Diseases affecting the glomerulus, the filtration unit of the kidney, are a major cause of chronic kidney disease. Glomerular disease is characterised by injury of glomerular cells and is often accompanied by an inflammatory response that drives disease progression. New strategies are needed to slow the progression to end-stage kidney disease, which requires dialysis or transplantation. Thymosin β4 (Tβ4), an endogenous peptide that sequesters G-actin, has shown potent anti-inflammatory function in experimental models of heart, kidney, liver, lung, and eye injury. In this review, we discuss the role of endogenous and exogenous Tβ4 in glomerular disease progression and the current understanding of the underlying mechanisms. The kidney glomerulus is a specialised capillary bed that constitutes the filtration unit of the kidney. The glomerular filtration barrier consists of endothelial cells, the glomerular basement membrane, and epithelial podocytes and is supported by mesangial cells. Glomerular injury is regarded as damage to one or more components of the glomerulus that hinders its ability to perform ultrafiltration of the blood. This can manifest in a diverse range of phenotypes, such as mesangial matrix expansion, collapse of capillary loops, podocyte foot process effacement, podocyte detachment, thickening of the glomerular basement membrane, macrophage infiltration, and glomerulosclerosis ,2,3,4,5.TMSB4X gene on the X chromosome [Thymosin β4 (Tβ4), a peptide encoded by the romosome , is pleiromosome  and moduromosome . In addiromosome  survivalromosome , and angromosome  and inhiromosome  and fibrromosome . As a reromosome , stroke romosome , dry eyeromosome , and pulromosome . Here, wromosome , and macromosome .Podocytes are specialised epithelial cells with a unique shape that is integral to the function of the glomerular filtration barrier . PrimaryA highly regulated network of filamentous actin (F-actin) is critical for maintaining podocyte shape and glomerular filtration . Early rTmsb4x was detected in developing glomeruli in embryonic day 16 [Tmsb4x as a transcript enriched in adult mouse podocyte cells [Tmsb4x transcripts were also detected in both developing and mature zebrafish podocytes by scRNAseq, suggesting that podocyte expression of Tβ4 is conserved in different species. Interestingly, this study identified a switch in aged podocytes from Tmsb4x to Tmsb1, another member of the beta thymosin family found in zebrafish and other bony fish [TMSB4X transcripts are detected in lysates from adult human glomeruli [TMSB4X in human podocytes. These studies demonstrate that Tβ4 is expressed in podocyte cells and therefore could play a role in maintaining podocyte structure and function.Several studies have demonstrated Tβ4 expression in podocytes. The mRNA transcript for c day 16 , embryonc day 16  with a lte cells  and morete cells ,33. Tβ4 te cells . Tmsb4x ony fish . TMSB4X lomeruli ; howeverTmsb4x mRNA levels were unchanged in whole kidney lysates from mice with nephrotoxic nephritis [TMSB4X mRNA levels were also unchanged in the glomerular lysates from kidney biopsy specimens obtained from patients with either rapidly progressive glomerulonephritis or lupus nephritis compared with living donor control kidneys [Tmsb4x expression in a cell-specific manner. A study by Chung et al. generated single-cell transcriptomic profiles of the glomerulus from healthy mice and mice with different types of glomerular injury, including mice with nephrotoxic nephritis; mice injured with Adriamycin, a chemotherapeutic drug which replicates some of the features of human focal segmental glomerulosclerosis; and BTBR ob/ob (Ob/ObLepr) mice with diabetic kidney disease [Tmsb4x was significantly reduced in all these disease models compared with Tmsb4x levels in the podocytes of healthy control mice [Tmsb10, was also downregulated in injured compared with healthy podocytes. Similar observations were made in vitro where injury of mouse immortalised podocytes with Adriamycin resulted in a reduction in the mRNA levels of Tmsb4x and Tmsb10 in a dose-dependent manner [Tmsb4x across multiple mouse models of glomerular disease and that these changes are not accurately reflected when assessing the expression of Tmsb4x in glomerular or whole kidney extracts.Given the presence of Tβ4 in podocytes and its role in actin binding , it is iephritis , an immuephritis , compare kidneys . Recent  disease . Analysirol mice . In addirol mice , Tmsb10,t manner . These fTmsb4x have been used to elucidate the role of endogenous Tβ4. Despite the association of podocyte injury with reduced Tmsb4x expression, kidneys from male −/yTmsb4x and +/yTmsb4x mice had similar glomerular morphology assessed by PAS staining, podocyte structure assessed by electron microscopy [−/yTmsb4x mice had normal levels of urinary albumin, plasma creatinine, and blood urea nitrogen [Mice with global deletion of croscopy , and procroscopy . In agrenitrogen ,37, indi−/yTmsb4x mice, which had significantly higher levels of albuminuria as well as increased plasma creatinine and blood urea nitrogen and a greater degree of glomerular injury as assessed by periodic acid Schiff (PAS) staining. Further experiments showed that nephrotoxic nephritis resulted in loss of podocytes, identified by immunofluorescent staining for Wilms tumour 1 (WT1), from the glomerular tuft in −/yTmsb4x mice. This was accompanied by increased WT1+ nuclei in the parietal epithelium lining the Bowman’s capsule, raising the possibility that Tβ4 deficiency results in aberrant migration of injured podocytes from the glomerular tuft to the Bowman’s capsule [−/yTmsb4x mice despite having similar levels of hypertension as wild-type mice. Podocyte number was not assessed directly in this study, but the protein levels of nephrin were lower in kidneys from hypertensive −/yTmsb4x compared with +/yTmsb4x mice [The pathophysiological role of endogenous Tβ4 was determined by further experiments in murine models of glomerular injury. Two distinct mouse models were examined: nephrotoxic nephritis , a model capsule . In a se+/y mice . ReducedTmsb4x by siRNA. However, lack of Tβ4 resulted in reorganisation of the F-actin cytoskeleton from predominantly cortical F-actin to cytoplasmic stress fibres and increased podocyte migration in a scratch wound assay. In addition, downregulation of Tβ4 increased RhoA activity, a master regulator of F-actin organisation, stress fibre formation, and migratory control [The direct effect of endogenous Tβ4 on podocyte cells was demonstrated by in vitro experiments. The viability of immortalised mouse podocytes  was unaf control , offerinKK Cg-Ay mouse model of type 2 diabetes [KK Cg-Ay mice were injected with either saline or 100 ng/10 g/day Tβ4 intraperitoneally for three months. Tβ4 injections suppressed albuminuria by 33% compared with saline-injected littermates [The findings that Tβ4 has a protective role in the glomerulus and that podocyte Tβ4 expression is reduced in murine models of glomerular disease raise the possibility that treatment with exogenous Tβ4 may slow glomerular disease progression. Initial evidence that exogenous Tβ4 may prevent glomerular injury came from a study using the diabetes . Twelve-termates . Tβ4 tretermates , providiTmsb4x. Tβ4 protein levels were assessed five weeks later, and it was shown that gene therapy with Tβ4 resulted in transduction of liver cells followed by secretion of Tβ4 and a twofold increase in Tβ4 plasma levels in mice injected with AAV-Tmsb4x compared with controls injected with AAV-LacZ. Validation experiments in -/yTmsb4x mice showed that AAV-delivered Tβ4 was internalised by podocyte cells, demonstrating that this is an effective strategy to systemically deliver Tβ4 to podocyte cells over a prolonged period [Subsequently, the mouse model of Adriamycin nephropathy, which primarily targets podocytes, was used to assess the effect of exogenous Tβ4 on podocyte injury  Figure . A partid period . A preved period . There wd period , suggestd period ,42 couldCollectively, the available literature illustrates how endogenous and exogenous Tβ4 protects the glomerular filtration barrier in pathological settings, likely by preserving the podocyte cytoskeleton and thus maintaining podocyte function in the glomerular tuft. However, the molecular mechanisms that underpin the protective effect of Tβ4 on podocytes have not been investigated in detail. The F-actin cytoskeleton links focal adhesion complexes to the foot processes maintaining anchorage to the glomerular basement membrane ; therefoThe protective effect of Tβ4 on podocytes may also be mediated by its metabolite, the tetrapeptide N-acetyl-seryl-aspartyl-lysyl-proline (Ac-SDKP), which is generated by successive cleavage of Tβ4 by the enzymes meprin-α  and prolOverall, these studies demonstrate that both endogenous and exogenous Tβ4 protect the podocyte cytoskeleton, prevent podocyte loss, and maintain the integrity of the glomerular filtration barrier during injury. However, it is currently not known whether Tβ4 can reverse podocyte injury, and therefore further studies administering Tβ4 after the onset of glomerular injury could be employed as a more clinically relevant approach to assess its efficacy in improving the progression of established glomerular disease. In addition, studies utilising human podocytes can provide evidence for the relevance of Tβ4 in human glomerular disease.Glomerular injury is often accompanied by an inflammatory response characterised by leukocyte infiltration and subsequent fibrosis which correlates with declining renal function . InflammInitial data from the rat remnant kidney model suggested that Tβ4 is not expressed in kidney macrophages identified by ED1 staining . Subsequ−/yTmsb4x and +/yTmsb4x mice. In contrast, at the later stage of the disease (day 21) there were more macrophages in both the glomerular tuft and the peri-glomerular region in −/yTmsb4x compared with +/yTmsb4x mice. This was accompanied by increased collagen IV and α-smooth muscle actin (SMA) staining in these regions, indicating increased fibrosis [−/yTmsb4x compared with +/yTmsb4x mice. This was accompanied by increased expression levels of Intercellular Adhesion Molecule 1 (ICAM-1), a pro-inflammatory molecule; collagen content assessed by picrosirius red staining; and α-SMA, quantified by Western blotting [Endogenous Tβ4 inhibits macrophage accumulation in the kidney cortex after injury, as demonstrated by both the studies that utilised Tβ4 knockout mice. In the mouse nephrotoxic nephritis model, the number of macrophages identified by F4/80 immunostaining was increased at the early stage of the disease (day 7) but did not differ between fibrosis . In the blotting . These rThe mechanisms that mediate the anti-inflammatory and anti-fibrotic effects of Tβ4 in glomerular disease are currently unclear. Tβ4 may regulate the production of cytokines and growth factors by injured glomeruli to limit monocyte infiltration and in situ macrophage proliferation. Alternatively, Tβ4 may act directly on macrophages to modulate their function. It is also currently not known if the anti-inflammatory role of Tβ4 in glomerular disease is dependent on its G-actin sequestering activity. Previous work has shown that Tβ4 inhibits tumour necrosis factor α (TNF-α)-induced nuclear factor κB (NF-κB) activation in human corneal cells independently of its G-actin sequestering activity . In addiGiven these findings, it is interesting to speculate whether administration of exogenous Tβ4 may also be effective in reducing macrophage accumulation in glomerular disease. The model of Adriamycin nephropathy that has been used to assess the effect of gene therapy with Tβ4 on glomerular disease does not result in inflammation within the time frame studied. This was illustrated by the low numbers of macrophages present in the renal cortex, which were similar in the mice that received Adriamycin and control mice that were administered saline . A numbeIn summary, Tβ4 has a protective role in glomerular disease as demonstrated in a range of experimental models. This effect is mediated by the ability of Tβ4 to protect the actin cytoskeleton of podocytes, thus preventing changes in the podocyte shape and podocyte loss and maintaining the integrity of the glomerular filtration barrier. At the same time, Tβ4 inhibits the accumulation of macrophages in the renal cortex, exerting an anti-inflammatory effect which is likely to slow disease progression as indicated by the concomitant reduction in fibrosis . It is cIt is unclear whether the effects of Tβ4 on podocytes and macrophages are distinct, or whether Tβ4 administration modulates signalling pathways that drive inflammation in response to podocyte injury. Irrespective of the underlying cellular and molecular mechanisms, the studies conducted to date have demonstrated that Tβ4 can inhibit the development and severity of glomerular disease. More studies are required to explore the therapeutic potential of exogenous Tβ4 in established glomerular disease to assess whether it can halt or reverse disease progression, which will strengthen the evidence for using Tβ4 as a novel treatment to reduce the morbidity and mortality associated with glomerular disease. Further studies are also needed to determine the relevance of Tβ4 and its therapeutic potential in human glomerular diseases.


