Creeping motion of a Jeffrey fluid in a small width porous-walled channel is presented with an application to flow in flat plate hemodialyzer. Darcy’s law is used to characterize the fluid leakage through channel walls. Using suitable physical approximations, approximate analytical solution of equations of motion is obtained by employing perturbation method. Expressions for velocity field and the hydrostatic pressure are obtained. Effects of filtration coefficient, the inlet pressure and Jeffrey fluid parameters on the flow characteristics are discussed graphically. The derived results are used to study the flow of filtrate in a flat plat hemodialyzer. Using the derived solutions, theoretical values of the filtration rate and the mean pressure difference in the hemodialyzer are calculated. On comparing the computed results with the available experimental data, a reasonable agreement between the two is found. It is concluded that the presented model can be used to study the hydrodynamical aspects of the fluid flow in a flat plate hemodialyzer. A common characteristic of such flows is the direct inapplicability of the usual Poiseuille law7 in these situations because of the existence of non-zero velocity components of fluid in both axial and normal directions. This happens because of the fluid leakage through porous walls of the channel.The study of hydrodynamics of fluid flow in porous-walled channels and tubes have been remained a subject of interest for researchers since decades. This is because of the occurrence of such flows in many areas of science and engineering, particularly in those processes where mass transfer and filtration are encountered. Desalination process due to reverse osmosis, transpiration cooling, ultrafiltration in the tubules of glomerulus and fluid reabsorption through permeable walls of renal proximal tubule in kidneys, and blood filtration during hemodialysis in an artificial kidney are examples of such flows12 by assuming different forms of fluid reabsorption at the walls. Berman8, Sellars9, and Yuan10 have studied the laminar flow of incompressible Newtonian fluid in a uniformly porous-walled channel. Solutions were obtained for a uniform suction or injection case using the regular perturbation method. Kozinski et al.11 and Siddiqui et al.12 also studied the creeping flow of a viscous fluid in a permeable channel. Exact solutions were found for the case in which the leakage has exponential and linear decaying rate along the channel length. Flow of a viscous fluid in a porous-walled channel was also studied by Marshall et al.5 who assumed that the fluid leakage across the channel walls is proportional to the pressure differences across the walls. For further studies of fluid flows under different flow conditions authors would refer the reader to19.Literature survey reveals that various researchers have attempted the problem of fluid flow in porous-walled channels and tubes20 and the classical Newton’s law of viscosity fails to describe the complex rheological properties of non-Newtonian fluids, a very little work has been done in order to study the non-Newtonian fluids flow in porous-walled channels and tubes. Amongst many non-Newtonian fluid models, one is the Jeffrey fluid model that has attracted many researchers due to its consideration as a better model for physiological fluids23. The Jeffrey model is recognized as a generalization of the frequently used Newtonian fluid model because of the fact tat its constitutive equation can be reduced to that of the Newtonian model’s as a special case. The Jeffrey fluid model is capable of describing the stress relaxation property of non-Newtonian fluids, which the usual viscous fluid model cannot describe. Class of non-Newtonian fluids having the characteristic memory time scale, also known as the relaxation time, can be described well by the Jeffrey fluid model. Therefore, this article is devoted to the study of an incompressible Jeffrey fluids’ flow in a porous-walled channel of small width. Fluid absorption at the channel wall is taken in accordance with the Darcy’s law. The approach of the present analysis seems better from that of 24. In the present approach, the fluid loss at the wall is taken as function of the wall permeability, the flow rate then determined can be found to decay linearly or exponentially along the channel wall as special case in our study. Whereas, in24 a flow rate that decays linearly or exponentially, along the channel and tube was assumed in advance.In the literature presented above, all studies were performed for the Newtonian fluid model only. Despite the fact that most of the industrial and biological fluids are non-NewtonianL distance 2a apart. A Cartesian coordinate system y = 0 as shown in Fig. Let us consider the steady and creeping motion of an incompressible Jeffrey fluid in a porous-walled channel comprising of two equidistant parallel flat plates of length mentclass2pt{minim23μ is the dynamic viscosity of the fluid, , λ1 is the ratio of relaxation time to the retardation time, and The extra stress tensor Lp is the mechanical filtration coefficient of the channel wall which is usually measured in the units of cm2, t is the wall thickness, and pm can be visualized as the back pressure that opposes the fluid leakage and it is equal to the difference of hydrostatic and the osmotic pressures outside the channel wall. Equation (Equations  and 6)  6) are tEquation  is the nEquation  and 10 aFollowing parameters are used to transform equations into dimensionless form:Using the above quantities, Eqs −3 take tions Eqs −10 are tS can be readily obtained in the following dimensionless formUsing Eq.  and the u, v and p and it is not possible to determine an exact solution of it. Since the channel is narrow and has small width as compared with its length, therefore the dimensionless parameter δ is very small. Thus it seems reasonable to ignore terms of the order δ2 and higher order. Note that this is also true for the flat plate hemodialyzer, for which the parameter δ2 is of the order 10−8 (see the data given in Table 27).The set of Eqs −14 contau, v and p in the power series of the dimensionless Jeffrey fluid parameter asNow expanding λ2):we obtain the following systems of initial-boundary-value problem up-to the Order  can be obtained asHence the difference of mean pressure ΔThe non-dimensional wall shear stress may be obtained asThe dimensionless volume flow rate at any cross-section of the channel can be computed asq(x) can be readily obtained as followingThe expression for leakage flux The fractional re-absorption (FR) is the amount of fluid that has been reabsorbed through the channel walls. It can be computed using the following expressionThe streamlines can be determined by using the following relationλ2 by the following equationThus streamlines can be obtained up to the order C5 is an arbitrary constant.where pi, wall permeability parameter K and the Jeffrey fluid parameters λ1 and λ2 on the axial and normal velocity components u, v, the mean pressure difference Δp(x) and the streamline patterns.This section describes effects of the inlet pressure u with y at the cross-section x = 0.3 of the channel for different values of K, pi, λ1 and λ2, respectively. A parabolic axial velocity is formed that has the maximum value at the center line of channel and is zero at the boundary. These figures reveal that the magnitude of axial velocity decreases rapidly as the inlet pressure and the wall permeability are increased. Similar effects are also noticed when the magnitudes of Jeffery fluid parameters is increased. However relatively small variations happen due to increase of λ1 and λ2 as compared to those due to pi and K.Figures v with y at the cross-section x = 0.3 of the channel for different values of K, pi, λ1 and λ2, respectively. Comparing with the axial velocity distribution, opposite effects of these parameters are observed on the normal velocity component. It can be seen clearly that v increases rapidly as the magnitudes of pi, K, λ1 and λ2 are increased. Thus, the wall seepage enhances by increasing these parameters. Effect of λ1 and λ2 on v are prominent as compared to those on u.Figures pi, K, λ1 and λ2 are shown in Figs p decreases rapidly as the values of these parameters are increased. It can also be seen that variations in Δp are dominant after the middle of the channel.Variations of the mean pressure difference in the axial direction for different values of K and (or) the inlet pressure pi increase to a certain value, a reverse flow phenomenon occurs. It happens due to the fact that if K or pi are increased, all the entering fluid is reabsorbed through seepage at the channel wall before the channel exit. Thus, a stagnation point flow can be seen in these two figures, Figs λ1 is increased.Streamline pattern of the flow is presented in Figs QA and the mean pressure drop ΔP in an artificial kidney (FPD) by using results of the former section. An FPD comprises of several compartments of blood. Every compartment involves two rectangular sheets that are composed of recovered cellulose. The two sheets are clipped at their edges by a couple of rectangular notched plastic sheets. The blood streams between the cellulose sheets whereas the dializing liquid goes in a counter-current or a cross-current stream along the sections in hemodialyzer board29. The volume of blood lost by the leakage through cellulose in a given time, from a known recycling volume is taken to be the ultrafiltration rate.In this section, we aim to derive equations for the computation of ultrafiltration rate L be the cellulose length, then we can compute the ultrafiltration rate for the presented model as followingQ0 = Q(0) and QL = Q(L). The non-dimensional expression for Let g use of , 49) an anL be tg use of  in 65),,L be thex = 0 and x = L. By using Eq.  and then solving the resulting equation we obtain a real root K = 6.23 × 10−4. The ultrafiltration coefficient Lp is then computed from Lp = 6.66 × 10−16 cm2 −pm have been found experimentally by Malino et al.31 and Mcdonald32. A series of experiments performed by Brown et al.33 also highlights the dependence of QA on the mechanical filtration coefficient, membrane thickness and the membrane area.Graphs of the ultrafiltration rate Lp, Eq. (QA with the trans-membrane pressure difference for different values of membrane thickness. The experimental curve in this graph is plotted by admitting the experimental result of Kauffmann et al.30 which states that Lp is 1.25 × 10−15 cm2. From this figure it can be seen that for experimental and theoretical curves to be in good agreement, the membrane thickness t should be approximately 1.5.0 × 10−3 cm. This thickness is approximately half of the estimated thickness obtained from the data of Funck-Bretano et al.29. The importance of membrane thickness in determining the ultrafiltration rate can also be seen from this graph. For example, it can be seen that magnitude of the ultrafiltration rate can be doubled if the membrane thickness is halved. In order to determine a desired ultrafiltration rate for variations of the dimensionless filtration coefficient K, theoretical values of the ultrafiltration rate are tabulated in Table K causes the higher ultrafiltration rate.For a given or desired mechanical filtration coefficient Lp, Eq.  can alsoλ1 and λ2 equal to zero. The derived equations for the ultrafiltration rate and the mean pressure difference can be confidently used in studying the flow in a flat plate hemodialyzer. In applying the current results to study the problem of flow in flat plat hemodialyzer, one should not overlook the physical aspects of the flow phenomenon. It is also concluded the presented results are theoretical in their soul, therefore one should perform more experimental and theoretical investigation in order to have a complete understanding of the flow in a flat plat hemodialyzer.The Jeffrey fluid model is a simpler model that describes well the physiological flows of non-Newtonian nature. In the study of fluid flow problems in porous-walled channels of small width, the presented model can serve as generalization of the usual Newtonian fluid model, since the obtained results can be reduced to the later one’s by substituting parameters


