Fluid vesicles in flow

Hydrodynamics of a multicomponent vesicle under strong confinement

We numerically investigate the hydrodynamics and membrane dynamics of a multicomponent vesicle in two strongly confined geometries. This serves as a simplified model for red blood cells undergoing large deformations while traversing narrow constrictions. We propose a new parameterization for the bending modulus that remains positive for all lipid phase parameter values. For a multicomponent vesicle passing through a stenosis, we establish connections between various properties: lipid phase coarsening, size and flow profile of the lubrication layers, excess pressure, and the tank-treading velocity of the membrane. For a multicomponent vesicle passing through a contracting channel, we find that the lipid always phase separates so that the vesicle is stiffer in the front as it passes through the constriction. For both cases of confinement we find that lipid coarsening is arrested under strong confinement, and resumes at a high rate upon relief from extreme confinement. The results may be useful for efficient sorting lipid domains using microfluidic flows by controlled release of vesicles passing through strong confinement.

Dynamics of fluid bilayer vesicles: Soft meshes and robust curvature energy discretization

Continuum models like the Helfrich Hamiltonian are widely used to describe fluid bilayer vesicles. Here we study the molecular dynamics compatible dynamics of the vertices of two-dimensional meshes representing the bilayer, whose in-plane motion is only weakly constrained. We show (i) that Jülicher's discretization of the curvature energy offers vastly superior robustness for soft meshes compared to the commonly employed expression by Gommper and Kroll and (ii) that for sufficiently soft meshes, the typical behavior of fluid bilayer vesicles can emerge even if the mesh connectivity remains fixed throughout the simulations. In particular, soft meshes can accommodate large shape transformations, and the model can generate the typical ℓ^{-4} signal for the amplitude of surface undulation modes of nearly spherical vesicles all the way up to the longest wavelength modes. Furthermore, we compare results for Newtonian, Langevin, and Brownian dynamics simulations of the mesh vertices to demonstrate that the internal friction of the membrane model is negligible, making it suitable for studying the internal dynamics of vesicles via coupling to hydrodynamic solvers or particle-based solvent models.

Three-dimensional numerical study on wrinkling of vesicles in elongation flow based on the immersed boundary method

We study the wrinkling dynamics of three-dimensional vesicles in a time-dependent elongation flow by utilizing an immersed boundary method. For a quasispherical vesicle, our numerical results well match the predictions of perturbation analysis, where similar exponential relationships between wrinkles' characteristic wavelength and the flow strength are observed. Using the same parameters as in the experiments by Kantsler et al. [V. Kantsler et al., Phys. Rev. Lett. 99, 178102 (2007)0031-900710.1103/PhysRevLett.99.178102], our simulations of an elongated vesicle are in good agreement with their results. In addition, we get rich three-dimensional morphological details, which are favorable to comprehend the two-dimensional snapshots. This morphological information helps identify wrinkle patterns. We analyze the morphological evolution of wrinkles using spherical harmonics. We find discrepancies in elongated vesicle dynamics between simulations and perturbation analysis, highlighting the importance of the nonlinear effects. Finally, we investigate the unevenly distributed local surface tension, which largely determines the position of wrinkles excited on the vesicle membrane.

Domain dynamics of phase-separated lipid membranes under shear flow

The dynamical behaviour of lateral domains on phase-separated lipid vesicles under external flow is reported. A microfluidic chamber was used for the immobilization of vesicles and the application of shear. Microscopic observation revealed that domains tended to be localized at the vortex center and to exhibit a stripe morphology as the flow speed increased. We clarified the dependency of domain behaviors on the flow speed and lipid mixing fraction. The cholesterol ratio in the membrane affected these domain behaviors. Next, we investigated the growth of domains under flow. We discuss the mechanism of these trends by considering the free energy of phase separation, and reproduce the experimental results by numerical simulations. These findings may lead to a better understanding of the dynamical properties of the membrane under nonequilibrium situations and the biophysical mechanism of cellular mechanotransduction.

Dynamics of polydisperse multiple emulsions in microfluidic channels

Multiple emulsions are a class of soft fluid in which small drops are immersed within a larger one and stabilized over long periods of time by a surfactant. We recently showed that, if a monodisperse multiple emulsion is subject to a pressure-driven flow, a wide variety of nonequilibrium steady states emerges at late times, whose dynamics relies on a complex interplay between hydrodynamic interactions and multibody collisions among internal drops. In this work, we use lattice Boltzmann simulations to study the dynamics of polydisperse double emulsions driven by a Poiseuille flow within a microfluidic channel. Our results show that their behavior is critically affected by multiple factors, such as initial position, polydispersity index, and area fraction occupied within the emulsion. While at low area fraction inner drops may exhibit either a periodic rotational motion (at low polydispersity) or arrange into nonmotile configurations (at high polydispersity) located far from each other, at larger values of area fraction they remain in tight contact and move unidirectionally. This decisively conditions their close-range dynamics, quantitatively assessed through a time-efficiency-like factor. Simulations also unveil the key role played by the capsule, whose shape changes can favor the formation of a selected number of nonequilibrium states in which both motile and nonmotile configurations are found.

