Vesicles are micrometric soft particles whose the membrane is a two-dimensional incompressible fluid governed by bending resistance leading to a zoology of shapes. The dynamics of deflated vesicles in shear flow with a bottom wall, a first minimal configuration to consider confined vesicles is investigated using numerical simulations. Coexistence under flow of oblate (metastable) and prolate (stable) shapes is studied in details. In particular, we discuss the boundaries of the region of coexistence in the (v, Ca) plane where v is the reduced volume of the vesicle and Ca the Capillary number. We characterize the transition from oblate to prolate and analyse the divergence of the transition time near the critical capillary number. We then analyse lift dynamics of oblate vesicle in the weak flow regime.
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, 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 sensitive dependence of int…
The axisymmetric electrohydrodynamic deformation of an elastic capsule with capacitive membrane obeying Skalak law under uniform AC electric field is investigated using analytical and boundary integral theory. The low capillary number (the ratio of destabilizing shear or electric force to the stabilizing elastic force) regime shows time-averaged prolate and oblate spheroid deformations, and the time-periodic prolate-sphere, oblate-sphere breathing modes are commensurate with the time averaged-deformation. A novel prolate-oblate breathing mode is observed due to an interplay of finite membrane …
We develop a coarse-grained particle-based model to simulate membranes with nematic liquid-crystal order. The coarse-grained particles form vesicles which, at low temperature, have orientational order in the local tangent plane. As the strength of coupling between the nematic director and the vesicle curvature increases, the vesicles show a morphology transition from spherical to prolate and finally to a tube. We also observe the shape and defect arrangement around the tips of the prolate vesicle.
The effect of membrane viscosity on the dynamics of vesicles in shear flow is studied. We present a new simulation technique, which combines three-dimensional multi-particle collision dynamics for the solvent with a dynamically-triangulated membrane model. Vesicles are found to transit from steady tank-treading to unsteady tumbling motion with increasing membrane viscosity. Depending on the reduced volume and membrane viscosity, shear can induce both discocyte-to-prolate and prolate-to-discocyte transformations. This dynamical behavior can be understood from a simplified model.
A numerical and systematic parameter study of three-dimensional vesicle electrohydrodynamics is presented to investigate the effects of different fluid and membrane properties. The dynamics of vesicles in the presence of DC electric fields is considered, both in the presence and absence of linear shear flow. For suspended vesicles it is shown that the conductivity ratio and viscosity ratio between the interior and exterior fluids, as well as the vesicle membrane capacitance, substantially affect the minimum electric field strength required to induce a full Prolate-Oblate-Prolate transition.In …
It is well known that understanding the transport properties of liquid crystals (LCs) is crucial to optimise their performance in a number of technological applications. In this work, we analyse the effect of shape anisotropy on the diffusion of rod-like and disk-like particles by Brownian dynamics simulations. To this end, we compare the dynamics of prolate and oblate nematic LCs incorporating particles with the same infinite-dilution translational or rotational diffusion coefficients. Under these conditions, which are benchmarked against the standard case of identical aspect ratios, we obser…
An analytic solution for Helfrich spontaneous curvature membrane model (H. Naito, M.Okuda and Ou-Yang Zhong-Can, Phys. Rev. E {\bf 48}, 2304 (1993); {\bf 54}, 2816 (1996)), which has a conspicuous feature of representing the circular biconcave shape, is studied. Results show that the solution in fact describes a family of shapes, which can be classified as: i) the flat plane (trivial case), ii) the sphere, iii) the prolate ellipsoid, iv) the capped cylinder, v) the oblate ellipsoid, vi) the circular biconcave shape, vii) the self-intersecting inverted circular biconcave shape, and viii) the se…
The external electric field deforms flaccid phospholipid vesicles into spheroidal bodies, with the rotational axis aligned with its direction. Deformation is frequency dependent: in the low frequency range (~ 1 kHz), the deformation is typically prolate, while increasing the frequency to the 10 kHz range changes the deformation to oblate. We attempt to explain this behaviour with a theoretical model, based on the minimization of the total free energy of the vesicle. The energy terms taken into account include the membrane bending energy and the energy of the electric field. The latter is calcu…
Predicting the macroscopic chiral behaviour of cholesteric liquid crystals from the microscopic chirality of the particles is highly non-trivial, even when the chiral interactions are purely entropic in nature. Here we introduce a novel chiral hard-particle model, namely particles with a twisted polyhedral shape and obtain, for the first time, a stable fully-entropy-driven cholesteric phase by computer simulations. By slightly modifying the triangular base of the particle, we are able to switch from a left-handed prolate to a right-handed oblate cholesteric using the same right-handed twisted …
The dynamics of fluid vesicles is studied under flow in microchannels, in which the width varies periodically along the channel. Three types of flow instabilities of prolate vesicles are found. For small quasi-spherical vesicles -- compared to the average channel width -- perturbation theory predicts a transition from a state with orientational oscillations of a fixed prolate shape to a state with shape oscillations of symmetrical ellipsoidal or bullet-like shapes with increasing flow velocity. Experimentally, such orientational oscillations are observed during the slow migration of a vesicle …