Coronal structures receive radiation not only from the solar disc, but also from the corona. This height-dependent incident radiation plays a crucial role in the excitation and the ionisation of the illuminated plasma. The aim of this article is to present a method for computing the detailed incident radiation coming from the solar corona, which is perceived at a point located at an arbitrary height. The coronal radiation is calculated by integrating the radiation received at a point in the corona over all of the corona visible from this point. The emission from the corona at all wavelengths of interest is computed using atomic data provided by CHIANTI. We obtain the spectrum illuminating points located at varying heights in the corona at wavelengths between 100 and 912 Å when photons can ionise H or He atoms and ions in their ground states. As expected, individual spectral lines will contribute most at the height within the corona where the local temperature is closest to their formation temperature. As there are many spectral lines produced by many ions, the coronal intensity cannot be assumed to vary in the same way at all wavelengths and so must be calculated for each separate height that is to be considered. This code can be used to compute the spectrum from the corona illuminating a point at any given height above the solar surface. This brings a necessary improvement to models where an accurate determination of the excitation and ionisation states of coronal plasma structures is crucial. To compmentclass2pt{minimet al. . The He ix 368 Å line mean intensity with height is shown in Figure The variation of the Mg entclass1pt{minimaix 171 line (x 174 Å line has a formation temperature of xv 284 Å line (Figure Although the mean intensities of the lines are integrated over the entire corona, the portion of the corona nearest to the point considered has the greatest effect on the incident spectrum. The mean intensity of each of these lines is strongest when viewed from a point in the corona closest to where they are formed.v 630 Å line contributes most of the total mean intensity within this range. Figure Each line’s mean intensity will vary with height in a different way from other lines, which means that for different heights, each line will have to be recalculated. It is not possible to simply calculate each line once for one height and then multiply the whole spectrum by some scaling factor, as each line scales differently with height. Summing the lines across wavelength ranges would not solve this issue, as the total mean intensity of different wavelength ranges will also scale differently with height.This article presents a method for obtaining the radiation from the quiet-Sun corona as observed from a location within the corona. We showed that the radiation from the corona illuminating a point within the corona depends on the height of said point above the solar surface, and why it is necessary to calculate this coronal spectrum separately for different heights within the corona.et al. (4Section Our code was tested in Section In Section Figure


Escherichia coli, self-propel in fluids by using specialised motors to rotate multiple helical filaments. The rotation of each motor is transmitted to a short flexible segment called the hook which in turn transmits it to a flagellar filament, enabling swimming of the whole cell. Since multiple motors are spatially distributed on the body of the organism, one would expect the propulsive forces from the filaments to push against each other leading to negligible swimming. We use a combination of computations and theory to show that the swimming of peritrichous bacteria is enabled by an elastohydrodynamic bending instability occurring for hooks more flexible than a critical threshold. Using past measurements of hook bending stiffness, we demonstrate how real bacteria are safely on the side of the instability that promotes systematic swimming.Peritrichously-flagellated bacteria, such as  Many bacteria self-propel in response to physical and chemical cues by actuating specialised, rotary motors in bulk fluid environments2. Each motor imposes a moment normal to the surface of the cell body transmitted to a helical flagellar filament via a short elastic segment called the hook that acts as a universal joint4. Due to the helical nature of flagellar filaments, the rotation imposed by each motor is not time-reversible and as a result bacteria are able to swim5. While a flagellar filament can take one of eleven polymorphic forms, the normal form used for swimming is left-handed and rotates counter-clockwise  propelling the bacterium cell-first7, a type of swimmer known as a pusher8. If the same left-handed helix were to rotate in the opposite direction then the cell would swim flagella first and be a puller9.Although out of sight, bacteria dominate chemical processes on our planet. They are the most abundant organisms on earth and, equipped with the ability to live in extreme and hostile conditions, they play crucial roles in both the environment and human health11. Well-studied examples include Escherichia coli . At the end of a tumble, the motors return to their normal CCW state, the bundle reforms and the bacterium swims in a new direction. Through a modulation of the tumbling frequency, bacteria can move towards favourable environments14. Crucial for the formation of the filament bundle, and successful swimming, is the flexible hook. When the hook is stiffened, bacteria are stuck in a tumble mode and can barely swim15. Hook flexibility is also crucial for singly flagellated bacteria, enabling changes in swimming directions via buckling16 but causing unstable locomotion if it is too flexible17, an effect itself stabilised by the presence of multiple flagella .Peritrichous bacteria possess multiple flagella that can grow from essentially any point on the cell body surfaceard Fig. . The mai18. Most studies assume a fixed relative position between helical filaments (or bundles) and the cell body, and modelling tools have been developed to address both swimming21 and the bundling/unbundling process23.Much theoretical work has been devoted to predicting the propulsion mechanisms of self-propelled bacteriaIf peritrichous bacteria have similar filaments distributed spatially around their cell body, why are the flagella not all pushing against each other leading to negligible swimming? In this paper we use a combination of computations and theory to show that swimming is enabled by an elastohydrodynamic instability of the hook. If hooks are too rigid, flagellar filaments always point normal to the cell body surface and never bundle. In contrast, when the bending rigidity of the hook is below a critical threshold, the feedback between the flow induced by the flagella and hook bending leads to a conformational instability resulting in all the flagellar filaments gathered at the back of the cell, and net locomotion. This sharp transition from negligible to successful swimming is observed numerically with decreasing hook stiffness and we show that this instability can be rationalised using a simple model of a cell propelled by two straight active filaments. By examining past measurements of hook flexibility, we demonstrate that bacteria are safely on the swimming side of the instability.Nf flagella  a helical flagellar filament of the normal left-handed polymeric form whose hydrodynamics is captured with slender-body theory24. Motor and filament parameters are chosen to match those of E. coli bacteria7 . The restoring elastic moment imposed by each motor on its flagellar filament is modelled as torsion spring of spring constant EI and 16. The magnitude of the restoring moment is thus given by K|θ| and the elasticity of the hook acts to align the helix axis with the normal to the cell body. The computational model solves for the instantaneous positions of the flagellar filaments and for the swimming velocity, Ub, and angular velocity, Ωb, of the cell body as a function of the hook stiffness.We start by building a computational model of the locomotion of a peritrichous bacterium, as outlined in the Methods section with mathematical details in supplementary information. We consider a bacterium propelled by lla Fig.  with a cNf = 4 flagella, the average number of flagella on an E. coli cell6. The motors are positioned symmetrically around the surface of the cell body. We start the computations with each flagellar filament tilted at some small angle away from the normal to the surface and march the system forward in time while tracking the position of the cell in the laboratory frame and of the flagellar filaments relative to the cell body. Associated movies are available online (see supplementary information).Examining the results of our computational model uncovers a remarkable elastohydrodynamic instability, illustrated in Fig. t = 200 . While both start at the same location (A), the cell with the flexible hook (K = 0.1) ends up with their flagellar filaments all wrapped in the back and is able to swim five times as fast (B) as the stiff-hooked cell (K = 100) whose flagellar filaments have remained in the same splayed configuration (C). This is quantified in Fig. 5. Importantly, the transition to fast swimming for flexible pusher bacteria does not occur smoothly with changes in the hook stiffness but instead it takes place at a critical dimensionless value of Kc ≈ 1 . Above Kc, all flagella remain normal to the cell (θ ≈ 0) leading to negligible swimming while below Kc, all flagella wrap behind the cell (|θ| ≈ π/2) leading to a net locomotion.In Fig. 16. Instead, the instability arises from the two-way coupling between the conformation of the flagella and cell locomotion. To unravel the physics of this instability, we consider in more detail the case of a spherical cell body and two flagella, which is the minimum configuration able to show the instability while capturing the same physics as geometrically-complex cases (see associated movies in supplementary information). The steady-state computational results in this case are shown in the