Simple production of cellulose nanofibril microcapsules and the rheology of their suspensions

Microcapsules are commonly used in applications ranging from therapeutics to personal care products due to their ability to deliver encapsulated species through their porous shells. Here, we demonstrate a simple and scalable approach to fabricate microcapsules with porous shells by interfacial complexation of cellulose nanofibrils and oleylamine, and investigate the rheological properties of suspensions of the resulting microcapsules. The suspensions of neat capsules are viscous liquids whose viscosity increases with volume fraction according to a modified Kreiger-Dougherty relation with a maximum packing fraction of 0.74 and an intrinsic viscosity of 4.1. When polyacrylic acid (PAA) is added to the internal phase of the microcapsules, however, the suspensions become elastic and display yield stresses with power-law dependencies on capsule volume fraction and PAA concentration. The elasticity appears to originate from associative microcapsule interactions induced by PAA that is contained within and incorporated into the microcapsule shell. These results demonstrate that it is possible to tune the rheological properties of microcapsule suspensions by changing only the composition of the internal phase, thereby providing a novel method to tailor complex fluid rheology.

Static interface profiles for contact lines on an elastic membrane with the Willmore energy

We consider a fluid interface in contact with an elastic membrane and study the static profiles of the interface and the membrane. Equilibrium conditions are derived by minimizing the total energy of the system with volume constraints. The total energy consists of surface energies and the Willmore energy; the latter penalizes the bending of the membrane. It is found that, while the membrane is locally flat at the contact line with the contact angle satisfying the Young-Dupré equation, the gradient of the mean curvature of the membrane exhibits a jump across the contact line. This jump balances the surface tension of the fluid interface in the normal direction of the membrane. Asymptotic solutions are obtained for two-dimensional systems in the limits as the reduced bending modulus ν tends to +∞ and 0, respectively. In the stiff limit as ν→+∞, the leading-order solution is given by that of a droplet sitting on a rigid substrate with the contact angle satisfying the Young-Dupré equation; in contrast, in the soft limit as ν→0, a transition layer appears near the contact line and the interfaces have constant curvatures in the outer region with apparent contact angles obeying Neumann's law. These solutions are validated by numerical experiments.

The vortex-driven dynamics of droplets within droplets

Understanding the fluid-structure interaction is crucial for an optimal design and manufacturing of soft mesoscale materials. Multi-core emulsions are a class of soft fluids assembled from cluster configurations of deformable oil-water double droplets (cores), often employed as building-blocks for the realisation of devices of interest in bio-technology, such as drug-delivery, tissue engineering and regenerative medicine. Here, we study the physics of multi-core emulsions flowing in microfluidic channels and report numerical evidence of a surprisingly rich variety of driven non-equilibrium states (NES), whose formation is caused by a dipolar fluid vortex triggered by the sheared structure of the flow carrier within the microchannel. The observed dynamic regimes range from long-lived NES at low core-area fraction, characterised by a planetary-like motion of the internal drops, to short-lived ones at high core-area fraction, in which a pre-chaotic motion results from multi-body collisions of inner drops, as combined with self-consistent hydrodynamic interactions. The onset of pre-chaotic behavior is marked by transitions of the cores from one vortex to another, a process that we interpret as manifestations of the system to maximize its entropy by filling voids, as they arise dynamically within the capsule.

Membrane permeability to water measured by microfluidic trapping of giant vesicles

We use a microfluidic method to estimate the water permeability coefficient (p) of membranes. As model lipid membranes we employ giant unilamellar vesicles (GUVs) composed of palmitoyloleoyl phosphatidylcholine and cholesterol (10 mol%). We have developed a microfluidic device with multiple chambers to trap GUVs and allow controlled osmotic exchange. Each chamber has a ring-shaped pressure-controlled valve which upon closure allows isolation of the GUVs in a defined volume. Opening the valves leads to a rapid fluid exchange between the trapping region and the microchannel network outside, thus allowing precise control over solution concentration around the GUVs contrary to other experimental approaches for permeability measurements reported in the literature. The area and volume changes of individual vesicles are monitored with confocal microscopy. The solute concentration in the immediate vicinity of the GUVs, and thus the concentration gradient across the membrane, is independently assessed. The data are well fitted by a simple model for water permeability which assumes that the rate of change in volume of a GUV per unit area is linearly proportional to concentration difference with permeability as the proportionality constant. Experiments of GUV osmotic deflation with hypertonic solutions yield the permeability of POPC/cholesterol 9/1 membranes to be p = 15.7 ± 5.5 μm s-1. For comparison, we also show results using two other approaches, which either do not take into account local concentration changes and/or do not resolve the precise vesicle shape. We point out the errors associated with these limitations. Finally, we also demonstrate the applicability of the microfluidic device for studying the dynamics of vesicles under flow.

Spatiotemporal Dynamics of Dilute Red Blood Cell Suspensions in Low-Inertia Microchannel Flow

Microfluidic technologies are commonly used for the manipulation of red blood cell (RBC) suspensions and analyses of flow-mediated biomechanics. To enhance the performance of microfluidic devices, understanding the dynamics of the suspensions processed within is crucial. We report novel, to our knowledge, aspects of the spatiotemporal dynamics of RBC suspensions flowing through a typical microchannel at low Reynolds number. Through experiments with dilute RBC suspensions, we find an off-center two-peak (OCTP) profile of cells contrary to the centralized distribution commonly reported for low-inertia flows. This is reminiscent of the well-known "tubular pinch effect," which arises from inertial effects. However, given the conditions of negligible inertia in our experiments, an alternative explanation is needed for this OCTP profile. Our massively parallel simulations of RBC flow in real-size microfluidic dimensions using the immersed-boundary-lattice-Boltzmann method confirm the experimental findings and elucidate the underlying mechanism for the counterintuitive RBC pattern. By analyzing the RBC migration and cell-free layer development within a high-aspect-ratio channel, we show that such a distribution is co-determined by the spatial decay of hydrodynamic lift and the global deficiency of cell dispersion in dilute suspensions. We find a cell-free layer development length greater than 46 and 28 hydraulic diameters in the experiment and simulation, respectively, exceeding typical lengths of microfluidic designs. Our work highlights the key role of transient cell distribution in dilute suspensions, which may negatively affect the reliability of experimental results if not taken into account.

