The relationship between cell density and velocity is often assumed to be negative, reflecting crowding-induced suppression of movement. However, observations across systems reveal a more nuanced picture: while some emphasize contact inhibition of locomotion, others suggest that dense regions exhibit enhanced activity due to force generation. Here, using experimental measurements we show that density–velocity relation in epithelial monolayers is inherently scale dependent. By coarse-graining cell motion over multiple spatial windows, we find that cell velocity magnitude correlates positively with local density at small scales, but negatively at large scales. Employing traction force measurements, we find that this crossover coincides with the emergence of mechanical pressure segregation, defining a characteristic length scale beyond which crowding dominates. A minimal model incorporating activity-induced shape changes reproduces this crossover and identifies the competition between active force generation and mechanical confinement as the underlying mechanism. Our results reconcile conflicting views of density-regulated migration and highlight an emergent length scale as a key factor in interpreting collective cell dynamics.
{"title":"Density–velocity relation is scale-dependent in epithelial monolayers","authors":"Hengdong Lu, Tianxiang Ma and Amin Doostmohammadi","doi":"10.1039/D5SM01054C","DOIUrl":"10.1039/D5SM01054C","url":null,"abstract":"<p >The relationship between cell density and velocity is often assumed to be negative, reflecting crowding-induced suppression of movement. However, observations across systems reveal a more nuanced picture: while some emphasize contact inhibition of locomotion, others suggest that dense regions exhibit enhanced activity due to force generation. Here, using experimental measurements we show that density–velocity relation in epithelial monolayers is inherently scale dependent. By coarse-graining cell motion over multiple spatial windows, we find that cell velocity magnitude correlates positively with local density at small scales, but negatively at large scales. Employing traction force measurements, we find that this crossover coincides with the emergence of mechanical pressure segregation, defining a characteristic length scale beyond which crowding dominates. A minimal model incorporating activity-induced shape changes reproduces this crossover and identifies the competition between active force generation and mechanical confinement as the underlying mechanism. Our results reconcile conflicting views of density-regulated migration and highlight an emergent length scale as a key factor in interpreting collective cell dynamics.</p>","PeriodicalId":103,"journal":{"name":"Soft Matter","volume":" 6","pages":" 1350-1357"},"PeriodicalIF":2.8,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146049579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Linsy Jane Selvin Robert, Ashish Chandra Das, Vida Jurečič, Vid Bobnar, Oleg D. Lavrentovich, Miha Ravnik and Igor Muševič
We use polarized optical microscopy and confocal fluorescence microscopy to explore electric-field induced swimming of direct laser written polymer microrods in a nematic liquid crystal in the regime of very low frequencies. The rods are of variable aspect ratio and swim in a liquid crystal layer with a thickness comparable to that of the longest rods. We observe significant spatial reorientation of the microrods under an applied electric field, which is characterized by their up and down movement along the applied electric field, oscillation in their tilting with respect to the field, sidewise wobbling of their center of mass and propulsion along the direction perpendicular to the electric field. The velocity of propulsion shows a power law behaviour on the electric field magnitude, vx ∝ Eα, where α is between 3 and 5 for different aspect ratio rods and can be partially explained by the shear thinning of the viscosity at higher velocity. The time analysis of 3D trajectories of swimming microrods shows a linear coupling of the microrod's center of mass to the applied electric field, and quadratic (i.e. dielectric) coupling of the microrod's tilt to the field, which appears to be the main driving mechanism for microrod propulsion.