main part of Fig. θ between the axis of the flagellar filaments and the cell body (A) and for the net lab-frame swimming speed U of the cell (B). While the flagella conformation of puller bacteria is independent of the hook stiffness and leads to zero swimming (light red circles), pusher cells clearly display a sudden jump to a wrapped conformation and a net locomotion for a hook stiffness below Kc ≈ 0.79 (dark blue circles).This sharp transition does not originate from a buckling instability of the hook which is only modelled here at the level of a torsional springa and are tilted by symmetric angles ±θ away from the body surface normal, K, pushes on the cell along their tangential direction with propulsive force density f < 0) and the cell is a pusher. In contrast, for CW motion, the propulsive forces point away from the cell (f > 0) and the swimmer is a puller.The observed dynamics can be captured by an analytical model demonstrating that swimming occurs as the result of a linear elastohydrodynamic instability. Consider the simple geometrical model illustrated in Fig. entclass1pt{minimaU) and the rate of change of the conformation of the filaments , the balance of forces on the whole cell in the direction of swimming, The swimming speed . We start with small perturbations around θ = 0 and compute the long-time steady state of Eq.  then the configuration with θ = 0, which is associated with no swimming U = 0, is always linearly stable to small perturbations for any value of K. In contrast, pushers with f < 0 are linearly unstable for K < Kc such that the right-hand side of Eq. (θ ≠ 0) with net swimming (U ≠ 0). Note that the simple theoretical model  would therefore not be subject to this instability, but peritrichous bacteria such as E. coli and Salmonella enterica would.How does this swimming instability affect real bacteria? We first note that for the instability to be relevant, the rotary motors need to be spatially distributed around the organism and therefore the instability would not occur if the rotary motors were all located around the same position on the cell body. Lophotrichous bacteria whose multiple flagella are positioned at the pole of the cell  and the pitch (2.22 μm) and frequency (110 Hz) of E. coli flagella7, we obtain Kc ≈ 9.6 × 10−19 Nm. Using a hook length 2, we therefore predict a critical hook stiffness of By examining past measurements on the bending stiffness of peritrichous bacterial hooks, we next discover that swimming bacteria are safely on the unstable side, explaining their ability to swim despite the presence of spatially distributed motors. The strength of the torsion spring in our model is given by 16. The physics of this instability lies in the feedback between the conformation of the flagella and the swimming of the cell. Flagellar filaments create propulsive forces which propel the cell forward. In the frame of the moving cell, the filaments experience hydrodynamic moments aligning them with the direction of swimming. The rigidity of the hook balances these hydrodynamic moments and below a critical rigidity, an elastohydrodynamic instability transitions the filaments from a splayed state to a conformation where they are gathered behind the cell. Our results rationalise the ability of real peritrichous bacteria to swim by showing that they are designed to undergo a successful transition to swimming after each tumble.In summary, we showed theoretically and computationally that pusher peritrichous bacteria can swim by exploiting an elastohydrodynamic instability while pullers never can. This instability is due to the bending rigidity of the hooks and is different from the buckling instability displayed by polar bacteriaUb, and angular velocity, Ωb, of the cell body by enforcing mechanical equilibrium at all time . At low Reynolds numbers, the balance of hydrodynamic forces and moments for the whole cell at its centre leads to a linear relationship between the swimming kinematics of the cell and the angular velocities of each filament, denoted by ωi for ith filament, of the formϒi depend on the hydrodynamic resistance of each individual component of the cell and on their geometrical arrangements.We give here a brief outline of the computational model, with all details found in supplementary information. Our computational model solves for the instantaneous positions of the flagellar filaments and for the swimming velocity, i may be written as Γi, Λi and Δi dependent on the geometry and relative configuration of the flagellar filament and cell body, and are proportional to the fluid viscosity. If we use the unit vector ki and The rotation rate of each filament has a prescribed value along its helical axis and we need two additional equations to solve for the other two components. This is obtained by examining the local balance of moments. In the frame of a filament, the swimming velocity and rotations are experienced as background flows which act to tilt the flagellum away from the normal to the motor while the hook applies an elastic restoring moment. The hydrodynamic moment acting on filament see Fig.  then theFigure 3 - Puller flexible swimmerFigure 3 - Puller stiff swimmerFigure 3 - Pusher flexible swimmerFigure 3 - Pusher stiff swimmerFigure 4 - Flexible spherical swimmerFigure 4 - Stiff spherical swimmerSupplementary Information


Droplet microfluidics has shown great potential for on-chip biological and chemical assays. However, fluid exchange in droplet microfluidics with high particle recovery is still a major bottleneck. Here, using acoustophoresis, we present for the first time a label-free method to achieve continuous background dilution in droplets containing cells with high sample recovery. The system comprises droplet generation, acoustic focusing, droplet splitting, picoinjection, and serpentine mixing on the same chip. The capacities of the picoinjection and the droplet split to dilute the background fluorescent signal in the droplets have been characterized. The sample recovery at different droplet split ratios has also been characterized. The results show a maximum of 4.3-fold background dilution with 87.7% particle recovery. We also demonstrated that the system can be used to dilute background fluorescent signal in droplets containing either polystyrene particles or endothelial cells. I.Droplet microfluidics provides a platform for the generation of monodisperse droplets at high throughput and the technology has found many applications in biological sciences, from single cell RNA sequencingTo enable the integration of complete biological assays into the droplet microfluidic format, different technical solutions to handle and analyze the droplets on-chip are needed. For example, unit operations have been developed to split,et al. presented a method to decrease the background fluorescent signal in droplets by first adding fresh medium to the original droplet and consecutively split the droplet in three succeeding T-junctions to return the droplet volume to its original value.et al.et al.et al. presented a method not requiring magnetic beads where they used surface acoustic waves to achieve droplet washing by first pushing the encapsulated polystyrene particles to the end of the droplet, splitting the droplet in half, followed by merging with a second droplet and splitting in half again.Different technical solutions to wash beads and cells encapsulated inside droplets have previously been demonstrated in the literature. For example, Mary The microfluidic platform we have developed for exchanging fluid inside droplets is operated by first using bulk acoustic waves to control the position of the particles in a trifurcation droplet split followed by injecting new fluid to restore the original droplet volume. Fluid is injected into the droplets by the widely used picoinjection technique as it is simple to design and fabricate, and the injected volume can be controlled precisely.II.Acoustophoresis is a common method to focus, enrich, and sort bioparticles in microfluidic channels.k is the wavenumber  droplet generation, (2) acoustic focusing, (3) droplet split, (4) picoinjection, and (5) serpentine mixing . The acoDroplets are generated in squeezing mode in a cross-flow channel at a rate between 0.5 Hz and 1.2 Hz. Both the dispersed phase and the continuous phase channels have separate inlets where the flow rate is controlled independently. As the droplets travel down the channel driven by the syringe pump, the encapsulated beads or cells are aligned in the center of the droplets by the acoustic radiation force. The droplets flow through the trifurcation channel where they are split into three daughter droplets with the particles remaining in the center daughter droplet due to the acoustic alignment. The two side split channels are joined to a common outlet channel, and the flow rate is controlled from a common syringe pump. The center daughter droplets then pass the picoinjector where clean water is injected to dilute the droplets. The serpentine channel enhances mixing of the injected fluid.The microfluidic channels were etched using a standard dry etching processB.H is the height of the channel, W is the width of the channel, and L is the length of the droplet. The width and length of the droplets were determined by an image processing program  from the threshold of the light intensity.Droplet images were captured using a camera with a CMOS sensor  mounted on a fluorescence microscope  at three different positions on the chip as indicated in C1 and V1 are the background concentration and volume of the original droplet, and C2 and V2 are the background concentration and volume of the droplet after the washing step, respectively.The initial concentration of the used solutions was known, so the concentration of the droplet at the end of the serpentine channel was calculated using the law of mass conservation,μm, ThermoFisher) were added to the dispersed aqueous phase to evaluate the particle recovery. The visual field of the microscope was set at the split channel so that a video could be captured of 20 individual droplet splits at position 3. Still images displaying the same droplet right before and directly after the split were acquired, and the encapsulated beads were manually counted. The particle recovery of each droplet was determined as the number of beads in the center daughter droplet after the split divided by the number of beads in the droplet before the split. We evaluated the precision of the measurements using 20 and 50 droplets when the flow rates of the continuous phase, the dispersed phase, and the split side channels were 2 μl min−1 for each inlet, 2 μl min−1, and 4.5 μl min−1, respectively. At a confidence level of 95%, the recovery of beads was 88.8 ± 6.8% for n = 50 and 87.5 ± 7.0% for n = 20 with acoustic actuation, and 28.9 ± 5.0% for n = 50 and 28.9 ± 5.0% for n = 20 without acoustic actuation. The F-ratio in ANOVA  is 0.9 with acoustic actuation and 1.3 without acoustic actuation, which is less than the critical F value of 1.8 from the F distribution table (95% confidence level). Therefore, there is no significant difference in recovery of beads between sampling 20 or 50 