Brassicaceae plants have the glucosinolate–myrosinase defense system, jointly active against herbivory. However, constitutive glucosinolate (GLS) defense is observed to occur at levels that do not deter all insects from feeding. That prompts the question of why Brassicaceae plants have not evolved a higher constitutive defense. The answer may lie in the contrasting relationship between plant defense and host plant preference of specialist and generalist herbivores. GLS content increases a plant's susceptibility to specialist insects. In contrast, generalists are deterred by the plant GLSs. Although GLSs can attract the natural enemies (predators and parasitoids) of these herbivores, enemies can reduce herbivore pressure to some extent only. So, plants can be overrun by specialists if GLS content is too high, whereas generalists can invade the plants if it is too low. Therefore, an optimal constitutive plant defense can minimize the overall herbivore pressure. To explain the optimal defense theoretically, we model the contrasting host selection behavior of insect herbivores and the emergence of their natural enemies by non‐autonomous ordinary differential equations, where the independent variable is the plant GLS concentration. From the model, we quantify the optimal amount of GLSs, which minimizes total herbivore  pressure. That quite successfully explains the evolution of constitutive defense in plants from the perspective of optimality theory. Specialist herbivores are attracted by constitutive plant defense while generalists are deterred by such a defense. Therefore, there is an optimal level of plant defense chemicals. By a mathematical model, we determine that optimum. However, the constitutive GLSs are detectable throughout the Brassicaceae plants at a moderate level only , Ceutorhynchus obstrictus (cabbage seed weevil), Dasineura brassicae (brassica pod midges), Delia radicum (cabbage root flies), Lipaphis erysimi (turnip aphids), Pieris rapae , and Plutella xylostella (diamondback moth)  of their preferred plants because they possess resistance (counter‐defense) mechanisms against the defense chemicals. They even use the GLS content  as a cue to identify plants for oviposition and feeding  on Arabidopsis , which leads to an increased load of Brevicoryne brassicae, a specialist aphid  on the Brassicaceae hosts , which describes the contrasting host selection behavior by specialist and generalist insect herbivores, as well as immigration of natural enemies with respect to the increasing constitutive plant defense (GLS) concentration  after deterrence and ND be the population of immigrated natural enemies at the constitutive defense (GLS) level D. Let specialists are attracted at a rate α per unit plant defense, whereas generalists per capita are deterred at a rate β per unit plant defense. For simplicity, we assume that the natural enemies  are attracted with a constant factor, which we denote by γ, that is, natural enemies increase linearly with the plant defense. Since natural enemies reduce the herbivore pressure by predation or parasitism, let μ and η be the per capita mortality rate (or death rate) of specialist and generalist herbivores, respectively, caused by the natural enemies. The differential equations read:Let μSN and ηGN) in Equations (βGD) in Equation , because the number of deterred insects is proportional to the generalist population size and the concentration of plant defense. The initial conditions for S and N are assumed as SD=0=0 and ND=0=0, meaning that no attracted specialists nor natural enemies are present without any plant defense.The mortality (or death) of herbivores is represented by bilinear functions  can be simplified as follows, where the third ODE has been integrated:dSdD should be non‐negative (≥0). The fixed point for the specialist population (S) is αθ, that is, dSdD=0 at S=αθ. Therefore, αθ can be considered as the carrying capacity of specialists, because it represents the maximum number of attracted specialists on a host plant (or patch of host plants).Remark 1αθ is very low (→0), the specialist population does not grow. That occurs only when the predation (or parasitism) by natural enemies is very strong.If As specialists are attracted by constitutive plant defense, the derivative S and G as functions of D:G0=GD=0≥1 is the maximum generalist population if the host plant (or patch of host plants) does not show any defense.By solving Equation , we can write SD+GD, denoted by TH. From Equations  is quations , 3b, TH TH is minimum at an optimal defense:From Equation , it can β+δ>θ and β+δG0>α, where G0≥1.The proof is given in Appendix Dopt) allows the host plant (or patch of host plants) to minimize the total herbivore pressure, shown in Figure Remark 2θ>β+δ and β+δG0>α, then plant defense cannot reduce the total herbivore pressure below its initial value. On the contrary, the total herbivore pressure increases from its initial value to reach a certain maximum at some level of plant defense, shown in Figure β+δ>θ or δ is practically always fulfilled  will noRemark 4Dopt in Equation (The predation (or parasitism) by natural enemies can be higher (or lower) on specialists than generalists. However, the optimum Equation  is not aThus, Equation  proves t3Eucalyptus grandis  to explain evolution of constitutive defense, applicable not only to the Brassicaceae plant family, but to all plants with chemical defenses. In nature, constitutive defenses are present in most plants  to include optimal defense theory (ODT)  resulted in the induction of proteinase inhibitors in potato (Solanum tuberosum) or tomato (Lycopersicon esculentum) leaves  larvae  on the generalist pressure (G) but also the inverse effect will be considered.Plants synthesize the constitutive defense compounds during their normal course of development and growth, notably in the absence of herbivory. These compounds are destined for a basic or initial protection to plants at the commencement of herbivory  is resistant to 52 different compounds from all the major insecticide classes ; formal analysis (lead); investigation (lead); methodology (lead); software (lead); validation ; visualization (lead); writing – original draft (lead); writing – review and editing . Jonathan Gershenzon: Project administration (supporting); supervision (supporting); validation ; writing – review and editing . Stefan Schuster: Formal analysis (supporting); funding acquisition (lead); investigation (supporting); methodology (supporting); project administration (lead); supervision (lead); validation ; writing – review and editing .The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.Data S1.Click here for additional data file.


