. u(t) assumed delta correlated in time, is presented. In this case, only the diffusive part at early times, To summarize this behavior we show a sketch of MSD(t), shown in Fig. D, and Dθ are taken as known from the above measurements). The extracted mean velocities do not seem to depend strongly on the length of the bacteria as shown in Fig. 16. However, we obtain a wide distribution of mean motor velocities showing clearly the variability from bacterium to bacterium, see Fig. Consider now the measured MSD(t) for two different concentrations of MC but averaged over several bacteria with roughly similar lengths in Fig. 16.In order to overcome this difficulty and obtain the mean velocity especially for low viscosity solutions, we show results of 16, we find smaller motor velocities. It is possible that the difference in the values of the measured velocities is related to the way velocities are estimated. Here we measure a velocity averaged over time while in previous work, the values are measured during the passage of a kink and correspond to a phase where the bacteria have their highest velocity16. In fact, and from the time trace of cell positions presented in Fig. 2 of ref.16, we extract mean velocities in reasonable agreement with our measurements. Further, and as we showed above, the motor velocity of the bacteria may show large velocity fluctuations in time. The measurements shown in Fig. Compared to previous studiesIn the preceding sections, we have therefore shown that the mobility of the bacteria is controlled by their motor velocity and by Brownian motion. This motor velocity has large variability from one bacterium to the next and large temporal variability. While the analysis of the bacteria’s mean square displacement gave us access to the mean velocity of the bacteria, the angular analysis of the velocity gave us access to the temporal variability. The main result is that this temporal variability is strong and both the mean velocity and the amplitude of the fluctuations increase as the viscosity increases. In the following, we will focus on the movement of a single bacterium and analyze its temporal dynamics by focusing both on the variations in its orientation and its instantaneous velocity. By using long trajectories where both the orientation and the position of a single bacterium can be tracked for long periods of time without the bacterium leaving the focal plane and without reorienting out of the plane of the measurement, we will illustrate the origin of these temporal fluctuations.16. The analysis carried out below is for short bacteria with lengths l < 4. μm for which we rarely observe the propagation of two kinks simultaneously and which renders the analysis simpler. The analysis we carry out in this section on single bacteria relies mainly on tracking the individual bacterium to measure its instantaneous center of mass velocity θ. We have visually inspected the images to identify the two ends of the bacterium and determine its orientation. We also measure the helicity of the bacterium especially during the propagation of a kink. Examples of these measurements are shown for θ and θ of the bacterium oscillates between two plateau values with a typical period of roughly 1 s. The plateau values differ by roughly 45° and are followed by short periods of rapid variation of the orientation. These short periods last roughly 0.2 to 0.3 s. The succession of plateaus in the orientation of the bacterium is directly correlated to a change in helicity of the bacterium.In order to further study the variability in mobility, we here analyze, in detail, the trajectories of individual bacteria in the more viscous case (1% MC). We only analyze trajectories for which the bacteria remain in the plane of observation so that the two ends of the bacteria can be followed in time continuously. This limits the analysis to fewer trajectories and to viscous solutions only compared to the statistical analysis carried out above. Nevertheless, such analysis of individual trajectories and for long periods of time allows to get more insight into the mobility of these bacteria. We have paid particular attention to the presence and displacement of kinks along the bacteria as has been described in16. Note that for these images and for the analysis of Fig. The sequence of images in Fig. θ(t) The velocity is highest (roughly 5 μm/s) during the rapid variations in orientation while in the plateaus, the velocity is very small. This observation confirms that the bacterium moves during the phase of kink propagation with the bacterium moving in the opposite direction to that of the kink. While most events propelled the bacterium in the same direction, a few events push the bacterium backwards as seen in Fig. Let us come back to the velocity time trace shown in Fig. 16, found that the velocity of propagation of a kink is roughly constant tpair. This time scale has a mean value of 0.26 s. The time between two such pairs tk was found to have a wide distribution which decays approximately exponentially with a time constant of the order of a second16. Our own observations confirm these previous measurements. We find tk has variability both in time and from bacterium to bacterium. Another example of the variation of the orientation is shown in Fig. Previous work35. In addition, our results show that the instantaneous velocity of the bacteria has large fluctuations with short periods of fast mobility and periods of slow movement. The time scale tk and the mean velocity of the bacteria are related in a simple way. Suppose that as a pair of kinks propagates along the bacterium, the cell moves a distance 2λ (one λ for each kink and assuming that the two kinks have moved in the