droplets. Hence, to simplify the workload of counting the beads, 20 droplets were analyzed for all particle recovery experiments.Fluorescent polystyrene beads  water, Sigma-Aldrich] either with or without microbeads or cells. Liquid was injected into the system using syringe pumps . Plastic syringes  were used for the continuous phase, and glass syringes  were used for the dispersed aqueous phase. The split ratio of the droplets was controlled by adjusting the withdrawal flow rate of the split side channels from a common syringe pump. Another glass syringe filled with clean water was connected to the picoinjector, and the fluid was injected using a syringe pump. At the end of the chip, the outlet was open to the air. All syringes were connected to the chip using polyethylene tubing .Light mineral oil (Sigma-Aldrich) with 2% Span-80 (Sigma-Aldrich) was used as the continuous phase. The dispersed aqueous phase used was a fluorescent solution [1 mg mlμM, DMEM Glutamax, Thermofisher). A solution of 2.3 × 107 cells ml−1 and the background concentration of 2 μM cell tracker were used for the experiments.To demonstrate the droplet background dilution, fluorescent solution was used as the dispersed phase when measuring the volume of the droplets. Polystyrene beads were added to the dispersed phase to show the particle recovery capability. The ability of cells in droplet washing was demonstrated by encapsulation of endothelial cells  stained with a green cell tracker  and after the droplet split (position 4) stayed constant at different flow rates of the picoinjector, which means the effect of back flow from the picoinjector can be neglected for droplet generation and droplet split.To characterize the capability of the picoinjector and identify its optimal flow rate, a set of experiments was performed where the injection flow rate of the picoinjector was systematically varied. The flow rate of the droplet generation and the droplet split was kept constant to ensure the same volume of the original droplets . The floB.When the droplet flows through the split channel, it is divided into three daughter droplets. The volume of each daughter droplet is determined by the ratio between the flow rates of the center and the split side channels and is controlled by the withdrawal flow rate of the split side channels. A higher flow rate of the split side channels results in smaller center daughter droplets after the split.μl min−1) to ensure the same volume of the original droplets. After the split, the volume of the droplet was returned to its original volume by injecting different volumes of clean water with the picoinjector. The volume and concentration of the droplets were measured at positions 3 and 4, as well as after the picoinjector at position 5, as described above [supplementary material).To evaluate the effect of the split ratio on the final droplet background dilution, the flow rates of the split side channels were varied systematically. The flow rate of the continuous and the dispersed phase was kept constant , the recovery of beads was still 87.5% ± 7.0% with the acoustics activated, as compared to only 28.2% ± 4.4% without acoustic actuation [In addition to the droplet background dilution, the particle recovery was characterized in relation to the flow rate ratios following the method described above. When the acoustics was off, the recovery of beads was reduced as the flow rate of the outlet channel increased, showing that the beads were randomly distributed in the daughter droplets. When the acoustic was on, the recovery of the beads reached ∼90% for all flow rates from 1.5 ctuation .C.supplementary material, additional characterization data on the effect of the original droplet size and the total flow rate on the background dilution efficiency and the recovery of beads are presented. The results show the ability to dilute the background signal in droplets with high particle recovery for different original droplet sizes and different total flow rates.The results in the previous sections show the characterization of all individual parts of the droplet washing system and their respective effect on reaching maximum droplet background dilution with a high particle recovery. In the μl min−1, and the flow rate of each inlet for the continuous phase was set to 1.7 μl min−1 to generate droplets with an original volume of 51.9 ± 0.7 nl. To minimize the volume of the center daughter droplet at the split, the withdrawal flow rate of the split side channels was set to 4 μl min−1, which was previously determined as the maximum flow rate with remained stability in the system. The average volume of the droplets after the split was decreased to 11.8 ± 0.7 nl. The flow rate of the picoinjector was set at 2 μl min−1, which is the maximum flow rate for stable operation in this design. From optical images of the droplets at the end of the serpentine mixing channel (position 5), it could be measured and calculated that the background concentration in the droplets was decreased from 1.00 mg ml−1 to only 0.23 mg ml−1, representing a 4.3-fold background dilution with a bead recovery of 87.7% ± 4.3%.To achieve maximum background dilution, the volume of the droplet after the split should be as small as possible and the volume of the droplet after picoinjection should be as large as possible. Based on the characterization above, the flow rate of the dispersed phase was set to 2.6 D.supplementary material). The same flow rates as in the maximum background dilution experiment were used. EX = 470–490 nm) channel of the microscope, although they had been labeled with a fluorescent stain. At position 5, the background noise was more than 4-fold diluted, and the cells could be observed in the FITC channel. The recovery of cells was high when the acoustic focusing was active, which was similar to what was demonstrated above using beads.To demonstrate the use of this new unit operator for on-chip background dilution with cells encapsulated in droplets, endothelial cells stained with a fluorescent cell tracker were used (Videos 3 and 4 in the V.μl min−1. This microfluidic system could achieve a maximum 4.3-fold background dilution (from 1.00 mg ml−1 to 0.23 mg ml−1) with a particle recovery of 87.7%. Moreover, we succeeded in applying this chip to performing background dilution in droplets with encapsulated cells at high cell recovery.We have designed and fabricated a microfluidic chip for on-chip background dilution of droplets with high particle recovery. This chip comprises five different unit operators that are integrated into a complete microfluidic circuit: droplet generation, acoustic focusing, droplet split, picoinjection, and serpentine mixing. We have characterized the capability of the picoinjection where the volume of the injected fluid can be controlled by the flow rate of the picoinjector. We have also characterized the droplet split by varying the withdrawal flow rate of the split side channels to minimize the volume of the daughter droplet. The main limitation for increasing the dilution efficiency in the current design is the droplet coalescence observed after the droplet split when the withdrawal flow rate of the split side channels exceeded 4.5 This microfluidic platform developed here has the ability to continuously dilute the background signal in droplets containing biological sample on-chip, and it should be straightforward to combine it with other droplet unit operators in the future.supplementary material, characterization data on the impact of the original droplet size and the total flow rate on background dilution and recovery are available, as well as videos showing acoustic focusing of beads and cells.In the


Pulmonary hypertension (PH) is a medical condition characterized by elevated pressures in the pulmonary vessels. Pulmonary arterial hypertension (PAH), or pre-capillary PH, is a subgroup of the broader PH definition. PAH is rare compared to other groups of PH; its prevalence is about 15 cases per million in the adult population. Several disease processes may lead to PAH; however, the most common cause of PAH is idiopathic. Until recently, treatment for PAH was very limited and prognosis was dismal. Limitations in management remain present today but more treatment options are available for patients suffering from this condition. Most of the information available regarding PAH comes from registries in the United States and Europe. Limited information about epidemiology, treatment options, and response to the treatment is available for other ethnic groups such as Hispanics. In the world of medicine, we have learned from other more common medical conditions that components, such as genetics, environment, and culture may affect how diseases manifest and how they respond to treatment. It is important to be aware of how different ethnic groups exposed to different environmental conditions respond to different treatment modalities. The aim of this paper is to review the limited data available regarding PAH in Hispanics. This paper will review the information regarding the etiology, diagnosis, and treatment modalities available in South American and Central American countries. This paper will also review the data available for Hispanics diagnosed with PAH living in the United States. The goal is to highlight the difference in how PAH manifests in Hispanics compared to other ethnic groups. We aim to emphasize the importance of the lack of data available for this group and how it may be affecting the way we are treating Hispanics with PAH.  