Gastroesophageal reflux disease (GERD) is a common disease which in the majority of patients is treated with proton pump inhibitors (PPI). However, up to 45% of the patients remain symptomatic on a standard dose of PPI. This study investigated the effectiveness and safety of an add-on therapy with the gel-forming chewable tablet Sobrade® in patients unsatisfied with PPI treatment. The bioadhesive gel covers the oesophagus and thereby protects the mucosa from reflux events.47 patients with symptomatic GERD despite PPI treatment participated in this study. The gel-forming tablets were taken up to four times daily after meals and prior to bedtime. Severity and frequency of GERD symptoms were evaluated during two onsite visits prior and following 14 days of treatment and used to calculate the GERD score of the Reflux Disease Questionnaire. Furthermore, patients recorded symptoms as well as onset and duration of symptoms relief daily in their electronic dairies. Effectiveness of treatment was analysed using non-parametric paired Wilcoxon test. In addition, anchor-based minimal important differences (MID) were assessed.Treatment resulted in significant reduction of GERD symptoms. Severity and frequency of 8 of the 9 assessed symptoms improved significantly during the treatment phase whereby most pronounced improvement was observed for heartburn. In agreement, all three subscales of the GERD score improved significantly. MID results suggest that patients considered a mean improvement of symptoms > 30% of initial severity as beneficial. Self-assessments by patients revealed first significant improvements of symptoms like heartburn and regurgitation from day 5 of treatment onwards. 49% of patients reported relief of symptoms within 15 min which lasted on average for 3.5 h. During the study no treatment emergent adverse events were reported and in 98% of all cases tolerability of the product was rated as very good or good.This study revealed a pronounced improvement of the symptoms after add-on treatment with the gel-forming medical device. The very good safety and tolerability profile indicate an advantageous risk-benefit ratio.This non-interventional study was prospectively positively evaluated by the responsible ethic-committees.The online version contains supplementary material available at 10.1186/s12876-023-02946-6. Gastroesophageal reflux disease (GERD) is a very common disease. Approximately 10–20% of the adult population in the Western world (Western Europe and North America) are affected . Clinica2 antagonists, proton pump inhibitors (PPIs) [The pathogenesis of gastroesophageal reflux disease is complex . Exposurs (PPIs) , 4, 8, 9s (PPIs) .Up to 45% of the patients report a limited therapeutic effect of PPIs with ongoing symptoms despite regular and correct intake of the medication. PartialNevertheless, medical products can serve as a low risk add-on therapy to the PPI treatment. An add-on therapy with an alginate-based medical device acting as a mechanical reflux barrier was shown to successfully control symptoms associated with GERD .Also, medical devices were developed for treatment of GERD symptoms like heartburn and acid regurgitation which differ in their composition but share a common mode of action .® chewable tablet is a low risk medical device and certified as class-I product. Its ingredients xanthan and carbomer are present in similar medical devices and the formation of a bioadhesive barrier to prevent the esophageal mucosa from further GERD induced damages was already confirmed in in-vitro and in-vivo studies [® acts as a symptomatically treatment of GERD symptoms.Sobrade studies , 16. In  studies , 18. ThiThe objectives were to evaluate the effectiveness of the medical device for the first time in patients suffering from GERD with unsatisfying PPI treatment for at least one year, when used in accordance with its intended use, the safety/tolerability during the treatment phase and the patients’ and investigators’ satisfaction.Patients qualified for this study if they suffered from symptoms of reflux disease such as pain or burning feeling behind the breastbone or acid taste in the mouth on at least 2 days per week with at least moderate severity despite PPI treatment for at least one year.This multicentre, uncontrolled prospective and open-label clinical study was performed according to § 23b German Medical Device Law and conducted at 2 general practitioners and 2 gastroenterologist sites located in the Federal States of North Rhine-Westphalia and Berlin, Germany. It complied to GCP guidelines, the Declaration of Helsinki and received prospectively, positive evaluation by the independent ethic committees of the medical councils of Nordrhein (File number 2020409) and Westfalen-Lippe (File number 2020-07-f-S) prior to enrolment of the first patient. The clinical phase lasted from January to November 2021 whereby recruitment was affected by the COVID-19 pandemic resulting in an unplanned extension of recruitment by 4 months.Before participating in the study, patients read and signed the informed consent form as well as a declaration on data protection. Patient identities were disguised by using a patient identification number. All patients met the inclusion criteria which were an age > 18 years; diagnosed GERD by the responsible physician with presence of at least 2 of the 3 symptoms “pain behind the breastbone”, “burning feeling behind the breastbone”, “acid taste in the mouth” with at least 3 points for frequency (2–3 days per week) and severity (moderate) on 6-point Likert scale (Appendix A) while receiving PPI treatment for at least one year; ability and willingness to complete self-assessment questionnaires; compliance with contra-indications, precautions for use and warnings mentioned in the Instructions for Use. Females with childbearing potential had to have a negative urine pregnancy test at baseline and had to agree to use a highly effective method of contraception for the duration of the clinical investigation.Heliobacter pylori within 2 weeks prior to the study; employee or direct relative of an employee of the site, CRO or sponsor; prisoner or lawfully kept in an institution.Patients were not eligible if one of the following exclusion criteria was met: illness or circumstance that could affect the study purpose in the opinion of the investigator; known or suspected disorders like Barrett’s esophagus or hereditary fructose intolerance; pregnancy or breastfeeding in females; participation in another clinical study within the last 6 months; triple therapy for eradication of The study and treatment phase started at Visit 1 and ended at Visit 2 after 14 ± 2 days. At Visit 1, patient’s demographics, body height, weight, concomitant medications and diseases as well as vital signs  and medical history were documented. Baseline assessments were collected from eligible patients by evaluating the frequency and severity of 9 GERD symptoms over the past seven days “burning feeling behind your breastbone”, “pain behind the breastbone”, “a burning feeling in the center of the upper stomach”, “pain in the center of the upper stomach”, “acid taste in the mouth”, “unpleasant movement of material upwards from the stomach”, “sore throat or hoarseness that is related to heartburn or acid reflux”, “symptoms that caused difficulties in getting a good night’s sleep” and “symptoms prevented eating” on ordinal 6-Point-Likert items (Appendix A). Patients were instructed on the use of an electronic diary (eDiary) for once daily recording of the number of meals and intake of tablets during the study and self-assessment of severity of the following clinical symptoms “heartburn”, “regurgitation”, “hoarseness”, “sleep disturbances” and “symptoms prevented eating” on ordinal 5-point Likert items (Appendix A). Patients received the tablets together with instructions on the correct intake: Sobrade® tablets are chewed slowly until complete dissolution and the forming gel is swallowed. The device should be used after each meal and prior to bedtime up to 4 times daily. Assessment of compliance considered the number of meals consumed daily to calculate the target number of tablets to be taken.Furthermore, time until onset of symptoms relief as well as duration of symptoms relief were documented whereby for analyses only data from patients with symptoms present on the day of entry were considered (Appendix A).Visit 2 took place after the 14 ± 2 days treatment period and the investigator evaluated again the frequency and severity of the same 9 GERD symptoms on the ordinal 6-Point-Likert items used for baseline assessments. Furthermore, patient and investigator rated the effectiveness of treatment as well as satisfaction and safety/tolerability of the device on 5-point-Likert items (Appendix A).Number of patients was based on a sample size calculation assuming a change of 1 from baseline scores for at least one symptom and a standard deviation of 1.7 resulting in 80% power for 48 evaluable patients in case of a paired t-test with 5% two-sided significance level. Furthermore, 50 patients were estimated to be sufficient to have a probability of 90% to detect adverse device effects (ADEs) with 5% incidence under assumption of Poisson distributed data.Effectiveness was assessed from change of symptom severity and frequency using the numeric versions of the 6-point-Likert items assessed at Visit 1 (baseline) and 2  with higher values of Likert items correspond to more severe (0: not present to 5: severe) and frequent (0: not present to 5: daily) symptoms. Symptoms obtained according to the German Reflux Disease Questionnaire (RDQ) were used to calculate its three subscales which consider mean severity and frequency of acid taste in mouth and movement of material upwards , pain or burning behind the breastbone  or pain or burning in the upper stomach  , 20. The2-test. Number of treatment responders was assessed using the following definition: improvement ≥ 1 point of at least one symptom without deterioration of another symptom for “pain behind the breastbone”, “burning behind the breastbone” and “acid taste in mouth”. If not stated otherwise correlation coefficients in the results represent Pearson’s r2. Based on the definition by Cohen, r values of 0.1, 0.3 and 0.5 correspond to weak, moderate and strong correlations, respectively [Effectiveness was analyzed using non-parametric paired Wilcoxon test for investigator- and self-assessed data without adaptation for multiple testing as data were not normally distributed, however, significance levels do not differ from results of paired t-tests. For diary data, day 1 was used as baseline, although symptoms could have already been alleviated by application of the first tablets. The number of patients with changed symptoms severity from Visit 1 to 2 was analyzed using chiectively .The minimal important difference (MID) was assessed for individual GERD symptoms as well as the RDQ scales regurgitation, heartburn and GERD score against the patient-reported outcomes effectiveness and satisfaction. MID analyses were restricted to significantly correlated parameters (> 0.3 Spearman correlation coefficient) and MID was calculated from change differences obtained for patients grouped based on ratings on 5-point Likert scales, whereby negative and neutral ratings were pooled. MID corresponded to differences of outcomes between patients’ groups with ratings of 1 compared to pooled patients with ratings of -2 to 0. Reliability of the applied anchor-based method was supported by the short treatment phase and similar initial mean values of symptoms in the groups obtained at Visit 1, both features reduce the potential for bias of ratings.Safety and tolerability of the investigational medicinal product (IMD) with regards to adverse device effects was evaluated in the safety evaluation set (SES) encompassing all patients who received at least one tablet. Effectiveness was analysed using the full analysis set (FAS) which encompassed all eligible patients participated Visit 1 and 2.Imputed data sets using Baseline observation carried forward (BOCF) including all patients