The effect of lipid phase on liposome stability upon exposure to the mechanical stress

Mechanical properties of a lipid bilayer are parameters determined mainly for giant unilamellar vesicles (GUVs). It is not clear if values obtained on the GUV model can be directly translated to submicron large unilamellar vesicles (LUVs). This ambiguity is a major obstacle in exploring the effect of lipid bilayer mechanics on membrane associated processes and effectiveness of liposome-based targeted drug delivery systems. In presented work extrusion, which is a common method to prepare LUVs, was used to study liposomes preparation and stability upon exposure to mechanical stress. The effect of parameters of the extrusion process (temperature, membrane pore size, extrusion force and volumetric flux) on the properties of liposome suspension (average liposome size, polydispersity index and lipid recovery ratio) was determined for model liposomes composed of DPPC lipid. The state of the DPPC lipid bilayer depends on temperature, therefore, the effect of lipid bilayer mechanics on the extrusion process can be quantitated without altering membrane composition. The extrusion process was carried out with the automated extruder delivering quantitative data on the extrusion force and volumetric flux. Obtained results have been interpreted in terms of mechanical properties of the lipid bilayer. Determined mechanical properties of the lipid bilayer and its dependence on temperature are in good agreement with the literature results determined for GUVs. This shows that mechanical properties of the lipid bilayer does not depend on the liposome size in the range from 100 nm to hundreds of microns.

Conformational dynamics and phase behavior of lipid vesicles in a precisely controlled extensional flow

Lipid vesicles play a key role in fundamental biological processes. Despite recent progress, we lack a complete understanding of the non-equilibrium dynamics of vesicles due to challenges associated with long-time observation of shape fluctuations in strong flows. In this work, we present a flow-phase diagram for vesicle shape and conformational transitions in planar extensional flow using a Stokes trap, which enables control over the center-of-mass position of single or multiple vesicles in precisely defined flows [A. Shenoy, C. V. Rao and C. M. Schroeder, Proc. Natl. Acad. Sci. U. S. A., 2016, 113(15), 3976-3981]. In this way, we directly observe the non-equilibrium conformations of lipid vesicles as a function of reduced volume ν, capillary number Ca, and viscosity contrast λ. Our results show that vesicle dynamics in extensional flow are characterized by the emergence of three distinct shape transitions, including a tubular to symmetric dumbbell transition, a spheroid to asymmetric dumbbell transition, and quasi-spherical to ellipsoid transition. The experimental phase diagram is in good agreement with recent predictions from simulations [V. Narsimhan, A. P. Spann and E. S. Shaqfeh, J. Fluid Mech., 2014, 750, 144]. We further show that the phase boundary of vesicle shape transitions is independent of the viscosity contrast. Taken together, our results demonstrate the utility of the Stokes trap for the precise quantification of vesicle stretching dynamics in precisely defined flows.

A theoretical study on the dynamics of a compound vesicle in shear flow

The dynamics of nucleate cells in shear flow is of great relevance in cancer cells and circulatory tumor cells where they determine the flow properties of blood. Buoyed by the success of giant unilamellar vesicles in explaining the dynamics of anucleate cells such as red blood cells, compound vesicles have been suggested as a simple model for nucleate cells. A compound vesicle consists of two concentric unilamellar vesicles with the inner, annular and outer regions filled with aqueous Newtonian solvents. In this work, a theoretical model is presented to study the deformation and dynamics of a compound vesicle in linear shear flow using small deformation theory and spherical harmonics with higher order approximation to the membrane forces. A coupling of viscous and membrane stresses at the membrane interface of the two vesicles results in highly nonlinear shape evolution equations for the inner and the outer vesicles which are solved numerically. The results indicate that the size of the inner vesicle (χ) does not affect the tank-treading dynamics of the outer vesicle. The inner vesicle admits a greater inclination angle than the outer vesicle. However, the transition to trembling/swinging and tumbling is significantly affected. The inner and outer vesicles exhibit identical dynamics in the parameter space defined by the nondimensional rotational (Λ_an) and extensional (S) strength of the general shear flow. At moderate χ, a swinging mode is observed for the inner vesicle while the outer vesicle exhibits tumbling. The inner vesicle also exhibits modification of the TU mode to IUS (intermediate tumbling swinging) mode. Moreover, synchronization of the two vesicles at higher χ and a Capillary number sensitive motion at lower χ is observed in the tumbling regime. These results are in accordance with the few experimental observations reported by Levant and Steinberg. A reduction in the inclination angle is observed with an increase in χ when the inner vesicle is replaced by a solid inclusion. Additionally, a very elaborate phase diagram is presented in the Λ_an-S parameter space, which could be tested in future experiments or numerical simulations.

