Drop deformation in shear flow is determined up to second order theory in Ca while considering kinetic effects on surfactants distributions in steady state. Surfactants inside the drop are adsorbed faster than those on the surface leading to an increase in total surfactants concentration on the semi-minor axis of the ellipsoidal droplet. New expressions for Taylor deformation and angle deviation are proposed involving kinetics effects. Theoretical calculations lead to a possibility of lesser deformation than the usual limit condition and a minor correction for the deviation angle.

The red blood cell (RBC) membrane is composed of a lipid bilayer and a cytoskeleton interconnected by protein junction complexes, allowing for potential sliding between the lipid bilayer and the cytoskeleton. Despite this biological reality, it is most often modelled as a single-layer model, a hyperelastic capsule or a fluid vesicle. Another approach involves incorporating the membrane's composite structure using double layers, where one layer represents the lipid bilayer and the other represents the cytoskeleton. In this paper, we computationally assess the various modelling strategies by analysing RBC behaviour in extensional flow and four distinct regimes that simulate RBC dynamics in shear flow. The proposed double-layer strategies, such as the vesicle-capsule and capsule-capsule models, account for the fluidity and surface incompressibility of the lipid bilayer in different ways. Our findings demonstrate that introducing sliding between the layers offers the cytoskeleton a considerable degree of freedom to alleviate its elastic stresses, resulting in a significant increase in RBC elongation. Surprisingly, our study reveals that the membrane modelling strategy for RBCs holds greater importance than the choice of the cytoskeleton's reference shape. These results highlight the inadequacy of considering mechanical properties alone and emphasise the need for careful integration of these properties. Furthermore, our findings fortuitously uncover a novel indicator for determining the appropriate stress-free shape of the cytoskeleton.

Margination, a fundamental process in which leukocytes migrate from the flowing blood to the vessel wall, is well-documented in physiology. However, it is still an open question on how the differences in cell size and stiffness of white and red cells contribute to this phenomenon. To investigate the specific influence of cell stiffness, we conduct experimental and numerical studies on the segregation of a binary mixture of artificially stiffened red blood cells within a suspension of healthy cells. The resulting distribution of stiffened cells within the channel is found to depend on the channel geometry, as demonstrated with slit, rectangular, and cylindrical cross sections. Notably, an unexpected central peak in the distribution of stiffened red blood cells, accompanied by fourfold peaks at the corners, emerges in agreement with simulations. Our results unveil a nonmonotonic variation in segregation/margination concerning hematocrit and flow rate, challenging the prevailing belief that higher flow rates lead to enhanced margination.

Drops in extensional flow undergo a deformation, which is primarily fixed by a balance between their surface tension and the viscous stress. This deformation, predicted and measured by Taylor on millimetric drops, is expected to be affected by the presence of surfactants but has never been measured systematically. We provide a controlled experiment allowing us to measure this deformation as a function of the drop size and of the shear stress for different surfactants at varying concentrations. Our observation is that the deformation predicted by Taylor is recovered at zero and high surfactant concentration, whereas it is smaller at concentrations close to the critical micellar concentration. This is in contradiction to the existing analytical models. We develop a new analytical model, taking into account the surfactant dynamics. The model predicts a transition between a deformation similar to that of a pure liquid and a smaller one. We show that the transition is driven by a parameter KL, which compares adsorption and desorption dynamics. Finally, the concentration C*, at which we observe this transition in the extensional flow is in good agreement with the one predicted by independent measurements of KL.

The controlled rupture of a core-shell capsule and the timely release of encapsulated materials are essential steps of the efficient design of such carriers. The mechanical and physico-chemical properties of their shells (or membranes) mainly govern the evolution of such systems under stress and notably the link between the dynamics of rupture and the mechanical properties. This issue is addressed considering weakly cohesive shells made by the interfacial complexation of Chitosan and PFacid in a planar extensional flow. Three regimes are observed, thanks to the two observational planes. Whatever the time of reaction in membrane assembly, there is no rupture in deformation as long as the hydrodynamic stress is below a critical value. At low times of complexation (weak shear elastic modulus), the rupture is reminiscent of the breakup of droplets: a dumbell or a waist. Fluorescent labelling of the membrane shows that this process is governed by continuous thinning of the membrane up to the destabilization. It is likely that the membrane shows a transition from a solid to liquid state. At longer times of complexation, the rupture has a feature of solid-like breakup (breakage) with a discontinuity of the membrane. The maximal internal constraint determined numerically marks the initial location of breakup as shown. The pattern becomes more complex as the elongation rate increases with several points of rupture. A phase diagram in the space parameters of the shear elastic modulus and the hydrodynamic stress is established.

