A simple model of a vesicle drop in a confined geometry

Physical Review Fluids, 2019

The dynamics of an adhesive two-dimensional vesicle doublet under various flow conditions is investigated numerically using a high-order, adaptive-in-time boundary integral method. In a quiescent flow, two nearby vesicles move slowly towards each other under the adhesive potential, pushing out fluid between them to form a vesicle doublet at equilibrium. A lubrication analysis on such draining of a thin film gives the dependencies of draining time on adhesion strength and separation distance that are in good agreement with numerical results. In a planar extensional flow we find a stable vesicle doublet forms only when two vesicles collide head-on around the stagnation point. In a microfluid trap where the stagnation of an extensional flow is dynamically placed in the middle of a vesicle doublet through an active control loop, novel dynamics of a vesicle doublet are observed. Numerical simulations show that there exists a critical extensional flow rate above which adhesive interaction is overcome by the diverging stream, thus providing a simple method to measure the adhesion strength between two vesicle membranes. In a planar shear flow, numerical simulations reveal that a vesicle doublet may form provided that the adhesion strength is sufficiently large at a given vesicle reduced area. Once a doublet is formed, its oscillatory dynamics is found to depend on the adhesion strength and their reduced area. Furthermore the effective shear viscosity of a dilute suspension of vesicle doublets is found to be a function of the reduced area. Results from these numerical studies and analysis shed light on the hydrodynamic and rheological consequences of adhesive interactions between vesicles in a viscous fluid.

2008

A coarse-grained model developed by Marrink et al. [J. Phys. Chem. B 111, 7812 (2007)] is applied to investigate vesiculation of lipid [dipalmitoylphosphatidylcholine (DPPC)] droplets in water. Three kinds of morphologies of micelles are found with increasing lipid droplet size. When the initial lipid droplet is smaller, the equilibrium structure of the droplet is a spherical micelle. When the initial lipid droplet is larger, the lipid ball starts to transform into a disk micelle or vesicle. The mechanism of vesicle formation from a lipid ball is analyzed from the self-assembly of DPPC on the molecular level, and the morphological transition from disk to vesicle with increasing droplet size is demonstrated. Importantly, we discover that the transition point is not very sharp, and for a fixed-size lipid ball, the disk and vesicle appear with certain probabilities. The splitting phenomenon, i.e., the formation of a disk/vesicle structure from a lipid droplet, is explained by applying a hybrid model of the Helfrich membrane theory. The elastic module of the DPPC bilayer and the smallest size of a lipid droplet for certain formation of a vesicle are successfully predicted.

Acta Mechanica Sinica, 2006

We develop a two dimensional model of a vesicle adhered on a curved substrate via long-range molecular interactions while subjected to a detachment force. The relationship between the force and displacement of the vesicle is investigated as a function of the substrate shape. It is shown that both the forcedisplacement relationship and the maximum force at pull-off are significantly dependent on the substrate shape. The results suggest that probes with different tip shapes may be designed for cell manipulation. For example, we demonstrate that a vesicle can be pulled off a flat surface using a probe with a curved tip.

International Journal for Numerical Methods in Fluids, 2014

The aim of this paper is to propose a new numerical model to simulate 2D vesicles interacting with a newtonian fluid. The inextensible membrane is modeled by a chain of circular rigid particles which are maintained in cohesion by using two different type of forces. First, a spring force is imposed between neighboring particles in the chain. Second, in order to model the bending of the membrane, each triplet of successive particles is submitted to an angular force.

Journal of Physics A: Mathematical and General, 2005

We present the exact solutions of various directed walk models of polymers confined to a slit and interacting with the walls of the slit via an attractive potential. We consider three geometric constraints on the ends of the polymer and concentrate on the long chain limit. Apart from the general interest in the effect of geometrical confinement, this can be viewed as a two-dimensional model of steric stabilization and sensitized flocculation of colloidal dispersions. We demonstrate that the large width limit admits a phase diagram that is markedly different from the one found in a half-plane geometry, even when the polymer is constrained to be fixed at both ends on one wall. We are not able to find a closed form solution for the free energy for finite width, at all values of the interaction parameters, but we can calculate the asymptotic behaviour for large widths everywhere in the phase plane. This allows us to find the force between the walls induced by the polymer and hence the regions of the plane where either steric stabilization or sensitized flocculation would occur.