Pulmonary arterial hypertension (PAH) is a subgroup of a broader medical condition known as pulmonary hypertension (PH). PH is a disease process which is characterized by elevated pressures in the pulmonary vessels. Different etiologies may cause the elevated pressures and therefore PH is classified into five different groups based on the etiology. Group 1 is pulmonary arterial hypertension, PAH, ; Group 2 is secondary to left-sided heart disease; Group 3 is due to chronic lung disease and hypoxemia; Group 4 is due to chronic thromboembolic disease , while Group 5 is due to unidentified mechanisms [The most common symptoms associated with PH are dyspnea and fatigue on exertion; such symptoms are secondary to inadequate increase in cardiac output during exercise. Other symptoms may include exertional chest pain, exertional syncope, weight gain from edema, and even abdominal pain and swelling due to hepatic congestion. Physical examination may reveal increased intensity of the pulmonic component of the second heart sound, as well as signs of right ventricular failure in more advanced cases, such as elevation of jugular venous pressure, murmur of tricuspid regurgitation, hepatomegaly, ascites, and peripheral edema . ImagingOnce PH is suspected, diagnostic testing is used to confirm the diagnosis, assess the severity, and identify the potential etiologies. Detailed history should focus on any evidence pointing towards connective tissue disease, history of smoking or chronic lung pathology, prior use of medications such as appetite suppressants or drugs such as cocaine, risk of having HIV or liver disease, and prior history of thromboembolic disease . Transthoracic echocardiography (TTE) is usually the initial step in diagnosing PH. Tricuspid regurgitant jet velocity may be used to estimate the pulmonary artery systolic pressure (ePASP). The right ventricle size, wall thickness, and function may be assessed, as well as the left ventricular function to assess potential contribution of left-sided heart disease. It is important to know that the ultimate diagnosis must be made from values obtained from a right heart catheterization (RHC), as studies have shown that ePASP has poor correlation with values obtained directly from RHC . Other sRight heart catheterization is the gold standard for the diagnosis of PH. It may be used to differentiate between the different groups of PH. It is particularly important for the diagnosis of Group 1 and Group 2 PH, as well as for suspected mixed etiology for PH. Left heart catheterization may also be useful to rule out ischemic cardiac disease. PAH, or Group 1 PH, is diagnosed when the mean pulmonary artery pressure is > 20 mmHg, the pulmonary wedge pressure (PCWP) is less than 15 mmHg, and when pulmonary vascular resistance is more than three wood units . RHC mayLittle is known about the epidemiology of PH outside of populations in the United States and Europe. These countries have extensive registries documenting the prevalence and etiology of the disease; however, the data in Latin American countries are scarce. Information regarding genetics and epidemiology for different ethnicities and geographical locations is important as the epidemiology and treatment of the disease may differ significantly between different ethnic groups. Literature review reveals limited studies and registries in Latin American countries which may shed some light on this topic .Most of the data available regarding the etiology, diagnosis, and treatment of PAH in Latin American countries come from three different registries. The information comes from registries in Argentina, Chile, and Brazil. Most of the data in these registries is for Group 1 PH, or PAH, and more specifically idiopathic PAH. The prevalence of PAH in these registries is higher than the registries available for the United States and Europe . It is also important to recognize that there are different common etiologies for PAH even between Latin American countries. For example, in Brazil, schistosomiasis is one of the main causes of PAH (about 20% of cases), while in Argentina congenital diseases are an important cause of PAH (about 28% of cases) -8. ConneAnother key difference is the severity of the disease. Most patients from the Latin American registries were in NYHA/WHO functional class III or IV (around 50%) which is lower than the documented cases in registries from the United States and Europe. The 6-minute walk distance was also higher in the three Latin American databases compared to the US REVEAL registry [It is important to mention that the three registries from Latin America showed the average age of diagnosis being much lower compared to registries in the US and European nations. Mean age of diagnosis varied between 34 and 51 in Latin American countries compared to over 50 in the US and European registries. All studies also showed a similar prevalence in females around 60%-86%) to the prevalence in the US and European countries (around 70%) [0%-86% toCuriously, in terms of survival, the Brazilian and Argentinian registries showed a slightly higher survival rate compared to US and European registries. This observation may be due to the younger age at diagnosis and lack of other comorbidities seen in these populations -8. Such Data regarding the prevalence and etiologies of PAH in Hispanics living in the United States are also limited. The NIH and the REVEAL registries in the United States provide the most information for different races/ethnicities in patients with the diagnosis of PAH. The NIH registry reports that about 2.3% of patients with the diagnosis of PAH are Hispanics . The REVThe conclusion from all the database analysis when it comes to the prevalence of PAH among Hispanics living in the United States as well as in Latin American countries is that the data for this population are very limited. The limitations are likely due to several reasons, including the lack of data coming from most Latin American countries, the small percentage of Hispanics enrolling in clinical trials in the United States, and socioeconomics. Socioeconomics is particularly important because in many cases the lack of resources in the Hispanic population leads to delay in diagnosis as well as medical treatment . UnfortuThe lack of data for the Latin American and US Hispanic population possibly also has implications when it comes to treatment and management of the disease. Genetics and environmental exposures likely play a role in the efficacy of different medications in different races and populations, in a way similar to how different races respond differently to medications such as angiotensin converting enzyme inhibitor (ACEi). One PAH medication that has shown to have different efficacy rates in different races is the class of medication known as endothelin-receptor antagonists. Gabler et al. completed an analysis of six randomized controlled trials comparing outcomes of using this medication based on demographic factors. The result was that in the white population the 6MWD increased by 41.6 m while in black patients it only increased by 3.5 m. It was hypothesized that black patients have higher levels of endothelin-1, and therefore need a higher dose of the medication compared to white patients . These fIn conclusion, it is important to raise awareness among Hispanics in Latin American countries and the United States regarding PH. Awareness of this disease is limited among these populations and this likely leads to under diagnosis as well as delayed treatment. It is also important to increase the percentage of this population participating in clinical trials and collect data based on different races. This would lead to better understanding in the interaction between environmental exposure, genetics, pharmacology, and response to treatment.


Recent molecular dynamics (MD) simulations of human hemoglobin (Hb) give results in disagreement with experiment. Although it is known that the unliganded (T Human hemoglobin is the paradigmatic model system for cooperativity in proteins. It transports oxygen from the lungs to the tissues and it is composed of two identical etramer.  Althoughetramer. , how it etramer. . The firetramer. , which setramer.  based onHigher resolution (2.8 Å) X-ray structures of unliganded and liganded hemoglobin  confirmeSeveral papers using different force fields and simulation conditions have been published recently  describi4, 2DN3) . Althougsee also . This ocR0 state , which i, we wondered whether the box size used for the MD simulations might be too small for the hydrophobic stabilization to be manifested. Because most of the simulation time is consumed by the waters, rather than the protein itself, which is of primary interest, a ‘lore’ has grown up about the minimal box size that can be used with periodic boundary conditions to carry out meaningful simulations. The standard requirement is that there must be at least five water molecules between any protein atom and the box boundary. , 2009 ThTo investigate the possibility that larger boxes were required for stabilizing Ttz model , were prsee also .If the free energy difference between the Tcule see  shows suBased on hydrodynamic arguments, The results described here suggest that the correct free energy of hemoglobin, at least to the extent that TSimulations for all box sizes have also been done with His146 deprotonated. The results for that system showed that Ttz model .To relate the above results to the hydrophobic effect, we use the construct of Chandler , who sho box see . The behThe full radial distribution function is reported in To summarize, the TAs a more local measure of the effect of undersolvation the radial distribution function In addition to the global behavior, local structural changes involving the two His146 residues were examined. The results –5 show tImportantly, the ability of the 150 Å box to stabilize the T-state starting from the R-like structure in the 120 Å box after 1 Given the increasing use of molecular dynamics simulations to study conformational transitions in large proteins and in an explicit solvent environment, the present result that much larger boxes than those used standardly are required for what appears to be the hydrophobic effect to be manifested is of general interest. It has wide ranging implications for the interpretation and validity of previous simulations, as well as those to be undertaken in the future. Given that the magnitude of the effect is expected to depend on the size (and shape) of the molecule and its hydrophobicity, as well as possibly other properties , the reqThe influence of solvent layers on the structural stability of hemoglobin tetramer is investigated using Molecular Dynamics (MD) simulations. Extended large-scale simulation were performed with the CHARMM36 all atom force-field  and the The coordinates of the starting structure are taken from the X-ray structure of tetrameric human hemoglobin in the deoxy form, PDB code 2DN2 (1.25 Å resolution) . The prootonated . The proFor the electrostatic interactions, particle-mesh Ewald (PME) was used with a grid spacing of 1 Å, a relative tolerance of lgorithm  was usedescaling   is −5 cm2/s . However−5 cm2/s . Thus, tperature . For dirIn order to directly compare with the literature  the 40 Å In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.eLife. Your article has been reviewed by three peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by John Kuriyan as the Senior Editor. The reviewers have opted to remain anonymous.Thank you for submitting your article "Valid Molecular Dynamics Simulations of Human Hemoglobin Require a Surprisingly Large Box Size" for consideration by The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.Summary:This is a potentially interesting study in which the authors suggest that the stability of the T state of hemoglobin in molecular dynamics (MD) simulations depends critically on the size of the simulation box and that the T state remains stable only with a sufficiently large box containing a relatively large portion of bulk-like solvent. While this observation may bear important practical implications to MD simulation of biomolecules , its statistical validity needs to be strengthened with further data, and the understanding of its origin requires further analyses.Essential revisions:1) The key observation was made based on four simulations in four different simulation boxes. Each simulation has been performed only once. Given the stochastic nature of protein conformational change in MD simulations, repeats of these simulations are essential to show that the observation is of statistical significance. Minimally, each simulation should be repeated once or twice, which should be practically manageable since each simulation is 1 microsecond long. Other simulations should be considered