of the SES were used for sensitivity analysis.All data are presented as mean ± 95% confidence intervals calculated under assumption of t-distributed data.A total of 47 patients at 4 sites participated in the study which was less than planned due to the COVID-19 induced difficulties in recruitment. Forty-two eligible patients completed the study and efficacy data from both visits were available. Complete cases were assigned to the FAS. Mean age of patients was 54.5 years of which 36% were females. PPI treatment lasted on average for 5 years with the majority of patients receiving pantoprazole (66%). Baseline characteristics of participating patients are summarized in Table On Visit 1, severity and frequency of all 9 symptoms were assessed whereby both characteristics were correlated. The symptoms with highest initial severity were “burning behind the breastbone” (3.5 ± 0.2), “pain behind the breastbone” (3.1 ± 0.1) and “acid taste in the mouth” (3.5 ± 0.4). Initially symptom frequencies were highest for “burning behind the breastbone” (3.6 ± 0.2), “pain behind the breastbone” (3.2 ± 0.2) and “acid taste in the mouth” (3.6 ± 0.4). Following 2 weeks treatment period, significant improvement of 8 of the assessed 9 symptoms assessed was observed. Changes of symptom severity and frequency assessed during the visits were comparable with slightly better improvement for severity.Frequencies of “burning behind the breastbone” (3.6 ± 0.2), “pain behind the breastbone” (3.2 ± 0.2) and “acid taste in the mouth” (3.6 ± 0.4) significantly improved at Visit 2 to 2.7 ± 0.5, 1.8 ± 0.4 and 2.6 ± 0.5, respectively . Based on the improvement of symptom severity after treatment, 90.5% of patients were considered as responders.The number of patients with “moderate”, “severe” and “not tolerable” severity for the symptom “burning behind the breastbone” decreased from initially 41 at Visit 1 to 22 at Visit 2. In parallel, number of patients with “mild”, “very mild” and “no symptoms” increased from 1 to 20  and “regurgitation” (r2: 0.89) were present  and “difficulties getting sleep” (p < 0.05) were reported from day 5 and 6 onward, respectively. Symptoms like “hoarseness”  and “symptoms prevented eating”  with low initial severity were significantly reduced only in the end of the study period. During the course of the study, linear correlations of daily mean severities of “sleeping disturbances” with “burning sensation”  and patients (r2: 0.65).73.8% of investigator ratings on the treatment effectiveness were positive which was confirmed by the ratings by patients (71.4%). Similarly, 73.8% of both, investigators and patients, were satisfied with the add-on therapy. Ratings of effectiveness and satisfaction on Likert items were highly correlated for both investigators . In comparison, in patients who perceived no effectiveness of treatment, symptoms improved by 0.15 and 0.27 (5.2 and 9.3%), respectively. Similar estimates were obtained based on treatment satisfaction. Thus, the average improvement achieved by patients during the treatment period exceeded MID.In patients with negative or neutral ratings of treatment, the symptoms sleeping disturbances and sore throat did not improve and were unchanged or even worsened whereas all other symptoms improved during the study period. These two worsened symptoms had pronounced effects on average change of symptoms. In contrast, MID analyses using the RDQ scores yielded no significant differences between patient groups without and with positive ratings of effectiveness (1.1 vs. 1.3 points) corresponding to 32.3 and 36.9%, respectively.No SAE or treatment emergent AE were reported during the 2 weeks treatment period. In 98% of all cases, investigators and patients, respectively, rated the tolerability of the product as very good or good.This non-interventional study investigated the effectiveness of a medical device in patients suffering from persistent reflux after PPI treatment for at least one year. Persistence of GERD can result from several causes, but may severely impact the quality of life and therefore requires adequate treatment . WhereasIn this study, treatment with the medical device resulted in a pronounced symptom relief of severity and frequency for 8 of the 9 symptoms assessed by investigators. In accordance, the symptoms derived subscales of the RDQ and the related GERD Score improved similarly. The reductions of self-assessed symptom severity reported in patient diaries became evident already within the first days of the study. Significant reductions of severity reported by patients for the symptoms “burning sensation in chest” and “regurgitation” were already observed from day 5 onwards. Beneficial effects were observed independently from the PPI applied and extend of improvement agrees with results obtained for chondroitin-sulphate based products which apply a comparable mode of action –30. ChonWith the decline of heartburn and regurgitation severity reported in patient diaries during the 2 weeks study period, sleep disorders were reduced in a secondary fashion. As nocturnal reflux events and resulting sleep disturbances are known to severely affect quality of life, alleviation of symptoms is expected to be highly beneficial for overall wellbeing and the quality of life . PatientThis study has its limitations as it was conducted using an open-label and uncontrolled design without adaption for multiple testing. Thus, the improvement of symptoms in this study results cannot be placed in context to similar marketed products or a placebo effect. A potential second limitation was use of different PPIs by patients during the trial and missing records of potentially changed patients’ compliance to PPI. The 2 weeks study duration did not allow assessments of long-term effectiveness and safety/tolerability as well as QoL. Finally, the small sample size only allowed to detect ADEs as well as device deficiencies with high incidences whereas rare events might not be noted. However, the low risk product characteristic and the absence of any adverse events suggest that application is most likely be considered as safe.Persistent GERD following PPI treatment is a heterogenous condition including among others reflux hypersensitivity, functional heartburn, or insufficient gastric acid suppression by PPI. Future studies with Sobrade® in well characterised patients suffering from GERD despite long-term PPI treatment may help to establish evidence-based therapies for these patients.The study revealed that the tested medical device can serve as a valuable add-on in PPI therapy of GERD as treatment resulted in a pronounced improvement of symptoms which was considered by patents as clinically relevant. The rapid onset of symptom relief within minutes and duration of relief of about 3 hours, suggests that Sobrade® may represent a treatment option for mild GERD symptoms on its own and allow partial tapering of long-term PPI use.Below is the link to the electronic supplementary materialSupplementary Material 1


Moreover, both experimental and numerical fractal dimensions correlate well with experimental HPMI porosity measurements. Multifractal parameters such as the non-uniformity degree of the pore structures Δα, the asymmetry degree in the vertical axis Δf(α), the concentration of pore size distribution α0 and the asymmetry degree in the horizontal axis Rd estimated from digital and experimental data correlated well and revealed ability to quantitatively describe samples heterogeneity. The ranges of digital and experimental multifractal parameters provided the means to differentiate between homogeneous and heterogeneous samples.Characterization and prediction of reservoir heterogeneity are crucial for hydrocarbon production. This study applies the multifractal theory using both numerical and experimental data to characterize quantitatively the heterogeneity of pore structures in Lower Cretaceous limestone reservoir from the United Arab Emirates. Fractal dimensions calculated from three dimensional digital images showed good correlation (R The concept of fractal dimension was introduced to describe the irregularity and complexity of structures, utilizing the idea of self-similarity in an object . Several studies investigated sandstone, shale, and carbonate reservoir rocks suggesting that they reveal fractal behaviour within a certain range of length7. The fractal dimension is a real number ranging from 1 to 2 for 2-D objects and from 2 to 3 for 3-D objects8. The main advantage of utilizing fractal theory is its ability to connect microscopic geometry patterns with macroscopic structural properties and it has been largely applied in geosciences to investigate carbonates pore space structures based on various experimental and digital imaging approaches. The concept of multifractals goes beyond the standard dimensions of fractals and can explain the hidden information that is not accounted by the conventional dimensions of fractals10. Several studies have applied fractal and multifractal theories using High Pressure Mercury Injection (HPMI) experimental measurements to investigate the irregularity of porous media and its impact on various rock properties such as permeability, pore throat diameter and porosity19. In the literature, several models relating capillary pressure and saturation introduced fractal dimension to consider geometric characteristics of the pore space21. A universal capillary pressure model was developed by Li and Horne11 to characterize heterogeneity in carbonate samples from the Geysers geothermal field by matching the capillary pressure model to the experimental data using experimental fractal dimension. Zhang et al.15investigated the heterogeneity in Lower Carboniferous carbonate reservoirs in the Marsel area in Kazakhstan using fractal dimensions computed from HPMI data and found relatively good correlations of fractal dimensions with several rock properties such as porosity, permeability, sorting coefficient, and skewness. Guan et al.22 and Zhang et al.23 implemented multifractal analysis based on HPMI experimental measurements to investigate samples heterogeneity using multifractals parameters such as the non-uniformity degree and the width of singularity spectra and found good correlations between the multifractals parameters and the heterogeneity degree of pore size distributions in studied samples.Carbonate reservoir rocks are highly heterogeneous and reveal complex pore geometry at various scales due to diagenesis and depositional processes. Pore structure is commonly characterized by the size, volume, connectivity, shape and distributions of pore radii and pore throats31. Technological advancements in 2D and 3D image acquisition systems allow exploring pore space at several length scales from millimetre to nanometre using 3D X-ray Micro-Computed Tomography (3D-MCT), Nano-Computed Tomography (NCT), and 2D Scanning Electron Microscopy (SEM). Following the image acquisition, the pore space is extracted using image segmentation methods to derive segmented binary images used to reveal the geometric distribution of pores32. Subsequently, techniques such as box-counting and gliding box methods can be applied on these images to estimate the fractal dimension33. Jouini et al.26 investigated the behavior of multifractal dimensions in SEM images of carbonate reservoir at several length scales and showed that fractal dimension concept can be used for a quantitative characterization of pore space heterogeneity. Following this study, Vega and Jouini27 proposed an analytical model to upscale porosity using the numerical fractal dimension values from SEM and thin section images of carbonate samples. Jouini et al.30 investigated heterogeneity at the pore scale for twenty rock samples from sandstone and carbonate reservoirs using multifractal theory based on 3D X-ray micro-computed tomography images. Authors showed that the capacity dimension D0 and the information dimension D1 correlate with porosity and permeability simulated from images, respectively. In addition, Jouini et al.30 showed the ability of multifractal parameters to classify groups of rock