Determining Gyration Tensor of Orienting Macromolecules through Their Scattering Signature

A method is presented for quantitatively evaluating the shape and size of deformed particles in dispersion from their two-dimensional anisotropic spectra by small-angle scattering. By means of real spherical harmonic expansion, we derive analytical expressions of the gyration tensor R in terms of experimentally measured anisotropic scattering functions, yielding a tensorial extension of the Guinier law. We demonstrate the usefulness of this approach by a model study of an affinely deformed Gaussian chain. We further show that radius of gyration R_g is the source term of intraparticle structure factor at the mean-field limit, and from this perspective, we address the connection between R and conformation asphericity. The developed method not only facilitates quantitative scattering studies of deforming materials, but also provides insightful information regarding their deformation behavior at the molecular level based on the symmetric properties of real spherical harmonics.

Flow-induced translocation of vesicles through a narrow pore

We use finite element method to investigate the flow-induced translocation of vesicles through a narrow pore from a dynamic point of view. In order to complete the coupling between fluid flow and the vesicle membranes, we employ the fluid-structure interactions with the arbitrary Lagrangian-Eulerian method. Our results demonstrate that the vesicle shows similar shape change from bullet-like to dumbbell-like, dumbbell-like to bulb-like, and bulb-like to parachute-like if it is pushed by flow field to pass through a narrow pore smaller than its size. We further find that the strain energy exhibits a higher peak and a lower peak in the whole translocation process, where the higher peak corresponds to the dumbbell-like shape and the lower peak corresponds to the parachute-like shape due to more stretching of the membrane for the dumbbell-like shape than that of the parachute-like shape. The translocation time of the vesicle from one side to the other side of the narrow pore decreases with the increase of inlet velocity, but the strain energy exhibits an increase, which implies that the vesicle needs more time to complete the translocation with the lower inlet velocity, but the requirement for the mechanical properties of the membrane is lower. Our work answers the mapping between the positions of the vesicles and deformed states with the stress distribution and change of strain energy, which can provide helpful information on the utilization of vesicles in pharmaceutical, chemical, and physiological processes.

Cytoplasmic flows in starfish oocytes are fully determined by cortical contractions

Cytoplasmic flows are an ubiquitous feature of biological systems, in particular in large cells, such as oocytes and eggs in early animal development. Here we show that cytoplasmic flows in starfish oocytes, which can be imaged well with transmission light microscopy, are fully determined by the cortical dynamics during surface contraction waves. We first show that the dynamics of the oocyte surface is highly symmetric around the animal-vegetal axis. We then mathematically solve the Stokes equation for flows inside a deforming sphere using the measured surface displacements as boundary conditions. Our theoretical predictions agree very well with the intracellular flows quantified by particle image velocimetry, proving that during this stage the starfish cytoplasm behaves as a simple Newtonian fluid on the micrometer scale. We calculate the pressure field inside the oocyte and find that its gradient is too small as to explain polar body extrusion, in contrast to earlier suggestions. Myosin II inhibition by blebbistatin confirms this conclusion, because it diminishes cell shape changes and hydrodynamic flow, but does not abolish polar body formation.

As already noted by Aristotle, life is motion. On the molecular scale, thermal motion leads to diffusive transport. On cellular scales, however, diffusion starts to become inefficient, due to the general property of random walks that their spatial excursions grow less than linear with time. Therefore more directed transport processes are needed on cellular scales, including transport by molecular motors or by hydrodynamic flows. This is especially true for oocytes and eggs in early animal development, which often have to be large in order to store sufficient amounts of nutrients. Here we use starfish oocytes as a convenient model system to investigate the nature and function of cytoplasmic flows in early development. These cells are very large and optically transparent, and therefore ideal for live cell imaging that here we combine with image processing and mathematical modelling. This approach allows us to demonstrate that the experimentally observed cytoplasmic flows during early development are a direct consequence of surface contraction waves that deform the soft and contractile eggs. Additionally we show that despite its microscopic complexity, the cytoplasm behaves like a Newtonian fluid on the cellular scale. Our findings impose strong physical limits on the potential biological function of these flows and suggest that also other cellular systems that are soft and contractile might experience large cytoplasmic flows upon cell shape changes, for example during cell migration or division.

Wall slip for complex liquids - Phenomenon and its causes

In this review, we tried to qualify different types and mechanisms of wall slip phenomenon, paying particular attention to the most recent publications and issues. The review covers all type of fluids - homogeneous low molecular weight liquids, polymer solution, multi-component dispersed media, and polymer melts. We focused on two basic concepts - fluid-solid wall interaction and shear-induced fluid-to-solid transitions - which are the dominant mechanisms of wall slip. In the first part of the review, the theoretical and numerical studies of correlation of wetting properties and wall slip of low molecular weight liquids and polymeric fluids are reviewed along with some basic experimental results. The influence of nanobubbles and microcavities on the effectiveness of wall slip is illuminated with regard to the bubble dynamics, as well as their stability at smooth and rough interfaces, including superhydrophobic surfaces. Flow of multi-component matter (microgel pastes, concentrated suspensions of solid particles, compressed emulsions, and colloidal systems) is accompanied by wall slip in two cases. The first one is typical of viscoplastic media which can exist in two different physical states, as solid-like below the yield point and liquid-like at the applied stresses exceeding this threshold. Slip takes place at low stresses. The second case is related to the transition from fluid to solid states at high deformation rates or large deformations caused by the strain-induced glass transition of concentrated dispersions. In the latter case, the wall effects consist of apparent slip due to the formation of a low viscous thin layer of fluid at the wall. The liquid-to-solid transition is also a dominant mechanism in wall slip of polymer melts because liquid polymers are elastic fluids which can be in two relaxation states depending on the strain rate. The realization of these mechanisms is determined by polymer melt interaction with the solid wall.