Core-shell configurations are ubiquitous in nature such as in the form of bacterial and cells. Inspired by this, microcapsules are designed with actives as the cores surrounded by thin shells. They not only play an increasing role as artificial models for understanding dynamic behaviors of biological cells in flows, but are also becoming a fundamental class of artificial vehicles at the heart of drug delivery and release in applications. The mechanical properties of the shells are of great importance in this context. Here, we review recent experimental and theoretical characterizations of microcapsules, focusing on the soft and deformable particles with liquid cores. We begin by exploring the concept and fabrication of artificial microcapsules, followed by a discussion of different methods on the mechanical characterization of the shell.

We report on a systematic numerical exploration of the vesicle dynamics in a channel, which is a model of red blood cells in microcirculation. We find a spontaneous transition, called swirling, from straight motion with axisymmetric shape to a motion along a helix with a stationary deformed shape that rolls on itself and spins around the flow direction. We also report on a planar oscillatory motion of the mass center, called three-dimensional snaking, for which the shape deforms periodically. Both emerge from supercritical pitch-fork bifurcation with the same threshold. The universality of these oscillatory dynamics emerges from Hopf bifurcations with two order parameters. These two oscillatory dy-namics are put in the context of vesicle shape and dynamics in the parameter space of reduced volume v, capillary number, and confinement. Phase diagrams are established for v = 0.95, v = 0.9, and v = 0.85 showing that oscillatory dynamics appears if the vesicle is sufficiently deflated. Stationary shapes (parachute/bullet/peanut, croissant, and slipper) are fixed points, while swirling and snaking are characterized by two limit cycles.

Controlling the assembly of polyelectrolytes and surfactant at liquid-liquid interfaces offers new ways to fabricate soft materials with specific physical properties. However, little is known of the relationships between the kinetics of interfacial assembly, structural and rheological properties of such interfaces. We studied the kinetics at water-oil interface of the assembly of a positively charged biopolymer, chitosan, with an anionic fatty acid using a multi-scale approach. The growth kinetics of the membrane was followed by interfacial rheometry and space- and time- resolved dynamic light scattering. This set of techniques revealed that the interfacial complexation was a multi-step process. At short time-scale, the interface was fluid and made of heterogeneous patches. At a 'gelation' time, the surface elastic modulus and the correlation between speckles increased sharply meaning that the patches percolated. Confocal and electron microscopy confirmed this picture, and revealed that the basic brick of the membrane was sub-micrometric aggregates of chitosan/ fatty acid.

The investigation of cell shapes mostly relies on the manual classification of 2D images, causing a subjective and time consuming evaluation based on a portion of the cell surface. We present a dual-stage neural network architecture for analyzing fine shape details from confocal microscopy recordings in 3D. The system, tested on red blood cells, uses training data from both healthy donors and patients with a congenital blood disease, namely hereditary spherocytosis. Characteristic shape features are revealed from the spherical harmonics spectrum of each cell and are automatically processed to create a reproducible and unbiased shape recognition and classification. The results show the relation between the particular genetic mutation causing the disease and the shape profile. With the obtained 3D phenotypes, we suggest our method for diagnostics and theragnostics of blood diseases. Besides the application employed in this study, our algorithms can be easily adapted for the 3D shape phenotyping of other cell types and extend their use to other applications, such as industrial automated 3D quality control.

Vesicles are soft elastic bodies with distinctive mechanical properties such as bending resistance, membrane fluidity, and their strong ability to deform, mimicking some properties of biological cells. While previous three-dimensional (3D) studies have identified stationary shapes such as slipper and axisymmetric ones, we report a complete phase diagram of 3D vesicle dynamics in a bounded Poiseuille flow with two more oscillatory dynamics, 3D snaking and swirling. 3D snaking is characterized by planar oscillatory motion of the mass center and shape deformations, which is unstable and leads to swirling or slipper. Swirling emerges from supercritical pitchfork bifurcation. The mass center moves along a helix, the preserved shape rolls on itself and spins around the flow direction. Swirling can coexist with slipper.

The voltage-dependent anion channel (VDAC) is the major pathway for metabolites and ions transport through the mitochondrial outer membrane. It can regulate the flow of solutes by switching to a low conductance state correlated with a selectivity reversal, or by a selectivity inversion of its open state. The later one was observed in non-plant VDACs and is poorly characterized. We aim at investigating the selectivity inversion of the open state using plant VDAC purified from Phaseolus coccineus (PcVDAC) to evaluate its physiological role. Our main findings are: (1) The VDAC selectivity inversion of the open state occurs in PcVDAC, (2) Ion concentration and stigmasterol affect the occurrence of the open state selectivity inversion and stigmasterol appears to interact directly with PcVDAC. Interestingly, electrophysiological data concerning the selectivity inversion of the PcVDAC open state suggests that the phenomenon probably does not have a significant physiological effect in vivo.