samples according to their degree of heterogeneity.Fractal and multifractal theories were implemented in other studies using digital images of reservoir samples34 established a correlation between image and experimental fractal dimensions in relatively homogeneous shale and tight gas sandstones using 3D MCT and NCT images. Chen et al.35 derived experimental fractal dimensions from HPMI data of six sandstone reservoirs and compared them with numerical fractal dimension calculated from 2-D SEM and 3-D MCT images. The fractal dimensions from 2-D and 3-D images were combined in a single parameter using a bridge function and results show that they are consistent with experimental fractal dimensions for only simple pore structure but not for more complex pore structures. Recently, Shi et al.36 calculated both experimental and digital fractal dimensions from HPMI and SEM data, respectively, in Lower carboniferous carbonate reservoir without discussing the relationship between image and experimental fractals due to the absence of representability between HPMI and SEM length scales. In addition to their scarcity, these studies did not investigate the relationship between experimental and digital multifractal parameters.Few studies have applied both numerical and experimental fractal concepts to analyse pore structures in clastic and carbonate reservoirs. Rahner et al.In this study, we investigated the pore structure distribution and heterogeneity of Lower Cretaceous carbonate reservoir from Abu Dhabi, United Arab Emirates (UAE) using coupled quantitative descriptors obtained from multifractal theory based on three dimensional digital images and HPMI experimental measurements. Furthermore, petrophysical properties were simulated numerically at pore scale to elucidate their correlation with multifractal descriptors. This study seeks to address the gap in analysing pore structure heterogeneity using the multifractal concept by applying the theory to both experimental and digital data.37. The carbonate samples were selected carefully to represent six different reservoir rock textures defined within the Upper Thamama Zone D. The Upper Thamama Zone D frequently is considered as low resistivity pay zone (LRPZ) due to the presence of multimodal pore network37.The Thamama Group (Barriasian-Aptian) is a carbonate reservoir that was deposited in shallow-marine, low-energy carbonate ramp and contains four formations: Habshan, Lekhwair, Kharaib and Shuaiba. Data from this study comes from Lekhwair Formation specifically from the Upper Thamama Zone D. The main depositional facies of Lekhwair Formation include high-frequency coarsening upward cycles of shallow-subtidal skeletal-Bacinella floatstones, skeletal-peloidal wackestones; mud-dominated packstones, capped by skeletal-ooidal grainstones1–S6 of 25 mm in diameter from Lower Cretaceous, shallow marine limestone reservoir in the UAE covering different depths and textural characteristics. The selected limestone samples are composed of allochems dominated by skeletal fragments, ooids, peloids, and oncoids  using a Zeiss Xradia X-ray micro-computed tomography scanner is the number of the units having a radius r needed to fill the whole fractal object, b is a factor of proportionality and Df is the fractal dimension. The model assumes that a pore is represented by capillary tube with a length of l and a volume equal to πlr2. The number of units N(r) can be calculated based on experimental capillary pressure curves measurements. Furthermore, a common assumption implemented in the model considers l independent of r. When the pore structure of the rock is fractal, Df the fractal dimension can be determined by finding the relationship between SHg the mercury saturation and Pc the capillary pressure as the following equation:HPMI measurements are extremely valuable because they: (i) represent valuable experimental information to characterize the distribution of fluids within the reservoir and rock transport properties, and (ii) provide capillary pressure curves that are commonly used to infer pore size distributions of rock samples. The capillary pressure and saturation relationship depends on several parameters including pore throats size distribution, grain and pore geometry. Depending on the implemented model, the calculated fractal dimensions may reflect specific characteristics of the pores. For example, Li et al.11. Moreover, the estimated fractal dimension model revealed high correlations with petrophysical properties of core plugs39. Other models can provide fractal dimension reflecting the characteristics of pore volume distributions in three dimension. Friesen et al.20 implemented a model describing measurements of the pore volume of a number of coal and char samples by mercury intrusion porosimetry. The fractal dimension was determined from the relationship in the following equation:b is a constant.This fractal dimension reflects the pore size distribution40. In our study, we focused on the model proposed by Li21 as one of our goals is to find the correlation between fractal dimension and petrophysical properties such as porosity and permeability in the samples.In addition, some models can provide a fractal dimension characterizing the roughness of the pore surface Zhang and LiSHg and Pc was obtained from HPMI experimental measurements for the Sample S1 as illustrated in Fig. 36% = 10 μm corresponding to the value log(Pc) = 0.87 PSI at SHg = 36%. Using (2), the fractal dimension of pores Df was estimated as 2.24. The plot revealed a poor linear relationship between the variables with a coefficient of determination R2 =  + 0.53. However, the curve showed a double-fractal characteristic depending on the range of the capillary pressure Pc. Figure SHg and Pc with a coefficient of determination R2 =  + 0.98 for all values less than log (Pc) = 0.87 PSI. The same strong relationship is observed for the values larger than log (Pc) =  + 0.87 PSI with a coefficient of determination R2 =  + 0.95. Similar result was observed in several previous studies when deriving fractal dimension Df from HPMI experimental measurements Lai and Wang41.Based on Eq.  the log rp where p is the percentage of saturation of the non-wetting phase43. Therefore, the Swanson’s method was implemented to determine the segmentation point for the fractal dimension from each HPMI curve for the studied samples44. Several researchers used the position of the maximum value of the plot of SHg/(Pc) versus SHg, which is known as the Swanson point, to find the transition between highly and poorly connected pores from HPMI curves43. The triangular purple point represents the Swanson point of the sample S1  of the kth interval is defined as the ratio between Ni(ε) the pore volume of a kth interval and Nt the total pore volume. The mass probability function is an exponential function of scale ε as defined as in the following equation:The Box-Counting (BC) method is a standard technique used to estimate multifractal parameters revealing the complexity of a data. This method analyses patterns at several length scales to capture self-similarities by zooming in and out in the data. Furthermore, the technique requires the measurements to be equally spaced with a scale of ε. In our study, HPMI measurements were irregularly spaced so linear interpolation were used to obtain regularly spaced data points divided into N(ε) increases exponentially with the scale ε as in the following equation:Nα(ε) represents the number of boxes with singular strength in the interval  and f(α) is the singularity spectrum12.Noted that the number of boxes Dq and the partition function χ are defined for q > 1 as in the following equation:The generalized dimensions q = 1, D1 is expressed as in the following equation:For τq and Dq the generalized dimension are related through the following equation:The mass exponent τ(q) reveals a linear relationship with moments q. Conversely, for heterogeneous objects, the slope of τ(q) may change with respect to q and the deviation is related to the degree of the heterogeneity.For homogeneous objects the mass exponent f(α) and the singularity α as in as in the following equations:In addition, the multifractal theory provides a relationship between the singularity spectrum 1.Figure 0 represents the concentration of pore size distribution corresponding to the maximum value of the singularity spectrum as illustrated in Fig. Δα = αmin-αmax denotes the non-uniformity degree of the pore structures analysed, the larger Δα the higher the data spatial complexity, where α belongs to the interval [αmin αmax]. The symmetry of the singularity spectrum curve f(α) helps for a quantitative assessment of data heterogeneity. Indeed, uniform data are characterized by symmetric curves whereas heterogeneous ones reveal curve asymmetry45. The parameter Δf = f(αmin) − f(αmax) denotes the shape characteristics of singularity spectra. The curve f(α) reveals an asymmetry to the right or to the left according to the dominant probability subset. Rd = (α0-αmax)-(α0-αmin) represents the asymmetry degree in the horizontal axis of the range  with respect to α0. When the value of Rd is positive, it indicates that the porosity distribution is mostly in sparse areas, and the opposite is true for negative values46.The variable α32. Indeed, every generated voxel inside the three-dimensional X-ray image represents a grey level, coded in 16 bits, associated to the density at this precise spatial location. High and low grey level values denote solid and porous phases, respectively. Standard approaches implement thresholding algorithms to find automatically grey level limits separating these different phases in the image. In this study, we use a common thresholding method called the bi-level segmentation technique. This approach includes the grey levels spatial distribution into the histogram shape information to calculate thresholds separating porous and solid phases. The main advantage of this method is the use of region growing strategy to cope with the fuzzy transition zone representing the unresolved micro porous phase by X-ray imaging. Nevertheless, limitations in image acquisition resolution may lead to an intermediate mode in the histogram related to the presence of micro pores below image resolution. In this paper, the bi-level segmentation method was implemented to find automatically the two thresholds separating the three phases. Lower and higher thresholding grey level values for the sample S1 were estimated respectively as 28,253 and 33,023  for a specific cube side length ε. The procedure was repeated by covering the 3D image by a sequence of boxes of descending cube side lengths ε. Subsequently, the fractal dimension was estimated by the slope of the regression straight line representing the relationship between ln(N(ε)) and ln(1/ε) as in the following equation:The 3D Box-Counting method was implemented to analyse patterns of self-similarities in 3D segmented images by breaking them into a grid of boxes. This approach is used, in general, to approximate the Hausdorff dimension of a fractal dimensionPk in each kth box as ε is the box size and kth box. Zhang et al.23 proposed the use of Pk of singularity strengths between α and α + dα. Additionally, the size of the boxes, ε, can be related to −f (α) where α corresponds to the singularity and f(α) is the singularity spectrum as in . Similarly, the mass exponent τq, the generalized dimension Dq, the partition function χ, concentration of pore size distribution α0, the non-uniformity Δα = (αmin-αmax), the asymmetry degree in the vertical axis Δf = f(αmin) − f(αmax) and the asymmetry degree in the horizontal axis Rd of the range  with respect to α0 were derived from the same equations in section "Dq and f(α) the singularity spectrum obtained for sample S1.The extension of the fractal theory is known as multifractal analysis, and it is used when the geometry of a system cannot be described by a single fractal dimension. Instead, a range of fractal dimensions is defined to fully define these objects. Multifractals are measured using a probability distribution n in Eq. , where