Steady state sedimentation of ultrasoft colloids

The structural and dynamical properties of ultra-soft colloids-star polymers-exposed to a uniform external force field are analyzed by applying the multiparticle collision dynamics technique, a hybrid coarse-grain mesoscale simulation approach, which captures thermal fluctuations and long-range hydrodynamic interactions. In the weak-field limit, the structure of the star polymer is nearly unchanged; however, in an intermediate regime, the radius of gyration decreases, in particular transverse to the sedimentation direction. In the limit of a strong field, the radius of gyration increases with field strength. Correspondingly, the sedimentation coefficient increases with increasing field strength, passes through a maximum, and decreases again at high field strengths. The maximum value depends on the functionality of the star polymer. High field strengths lead to symmetry breaking with trailing, strongly stretched polymer arms and a compact star-polymer body. In the weak-field-linear response regime, the sedimentation coefficient follows the scaling relation of a star polymer in terms of functionality and arm length.

Computer simulations of drug release from a liposome into the bloodstream

I propose two-dimensional simulations of drug release from a liposome into the bloodstream. I perform the fluid-structure coupling, between the particles deformation (the liposome and the red blood cells) and the plasma flow, using the immersed boundary method. I compute both the flow and the drug mass transport using the lattice Boltzmann method. The simulations allow computing the instantaneous amount of the released drug, its distribution and its accumulation in the blood vessel wall. These quantities are sensitive to multiple factors and parameters. Here, I briefly explore the impact of having surrounding red blood cells, which are found to enhance slightly the drug release at large Schmidt numbers. In the limit of extremely large permeability of the particles, the drug transport is mainly affected by the complex flow induced by the interplay between the applied flow and the collective motion of the particles.

Elastic particle deformation in rectangular channel flow as a measure of particle stiffness

In this study, we experimentally observed and characterized soft elastic particle deformation in confined flow in a microchannel with a rectangular cross-section. Hydrogel microparticles of pNIPAM were produced using two different concentrations of crosslinker. This resulted in particles with two different shear moduli of 13.3 ± 5.5 Pa and 32.5 ± 15.7 Pa and compressive moduli of 66 ± 10 Pa and 79 ± 15 Pa, respectively, as measured by capillary micromechanics. Under flow, the particle shapes transitioned from circular to egg, triangular, arrowhead, and ultimately parachute shaped with increasing shear rate. The shape changes were reversible, and deformed particles relaxed back to circular/spherical in the absence of flow. The thresholds for each shape transition were quantified using a non-dimensional radius of curvature at the tip, particle deformation, circularity, and the depth of the concave dimple at the trailing edge. Several of the observed shapes were distinct from those previously reported in the literature for vesicles and capsules; the elastic particles had a narrower leading tip and a lower circularity. Due to variations in the shear moduli between particles within a batch of particles, each flow rate corresponded to a small but finite range of capillary number (Ca) and resulted in a series of shapes. By arranging the images on a plot of Ca versus circularity, a direct correlation was developed between shape and Ca and thus between particle deformation and shear modulus. As the shape was very sensitive to differences in shear modulus, particle deformation in confined flow may allow for better differentiation of microparticle shear modulus than other methods.

Pitfalls in Size Characterization of Soft Particles by Dynamic Light Scattering Online Coupled to Asymmetrical Flow Field-Flow Fractionation

An asymmetrical flow field-flow fractionation (AF4) technique coupled to a multiangle light scattering (MALS) detector with an embedded dynamic light scattering (DLS) module was introduced to study the size characteristics and shape of soft particles of various size and type: polystyrene nanosphere size standards, lipid droplets (LDs), and large unilamellar vesicles (LUVs). A range of flow velocities through the LS detector, at which accurate hydrodynamic size can be extracted from the DLS in flow mode, was studied since the particles subjected to a longitudinal flow exhibit not only the Brownian motion due to diffusion but also the translational movement. In addition, the impact of the longitudinal flow velocity on the shape of the artificial LUV of two different sizes and two different compositions was studied by MALS. For comparison, the conventional batch DLS and static light scattering (SLS) experiments without prior sample separation by size were performed. From a combination of batch and flow light scattering results, we concluded that the passage flow velocities at the detector used in this study, 0.2, 0.5, and 1 mL/min, have no significant impact on the shape of spherical vesicles; however, the flow DLS experiments give accurate hydrodynamic radius (R_h) only at the lowest investigated passage flow rate at the detector (0.2 mL/min). With increasing rate of passage flow at the DLS detector, the error in the accuracy of the R_h determination rapidly increases. The error in R_h depends solely on the detector flow rate and particle size but not on the type of the soft particle.