Figure 1: a: We performed a long term membrane formation for a single case (0.1% w/w chitosan, 0.1% w/w PFacid , f= 0.5 Hz, γ=0.03%) in order to perform a strain sweep on a thick membrane and define the limits of linear elastic regime. B: We observed that for long term formed membranes (>24 hours) the linear elastic regime was limited to surprisingly low values of strain (<0.1 % ). The direct microscopic observation of the membrane decorated with tracing particles during the strain sweep experiments showed that this highly non-linear behaviour was caused by wrinkling instability of the membrane. The deformation of ≈ 20 % lead to the rapid decline in Gi. The direct observation showed that it was caused by the loss of connectivity between the membrane and the bicone.

Giant unilamellar vesicles subjected to pulsed direct-current (pulsed-DC) fields are promising biomimetic systems to investigate the electroporation of cells. In strong electric fields, vesicles undergo significant deformation, which strongly alters the transmembrane potential, and consequently the electroporation. Previous theoretical studies investigated the electrodeformation of vesicles in DC fields (which are not pulsed). In this work, we computationally investigate the deformation of a deflated vesicle under unipolar, bipolar, and two-step unipolar pulses and show the sensitive dependence of intermediate shapes on the type of pulse and pulse width. Starting with the stress-free initial shape of a deflated vesicle, which is similar to a prolate spheroid, the analysis is presented for the cases with higher and lower conductivities of the inner fluid medium relative to the outer fluid medium. For the ratio of inner to outer fluid conductivity, σr = 10, the shape always remains prolate, including when the field is turned off. For σr=0.1, several complex dynamics are observed, such as the prolate-to-oblate (PO), prolate-to-oblate-to-prolate (POP) shape transitions in time depending upon the strength of the field and the pulse properties. In this case, on turning off the field, a metastable oblate equilibrium shape is seen, which seems to be a characteristic of a deflated vesicle leading to POPO transitions. When a two-step unipolar pulse (a combination of a strong and a weak subpulse) is applied, a vesicle can reach an oblate or a prolate final shape depending upon the relative durations of the two subpulses. This study suggests that the transmembrane potential can be regulated using a bipolar pulsed-DC field. It also shows that the shapes admitted in the dynamics of a vesicle depend upon whether the pulse is unipolar or bipolar. Parameters are suggested wherein the simulation results can be demonstrated in experiments.

Controlling the assembly of colloids at liquid-liquid interfaces offers new ways to fabricate soft materials with specific physical properties. However, little is known of the relationships between the kinetics of interfacial assembly, structural and rheological properties of such interfaces. We studied the kinetics of the assembly of two oppositely charged polyelectrolytes using a multi-scale approach. Soft interfaces were formed from the complexation at water-oil interface of chitosan, a polysaccharide carrying positively charged groups, and a fatty acid exhibiting negative charges. The growth kinetics of the membrane was followed by interfacial rheometry and space- and time- resolved dynamic light scattering. This set of techniques revealed that the interfacial complexation was a multi-step process. At short time-scale, the interface was fluid and made of heterogeneous patches. At a gelation time, the surface elastic modulus and the correlation between speckles increased sharply meaning that the patches percolated. Confocal and electron microscopy confirmed this picture, and revealed that the basic brick of the membrane was sub-micrometric aggregates of polyelectrolytes.

The stability of copolymer tethers is investigated theoretically. Self-assembly of diblock or triblock copolymers can lead to tubular polymersomes, which are known experimentally to undergo shape instability under thermal, chemical, and tension stresses. It leads to a periodic modulation of the radius, which evolves to assembly line pearls connected by tiny tethers. We study the contributions of shear surface viscosity and spontaneous curvature and their interplay to understand the pearling instability. The performed linear analysis of stability of this cylinder-to-pearls transition shows that such systems are unstable if the membrane tension is larger than a finite critical value contrary to the Rayleigh–Plateau instability, an already known result, or if the spontaneous curvature is in a specific range, which depends on membrane tension. For the case of spontaneous curvature-induced shape instability, two dynamical modes are identified. The first one is analog to the tension-induced instability with a marginal mode. Its wavenumber associated with the most unstable mode decreases continuously to zero as membrane viscosity increases. The second one has a finite range of unstable wavenumbers. The wavenumber of the most unstable mode tends to be constant as membrane viscosity increases. In this mode, its growth rate becomes independent of the bulk viscosity in the limit of high membrane viscosity and behaves as a pure viscous surface.