to help establish the key observation. For example, in the cover letter, the authors stated that they "ran simulations starting with a partially decayed (i.e. R-state-like) structure from a 120 ˚A3 box in the 150 ˚A3 box and demonstrated that it progressed toward the T0 structure." These data would be very important, but it is not shown in the manuscript. The authors should show plots of all the distance, angles and RMSDs for this simulation so that it would be easier to assess the significance of their finding. They should also run the same system for an additional 1μs in the 120A box, to provide a fair comparison between the two. Various attempts by the authors to stabilize the T state, which is mentioned in the cover letter but largely not discussed in the main text or the supplemental information, should be reported with some details as well.2) A possible reason for the instability of the T state would be inaccuracies in the potential energy function, in particular for the Heme group. Also, the 3-point models used to describe water in the simulations are known to provide only a rather rough description of liquid water properties and there is no reason to believe that they would accurately capture the subtle balance of electrostatic and hydrophobic forces that modulate the relative stability of the T and R states. Comparison with previous works is complicated by the use of a different force-field (CHARMM36 (?), instead of the Amber and the Gromos force-fields used in previous works). These issues need to be discussed. Also, the reference for the Charmm36 force-field, which refers to paper for parametrization of the Charmm lipid force-field by mistake, needs to be corrected.3) The analyses to understand the origin of the possible phenomenon consisted of three parts, respectively concerning hydrogen bonds, diffusion, and radial distribution function of water molecules. The first two analyses showed that, with a larger simulation box, an average water molecule in the simulation increasingly takes up the bulk-water behavior. This is certainly sensible but also to be expected, as in a large box a larger portion of waters are not in the vicinity of the protein. Hemoglobin is a protein that contains a number of cavities and a water-filled channel. It is expected that water molecules in the cavities or in the channel will have a smaller diffusion coefficient and a smaller number of hydrogen bonds with respect to the bulk water. The analysis of the average water diffusion coefficient and number of hydrogen bonds as a function of box size  is merely showing convergence towards the bulk as the ratio between (water in cavities)/(bulk water) becomes smaller and smaller. The authors need to more clearly state their connection with the T stability of hemoglobin.4) The authors' underlying hypothesis appears to be that the deviation of water molecules in small boxes from the bulk behavior affects the magnitude of the hydrophobic effect, and that this effect differentially impacts the stability of the two states because the T state is structurally more compact and with less solvent exposed area than the R state. If so, this reasoning should be stated explicitly with necessary data.g(r) presented in Figure 5A, as bulk water behavior seems to be achieved only ~2.5 nm away from Hemoglobin. Figure 5—figure supplement 1 presents the whole RDF profile. This RDF calculated in this manuscript appears to be wrong, as there is water in the center of Hemoglobin, so the RDF should have value close to 1 in the center. If this is a mistake, it should be corrected. Did the authors checked that at the beginning of the simulation water was actually placed in the central cavities of the protein and that this water was properly equilibrated?5) Figure 5A shows that the water RDF around a spherical solute approaches bulk behavior ~0.5-1 nm away from the solute, suggesting that a periodic box that is ~2 nm larger than the solute should give acceptable result. Figure 5B, however, is apparently at odds with the  Essential revisions:1) The key observation was made based on four simulations in four different simulation boxes. Each simulation has been performed only once. Given the stochastic nature of protein conformational change in MD simulations, repeats of these simulations are essential to show that the observation is of statistical significance. Minimally, each simulation should be repeated once or twice, which should be practically manageable since each simulation is 1 microsecond long. Other simulations should be considered to help establish the key observation. For example, in the cover letter, the authors stated that they "ran simulations starting with a partially decayed (i.e. R-state-like) structure from a 120 ˚A3 box in the 150 ˚A3 box and demonstrated that it progressed toward the T0 structure." These data would be very important, but it is not shown in the manuscript. The authors should show plots of all the distance, angles and RMSDs for this simulation so that it would be easier to assess the significance of their finding. They should also run the same system for an additional 1μs in the 120A box, to provide a fair comparison between the two. Various attempts by the authors to stabilize the T state, which is mentioned in the cover letter but largely not discussed in the main text or the supplemental information, should be reported with some details as well.As agreed with the Editor we did not repeat these simulations.2) A possible reason for the instability of the T state would be inaccuracies in the potential energy function, in particular for the Heme group. Also, the 3-point models used to describe water in the simulations are known to provide only a rather rough description of liquid water properties and there is no reason to believe that they would accurately capture the subtle balance of electrostatic and hydrophobic forces that modulate the relative stability of the T and R states. Comparison with previous works is complicated by the use of a different force-field (CHARMM36 (?), instead of the Amber and the Gromos force-fields used in previous works). These issues need to be discussed. Also, the reference for the Charmm36 force-field, which refers to paper for parametrization of the Charmm lipid force-field by mistake, needs to be corrected.Given that other simulations  using different MD codes and force fields find similar instabilities it is unlikely that the FF parametrizations are the prime reason for the thermodynamic instability, see main text, third paragraph. Also, some of the additional tests that were carried out included FF-modifications which, however, did not lead to stabilization in the small water boxes. The reference to the CHARMM36 force field was corrected.3) The analyses to understand the origin of the possible phenomenon consisted of three parts, respectively concerning hydrogen bonds, diffusion, and radial distribution function of water molecules. The first two analyses showed that, with a larger simulation box, an average water molecule in the simulation increasingly takes up the bulk-water behavior. This is certainly sensible but also to be expected, as in a large box a larger portion of waters are not in the vicinity of the protein. Hemoglobin is a protein that contains a number of cavities and a water-filled channel. It is expected that water molecules in the cavities or in the channel will have a smaller diffusion coefficient and a smaller number of hydrogen bonds with respect to the bulk water. The analysis of the average water diffusion coefficient and number of hydrogen bonds as a function of box size  is merely showing convergence towards the bulk as the ratio between (water in cavities)/(bulk water) becomes smaller and smaller. The authors need to more clearly state their connection with the T stability of hemoglobin.0 is stable. Figure 3—figure supplement 1 was added to substantiate this. The shape of the radial distribution functions is rather a consequence than the origin of the T0 stability.In the sixth paragraph of the Results and Discussion it is now clarified that if the water self diffusivity and the hydration network resemble that of bulk water, T4) The authors' underlying hypothesis appears to be that the deviation of water molecules in small boxes from the bulk behavior affects the magnitude of the hydrophobic effect, and that this effect differentially impacts the stability of the two states because the T state is structurally more compact and with less solvent exposed area than the R state. If so, this reasoning should be stated explicitly with necessary data.0 state. What we do observe is, that the T0 state is thermodynamically stable if the water box is sufficiently large such that solvent water behaves as bulk water as judged from the self diffusion coefficient  and the hydrogen bonded network .We have added a statement to the first paragraph of the Results and Discussion which makes clear what is in the papers of Chothia et al. (1976) and Lesk et al. (1985) concerning the role of the hydrophobic effect in stabilizing the T5) Figure 5A shows that the water RDF around a spherical solute approaches bulk behavior ~0.5-1 nm away from the solute, suggesting that a periodic box that is ~2 nm larger than the solute should give acceptable result. Figure 5B, however, is apparently at odds with the g(r) presented in Figure 5A, as bulk water behavior seems to be achieved only ~2.5 nm away from Hemoglobin. Figure 5—figure supplement 1 presents the whole RDF profile. This RDF calculated in this manuscript appears to be wrong, as there is water in the center of Hemoglobin, so the RDF should have value close to 1 in the center. If this is a mistake, it should be corrected. Did the authors checked that at the beginning of the simulation water was actually placed in the central cavities of the protein and that this water was properly equilibrated?g(r). The time series confirm that the central cavity is filled and that the two counts are consistent.There are ∼ 130 water molecules in the central cavity of Hb, see new Figure 5—figure supplements 2 and 3. This is from two different analyses. One involves explicit counting and the other one integration of