Dynamic behaviour of multilamellar vesicles under Poiseuille flow

Surfactant solutions exhibit multilamellar surfactant vesicles (MLVs) under flow conditions and in concentration ranges which are found in a large number of industrial applications. MLVs are typically formed from a lamellar phase and play an important role in determining the rheological properties of surfactant solutions. Despite the wide literature on the collective dynamics of flowing MLVs, investigations into the flow behavior of single MLVs are scarce. In this work, we investigate a concentrated aqueous solution of linear alkylbenzene sulfonic acid (HLAS), characterized by MLVs dispersed in an isotropic micellar phase. Rheological tests show that the HLAS solution is a shear-thinning fluid with a power law index dependent on the shear rate. Pressure-driven shear flow of the HLAS solution in glass capillaries is investigated using high-speed video microscopy and image analysis. The so obtained velocity profiles provide evidence for a power-law fluid behaviour of the HLAS solution and images show a flow-focusing effect of the lamellar phase in the central core of the capillary. The flow behavior of individual MLVs shows analogies with that of unilamellar vesicles and emulsion droplets. Deformed MLVs exhibit typical shapes of unilamellar vesicles, such as parachute and bullet-like. Furthermore, MLV velocity follows the classical Hetsroni theory for droplets provided that the power law shear dependent viscosity of the HLAS solution is taken into account. The results of this work are relevant for the processing of surfactant-based systems in which the final properties depend on the flow-induced morphology, such as cosmetic formulations and food products.

Electrohydrodynamics of a compound vesicle under an AC electric field

Compound vesicles are relevant as simplified models for biological cells as well as in technological applications such as drug delivery. Characterization of these compound vesicles, especially the inner vesicle, remains a challenge. Similarly their response to electric field assumes importance in light of biomedical applications such as electroporation. Fields lower than that required for electroporation cause electrodeformation in vesicles and can be used to characterize their mechanical and electrical properties. A theoretical analysis of the electrohydrodynamics of a compound vesicle with outer vesicle of radius R _o and an inner vesicle of radius [Formula: see text], is presented. A phase diagram for the compound vesicle is presented and elucidated using detailed plots of electric fields, free charges and electric stresses. The electrohydrodynamics of the outer vesicle in a compound vesicle shows a prolate-sphere and prolate-oblate-sphere shape transitions when the conductivity of the annular fluid is greater than the outer fluid, and vice-versa respectively, akin to single vesicle electrohydrodynamics reported in the literature. The inner vesicle in contrast shows sphere-prolate-sphere and sphere-prolate-oblate-sphere transitions when the inner fluid conductivity is greater and smaller than the annular fluid, respectively. Equations and methodology are provided to determine the bending modulus and capacitance of the outer as well as the inner membrane, thereby providing an easy way to characterize compound vesicles and possibly biological cells.

Theory and algorithms to compute Helfrich bending forces: a review

Cell membranes are vital to shield a cell's interior from the environment. At the same time they determine to a large extent the cell's mechanical resistance to external forces. In recent years there has been considerable interest in the accurate computational modeling of such membranes, driven mainly by the amazing variety of shapes that red blood cells and model systems such as vesicles can assume in external flows. Given that the typical height of a membrane is only a few nanometers while the surface of the cell extends over many micrometers, physical modeling approaches mostly consider the interface as a two-dimensional elastic continuum. Here we review recent modeling efforts focusing on one of the computationally most intricate components, namely the membrane's bending resistance. We start with a short background on the most widely used bending model due to Helfrich. While the Helfrich bending energy by itself is an extremely simple model equation, the computation of the resulting forces is far from trivial. At the heart of these difficulties lies the fact that the forces involve second order derivatives of the local surface curvature which by itself is the second derivative of the membrane geometry. We systematically derive and compare the different routes to obtain bending forces from the Helfrich energy, namely the variational approach and the thin-shell theory. While both routes lead to mathematically identical expressions, so-called linear bending models are shown to reproduce only the leading order term while higher orders differ. The main part of the review contains a description of various computational strategies which we classify into three categories: the force, the strong and the weak formulation. We finally give some examples for the application of these strategies in actual simulations.

Controlled shaping of lipid vesicles in a microfluidic diffusion chamber

The chemical environment around flaccid lipid vesicles, i.e., the osmotic conditions and the concentration of membrane-shaping molecules, is regulated only by diffusion without any hydrodynamic flow.

Extracting Cell Stiffness from Real-Time Deformability Cytometry: Theory and Experiment

Cell stiffness is a sensitive indicator of physiological and pathological changes in cells, with many potential applications in biology and medicine. A new method, real-time deformability cytometry, probes cell stiffness at high throughput by exposing cells to a shear flow in a microfluidic channel, allowing for mechanical phenotyping based on single-cell deformability. However, observed deformations of cells in the channel not only are determined by cell stiffness, but also depend on cell size relative to channel size. Here, we disentangle mutual contributions of cell size and cell stiffness to cell deformation by a theoretical analysis in terms of hydrodynamics and linear elasticity theory. Performing real-time deformability cytometry experiments on both model spheres of known elasticity and biological cells, we demonstrate that our analytical model not only predicts deformed shapes inside the channel but also allows for quantification of cell mechanical parameters. Thereby, fast and quantitative mechanical sampling of large cell populations becomes feasible.