{"title":"Propulsion of laser printed polymer micro-rods by a low frequency electric field in nematic liquid crystals","authors":"Linsy Jane Selvin Robert, Ashish Chandra Das, Vida Jurečič, Vid Bobnar, Oleg D. Lavrentovich, Miha Ravnik and Igor Muševič","doi":"10.1039/D5SM01104C","DOIUrl":"10.1039/D5SM01104C","url":null,"abstract":"<p >We use polarized optical microscopy and confocal fluorescence microscopy to explore electric-field induced swimming of direct laser written polymer microrods in a nematic liquid crystal in the regime of very low frequencies. The rods are of variable aspect ratio and swim in a liquid crystal layer with a thickness comparable to that of the longest rods. We observe significant spatial reorientation of the microrods under an applied electric field, which is characterized by their up and down movement along the applied electric field, oscillation in their tilting with respect to the field, sidewise wobbling of their center of mass and propulsion along the direction perpendicular to the electric field. The velocity of propulsion shows a power law behaviour on the electric field magnitude, <em>v</em><small><sub><em>x</em></sub></small> ∝ <em>E</em><small><sup><em>α</em></sup></small>, where <em>α</em> is between 3 and 5 for different aspect ratio rods and can be partially explained by the shear thinning of the viscosity at higher velocity. The time analysis of 3D trajectories of swimming microrods shows a linear coupling of the microrod's center of mass to the applied electric field, and quadratic (<em>i.e.</em> dielectric) coupling of the microrod's tilt to the field, which appears to be the main driving mechanism for microrod propulsion.</p>","PeriodicalId":103,"journal":{"name":"Soft Matter","volume":" 10","pages":" 2107-2121"},"PeriodicalIF":2.8,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://pubs.rsc.org/en/content/articlepdf/2026/sm/d5sm01104c?page=search","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146163080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Aqueous foams are subject to coarsening, whereby gas from the bubbles diffuses through the liquid phase. Gas is preferentially transported from small to large bubbles, resulting in a gradual decrease of the number of bubbles and an increase in the average bubble size. Coarsening foams are expected to approach a scaling state at late times in which their statistical properties are invariant. However, a model predicting the experimentally observed bubble-size distribution in the scaling state of foams with moderate liquid content, as a function of the liquid fraction ϕ, has not yet been developed. To this end, we propose a three-dimensional mean-field bubble growth law for foams without inter-bubble adhesion, validated against bubble-scale simulations, and use it to derive a prediction of the scaling-state bubble-size distribution for any ϕ from zero up to the unjamming transition ϕc ≈ 36%. We verify that the derived scaling state is approached from a variety of initial conditions using mean-field simulations implementing the proposed growth law. Comparing our predicted bubble-size distribution with previous simulations and experimental results, we likewise find a large population of small bubbles when ϕ > 0, but there are qualitative differences from prior results which we attribute to the absence of rattlers, i.e. bubbles not pressed into contact with their neighbours, in our model.
{"title":"Mean-field model for the bubble size distribution in coarsening wet foams","authors":"Jacob Morgan and Simon Cox","doi":"10.1039/D5SM01007A","DOIUrl":"10.1039/D5SM01007A","url":null,"abstract":"<p >Aqueous foams are subject to coarsening, whereby gas from the bubbles diffuses through the liquid phase. Gas is preferentially transported from small to large bubbles, resulting in a gradual decrease of the number of bubbles and an increase in the average bubble size. Coarsening foams are expected to approach a scaling state at late times in which their statistical properties are invariant. However, a model predicting the experimentally observed bubble-size distribution in the scaling state of foams with moderate liquid content, as a function of the liquid fraction <em>ϕ</em>, has not yet been developed. To this end, we propose a three-dimensional mean-field bubble growth law for foams without inter-bubble adhesion, validated against bubble-scale simulations, and use it to derive a prediction of the scaling-state bubble-size distribution for any <em>ϕ</em> from zero up to the unjamming transition <em>ϕ</em><small><sub>c</sub></small> ≈ 36%. We verify that the derived scaling state is approached from a variety of initial conditions using mean-field simulations implementing the proposed growth law. Comparing our predicted bubble-size distribution with previous simulations and experimental results, we likewise find a large population of small bubbles when <em>ϕ</em> > 0, but there are qualitative differences from prior results which we attribute to the absence of rattlers, <em>i.e.</em> bubbles not pressed into contact with their neighbours, in our model.</p>","PeriodicalId":103,"journal":{"name":"Soft Matter","volume":" 7","pages":" 1601-1617"},"PeriodicalIF":2.8,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://pubs.rsc.org/en/content/articlepdf/2026/sm/d5sm01007a?page=search","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146117228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Droplet formation and breakup in branched microchannels with asymmetric constrictions were investigated using shear-thinning xanthan gum solutions as the continuous phase and soybean oil as the dispersed phase. Experiments at concentrations of 400–1500 ppm were complemented by validated three-dimensional simulations to assess the influence of the power-law index (n) on droplet dynamics. Time-resolved analyses revealed periodic upstream pressure oscillations whose amplitude increased as n decreased, linking rheology directly to droplet size and formation frequency. Normalized droplet length data from all cases collapsed onto a single power-law curve when rescaled by the effective capillary number, providing a universal representation of breakup dynamics. With increasing n, droplet volumes grew while front-tip velocities declined, demonstrating the coupled effect of rheology on both size and transport. Velocity fields further confirmed flatter core profiles in shear-thinning systems, characteristic of power-law fluids, in contrast to the parabolic distributions observed for Newtonian flows. Collectively, the results establish how shear-thinning rheology and downstream asymmetry interact to control droplet breakup and partitioning, offering design principles for predictive scaling in multiphase microfluidics.