εf of the particles at each iteration, taking into account both the streaming and colliding terms, where x represents the location and t represents the time as in the following equation:Simulating permeability at pore scale using Lattice Boltzmann (LB) method on 3D X-ray images involves the following steps: (1) acquisition of 3D images of a porous material, (2) segmentation of the images to extract pore network and solid matrix, (3) assignment of boundary conditions and fluid properties to the pore network, (4) simulation of fluid flow through the pore network, and (5) calculation of permeability from the simulated fluid flow. The method considers the micro-scale features of the porous material, providing a more accurate representation of permeability compared to macro-scale models. In this approach, the fluid is modelled as particles moving in a lattice structure and their movement is described using a time and space distribution function. The governing equation calculates the density ei, where i is the index for a specific direction. The particle velocity is ui, τ is the relaxation time controlling the rate of approach to equilibrium, Ω is a collision operator required to satisfy the conservation of total mass and total momentum, and F is an external force term. The LB method has several advantages as it calculates the particle velocity at each iteration using only the velocities of surrounding particles, making it easily implementable on high performance computer clusters. A multi-relaxation-time model based on the Lattice Bhatnagar–Gross–Krook (LBGK) scheme for the 3D lattice was used in this study, following a D3Q19 lattice model47. The flow was set to be periodic between the inlet and outlet and the bounce-back rule was used to manage solid–fluid boundaries. Additionally, a no-slip boundary condition was implemented at the solid–fluid interface. When the steady state is reached, the permeability is estimated using the unidirectional Darcy’s law as in the following equation:The particle movement direction in the lattice is indicated by  K is the absolute permeability, ΔP represents the pressure difference along the length of the sample, A is the surface section area, Q stands for the flow rate and µ is the dynamic fluid viscosity. The permeability value estimated is in lattice units and are converted to a real value using the resolution of the scanned image. Moreover, the porosity can be determined by calculating the ratio of the number of voxels within the segmented pore space to the total number of voxels in the image. This value is calculated directly from the segmented 3D images.where2 =  + 0.69 and R2 =  + 0.98, respectively  between the image fractal dimension and the experimental permeability measurements obtained from HPMI. Indeed, the fractal dimension FDL also called capacity dimension usually captures the average presence of pores rather than their connectivity29. Furthermore, a positive correlation was revealed between the fractal dimension FDL and the radius at Swanson’s segmentation point with a relatively fair coefficient of determination R2 =  + 0.45 . A brief description of the six samples features and their limestone textures is provided in Table 3 acquired at 0.5 µm resolution showed a well-connected macropore system and presence of dolomite rhombs within the micrite matrix. The 3D-MCT scan of sample S4 at 0.5 µm resolution showed that the micro-porous phase exits inside the leached grains in grain supported texture. The HPMI data of samples S5 and S6 revealed unimodal pore throat size distributions with a major peak at 0.27 µm and 0.14 µm, respectively. Both samples display relatively narrow distributions by comparison to the other four samples . Figure SHg and Pc samples S2 to S6. As for sample S1 the plot showed poor linear relationships fitting between the variables. Nevertheless, Fig. SHg versus SHg/Pc denoted sharp apex for each sample  versus log(Shg) curves. However, the estimation of the fractal dimension in the intermediary section provided also a fractal dimension larger than 3.0 contradicting the Euclidean dimension. Therefore, we used only DL revealing the fractal behaviour for macro-pores.The double-fractal characteristic is revealed by piecewise linear regressions showing good fits with a positive coefficient of determination Rτ(q) and the singularity spectra f(α) were calculated for the six samples. Figure τ with respect to q for the six samples. Samples S1 and S2 show higher changes in slopes values compared to the other four samples. These large variations are due to the higher heterogeneity in pore throat size distributions in these two samples described in both HPMI data and observed in 3D X-Ray images. This observation confirms the ability of multifractal parameters to assess quantitatively heterogeneity in HPMI measurements. The singularity curves for the six samples revealed convex parabolic shape as illustrated in Fig. 1, S4 and S6 revealed singularity spectra curves f(α) with a left asymmetry around α equals to 1. Singularity curves of samples S1, S4 and S6 showed wider left portions with sharper slopes than the right ones. However, asymmetric singularity curves of samples S2, S3 and S5 revealed wider right portions with sharper slopes than the left ones. These behaviours indicate that distributions of pores reveal a multifractal behaviour for all six samples. Moreover, singularity parameters Δα and Δf(α) were calculated to assess heterogeneities characteristics of the samples. Table 0 values were in the range  for the six samples. Smaller α0 values indicate larger concentrated distributions. The degree of heterogeneity in the distribution of probability measures of physical quantities over the entire fractal structure is indicated by the width of the multifractal spectra Δα. Samples S1 and S2 revealing strongest heterogeneity of pore distributions revealed largest Δα values among the six samples of 1.22 and 1.91, respectively. The range of non-uniformity degree Δα was  for the other four samples. The most homogeneous sample in term of pore size distribution appears is sample S5 with the Δα value of 0.47. These results confirm the ability of this multifractal parameter to describe quantitatively the heterogeneity in samples. In addition, Δf(α) values were positive for samples S1, S4 and S6 indicating that a large probability subset was dominant in these samples. The samples S2, S3 and S5 show Δf values that are negative indicating that a small probability subset was dominant in these samples.Moreover, several multifractal parameters were calculated based on the HPMI measurements of the six samples. The mass exponent 1–S4 produced fractal dimensions values D ranging from 2.53 to 2.64, whereas NCT images gave fractal dimensions 2.59 and 2.74 for samples S5 and S6, respectively. The image fractal dimensions D values (Table FDL) were recalculated keeping only pores with sizes larger than the Swanson’s segmentation points. Figure 23. Consequently, the decrease of fractal dimension values is in agreement with results reported in these previous studies.The analysis of 3D-MCT images of samples S1 and S2 revealed image fractal dimensions FDL values of respectively 2.27 and 2.38 larger than the four other samples with values ranging in the interval . This observation indicates the effectiveness of fractal dimensions in capturing complexity in pore structures of samples through the imaged pore network.Furthermore, samples Sf(α) for the six samples showed right sided asymmetric convex parabolic shapes as illustrated in Fig. 0 ranged between 2.977 and 2.988. Larger α0 values indicate smaller concentrated distributions. Samples S1 and S2 revealed largest Δα values among the six samples respectively 0.413 and 0.416 whereas Δα was in the range  for the other four samples. This observation confirms that the non-uniformity degree of the pore structures Δα captures heterogeneity from 3-dimensional image data. Moreover, Δf(α) values were negative for the six samples indicating that a small probability subset was dominant in these samples.The singularity curves 2 =  + 0.73. Furthermore, the concentration of pore size distribution α0 showed also a relatively good linear relationship with a determination coefficient R2 =  + 0.69  in carbonate rocks. These parameters serve as quantitative indicators for classifying the degree of heterogeneity in carbonate formations. Subsequently, in a secondary phase of the research, the goal is to identify the most significant multifractal parameters among these, influencing key rock properties such as porosity, permeability, and elasticity. Ultimately, our aim will be to integrate the most influential parameters among Δα, Δf(α), Rd, and α0 as quantitative heterogeneity indicators into rock physics models for carbonate formations.In future studies, it is imperative to explore a broader spectrum of experimental and digital measurements to establish statistically more comprehensive parameter ranges for Δα, αThe primary advantage of this study is to offer a quantitative tool for categorizing rock samples based on their heterogeneity within this reservoir. Indeed, multifractal analysis can effectively capture the heterogeneity present in carbonate samples, whether derived from experimental data or digital rock images. Furthermore, we establish the presence of a correlation between these multifractal parameters, even when estimated at various scales. These observations should be investigated for more samples in future studies to have statistically more representative and accurate results.The image simulated rock properties agree with experimental measurements suggesting that 3D imaging, and simulation are effective methods to represent HPMI experimental measurements. Image fractal dimensions values span from 2.05 to 2.38 and revealed fair correlation with experimental HPMI measurement of porosity. Overall, a good correlation was revealed with pore throat radius at Swanson segmentation point.Higher correlation between experimental and simulated permeability than porosity values due to larger magnitude of permeability variation indicates that 3-dimensional images captured successfully digital pore networks representative of the real pore space in subsets used for HMPI experiments.A double fractal behaviour was revealed in the curves relating mercury saturation to capillary pressure. The intervals with fractal characteristics are characterized by Swanson segmentation points. Fractal dimensions calculated from HPMI measurements showed a good correlation with experimental HPMI measurement of porosity.The existence of good correlation between image and experimental multifractal parameters suggest that the description of pore scale morphologies can be described accurately by 3-D X-ray images representing a foundation for further research.The main findings of this study on pore structures investigation of the Lower Cretaceous, shallow marine limestone reservoir by HPMI and 3D X-Ray MCT and NCT in combination with fractal and multifractal theories are listed as below (Supplementary Information Supplementary Information.