Wrinkling dynamics of fluctuating vesicles in time-dependent viscous flow

We study the fully nonlinear, nonlocal dynamics of two-dimensional vesicles in a time-dependent, incompressible viscous flow at finite temperature. We focus on a transient instability that can be observed when the direction of applied flow is suddenly reversed, which induces compressive forces on the vesicle interface, and small-scale interface perturbations known as wrinkles develop. These wrinkles are driven by regions of negative elastic tension on the membrane. Using a stochastic immersed boundary method with a biophysically motivated choice of thermal fluctuations, we investigate the wrinkling dynamics numerically. Different from deterministic wrinkling dynamics, thermal fluctuations lead to symmetry-breaking wrinkling patterns by exciting higher order modes. This leads to more rapid and more realistic wrinkling dynamics. Our results are in excellent agreement with the experimental data by Kantsler et al. [Kantsler et al., Phys. Rev. Lett., 2007, 99, 17802]. We compare the nonlinear simulation results with perturbation theory, modified to account for thermal fluctuations. The strength of the applied flow strongly influences the most unstable wavelength characterizing the wrinkles, and there are significant differences between the results from perturbation theory and the fully nonlinear simulations, which suggests that the perturbation theory misses important nonlinear interactions. Strikingly, we find that thermal fluctuations actually have the ability to attenuate variability of the characteristic wavelength of wrinkling by exciting a wider range of modes than the deterministic case, which makes the evolution less constrained and enables the most unstable wavelength to emerge more readily. We further find that thermal noise helps prevent the vesicle from rotating if it is misaligned with the direction of the applied extensional flow.

Membranes under shear stress: visualization of non-equilibrium domain patterns and domain fusion in a microfluidic device

In this study we investigate the effect of shear force on lipid membranes induced by external fluid flow. We use giant unilamellar vesicles (GUVs) as simple cell models and chose a ternary lipid mixture that exhibits liquid-ordered and liquid-disordered domains. These domains are stained with different dyes to allow visualization of changes within the membrane after the application of flow. A microfluidic device served as a valuable platform to immobilize the vesicles and apply shear forces of a defined strength. Moreover, integration of valves allowed us to stop the flow instantaneously and visualize the relaxing domain patterns by means of high-resolution fluorescence microscopy. We observed the formation of transient, non-deterministic patterns of the formerly round domains during application of flow. When the flow is stopped, round domains are formed again on a time scale of ms to s. At longer time scales of several seconds to minutes, the domains fuse into larger domains until they reach equilibrium. These processes are accelerated with increasing temperature and vesicles with budding domains do not fuse unless the temperature is elevated. Our results show the strong effect of the flow on the lipid membrane and we believe that this phenomenon plays a crucial role in the processes of mechanotransduction in living cells.

Experimental observation of the asymmetric instability of intermediate-reduced-volume vesicles in extensional flow

Vesicles provide an attractive model system to understand the deformation of living cells in response to mechanical forces. These simple, enclosed lipid bilayer membranes are suitable for complementary theoretical, numerical, and experimental analysis. A recent study [Narsimhan, Spann, Shaqfeh, J. Fluid Mech., 2014, 750, 144] predicted that intermediate-aspect-ratio vesicles extend asymmetrically in extensional flow. Upon infinitesimal perturbation to the vesicle shape, the vesicle stretches into an asymmetric dumbbell with a cylindrical thread separating the two ends. While the symmetric stretching of high-aspect-ratio vesicles in extensional flow has been observed and characterized [Kantsler, Segre, Steinberg, Phys. Rev. Lett., 2008, 101, 048101] as well as recapitulated in numerical simulations by Narsimhan et al., experimental observation of the asymmetric stretching has not been reported. In this work, we present results from microfluidic cross-slot experiments observing this instability, along with careful characterization of the flow field, vesicle shape, and vesicle bending modulus. The onset of this shape transition depends on two non-dimensional parameters: reduced volume (a measure of vesicle asphericity) and capillary number (ratio of viscous to bending forces). We observed that every intermediate-reduced-volume vesicle that extends forms a dumbbell shape that is indeed asymmetric. For the subset of the intermediate-reduced-volume regime we could capture experimentally, we present an experimental phase diagram for asymmetric vesicle stretching that is consistent with the predictions of Narsimhan et al.

Dynamics of prolate spheroidal elastic particles in confined shear flow

We investigate through numerical simulations the dynamics of a neo-Hookean elastic prolate spheroid suspended in a Newtonian fluid under shear flow. Both initial orientations of the particle within and outside the shear plane and both unbounded and confined flow geometries are considered. In unbounded flow, when the particle starts on the shear plane, two stable regimes of motion are found, i.e., trembling, where the particle shape periodically elongates and compresses in the shear plane and the angle between its major semiaxis and the flow direction oscillates around a positive mean value, and tumbling, where the particle shape periodically changes and its major axis performs complete revolutions around the vorticity axis. When the particle is initially oriented out of the shear plane, more complex dynamics arise. Geometric confinement of the particle between the moving walls also influences its deformation and regime of motion. In addition, when the particle is initially located in an asymmetric position with respect to the moving walls, particle lateral migration is detected. The effects on the particle dynamics of the geometric and physical parameters that rule the system are investigated.