{"title":"Shear-thinning rheology and geometric asymmetry govern droplet dynamics in branched microchannels","authors":"Rakesh Kumar, Rajaram Lakkaraju and Arnab Atta","doi":"10.1039/D5SM00957J","DOIUrl":"10.1039/D5SM00957J","url":null,"abstract":"<p >Droplet formation and breakup in branched microchannels with asymmetric constrictions were investigated using shear-thinning xanthan gum solutions as the continuous phase and soybean oil as the dispersed phase. Experiments at concentrations of 400–1500 ppm were complemented by validated three-dimensional simulations to assess the influence of the power-law index (<em>n</em>) on droplet dynamics. Time-resolved analyses revealed periodic upstream pressure oscillations whose amplitude increased as <em>n</em> decreased, linking rheology directly to droplet size and formation frequency. Normalized droplet length data from all cases collapsed onto a single power-law curve when rescaled by the effective capillary number, providing a universal representation of breakup dynamics. With increasing <em>n</em>, droplet volumes grew while front-tip velocities declined, demonstrating the coupled effect of rheology on both size and transport. Velocity fields further confirmed flatter core profiles in shear-thinning systems, characteristic of power-law fluids, in contrast to the parabolic distributions observed for Newtonian flows. Collectively, the results establish how shear-thinning rheology and downstream asymmetry interact to control droplet breakup and partitioning, offering design principles for predictive scaling in multiphase microfluidics.</p>","PeriodicalId":103,"journal":{"name":"Soft Matter","volume":" 8","pages":" 1797-1808"},"PeriodicalIF":2.8,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146148588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Steffen M. Recktenwald, Vincenzo Calabrese, Amy Q. Shen, Giovanniantonio Natale and Simon J. Haward
We perform a combined experimental and theoretical investigation of the orientational dynamics of colloidal rods subjected to time-dependent homogeneous planar elongational flow. Our experimental approach involves the flow of dilute suspensions of cellulose nanocrystals (CNC) within a cross-slot-type microfluidic device through which the extension rate is modulated sinusoidally over a wide range of Péclet number amplitudes (Pe0) and Deborah numbers (De). The time-dependent orientation of the CNC is assessed via quantitative flow-induced birefringence measurements. For small Pe0 ≲ 1 and small De ≲ 0.03, the birefringence response is sinusoidal and in phase with the strain rate. With increasing Pe0, the response becomes non-sinusoidal (i.e., nonlinear) as the birefringence saturates due to the high degree of particle alignment at higher strain rates during the cycle. With increasing De, the CNC rods have insufficient time to respond to the rapidly changing strain rate, leading to asymmetry in the birefringence response around the minima and a residual effect as the strain rate approaches zero. These dynamical responses of the CNC are captured in a detailed series of Lissajous plots of the birefringence versus the strain rate. Experimental measurements are compared with simulations performed on both monodisperse and polydisperse systems, with rotational diffusion coefficients Dr matched to the CNC. A semiquantitative agreement is found for polydisperse simulations with Dr heavily weighted to the longest rods in the measured CNC distribution. The results will be valuable for understanding, predicting and optimizing the orientation of rod-like colloids during transient processing flows such as fiber spinning and film casting.