The data in this article were obtained from a research designed to investigate the effects of choice of solvent, mixing speed, temperature and solvent to oil ratio on the treatment process of used lubricating oils using solvent extraction and adsorption method. Various data on the performance of the three solvents chosen were studied and compared based on certain parameters are presented and discussed. From the results obtained, it was observed that MEK (Methyl Ethyl Ketone) had the best performance because it gave the highest sludge removal and closest properties to the fresh lubricating base stock. Furthermore, it was also determined that increase in temperature improved the quality of oil obtained up till 50 °C above this temperature poorer quality of oil was observed. But above all the factors investigated, it was concluded that solvent to oil ratio has a greater effect on the quality of oil produced after treatment. Specifications TableValue of the data•The data could be helpful in different brands of used lubricating oil characterization.•The data presents varying capabilities of how the solvents used could effectively treat and remove contaminants from the used engine oil.•Multivariate analysis can be used to establish relationships among the variables.•The data presents evidence of cost effectiveness of the solvent extraction to adsorption method.1The data describe research findings of the effects of choice of solvent, mixing speed, temperature and solvent to oil ratio on the treatment process of used oils using solvent extraction and adsorption method. The performance of the three solvents chosen were studied (process characterization) and compared based on certain parameters. To achieve this the oil was dehydrated using an atmospheric distillation setup and light ends were removed using a vacuum distillation setup. It was mixed with a solvent at different solvent to oil ratios and let to settle for 48 h before the solvent was recovered and activated charcoal was used to improve its colour amongst other properties. From results attained, it was observed that MEK (Methyl Ethyl Ketone) had the best performance because it gave the highest sludge removal and closest properties to the fresh lubricating base stock. Furthermore, it was also determined that increase in temperature, improved the quality of oil obtained up till 50 °C above this temperature poorer quality of oil was observed. But above all the factors investigated it was concluded that solvent to oil ratio has a greater effect on the quality of oil produced after treatment.1.1Lubricants are used in many industries as they perform a variety of functions ranging from reducing friction between metal parts in contact with each other, heat dissipation, power transmission amongst many others Lubricant Oil (LO) in use degrade over time, the degree of this degradation is dependent on the environment and operating conditions where the oil was used, however, a point is reached where the engine oil would no longer be able to perform its functions Recycling of used lubricating oil deals with subjecting the oils to a series of processes that are able to eliminate most contaminants, including water, oxidation products, additives and thereby allowing the initial characteristics of the base oil to be re-established. Several methods have been proven feasible in the recycling of used lubricating oil, although not all of them are economically feasible principally because of high energy consumption during the recovery process.Some of them include vacuum distillation, solvent extraction, acid-clay treatment, hydro finishing, to mention but few 22.1Two different used oil samples were used for the experimental analysis of this research. The first sample of oil was obtained from an auto repair shop in Lagos, Nigeria from a drum where oils from different vehicles had been drained. The second sample of oil was drained directly from one of the generators in Covenant University campus. The solvents used include MEK, propan-2-ol, a composite mixture of 75% MEK and 25% propan-2-ol and the adsorbent activated carbon.2.22.2.1A pre-measured quantity of the used oil is placed in a round bottom flask. A setup like the one below was erected in order to perform the dehydration process. The dehydration of both samples of used lubricating oil was carried out using a simple atmospheric distillation setup at a temperature of 120 °C because at this temperature water will evaporate. The dehydration process was done until no distillate was produced.2.2.2Elimination of light ends as well as gasoline was made possible with the use of a simple batch vacuum distillation setup operated at a temperature of 210 °C and a pressure of about 3 inHg. The vacuum distillation process was carried out for an hour. The vacuum distillation setup is similar to that of the atmospheric distillation setup in 2.2.3Three different types of solvents were used, two single solvents and a composite solvent. The single solvents used were MEK and propan-2-ol while the composite solvent comprised of 75% MEK and 25% propan-2-ol. The constituents of the composite solvent are stirred together for 30 min to ensure proper interaction between both of the solvents. A 100 ml sample of the oil is poured into a 600 ml beaker. Different quantities of either of the solvents were added to the oil sample in the beaker in these varying ratios, 1:1, 1:2, 1:3, 1:4 and 1:5. The oil and the solvent are then stirred for one hour to ensure that the mixture is adequately mixed using an electric hot plate at a speed of 500 rpm. The mixture was allowed to settle at a constant temperature for 48 h in a separating funnel. It separates into two phases, the extract and the raffinate phase. The extract phase is made up of the solvent and base oil components while the raffinate phase contains sludge. The raffinate phase was a black and semisolid and the extract phase was a brownish-black liquid. The sludge contains both solid and liquid contaminants found in the oil. The sludge collected from the separating funnel is then weighed and its volume recorded. The solvent and oil mixture (extract phase) undergoes further distillation for recovery.2.2.4The solvent is recovered from the extract phase using an atmospheric distillation setup. The oil and solvent from the extract phase is heated with an electric mantle to a temperature of 85 °C. This is slightly higher than the boiling point either of the solvents used so as to ensure the total removal of the solvent from the oil and solvent mixture.2.2.5Activated carbon was the adsorbent of choice because of its strong affinity for PAH’s as well as its capacity to absorb fifty times its weight. A 40 g sample of oil was weighed alongside a five percent weight by weight of activated carbon. This was mixed for 15 min at ambient temperature at 500 rpm. The activated carbon is left in contact with the oil for four hours after which it must have settled by gravity and then the oil sample is collected.2.32.3.1A volume of the oil sample was put into a graduated cylinder till it was three quarters full and a hydrometer is inserted at a relatively slow pace into this sample. While the device is floating, the point on the liquid surface where the hydrometer rests is the specific gravity.2.3.2The oil sample was placed in an open cup where it was heated, its temperature was monitored using a thermometer. At specified time intervals the ignition source which is a flame is passed over it, this is done until the oil sample has flashed. An oil sample has flashed when a flame spreads on the entirety of the oil sample.2.3.3If the temperature at which a viscosity reading is taken is not specified the reading is meaningless. Typically, the viscosity reading is usually reported at either 40 °C (100 °F) or 100 °C (212 °F). A capillary Viscometer is used to determine the kinematic viscosity of an oil sample used. The oil sample is placed inside a glass capillary U-tube and part of the sample is drawn through the tube using suction until it reaches the start position indicated on the tube’s side. The suction is then released, allowing the sample to flow back through the tube under gravity.2.3.4The metal content of different metals found in the oil samples was obtained by atomic absorption spectrometry using an atomic absorption spectrometer. A measured mass of used lube oil is heated to 60 °C and stirred. The used oil is then mixed with kerosene in the ratio 1:10. Sets of organometallic standards of metal  4-cyclohexylbutyric acid salts were prepared and metal concentrations were determined by introducing the test solutions of engine oil samples into the flame of the atomic absorption spectrophotometer and thereafter recording the responses. Metal concentrations were determined from the calibration curve that is obtained from standard solutions. Standard solutions for all metals in engine oil samples were prepared according ASTM D 4628-2.2.3.5Viscosity index is a value that indicates the effect of temperature on the kinematic viscosity of an oil sample. This test is usually done using viscosity values attained at 40 and 100 °C. A table where viscosity values and reference series are listed is used in calculating the viscosity index value. The accuracy of this method is dependent on the accuracy of the kinematic viscosity value determination.2.3.6This test was carried out according to the ASTM D2896 method for testing the total base number of used and treated oils. The oil sample is dissolved in a chlorobenzene and glacial acetic acid. It is then titrated with Perchloric acid in glacial acetic acid.The endpoint is obtained by potentiometric titration with a glass indicating electrode inside the solution and a reference electrode linked to the sample solution by a salt bridge.2.41.Choice of solvent2.Mixing speed3.Temperature4.Effect of vacuum distillation.Many factors were varied in order to study the effect that they would have on the solvent extraction and adsorption process as well as the characteristics of the treated oil. These factors include:3The data are presented in subsections.3.1Several factors such as high molecular weight, solubility, sludge formation as well as ease of recovery were put into consideration before solvent choices were made. The ability of a polar solvent to form flocs from pre-treated lubricating oil depends on solubility parameters. According to Burrel’s classification of solvent alcohols are solvents with high capacity, ketones are solvents with medium capacity while hydrocarbons have relatively low capacity. To prove this theory, an alcohol propan-2-ol, a ketone methyl ethyl ketone and a 75% and 25% mixture of methyl ethyl ketone and propan-2-ol respectively. From the analysis, the greatest sludge formation can be attributed to MEK closely followed by the composite mixture then propan-2-ol. Upon the use of propan-2-ol it was discovered that compounds that have low molecular weight do not form a distinct layer of sludge after settling for up to four days, but on heating to recover the solvent a layer of sludge is deposited on the body of the containing vessel of the solvent and oil mixture.3.2Solvent to oil ratio has a very prominent effect on the quality of oil produced (its characteristics) as well the percentage of oil recovered from a pre-treated oil sample. Usually the higher the solvent to oil ratio the greater its ability to remove contaminants in the form of sludge from the oil sample another important property gotten from increasing the solvent to oil ratio is the increase in the percentage recovery of the oil. For MEK the optimum solvent to oil ratio is 4:1 for all the solvents because this was the point where the properties of the oil changed best with respect to the quantity of solvent used. On comparing properties such as viscosity at 40 °C and 100 °C of used and treated oil samples there is a decreasing trend in the values obtained this shows that increasing the solvent to oil ratios increases the sludge forming capabilities. This is portrayed in From observation the oil recovery was much higher with increasing solvent to oil ratio this is because at lower solvent to oil ratios the base oil might be