Numerical computations of the dynamics of fluidic membranes and vesicles

Vesicles and many biological membranes are made of two monolayers of lipid molecules and form closed lipid bilayers. The dynamical behavior of vesicles is very complex and a variety of forms and shapes appear. Lipid bilayers can be considered as a surface fluid and hence the governing equations for the evolution include the surface (Navier-)Stokes equations, which in particular take the membrane viscosity into account. The evolution is driven by forces stemming from the curvature elasticity of the membrane. In addition, the surface fluid equations are coupled to bulk (Navier-)Stokes equations. We introduce a parametric finite-element method to solve this complex free boundary problem and present the first three-dimensional numerical computations based on the full (Navier-)Stokes system for several different scenarios. For example, the effects of the membrane viscosity, spontaneous curvature, and area difference elasticity (ADE) are studied. In particular, it turns out, that even in the case of no viscosity contrast between the bulk fluids, the tank treading to tumbling transition can be obtained by increasing the membrane viscosity. Besides the classical tank treading and tumbling motions, another mode (called the transition mode in this paper, but originally called the vacillating-breathing mode and subsequently also called trembling, transition, and swinging mode) separating these classical modes appears and is studied by us numerically. We also study how features of equilibrium shapes in the ADE and spontaneous curvature models, like budding behavior or starfish forms, behave in a shear flow.

Shapes of sedimenting soft elastic capsules in a viscous fluid

Soft elastic capsules which are driven through a viscous fluid undergo shape deformation coupled to their motion. We introduce an iterative solution scheme which couples hydrodynamic boundary integral methods and elastic shape equations to find the stationary axisymmetric shape and the velocity of an elastic capsule moving in a viscous fluid at low Reynolds numbers. We use this approach to systematically study dynamical shape transitions of capsules with Hookean stretching and bending energies and spherical rest shape sedimenting under the influence of gravity or centrifugal forces. We find three types of possible axisymmetric stationary shapes for sedimenting capsules with fixed volume: a pseudospherical state, a pear-shaped state, and buckled shapes. Capsule shapes are controlled by two dimensionless parameters, the Föppl-von-Kármán number characterizing the elastic properties and a Bond number characterizing the driving force. For increasing gravitational force the spherical shape transforms into a pear shape. For very large bending rigidity (very small Föppl-von-Kármán number) this transition is discontinuous with shape hysteresis. The corresponding transition line terminates, however, in a critical point, such that the discontinuous transition is not present at typical Föppl-von-Kármán numbers of synthetic capsules. In an additional bifurcation, buckled shapes occur upon increasing the gravitational force. This type of instability should be observable for generic synthetic capsules. All shape bifurcations can be resolved in the force-velocity relation of sedimenting capsules, where up to three capsule shapes with different velocities can occur for the same driving force. All three types of possible axisymmetric stationary shapes are stable with respect to rotation during sedimentation. Additionally, we study capsules pushed or pulled by a point force, where we always find capsule shapes to transform smoothly without bifurcations.

Selective flow-induced vesicle rupture to sort by membrane mechanical properties

Vesicle and cell rupture caused by large viscous stresses in ultrasonication is central to biomedical and bioprocessing applications. The flow-induced opening of lipid membranes can be exploited to deliver drugs into cells, or to recover products from cells, provided that it can be obtained in a controlled fashion. Here we demonstrate that differences in lipid membrane and vesicle properties can enable selective flow-induced vesicle break-up. We obtained vesicle populations with different membrane properties by using different lipids (SOPC, DOPC, or POPC) and lipid:cholesterol mixtures (SOPC:chol and DOPC:chol). We subjected vesicles to large deformations in the acoustic microstreaming flow generated by ultrasound-driven microbubbles. By simultaneously deforming vesicles with different properties in the same flow, we determined the conditions in which rupture is selective with respect to the membrane stretching elasticity. We also investigated the effect of vesicle radius and excess area on the threshold for rupture, and identified conditions for robust selectivity based solely on the mechanical properties of the membrane. Our work should enable new sorting mechanisms based on the difference in membrane composition and mechanical properties between different vesicles, capsules, or cells.

Deformation of phospholipid vesicles in an optical stretcher

Phospholipid vesicles are common model systems for cell membranes. Important aspects of the membrane function relate to its mechanical properties. Here we have investigated the deformation behaviour of phospholipid vesicles in a dual-beam laser trap, also called an optical stretcher. This study explicitly makes use of the inherent heating present in such traps to investigate the dependence of vesicle deformation on temperature. By using lasers with different wavelengths, optically induced mechanical stresses and temperature increase can be tuned fairly independently with a single setup. The phase transition temperature of vesicles can be clearly identified by an increase in deformation. In the case of no heating effects, a minimal model for drop deformation in an optical stretcher and a more specific model for vesicle deformation that takes explicitly into account the angular dependence of the optical stress are presented to account for the experimental results. Elastic constants are extracted from the fitting procedures, which agree with literature data. This study demonstrates the utility of optical stretching, which is easily combined with microfluidic delivery, for the future serial, high-throughput study of the mechanical and thermodynamic properties of phospholipid vesicles.

Microfluidic Strategies for Understanding the Mechanics of Cells and Cell-Mimetic Systems

Microfluidic systems are attracting increasing interest for the high-throughput measurement of cellular biophysical properties and for the creation of engineered cellular microenvironments. Here we review recent applications of microfluidic technologies to the mechanics of living cells and synthetic cell-mimetic systems. We begin by discussing the use of microfluidic devices to dissect the mechanics of cellular mimics, such as capsules and vesicles. We then explore applications to circulating cells, including erythrocytes and other normal blood cells, and rare populations with potential disease diagnostic value, such as circulating tumor cells. We conclude by discussing how microfluidic devices have been used to investigate the mechanics, chemotaxis, and invasive migration of adherent cells. In these ways, microfluidic technologies represent an increasingly important toolbox for investigating cellular mechanics and motility at high throughput and in a format that lends itself to clinical translation.