{"title":"Colloidal rod dynamics under large amplitude oscillatory extensional flow","authors":"Steffen M. Recktenwald, Vincenzo Calabrese, Amy Q. Shen, Giovanniantonio Natale and Simon J. Haward","doi":"10.1039/D5SM01122A","DOIUrl":"10.1039/D5SM01122A","url":null,"abstract":"<p >We perform a combined experimental and theoretical investigation of the orientational dynamics of colloidal rods subjected to time-dependent homogeneous planar elongational flow. Our experimental approach involves the flow of dilute suspensions of cellulose nanocrystals (CNC) within a cross-slot-type microfluidic device through which the extension rate is modulated sinusoidally over a wide range of Péclet number amplitudes (Pe<small><sub>0</sub></small>) and Deborah numbers (De). The time-dependent orientation of the CNC is assessed <em>via</em> quantitative flow-induced birefringence measurements. For small Pe<small><sub>0</sub></small> ≲ 1 and small De ≲ 0.03, the birefringence response is sinusoidal and in phase with the strain rate. With increasing Pe<small><sub>0</sub></small>, the response becomes non-sinusoidal (<em>i.e.</em>, nonlinear) as the birefringence saturates due to the high degree of particle alignment at higher strain rates during the cycle. With increasing De, the CNC rods have insufficient time to respond to the rapidly changing strain rate, leading to asymmetry in the birefringence response around the minima and a residual effect as the strain rate approaches zero. These dynamical responses of the CNC are captured in a detailed series of Lissajous plots of the birefringence <em>versus</em> the strain rate. Experimental measurements are compared with simulations performed on both monodisperse and polydisperse systems, with rotational diffusion coefficients <em>D</em><small><sub>r</sub></small> matched to the CNC. A semiquantitative agreement is found for polydisperse simulations with <em>D</em><small><sub>r</sub></small> heavily weighted to the longest rods in the measured CNC distribution. The results will be valuable for understanding, predicting and optimizing the orientation of rod-like colloids during transient processing flows such as fiber spinning and film casting.</p>","PeriodicalId":103,"journal":{"name":"Soft Matter","volume":" 6","pages":" 1389-1401"},"PeriodicalIF":2.8,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://pubs.rsc.org/en/content/articlepdf/2026/sm/d5sm01122a?page=search","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146049645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yara Alvarez-Braña, Andreu Benavent-Claró, Fernando Benito-Lopez, Aurora Hernandez-Machado and Lourdes Basabe-Desmonts
To enhance the portability of Lab-on-a-Chip technology, avoiding bulky electronic flow control systems is crucial. Self-powered microfluidics can significantly improve portability by eliminating the need for electronic components. Traditionally, self-powered microsystems handle small fluid volumes for up to one or two hours. However, many experiments, such as cell culture or real-time biomarker detection assays, require flow control for longer periods. In this study, we demonstrate that polymeric micropumps can provide self-powered flow control for intermediate durations, ranging from several to more than 10 hours. By monitoring the fluid front dynamics of a solution flowing through a microchannel over 1.5 meters long, we developed calibration curves for various micropump types. Our findings reveal that the pump's actuation time is influenced by degassing time, and effective surface area. Using these calibration curves, we compare mathematical models to predict flow rates and actuation times, facilitating the design of customized self-powered microsystems for both short and long-term applications. Epoxy-coated PDMS pumps represent a notable example of a long-operating self-powered microsystem, which holds significant potential for applications requiring controlled flow over extended periods.