Physical Review Letters, 2004

The dynamics of phase separation in multi-component bilayer fluid vesicles is investigated by means of large-scale dissipative particle dynamics. The model explicitly accounts for solvent particles, thereby allowing for the very first numerical investigation of the effects of hydrodynamics and area-to-volume constraints. We observed regimes corresponding to coalescence of flat patches, budding and vesiculation, and coalescence of caps. We point out that the area-to-volume constraint has a strong influence on crossovers between these regimes. 64.75.+g, 68.05.Cf Apart from partitioning the inner and outer environments of the cell, biomembranes also act as support for complex and specialized molecular machinery, crucial for various physiological functions and trans-membrane transport . It is believed that membranes maintain inplane compositional organization that is essential for its function. Though biological membranes are very complex and can in general be far from equilibrium, knowledge of the equilibrium properties of simple model membranes will be extremely useful in providing understanding of this molecular machinery. Such a study should also be essential for developing new applications involving liposomes. This has recently resulted in a surge of theoretical and experimental investigations on domain formation in multicomponent vesicles .

Journal of Physics A: Mathematical and Theoretical, 2014

We study a model of two polymers confined to a slit with sticky walls. More precisely, we find and analyse the exact solution of two directed friendly walks in such a geometry on the square lattice. We compare the infinite slit limit, in which the length of the polymer (thermodynamic limit) is taken to infinity before the width of the slit is considered to become large, to the opposite situation where the order of the limits are swapped, known as the half-plane limit when one polymer is modelled. In contrast with the single polymer system we find that the half-plane and infinite slit limits coincide. We understand this result in part due to the tethering of polymers on both walls of the slit. We also analyse the entropic force exerted by the polymers on the walls of the slit. Again the results differ significantly from single polymer models. In a single polymer system both attractive and repulsive regimes were seen, whereas in our two walk model only repulsive forces are observed. We do, however, see that the range of the repulsive force is dependent on the parameter values. This variation can be explained by the adsorption of the walks on opposite walls of the slit.

Journal of Physics: Condensed Matter, 2011

We examined the dynamics of the deformation and phase separation of two-component vesicles. First, we numerically investigated the effects of (i) thermal noise, (ii) hydrodynamic flow induced by the line tension of the domain boundary and (iii) composition-dependent bending rigidity on the coarsening dynamics of a phase-separated pattern on the surfaces of vesicles with fixed shapes. The dynamical exponent z (NDB ∼ t −z , the total length of the domain boundaries) of the coarsening of phase-separated pattern was found to decrease from z = 1/3 under no thermal noise to 1/5 < z < 1/4 when including the effects of thermal noise. We also found that the hydrodynamic effect enhances the coarsening in a bicontinuous phase separation for a spherical vesicle. In phase separations of a shape-fixed tubular vesicle, a band-like phase separation with periodicity along the longer axis of the tube occurs because of the composition-dependent bending rigidity and the higher curvatures at the tube end-caps. Second, we also explored the dynamics of shape deformation coupled with phase separation through the bending rigidity of the membrane which depends on the local composition in lipid, and found that the composition-dependent bending rigidity crucially influences the phase separation and deformation of the vesicle. The results of simulations are in good agreement with experimentally observed behaviors known as "shape convergence" [

The European Physical Journal E, 2007

The adhesion of fluid vesicles at chemically structured substrates is studied theoretically via Monte Carlo simulations. The substrate surface is planar and repels the vesicle membrane apart from a single surface domain γ, which strongly attracts this membrane. If the vesicle is larger than the attractive γ domain, the spreading of the vesicle onto the substrate is restricted by the size of this surface domain. Once the contact line of the adhering vesicle has reached the boundaries of the γ domain, further deflation of the vesicle leads to a regime of low membrane tension with pronounced shape fluctuations, which are now governed by the bending rigidity. For a circular γ domain and a small bending rigidity, the membrane oscillates strongly around an average spherical cap shape. If such a vesicle is deflated, the contact area increases or decreases with increasing osmotic pressure, depending on the relative size of the vesicle and the circular γ domain. The lateral localization of the vesicle's center of mass by such a domain is optimal for a certain domain radius, which is found to be rather independent of adhesion strength and bending rigidity. For vesicles adhering to stripe-shaped surface domains, the width of the contact area perpendicular to the stripe varies nonmonotonically with the adhesion strength.

Chemical Physics, 2009

A coarse-grained model developed by Marrink et al. (J. Phys. Chem. B 111, 7812, 2007) is applied to 6 investigate vesiculation of lipid (DPPC) droplets in water. Three kinds of morphologies of micelles are found with 7 increasing lipid droplet size. When the initial lipid droplet is smaller, the equilibrium structure of the droplet is a 8 spherical micelle. When the initial lipid droplet is larger, the lipid ball starts to transform into a disk micelle or vesicle. 9