same direction). The mean velocity λ/tk. Figure tk for a solution of 1% MC. The measurements show a roughly linear correlation between the two quantities with a slope of 1.4 giving λ ~ 0.7 μm. This type of measurement was more difficult to carry out for lower viscosity solutions.It has already been noted that the passage of the kink is responsible for the motility of the bacterias at a frame rate of 10 images per second. The distribution of Vm(t). This distribution is more complex with a central peak due to Brownian motion and roughly similar to that of the transverse velocity. This distribution is however asymmetric with positive velocities that are more probable than negative velocities and is very broad. While positive velocities are associated with kinks moving forward, on a few occasions kinks may propagate in the opposite direction giving negative velocities but these events are not as frequent.Figure By tracking individual spiroplasmas we have shown that they move in the direction of their long axis with a motor velocity which presents a large variability from one bacterium to the next and a large temporal variability. From a statistical analysis using a Langevin equation for both the translational and the rotational dynamics of the bacteria approximated as ellipsoids, the rotational motion was found to follow Brownian dynamics with angular diffusion coefficients determined by the size of the bacteria and the viscosity of the medium. This statistical analysis allowed us to disentangle the Brownian motion from the motor velocity and its fluctuations. This motor velocity was found to increase with solution viscosity. The amplitude of the temporal fluctuations of the motor velocity were also obtained and found to be large and comparable to the mean motor velocity. This temporal variability is due to the way these bacteria are propelled. This propulsion is controlled by the passage of kinks that travel from one end of the bacterium to the other. The passage of each kink gives rise to a large variation of the orientation of the bacterium and propels it forward in a short time period. Once the kink has propagated from one end to the other, the bacterium remains roughly static. It is this process of mobility, large movements followed by periods of rest which give rise to large temporal variations in the velocity of the bacteria. The kinks actually come in pairs, which propagate in the same direction and are separated by a short time interval. The time period between the passage of pairs of kinks is longer and is correlated to the mean velocity of these bacteria. An interesting point here is the presence of long waiting times between the passage of pairs of kinks. These times and their distribution is probably an intrinsic property of the motility of these bacteria. This waiting time maybe simply related to the time necessary for recharging the intracellular ATP pool and allow the bacteria to find the necessary energy for a subsequent kink generation. These waiting periods or pausing could enable the cell reorientation by Brownian motion for example. The variability from one bacterium to the next is probably a consequence of the variability in the time period between the passage of pairs of kinks; it is possible that the mean period is specific to each bacterium.S. citri for example to explore links between their mobility and their pathogenicity.The proposed analysis here allows to disentangle the different contributions to the mobility of these bacteria: Brownian motion and motor velocity. The analysis also allows to unambiguously show the variability in motor velocity from bacterium to bacterium. The mean velocity as well as the amplitude of the temporal fluctuations of the velocity both increase with the medium viscosity. In fact, for low viscosity fluids (near the viscosity of water), Brownian motion is dominant and the motor velocity is small. Using such a quantitative approach may help in characterizing the motility of variants of 36. The polymer solutions used here are however Newtonian considering the small molecular weight of the polymer and the concentrations used . Different diagnostics point to this fact including the shear rheology and the microrheology used here. In fact, and in order for solutions of MC to acquire Non Newtonian behavior, high molecular weights are required37. Consider for example the determination of the viscosity using Brownian particles of roughly 1 micron in diameter. Their mean square displacement was found to be given by the viscosity of the solution measured using a capillary viscometer or a rheometer. Further, the diffusion constants of the bacteria  are given by the viscosity of the solution. Basically, microrheology measurements show that no anisotropy is observed and that the solution properties are governed by the viscosity of the solution as measured on a macroscopic scale32. This, coupled to the linearity of the viscosity versus concentration of the solutions used, all indicate that Non-Newtonian effects as well as entanglement effects can be excluded. Few mechanisms have been proposed to explain this enhanced swimming speed without invoking the entangled nature of the solution or its non Newtonian character. Perhaps the most relevant is depletion effects of polymers near the bacterium which coupled to the rotational motion of the bacterium may give swimming speed enhancement as proposed in38. However, this remains to be tested carefully.One of the main questions raised by our analysis concerns the mechanisms behind the enhancement of the swimming speed versus viscosity. It has been argued before that such an enhancement is due to viscoelastic effects and possible entanglement of the polymer solutions