{"title":"Epoxy coating to prolong actuation time in degas-driven PDMS micropumps","authors":"Yara Alvarez-Braña, Andreu Benavent-Claró, Fernando Benito-Lopez, Aurora Hernandez-Machado and Lourdes Basabe-Desmonts","doi":"10.1039/D5SM00964B","DOIUrl":"10.1039/D5SM00964B","url":null,"abstract":"<p >To enhance the portability of Lab-on-a-Chip technology, avoiding bulky electronic flow control systems is crucial. Self-powered microfluidics can significantly improve portability by eliminating the need for electronic components. Traditionally, self-powered microsystems handle small fluid volumes for up to one or two hours. However, many experiments, such as cell culture or real-time biomarker detection assays, require flow control for longer periods. In this study, we demonstrate that polymeric micropumps can provide self-powered flow control for intermediate durations, ranging from several to more than 10 hours. By monitoring the fluid front dynamics of a solution flowing through a microchannel over 1.5 meters long, we developed calibration curves for various micropump types. Our findings reveal that the pump's actuation time is influenced by degassing time, and effective surface area. Using these calibration curves, we compare mathematical models to predict flow rates and actuation times, facilitating the design of customized self-powered microsystems for both short and long-term applications. Epoxy-coated PDMS pumps represent a notable example of a long-operating self-powered microsystem, which holds significant potential for applications requiring controlled flow over extended periods.</p>","PeriodicalId":103,"journal":{"name":"Soft Matter","volume":" 7","pages":" 1679-1686"},"PeriodicalIF":2.8,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://pubs.rsc.org/en/content/articlepdf/2026/sm/d5sm00964b?page=search","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146148520","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Siripanyo Promnil, Daniele Liprandi, Tom Illing, Maitry Jani, Paula Heinz and Jonas O. Wolff
Spider silk is known for its outstanding toughness at low density, making it a promising model for the biomimetic design of advanced fibre materials. Spiders naturally do not spin single silk fibres but instead produce bundles, or threads, composed of two or more fibres that may originate from the same or different silk glands. Despite their ubiquity, the mechanical properties of these fibre bundles have been largely overlooked. In this study, both naturally spun and forcibly silked fibre bundles from the cosmopolitan cellar spider Pholcus phalangioides (Pholcidae) and naturally spun bundles from the comb-footed cellar spider Nesticus cellulanus (Nesticidae) were examined to test whether post-spinning combinations of different silk materials, such as stiff and soft fibres, enhance the toughness of silk bundles. Despite their compositional diversity, tensile tests showed that the performance of fibre bundles cannot be predicted solely from the properties or the number of the individual fibres. These findings reveal that silk fibre bundles exhibit more complex tensile behaviour than previously recognised and demonstrate that spiders can produce a wide range of mechanical properties through the specific post-processing and combination of silk fibres. This principle of forming heterogeneous bundles may inspire biomimetic approaches to the post-spinning processing of recombinant silks and the design of advanced fibre materials.
{"title":"Tensile properties of single- and multi-type mixed fibre bundles of spider silk","authors":"Siripanyo Promnil, Daniele Liprandi, Tom Illing, Maitry Jani, Paula Heinz and Jonas O. Wolff","doi":"10.1039/D5SM01141H","DOIUrl":"10.1039/D5SM01141H","url":null,"abstract":"<p >Spider silk is known for its outstanding toughness at low density, making it a promising model for the biomimetic design of advanced fibre materials. Spiders naturally do not spin single silk fibres but instead produce bundles, or threads, composed of two or more fibres that may originate from the same or different silk glands. Despite their ubiquity, the mechanical properties of these fibre bundles have been largely overlooked. In this study, both naturally spun and forcibly silked fibre bundles from the cosmopolitan cellar spider <em>Pholcus phalangioides</em> (Pholcidae) and naturally spun bundles from the comb-footed cellar spider <em>Nesticus cellulanus</em> (Nesticidae) were examined to test whether post-spinning combinations of different silk materials, such as stiff and soft fibres, enhance the toughness of silk bundles. Despite their compositional diversity, tensile tests showed that the performance of fibre bundles cannot be predicted solely from the properties or the number of the individual fibres. These findings reveal that silk fibre bundles exhibit more complex tensile behaviour than previously recognised and demonstrate that spiders can produce a wide range of mechanical properties through the specific post-processing and combination of silk fibres. This principle of forming heterogeneous bundles may inspire biomimetic approaches to the post-spinning processing of recombinant silks and the design of advanced fibre materials.</p>","PeriodicalId":103,"journal":{"name":"Soft Matter","volume":" 6","pages":" 1455-1472"},"PeriodicalIF":2.8,"publicationDate":"2026-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://pubs.rsc.org/en/content/articlepdf/2026/sm/d5sm01141h?page=search","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146058264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Swapnil Daxini, Jack A. Barnes and Hans-Peter Loock
Crank's solutions for Fick's second law remain the foundation of diffusion kinetics models, yet many studies use simplified forms of these solutions for fitting experimental data. Here, we derive and summarize the exact diffusion equations that can be used to model the analyte uptake and release in permeable films, with emphasis on two cases: a free-standing film and a film mounted on an impermeable substrate. For both cases, we present the analytical expressions and their integrated forms. The integrations consider two different experimental scenarios that are common when measuring the kinetics of analyte uptake and desorption: (1) the average analyte concentration is determined across the entire film and (2) the average concentration of analyte is determined in a localized region of interest. While the former is relevant to, e.g. gravimetric measurements, the latter is particularly relevant to plasmonic sensing applications and evanescent field interactions, where the measurable signal is dependent on the analyte concentration near the film interface. We provide a comprehensive framework for fitting experimental diffusion curves to physically meaningful models, enabling a more accurate determination of diffusion coefficients across a range of polymer–analyte systems.