The proposed battery chemistry is expandable to other metal chlorides, which widens the cathode materials available for aqueous chloride ion batteries.The zinc-copper redox couple exhibits several merits, which motivated us to reconstruct the rechargeable Daniell cell by combining chloride shuttle chemistry in a zinc chloride-based aqueous/organic biphasic electrolyte. An ion-selective interface was established to restrict the copper ions in the aqueous phase while ensuring chloride transfer. We demonstrated that the copper-water-chloro solvation complexes are the descriptors, which are predominant in aqueous solutions with optimized concentrations of zinc chloride; thus, copper crossover is prevented. Without this prevention, the copper ions are mostly in the hydration state and exhibit high spontaneity to be solvated in the organic phase. The zinc-copper cell delivers a highly reversible capacity of 395 mAh g 2 aqueous/organic biphasic electrolyte, delivering a high energy density with stable cycling performanceThe zinc-copper (Zn-Cu) Daniell cell is regarded as primary battery due to the crossover of the copper species. Here, the authors report a rechargeable Zn-Cu battery with the combination of chloride shuttle chemistry in a ZnCl Although rechargeable lithium-ion batteries are the focus of the current energy storage market/industry, ubiquitous issues, including safety, toxicity, and resource limitation, have impeded their large-scale and/or security-critical applications4. Alternatively, aqueous zinc batteries combine several advantages, including intrinsic safety, high energy density, and abundant resources, and have been intensively studied recently as the most compelling substitutes for large-scale energy storage6. Although encouraging, aqueous zinc batteries are challenged by the sluggish intercalation/deintercalation kinetics of metal oxide cathodes due to the large electron density of Zn2+ ions; therefore, only a limited rate capability and low capacity can be delivered7. The development of novel battery systems that incorporate aqueous zinc chemistry and new operating mechanisms would be a solution for the application of aqueous zinc batteries8.The worldwide exploitation of alternative renewable energies (wind and solar) has led to an increase in demand for the storage of electrical energy, particularly for advanced batteries that show practical potential for grid-scale applications10; however, the Daniell cell is regarded as a primary cell due to the irreversibility  or passivation of Cu2O formed during discharge 11. It is currently used in chemistry curricula to demonstrate the battery working principle by using a salt bridge to facilitate SO42− anion shuttling between the cathode and anode. The total electrochemical reaction on the cathode and anode could be interpreted as [Zn(s) + Cu2+(aq) ⇄ Zn2+(aq) + Cu(s)], for which the crossover of the copper ion leads to a direct chemical reaction in the absence of a salt bridge. Efforts have been dedicated to making the Zn–Cu Daniell battery reversible, in which ion-exchange membrane/ceramics are used to prevent Cu crossover in the neutral electrolyte14, or transfer the redox electrochemistry to hydroxyl (OH−) involved precipitation process to minimize the copper ion dissolution in alkaline electrolyte15. The incorporation of CuO and Bi2O3 could further mitigate Cu2O passivation for the alkaline Zn–CuO battery, which affords a reversible Zn–CuO alkaline battery11. Nevertheless, the ion-exchange membrane approach significantly increases the cost of the technology, while the hydroxyl strategy results in a large polarization during charge and discharge due to the slow kinetics of the solid‒solid conversion. These approaches provide valuable inspiration for the promising design of rechargeable Zn–Cu batteries, namely, the dissolution and crossover of copper species should be dialectically considered.The historic Daniell cell, invented by the British chemist John Frederic Daniell in 1836, is popularly known as the zinc-copper battery, which integrates the merits of high theoretical capacity and abundant resources for both Zn and Cu. Several modern battery designs have been developed to satisfy different application scenarios17. In addition to the large variety of abundant chloride-containing electrode materials, CIB technology is attractive due to the wide array of possible electrochemical couples with high theoretical energy densities19. Moreover, the fast chloride anion transfer in the electrolyte solution provides relatively fast reaction kinetics for the electrochemical reaction in theory; the chloride ion radius in solvated cations is significantly smaller than that of the solvated cations. In principle, CIBs are also challenged by poor cycling stability due to the dissolution of metal chlorides20. Therefore, anion hosts such as metal oxychlorides22, layered double hydroxides24, and chloride ion-doped polymers26 have been developed as cathode materials, but the poor structural stability of these frameworks has yet to be resolved19.The electrochemistry of the Daniell cell  is analogous to that of the typical chloride ion battery (CIB), which alternatively uses a chloride ion shuttle between the metal chloride/metal electrochemical couple2 aqueous solution and a Tf2N-based ionic liquid, in which the cathode is located in the aqueous phase while the zinc anode is immersed in the organic phase. The crossover of Cu ions across the interface of the biphasic electrolyte is strongly correlated to the coordination structure of Cu ions, which is rationally tunable according to the ZnCl2 concentration in the aqueous phase. We demonstrated that the copper-water-chloro complexes are the descriptors that inhibits the occurrence of Cu in the organic phase, which is dominant in the aqueous solution with > 15 m ZnCl2; otherwise, the copper ions are mostly in their hydration states with spontaneity to be solvated in the organic phase. This enables a large Cu2+ distribution ratio of 2700 between the 15 m ZnCl2 aqueous phase and organic phase, which affords highly reversible copper electrochemistry with stepwise redox reactions between CuII – CuI – Cu0. The solution solvation structure-related ion selective interface of the biphasic electrolyte in this work could greatly alleviate the active material crossover and provide fast conversion kinetics. In addition, utilization of the active material was improved because the active material species were partially solubilized in the aqueous phase. We further demonstrated that this strategy of eliminating metal ions in the organic phase is expandable to iron chloride, nickel chloride, and vanadium oxides, representing a robust approach to improve the performance of chloride shuttle batteries.In this report, we combine the advantages of the Zn–Cu redox and the glamorous chloride anion shuttle to develop a rechargeable historic Daniell cell. It was achieved by exploiting an aqueous/organic biphasic electrolyte, which established an ion selective interface that allows the restriction of the copper ions in the aqueous phase, along with chloride ions, which served as the charge carrier between the two phases to keep electrical neutrality. This biphasic electrolyte is composed of ZnCl4 aqueous electrolyte and the super P-CuCl2 cathode renders fast capacity decay, which is attributed to the serious copper ion dissolution and its rapid chemical reactions with the zinc anode   Fig. . EDS resor) Fig. .Fig. 1Th2 aqueous solution  and a Tf2N-based ionic liquid phase with large hydrophobic cations (named ZnCl2-based biphasic electrolyte), in which the dissolved electroactive CuCl2 is automatically restricted in the aqueous phase. Due to the strong water repulsion of the hydrophobic anion and cation of the organic phase, the water-favorable metal ions show a distinct distribution in the biphasic electrolyte, most likely in the aqueous phase, which will be discussed in the next section. Note that low CE and rapid capacity fading are observed in the Zn–Cu batteries based on the single phase aqueous electrolyte with 5 m ZnCl2, 15 m ZnCl2, and 25 m ZnCl2  is 395 and 388 mAh g−1 based on the mass of CuCl2, respectively, indicating CuCl2 was fully converted with two-electron transfer . EDS analysis on the zinc surface after cycling in the 15 m ZnCl2-based biphasic electrolyte confirms free Cu deposition, indicating suppressed Cu species crossover , especially for the Ni–Zn and Fe–Zn chemistries with moderate reversibility and abundance of the active materials. We further expanded the anode to Li metal, which was immersed in the organic phase of the electrolyte to provide a higher discharge potential to the battery  or the ratios between the cathode and the aqueous phase of the biphasic electrolyte. CuCl2 (1 m) in various ZnCl2 solutions was contacted with the [bmmim][Tf2N] ionic liquid, which showed distinct phase separation, as exemplified by the CuCl2−15 m ZnCl2-based biphasic electrolyte  is reported in Fig. 2N]-based biphasic electrolyte. The occurrence of the ionic liquid in the aqueous phase was investigated via Raman spectra and 19F NMR. The Raman band at approximately 740 cm−1 is assigned to the C-F vibration of the ionic liquid; however, it is absent in the aqueous phase of the biphasic electrolyte, indicative of immiscibility  in the aqueous phase was detected by 19F NMR, corresponding to a distribution ratio of 494 between the organic phase and the aqueous phase  calculations also confirmed the stability of the interface of the biphasic system within a nanoscale, in which the aqueous phase and ionic liquid are stratified along the axis with a length of 7 nm in the simulation box. The calculations illustrate a sharp interface and inerratic distribution of ions between the two phases Fig. . Althoug2+ in aqueous solutions is essential for understanding the distinct distribution of Cu species among the biphasic electrolyte. Classic computations and experiments validated that Cu2+ are solvated hydrates ([Cu(H2O)6]2+) with a distorted octahedral structure at low chloride concentrations, whereas at high concentrations [CuCl]+, [CuCl2] and [CuCl4]2− coordinated with H2O ligands are dominant species (copper–water–chloro complexes)34. This is due to the stronger dipole moment-derived electronegativity of Cl− than that of H2O35, which induces the displacement of the aqua ligands at the axial position of [Cu(H2O)6]2+ by Cl− at high chloride concentrations36. We experimentally observed this speciation by Raman spectroscopy 6]2+ hydrates remained in the 5 m CuCl2 solution (440 cm−1)37. While the solubility of CuCl2·2H2O beads in the ionic liquid was significantly lower than that of anhydrous CuCl2 2]2− units39, which is similar to the composition of distorted octahedron CuCl42− dimers with two aqua ligands in concentrated CuCl2 aqueous solution40.Knowledge of the local coordination environment around Cuopy Fig. ; however2O)6]2+ hydrates to Cu(H2O)2(Tf2N)2 was thermodynamically considered to mimic the crossover of copper ions into the organic phase. The spontaneity of the CuII cluster shuttle can be quantified by the Gibbs free energy changes42. Figure 2O)6]2+ and [CuCl2(H2O)4] in the organic phase, suggesting that the former is a spontaneous process and the latter is thermodynamically unfavorable. This hypothesis was also experimentally verified by the CuCl2-based biphasic electrolyte without ZnCl2, where both the 0.5 m CuCl2 and 5 m CuCl2 aqueous solutions show good stratifications with IL 6]2+) clusters but was prone to copper-water-chloro complexes. In pure ZnCl2 solution, the intense Raman band at approximately 283 cm−1 represents [ZnCl2+x(H2O)y]x− hydrates 6]2+44. The [ZnCl4]2− clusters rapidly dominate the solution with increasing ZnCl2 concentration (239 cm−1), indicating the share of chloride corners of the tetrahedral [ZnCl4]2− aggregates47. Although the Raman bands of chloride-associated zinc hydrates and that of copper coincide in the CuCl2-ZnCl2 solution, the solvation structure of copper can roughly be described by the presence of complete hydration ([Cu(H2O)6]2+) clusters. The copper hydration structure at 440 cm−1 gradually weakened with increasing ZnCl2 concentration and vanished in concentrated ZnCl2 solutions (>10 m)  Fig. . This inork Fig. , which i2-ZnCl2 solutions. Because the detection limit for Cu2+ is less than 0.05 m for UV spectroscopy x]+ at 250 nm and [CuCl2(H2O)x] at 260 nm are dominant copper-water-chloro complexes in low concentration (5 m) and high concentration (15 m) ZnCl2 solutions35, respectively . We further provide other zinc salts as control samples in the aqueous phase to highlight the critical role of chloride ions. The aqueous solution of ZnSO4, Zn(ClO4)2, and Zn(NO3)2 shows distinct phase separation with the organic phase, forming a biphasic electrolyte solution as the ZnCl2 salt 2, and 5 m Zn(NO3)2-based biphasic electrolytes decays rapidly -water-chloro complexes, i.e., The main peaks of CuCl and CuCl2 in 15 m ZnCl2 are both located at approximately 260 nm  after discharge, while those of the N signal from the absorbed Tf2N anions remain unchanged compared to the charged electrode 