Understanding the flow of deformable particles such as liquid drops, synthetic capsules and vesicles, and biological cells confined in a small channel is essential to a wide range of potential chemical and biomedical engineering applications. Computer simulations of this kind of fluid-structure (membrane) interaction in low-Reynolds-number flows raise significant challenges faced by an intricate interplay between flow stresses, complex particles' interfacial mechanical properties, and fluidic confinement. Here, we present an isogeometric computational framework by combining the finite-element method (FEM) and boundary-element method (BEM) for an accurate prediction of the deformation and motion of a single soft particle transported in microfluidic channels. The proposed numerical framework is constructed consistently with the isogeometric analysis paradigm; Loop's subdivision elements are used not only for the representation of geometry but also for the membrane mechanics solver (FEM) and the interfacial fluid dynamics solver (BEM). We validate our approach by comparison of the simulation results with highly accurate benchmark solutions to two well-known examples available in the literature, namely a liquid drop with constant surface tension in a circular tube and a capsule with a very thin hyperelastic membrane in a square channel. We show that the numerical method exhibits second-order convergence in both time and space. To further demonstrate the accuracy and long-time numerically stable simulations of the algorithm, we perform hydrodynamic computations of a lipid vesicle with bending stiffness and a red blood cell with a composite membrane in capillaries. The present work offers some possibilities to study the deformation behavior of confining soft particles, especially the particles' shape transition and dynamics and their rheological signature in channel flows.

A way forward for high throughput fabrication of microcapsules with uniform size and mechanical properties was reported irrespective of the kinetic process of shell assembly. Microcapsules were produced using lab-scale emulsification equipment with a micro-engineered membrane in the size range 10-100 $\mu$m. The shell of the microcapsules was assembled at the water-oil interface by complexation of polyelectrolytes or cross-linking of proteins providing two different kinetic processes. Elasticity of microcapsules was characterized with an automated extensional flow chamber. Process parameters were optimized to obtain suspensions with size variations of 15%. Some strategies were developed to obtain uniform elastic properties according to the kinetics of shell assembly. If kinetics is limited by diffusion, membrane emulsification and shell assembly have to be split into two steps. If kinetics is limited by the quantity of reactants encapsulated in the droplet, variations of elastic properties result only from size variations.

Giant unilamellar vesicles (GUVs) under pulsed direct current (pulsed-DC) fields are promising biomimetic systems to investigate electroporation of cells and vesicles. A question of relevance is the shape deformation of a vesicle when a DC-pulse is applied. Previous theoretical studies have looked at vesicles in DC fields (which are not pulsed). However, a pulsed-DC field yields electric stresses that can push a long time prolate spheroidal shape into an oblate spheroid. In this work, we computationally investigate the deformation of a vesicle under unipolar, bipolar, and two-step unipolar pulses. Our study indicates that the transmembrane potential can be regulated using a bipolar pulsed-DC field. For the ratio of inner to outer fluid conductivity, $\sigma_\mathrm{r}$ = 10, the shape always remains prolate, including when the field is turned off. For $\sigma_\mathrm{r} = 0.1$ and the electric field strength $\beta$ (the ratio of electric to viscous force), $\beta \beta_c$, a metastable oblate equilibrium shape is predicted in pulsed-DC fields similar to that in the DC field. A prolate-to-oblate transition on turning off the field is an important characteristic of the dynamics in unipolar and bipolar pulsed-DC electric fields. When a two-step unipolar pulse (a combination of a strong and a weak subpulse) is applied, a vesicle can reach an oblate or a prolate final shape depending upon the relative durations of the two subpulses. The simulation results can be demonstrated in an experiment under typical experimental conditions.

The steady motion and deformation of a lipid-bilayer vesicle translating through a circular tube in low Reynolds number pressure-driven flow are investigated numerically using an axisymmetric boundary element method. This fluid-structure interaction problem is determined by three dimensionless parameters: reduced volume (a measure of the vesicle asphericity), geometric confinement (the ratio of the vesicle effective radius to the tube radius), and capillary number (the ratio of viscous to bending forces). The physical constraints of a vesicle -- fixed surface area and enclosed volume when it is confined in a tube -- determine critical confinement beyond which it cannot pass through without rupturing its membrane. The simulated results are presented in a wide range of reduced volumes [0.6, 0.98] for different degrees of confinement; the reduced volume of 0.6 mimics red blood cells. We draw a phase diagram of vesicle shapes and propose a shape transition line separating the parachute-like shape region from the bullet-like one in the reduced volume versus confinement phase space. We show that the shape transition marks a change in the behavior of vesicle mobility, especially for highly deflated vesicles. Most importantly, high-resolution simulations make it possible for us to examine the hydrodynamic interaction between the wall boundary and the vesicle surface at conditions of very high confinement, thus providing the limiting behavior of several quantities of interest, such as the thickness of lubrication film, vesicle mobility and its length, and the extra pressure drop due to the presence of the vesicle. This extra pressure drop holds implications for the rheology of dilute vesicle suspensions. Furthermore, we present various correlations and discuss a number of practical applications.