{"title":"Exact integrated equations to describe diffusion kinetics","authors":"Swapnil Daxini, Jack A. Barnes and Hans-Peter Loock","doi":"10.1039/D5SM01209K","DOIUrl":"10.1039/D5SM01209K","url":null,"abstract":"<p >Crank's solutions for Fick's second law remain the foundation of diffusion kinetics models, yet many studies use simplified forms of these solutions for fitting experimental data. Here, we derive and summarize the exact diffusion equations that can be used to model the analyte uptake and release in permeable films, with emphasis on two cases: a free-standing film and a film mounted on an impermeable substrate. For both cases, we present the analytical expressions and their integrated forms. The integrations consider two different experimental scenarios that are common when measuring the kinetics of analyte uptake and desorption: (1) the average analyte concentration is determined across the entire film and (2) the average concentration of analyte is determined in a localized region of interest. While the former is relevant to, <em>e.g.</em> gravimetric measurements, the latter is particularly relevant to plasmonic sensing applications and evanescent field interactions, where the measurable signal is dependent on the analyte concentration near the film interface. We provide a comprehensive framework for fitting experimental diffusion curves to physically meaningful models, enabling a more accurate determination of diffusion coefficients across a range of polymer–analyte systems.</p>","PeriodicalId":103,"journal":{"name":"Soft Matter","volume":" 8","pages":" 1816-1824"},"PeriodicalIF":2.8,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://pubs.rsc.org/en/content/articlepdf/2026/sm/d5sm01209k?page=search","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146155597","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Two typical morphologies of two-dimensional aggregates are considered: compact crystalline clusters and string-like non-compact conformations. Simulated trajectories of both types of aggregates are analysed with fine spatial resolution. While the long-time geometry of such trajectories appears to be statistically identical for the two conformations, the self-overlap statistics reveal two distinct short-time pre-caging mechanisms. While the length-scale is directly proportional to the time-scale for particles in compact aggregates, a non-monotonic relationship holds for non-compact clusters. The relationship between short length-scale and fast time-scale for particle localization might hold the key to the structure–function relationship of aggregate forming systems and other non-equilibrium soft materials.