2  across the interface of the biphasic electrolyte was accessed from the Bruce–Vincent–Evans equation based on chronoamperometry of the symmetric cell using the Ag/AgCl electrode51. The Ag/AgCl electrode is a chloride active electrode, which shows stable Cl− absorption/extraction reactions in the biphasic electrolyte  collected by the same method with the zinc symmetric cell. This indicates that chloride ions are the main charge carriers across the interface of the biphasic electrolyte. Moreover, we use an ion exchange membrane to separate the biphasic electrolyte  and deposition-dissolution (CuI – Cu0) in the cathode are discussed separately. The diffusion coefficients of the liquid phase conversion are on the order of 10−6–10−8 cm2 s−1  was conducted to assess the reaction kinetics. The quasiequilibrium potentials are approximately 1.3 V for Cus−1 Fig. , while tons Fig. 52. The c2 aqueous solution and 10 µL of organic phase (see methods for details). Furthermore, Zn–Cu batteries in biphasic electrolytes with different aqueous/organic phase ratios were evaluated   at a current density of 400 mA g−1, which is higher than that of state-of-art zinc ion batteries, e.g., MnO2-Zn, VOx-Zn, spinel structured oxides-Zn, and Prussian blue-Zn53. This corresponds to a remarkable energy density of 380 Wh kg−1. A specific capacity of 385 mAh g−1 is obtained at a high current density of 800 mA g−1, and the capacity retention is calculated to be 93.5% after 100 cycles with an average coulombic efficiency > 99.5% and an energy efficiency of 83.6%. The Zn–Cu battery was tested for more than 300 cycles at 1600 mA g−1 with a capacity retention of 76%. Supplementary Fig. −1 between 0.4 and 1.6 V; EDS also confirms that there is no copper deposition on the zinc anode. While the close-to-unit coulombic efficiency is indicative of controlled crossover of the copper species in the cell, the capacity fading of this cell at high current density is mostly attributed to the incompatibility of the nonpolar carbon host for the nucleation of the copper polyhedrons. This is evidenced by the “knee” points at the beginning of the second discharge plateau, in which supersaturated CuI in the aqueous phase is essential to drive the nucleation of copper metal. This overpotential feature to initiate nucleation was well studied for metal electrodeposition and could be manipulated by altering the surface properties of the substrate; however, it is not the scope of this study.The biphasic electrolyte for cycling performance assessment is composed of 30 µL of 15 m ZnClII – CuI being activated. It delivers a high discharge capacity of 192 mAh g–1 at a rate of 200 mA g−1, corresponding to complete conversion of CuII to CuI. The capacity retention is 85.9% after 150 cycles with a coulombic efficiency of 99.9% and an improved energy efficiency of approximately 94.5%  was dissolved in the biphasic electrolyte instead of blended within the electrode (see Methods). As a result of its flexible components, the Zn–Cu pouch is expected to possess a high flexibility. The hydrophilic carbon cloth and lipophilic PP membrane also endow the battery with gravity independence. The flexible device was connected to a multifunction digital clock  with nearly 100% coulombic efficiency, or 199 mAh g−1 for the CuII – CuI conversion with stable cycling performance. The energy density of the rechargeable Zn–Cu was up to 380 Wh kg−1, which is competitive among other aqueous zinc ion batteries. We elucidated that the local coordination environment around CuII in aqueous solutions is essential for preventing the crossover of Cu ions, which is rationally tunable according to the ZnCl2 concentration with the aim of suppressing the complete hydration of Cu ions. It was demonstrated that the copper-water-chloro complexes are the descriptors that inhibit the presence of Cu in the organic phase, which are dominant in the aqueous solution with >15 m ZnCl2; without these complexes, the copper ions are mostly in their hydration states with spontaneity to be solvated in the organic phase. The strategy of eliminating metal ions in the organic phase is further expanded to iron chloride, nickel chloride, and vanadium oxides, providing a new promising approach and sustainable power source for large-scale energy storage. The merits of the solution solvation structure-related ion-selective interface of the biphasic electrolyte might also be applicable for the design of advanced chloride ion batteries and flow batteries.In summary, we have successfully rebuilt the primary Daniell cell as a secondary battery with an aqueous/organic biphasic electrolyte. An ion-selective interface was established that confines copper ions in the aqueous phase instead of a crossover between the cathode and anode, along with chloride ions serving as the charge carrier between the two phases to maintain electrical neutrality. Such an ion-selective interface was enabled by the combination of immiscible ZnCl2 cathode was prepared by mixing 20 wt% Super P carbon, 70 wt% CuCl2, 10 wt% PTFE, then the mixture was compressed onto Ti mesh . The electrodes of iron chloride, nickel chloride, and vanadium oxides were prepared in the same procedure. The areal loading of the active material on these electrodes was about 4-5 mg cm−2. Ag/AgCl electrode was prepared by mixing 20 wt% Super P carbon, 70 wt% AgCl, 10 wt% PVDF, with NMP as the solvent. The slurry was cast onto the Ag foam  and was vacuum dried at 60 °C for 12 h. The areal loading of AgCl is about 20 mg cm−2 for each electrode. Carbon cloth (CeTech W0S1011), PP membrane (Celgard 2300), Glass fiber (Whatman GF/A), anion exchange membrane (Fumasep FAB-PK-130), and cation exchange membrane (Nafion N-117) were purchased from sci materials hub. Nafion N-117 was pretreated with 5 wt% H2O2 solution at 80 °C for 1 h to remove the organic impurities, then soaked in the deionized water at 80 °C for 1 h to remove the H2O2. Both anion exchange membrane and cation exchange membrane were pre-soaked in the 15 m ZnCl2 solution before the battery assembly. Carbon cloth was chemically activated by the oxidation method by soaking carbon cloth in a mixture of acids (H2SO4: HNO3 = 1:3) for 12 h.All reagents were purchased from Shanghai Aladdin Biochemical Technology Co. and used as received without any further purification. Aqueous solutions were prepared by molality . CuCl−1. All the solutions were sealed in the capillary for Raman tests. 1 wt% HCl was added to the aqueous phase in case of coprecipitation of paratacamite at high CuCl2 concentration. XPS spectra were collected on Thermo Scientific K-Alpha system with a monochromatic Al-Ka (1486.6 eV) X-ray source to investigate the chemicals on the Zn anode. 19F NMR spectra were monitored by a Bruker Ascend HD 400 MHz with deuterium oxide as NMR solvent and trifluoroacetic acid as internal standard. XRD measurements were carried out on a Bruker D8-Advance powder X-ray diffractometer operating at 40 kV and 40 mA, using Cu-Kα radiation (λ = 0.15405 nm). SEM studies were carried out on a TESCAN MIRA3 field-emission SEM instrument. Electrodes were gently washed with deionized water and dried at 60 °C before the SEM tests.ICP-OES results were conducted on a Varian Agilent 720ES spectrometer. The biphasic electrolytes were equilibrated for a least one week before the ICP tests. UV–vis spectra characterization was carried out on a UV1902PC with a range from 200 to 600 nm. Raman analyses were carried out on a bench Raman dispersive microspectrometer  using a laser (wavelength of 532 nm) at frequencies from 100 to 4000 cm−5 kcal mol−1 and force convergence criteria of 1.0 × 10−3 kcal mol−1 Å−1 was used to get a global minimum energy configuration. To further equilibrate the model, the simulations were initially relaxed under the constant pressure and the constant temperature (NPT ensemble) for 1 ns at a room temperature of 298.15 K and atmospheric pressure. During the simulation, Nose thermostat and Berendsen barostat algorithm were applied in the temperature and pressure control. Later, the equilibrated simulations run at constant NVT ensemble for 10 ns in order to get authentic data. All DFT calculations were performed using the DMol package. The treatment of core electrons was described by the all-electron relativistic method which is the most accurate and also the most computationally expensive of the available type. The generalized gradient approximation of Perdew–Burke–Ernzerhof (GGA–PBE) was used to account for the exchange-correlation functional. The double numerical plus polarization (DNP) basis was used for the best accuracy but highest cost. The global orbital cutoff was set to 4.5 Å. The Grimme correction method was employed in order to include VDW interactions. The energy, force and displacement convergence criterion was set to 1.0 × 10−5 Hartree, 2.0 × 10−3 Hartree Å−1 and 5.0 × 10−3 Å for optimization.All MD simulations were performed within Forcite Package. The COMPASS force-field was used. The Ewald method and the atom-based method were employed for analyzing the Coulomb interactions and the van der Waals (VDW) interactions. In order to obtain a reasonable interaction configuration, a geometry optimization using smart method which is a cascade of the steepest descent, ABNR, and quasi-Newton methods with an energy convergence criterion of 2.0 × 10−2, 0.1 mm, Hebei Qingyuan Technology Co.) was used as anodes. Glass fiber  was used as the separator for the cells with the single-phase electrolyte. For the batteries based on biphasic electrolyte, a hydrophilic glass fiber near the cathode was wetted by the ZnCl2 aqueous solution, and a hydrophobic PP membrane  near the anode was wetted by the organic solution. The battery was assembled by simply stacking the electrodes and the wetted separators layer by layer. The different hydrophilies of the separators facilitate the combination of two immiscible liquids into a robust biphasic system. The aqueous solution of the biphasic electrolyte for each cell was 30 μL, while that of the organic phase was 10 μL. The Zn–Cu batteries based on the bi-phasic electrolyte with the anion or cation exchange membranes were assembled in the same procedure, except that the anion exchange membrane (Fumasep FAB-PK-130), or cation exchange membrane (Nafion N-117) was placed between 30 μL organic phase and 10 μL aqueous phase. The flexible pouch cell (size: 6 × 6 × 0.06 cm3) was readily fabricated in a transparent PE bag. The biphasic electrolyte for the pouch cell was composed by 800 μL aqueous solution with 1 m CuCl2 and 200 μL organic phase. Hydrophilic carbon cloth with a thickness of 0.36 mm (CeTech W0S1011) was used as the cathode current collector and also as the aqueous phase absorbent, and a hydrophobic PP membrane (Celgard 2300) near the anode was wetted by the organic solution. Hydrophilic glass fiber membrane was not used in the pouch cell. More details please see Supplementary Note All electrochemical studies were conducted in Swagelok-type cells with titanium rod current collectors. The diameter of electrodes are 12 mm. The 0.1 mm thickness zinc foil . In consistent with the structure of the battery, separators were used as absorbent for the electrolyte solution  was measured with combination measurements of alternating current impedance and direct current polarization using the Zn//Zn and Ag/AgCl//Ag/AgCl cells based biphasic electrolyte, respectively. The polarization currents of cell including initial (I0) and steady-state (Iss) were recorded under a direct current polarization voltage of 20 mV (ΔV). The interfacial resistances before (R0) and after (Rss) polarization were tested by EIS. Afterwards, ion transference number was calculated from Bruce–Vincent–Evans Equation:Cells were galvanostatically tested on a Neware CT-4008T battery test system  at room temperature (25 °C). Cyclic voltammetry and linear sweep voltammetry measurements were performed on an Interface 1010 electrochemical workstation  in a three-electrode cell with the Ag/AgCl reference electrode. The electrochemical stability windows (ESW) of [bmmim][TfSupplementary InformationPeer Review File