saturated in the extraction phase leading to low oil recovery and greater oil losses The effect of solvent to oil ratio on the metals calcium and zinc and the non- metal sulphur was investigated as seen in 3.3The effect of temperatures ranging from 40 °C to 60 °C on the process was tested for the same solvent to oil ratio. At room temperature to 40 °C there is little effect felt by the process as a result of the temperature change, but above this the solvent started vaporizing faster as MEK is volatile. Temperature affects the solubility of base oil and spent oil impurities in solvents. The experiments were conducted in order to observe the characteristics of the treated oil above room temperature. Temperatures above 60 °C were not tested as they enhance the rate of solvent vaporization.Previously conducted studies show that temperature has a great effect on the extraction process, especially those above 45 °C 3.4It was observed that for the same solvent to oil ratio there was an increase in the yield of the oil at different mixing speeds as well as an increase in the amount of sludge formed while mixing. This is presented in 3.5The optimum quantity and contact time between the adsorbent and the oil was investigated this is because the increase in the quantity of adsorbent used can retard the rate of the adsorption process. This is in line with studies made by previous researchers. It was determined that a 5%w/w oil of adsorbent was used for a contact period of four.3.63.6.1The metal content of base oil is a very important parameter as the metal content in an oil sample as it can increase the rate of corrosion of the metal parts it is in contact with. The metal and nonmetal content of oil mainly come from the additives added to the oil. Calcium comes mainly from detergents and dispersants, sulphur from extreme pressure additives and Zinc is introduced to base oil in the form of additives packaged as anti-oxidant, corrosion inhibitor, anti-wear, detergent. MEK has the most effect on the metals, zinc and calcium as well as the non-metal sulphur as can be seen in 3.6.2The type of viscosity measured is the kinematic viscosity. It is the ratio of dynamic viscosity to density. In addition, it is affected by pressure and temperature. Like the general definition of viscosity as temperature increases, viscosity decreases and vice-versa the same also applies to kinematic viscosity. Generally in the treatment process vacuum distillation has the most effect on the viscosity of the oil, but the effect of solvent extraction alone on certain properties such as viscosity and flash point was investigated. At the end of the treatment with the various solvents, it was determined that no matter the solvent used the effect it would have on the viscosity is marginal compared to the viscosity of an unused lube base stock. But the effect of the different solvents on oil can be seen in 3.6.3Combustion engines of most automotive vehicles are blended with additives that are highly alkaline in nature this is to ensure that the oil would be able to neutralize the corrosive products formed from oxidation. The higher the TBN value of the oil the better it would be at neutralizing acids, but since the oil has been used the TBN value is relatively low but despite this these highly alkaline additives are not completely depleted. The data presented in this article has shown that all the solvents used could effectively treat and remove contaminants from the used engine oil though not with the same capabilities. From the characteristics compared, it can be seen that MEK gave the most favourable characteristics at an optimum solvent to oil ratio of 4:1. Different factors affect the quality of treated oil gotten from used lubricating oil. Temperature helps improve the solubility of oil in the solvent up till a temperature of 60 °C with an improvement in the properties above this temperature poorer quality of oil is attained. Also the mixing speed increases the yield at the same solvent to oil ratio. Solvent to oil ratio had a greater effect on the properties of the oil than temperature. As a result of the cost effectiveness of the solvent extraction to adsorption method, it can be prescribed for use. Furthermore, several statistical methods can be applied to improve the usefulness, variable characterization and reliability of the data. Data obtained from various experiments are refined, analyzed and interpreted with the aid of statistical methods. Readers are refer to the following articles


The use of solid cavities around electromagnetic sources has been recently reported as a mechanism to provide enhanced images at microwave frequencies. These cavities are used as measurement randomizers; and they compress the wave fields at the physical layer. As a result of this compression, the amount of information collected by the sensing array through the different excited modes inside the resonant cavity is increased when compared to that obtained by no-cavity approaches. In this work, a two-dimensional cavity, having multiple openings, is used to perform such a compression for ultrasound imaging. Moreover, compressive sensing techniques are used for sparse signal retrieval with a limited number of operating transceivers. As a proof-of-concept of this theoretical investigation, two point-like targets located in a uniform background medium are imaged in the presence and the absence of the cavity. In addition, an analysis of the sensing capacity and the shape of the point spread function is also carried out for the aforementioned cases. The cavity is designed to have the maximum sensing capacity given different materials and opening sizes. It is demonstrated that the use of a cavity, whether it is made of plastic or metal, can significantly enhance the sensing capacity and the point spread function of a focused beam. The imaging performance is also improved in terms cross-range resolution when compared to the no-cavity case. According to Compressive Sensing (CS) theory, unknown signals sampled at a rate smaller than that required by the Shannon–Nyquist theorem  may be rSeveral sensing and imaging applications  have beeMetamaterials have also been used to create randomness in the sensing system for applications such as microwave imaging ,9,10, opy axis.In order to design the cavity, a baseline configuration is defined as shown in The parameters listed on the right side of In this section, the algorithms used to perform compressive sensing and imaging are introduced. Specifically, a computational forward model is used to simulate the sensing process and measured acoustic wave fields, the inverse model is formulated and the first-order Born approximation is used as a simple approach to linearize the imaging problem. Moreover, the sensing capacity and the Point Spread Function (PSF) of the system are defined, and they will be used as extra metrics to assess how the addition of the cavity affects the performance of the imaging system.f denoting the frequency, For an inhomogeneous medium, with its density and speed of sound defined as a function of the location vector  follows :1)ρ(r)∇ms, then (2)F∇ms, The computed total and background fields in the forward modeling inside the imaging domain can be denoted with Equation :3),,6)(∇2+k(∇2+k(6) is employed to find an optimized solution for Q levels, and it is formulated as follows [Q submatrices Algorithm 1 Consensus ADMM.Inputs:        Initialize ▹ Initialization Compute the inverse factor  repeat    ▹ Update    ▹ Mean of    ▹ Mean of    ▹ Update    ▹ Update    k▹ Increment until ▹ Check for convergenceOutput: Discretizing Equation  into P pectively . If the equation:A(M×P)x^mmP pixelsltiplier  (§3.1.1)i and In the algorithm, tions as ,40:(12)STo calculate the inversion of ribed in .When there is noise in the measurements, Equation  can be ri at location The performance of the sensing array with and without the cavity can be seen through its PSF, which is the field distribution that results from coherently adding up the pressure field of each transmitter (or receiver), multiplied by a phase term that produces a constructive interference at the focusing point, when the transmitter (or receiver) is excited by a unit impulse function. The described procedure is named phase-based beam focusing, and the resulting PSF for transmitters is given by the following equation ,41:(14)Br is the Signal-to-Noise Ratio CThe goal of this section is to compare the performance of the imaging system with and without the cavity. Specifically, the performance will be assessed in terms of the sensing capacity, the PSF of a focused beam and the image quality. A typical ultrasound imaging medium, which satisfies both the density and contrast conditions, is used as a case study in this paper according to the geometry shown in x and y direction, in order, leading to a vector signal size of M and P make the system in  are kept constant as the size of the holes at the bottom of the cavity was changed. The number of holes is maximized in each case by fitting as many openings as possible at the bottom of the cavity, with the assumption that 3D printing technology has made prototype fabrication much easier for many applications ,54,55. Hained by  in the pAlthough the addition of the plastic cavity to the domain has increased the sensing capacity, its effect is not as strong as that of the steel or the aluminum cavity. Since aluminum is lighter than steel, it can be made into thin layers, and its effect in the cavity is close to that of steel, so it was selected as the material for the cavity. It is noteworthy to remark that the maximum capacity difference occurs when the The cavity effect on the PSF of a focused beam is shown for three cases in Q is selected such that a relatively quick consensus-based solution is achieved. Selecting Q to be relatively small increases the computational speed in the variable convergence while increasing the computation time in the initial matrix inversions; yet, selecting it to be relatively large could unnecessarily elevate the computational load and time in overall, as many parameters must reach consensus.The selection of diagonal , can be x direction. The Relative Half-Power Width (RHPW) (equivalent to a To better show how well the imaging in each case has performed, the normalized signals restored by the ADMM at the line passing through The results generated by the ADMM are also compared to those provided by traditional Hermitian matrix imaging in The imaging results discussed so far did not account for any noise in the measurements. In this work, a theoretical study of using solid cavities enclosing ultrasound sources to randomize the measurements was presented. Such a novel measurements scheme was combined with CS theory to retrieve the image of two objects using a reduced number of transmitters. It was shown that the sensing capacity and the PSF of the focused beam were significantly improved when a cavity, made of aluminum or plastic, was utilized. The recovered images of two point-like targets inside a uniform medium showed that the use of the cavity enhances the cross-range resolution, but they might still possess some weak artifacts when the