{"title":"Spatially resolved fast dynamics reveal the aggregation mechanism in two-dimensions","authors":"Tamoghna Das and Mahesh M. Bandi","doi":"10.1039/D5SM00672D","DOIUrl":"10.1039/D5SM00672D","url":null,"abstract":"<p >Two typical morphologies of two-dimensional aggregates are considered: compact crystalline clusters and string-like non-compact conformations. Simulated trajectories of both types of aggregates are analysed with fine spatial resolution. While the long-time geometry of such trajectories appears to be statistically identical for the two conformations, the self-overlap statistics reveal two distinct short-time pre-caging mechanisms. While the length-scale is directly proportional to the time-scale for particles in compact aggregates, a non-monotonic relationship holds for non-compact clusters. The relationship between short length-scale and fast time-scale for particle localization might hold the key to the structure–function relationship of aggregate forming systems and other non-equilibrium soft materials.</p>","PeriodicalId":103,"journal":{"name":"Soft Matter","volume":" 7","pages":" 1562-1568"},"PeriodicalIF":2.8,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://pubs.rsc.org/en/content/articlepdf/2026/sm/d5sm00672d?page=search","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146103189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yi Guo, Jiaqing Zhang, Dongsheng Wang, Pengran Gao and Depeng Kong
To investigate the effects of water hardness on aqueous film-forming foam (AFFF) extinguishing agents, this study prepared AFFFs using water with varying concentrations and mixing ratios of Ca2+ and Mg2+. The effects of different hardness levels and ion compositions on conductivity, dynamic surface tension, drainage time, and initial foam height are quantitatively analyzed. The results indicate that, due to interactions between the ions and surfactants, solution conductivity initially increases and then decreases with rising ion concentration. Dynamic surface tension analysis reveals that increasing water hardness slows the adsorption of surfactants at the gas–liquid interface. Notably, when the ion concentration exceeds 60 mM, the characteristic adsorption time increases significantly, with Ca2+ exerting a stronger inhibitory effect than Mg2+. Moderate water hardness enhances foaming by shielding electrostatic repulsion. Dynamic surface tension analysis indicates that increasing water hardness slows the adsorption of surfactants at the gas–liquid interface. When the total ion concentration exceeds 60 mM, the characteristic adsorption time rises significantly, with Ca2+ exhibiting a stronger inhibitory effect than Mg2+. Moderate water hardness promotes foaming by shielding electrostatic repulsion, while extreme hardness leads to excessive ion aggregation and the formation of insoluble precipitates, which compromise foam stability and shorten drainage time. In mixed hardness systems, increasing the proportion of Mg2+ at the same overall hardness lessens the negative impact on AFFF performance, resulting in prolonged foam drainage time and delayed foam coarsening. This study provides valuable data support for optimizing AFFF formulations with respect to varying water hardness conditions.
{"title":"Mechanistic insights into water hardness effects on AFFF foam behavior: the dominant role of Ca2+ and Mg2+","authors":"Yi Guo, Jiaqing Zhang, Dongsheng Wang, Pengran Gao and Depeng Kong","doi":"10.1039/D5SM01131K","DOIUrl":"10.1039/D5SM01131K","url":null,"abstract":"<p >To investigate the effects of water hardness on aqueous film-forming foam (AFFF) extinguishing agents, this study prepared AFFFs using water with varying concentrations and mixing ratios of Ca<small><sup>2+</sup></small> and Mg<small><sup>2+</sup></small>. The effects of different hardness levels and ion compositions on conductivity, dynamic surface tension, drainage time, and initial foam height are quantitatively analyzed. The results indicate that, due to interactions between the ions and surfactants, solution conductivity initially increases and then decreases with rising ion concentration. Dynamic surface tension analysis reveals that increasing water hardness slows the adsorption of surfactants at the gas–liquid interface. Notably, when the ion concentration exceeds 60 mM, the characteristic adsorption time increases significantly, with Ca<small><sup>2+</sup></small> exerting a stronger inhibitory effect than Mg<small><sup>2+</sup></small>. Moderate water hardness enhances foaming by shielding electrostatic repulsion. Dynamic surface tension analysis indicates that increasing water hardness slows the adsorption of surfactants at the gas–liquid interface. When the total ion concentration exceeds 60 mM, the characteristic adsorption time rises significantly, with Ca<small><sup>2+</sup></small> exhibiting a stronger inhibitory effect than Mg<small><sup>2+</sup></small>. Moderate water hardness promotes foaming by shielding electrostatic repulsion, while extreme hardness leads to excessive ion aggregation and the formation of insoluble precipitates, which compromise foam stability and shorten drainage time. In mixed hardness systems, increasing the proportion of Mg<small><sup>2+</sup></small> at the same overall hardness lessens the negative impact on AFFF performance, resulting in prolonged foam drainage time and delayed foam coarsening. This study provides valuable data support for optimizing AFFF formulations with respect to varying water hardness conditions.</p>","PeriodicalId":103,"journal":{"name":"Soft Matter","volume":" 6","pages":" 1434-1445"},"PeriodicalIF":2.8,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146058151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}