We systematize and extend the description of vesicle growth and shape change using linear nonequilibrium thermodynamics. By restricting the study to shape changes from spheres to axisymmetric ellipsoids, we are able to give a consistent formulation which includes the lateral tension of the vesicle membrane. This allows us to generalize and correct a previous calculation. Our present calculations suggest that, for small growing vesicles, a prolate ellipsoidal shape should be favored over oblate ellipsoids, whereas for large growing vesicles oblates should be favored over prolates. The validity …
As a model of soft confinement for polymers, we investigated equilibrium shapes of a flexible vesicle that contains a phase-separating polymer solution. To simulate such a system, we combined the phase field theory (PFT) for the vesicle and the self-consistent field theory (SCFT) for the polymer solution. We observed a transition from a symmetric prolate shape of the vesicle to an asymmetric pear shape induced by the domain structure of the enclosed polymer solution. Moreover, when a non-zero spontaneous curvature of the vesicle is introduced, a re-entrant transition between the prolate and th…
We investigate Brownian noise effects on magnetic focusing of prolate and oblate spheroids carrying permanent magnetic dipoles in channel (Poiseuille) flow subject to a uniform magnetic field. The focusing is effected by the low-Reynolds-number wall-induced hydrodynamic lift which can be tuned via tilt angle of the field relative to the flow direction. This mechanism is incorporated in a steady-state Smoluchowski equation that we solve numerically to analyze the noise effects through the joint position-orientation probability distribution function of spheroids within the channel. The results f…
While the behavior of vesicles in thermodynamic equilibrium has been studied extensively, how active forces control vesicle shape transformations is not understood. Here, we combine theory and simulations to study the shape behavior of vesicles containing active Brownian particles. We show that the combination of active forces, dimensionality and membrane bending free energy creates a plethora of novel phase transitions. At low swim pressure, the vesicle exhibits a discontinuous transition from a spherical to a prolate shape, which has no counterpart in two dimensions. At high swim pressure it…
Orientational ordering and close packing properties of quasi-one-dimensional hard Gaussian overlap particles
Institute for Applied Physics, University of Tübingen（蒂宾根大学应用物理研究所）；Physics Department, Centre for Natural Sciences, University of Pannonia（佩奇大学自然科学中心物理系）
We present computer simulations of the vapour-nematic interface of the Gay-Berne model. We considered situations which correspond to either prolate or oblate molecules. We determine the anchoring of the nematic phase and correlate it with the intermolecular potential parameters. On the other hand, we evaluate the surface tension associated to this interface. We find a corresponding states law for the surface tension dependence on the temperature, valid for both prolate and oblate molecules.
Using field theoretic approach, we study equilibrium shape deformation of a vesicle induced by the presence of enclosed flexible polymers, which is a simple model of drug delivery system or endocytosis. To evaluate the total free energy of this system, it is necessary to calculate the bending elastic energy of the membrane, the conformation entropy of the polymers and their interactions. For this purpose, we combine phase field theory for the membrane and self-consistent field theory for the polymers. Simulations on this coupled model system for axiosymmetric shapes show a shape deformation of…
The shape transformations of fluid membranes induced by curved protein rods are studied using meshless membrane simulations. The rod assembly at low rod density induces a flat membrane tube and oblate vesicle. It is found that the polyhedral shapes are stabilized at high rod densities. The discrete shape transition between triangular and buckled discoidal tubes is obtained and their curvature energies are analyzed by a simple geometric model. For vesicles, triangular hosohedron and elliptic-disk shapes are formed in equilibrium, whereas tetrahedral and triangular prism shapes are obtained as m…
The surface free energy of ideal hard rods near curved hard surfaces is determined to second order in curvature for surfaces of general shape. In accordance with previous results for spherical and cylindrical surfaces it is found that this quantity is non-analytical when one of the principal curvatures changes signs. This prohibits writing it in the common Helfrich form. It is shown that the non-analytical terms are the same for any aspect ratio of the rods. These results are used to find the equilibrium shape of vesicles immersed in solutions of rod-like (colloidal) particles. The presence of…
Can the presence of molecular-tilt order significantly affect the shapes of lipid bilayer membranes, particularly membrane shapes with narrow necks? Motivated by the propensity for tilt order and the common occurrence of narrow necks in the intermediate stages of biological processes such as endocytosis and vesicle trafficking, we examine how tilt order inhibits the formation of necks in the equilibrium shapes of vesicles. For vesicles with a spherical topology, point defects in the molecular order with a total strength of $+2$ are required. We study axisymmetric shapes and suppose that there …
Phase-contrast microscopy is used to monitor the shapes of micron-scale fluid-phase phospholipid-bilayer vesicles in aqueous solution. At fixed temperature, each vesicle undergoes thermal shape fluctuations. We are able experimentally to characterize the thermal shape ensemble by digitizing the vesicle outline in real time and storing the time-sequence of images. Analysis of this ensemble using the area-difference-elasticity (ADE) model of vesicle shapes allows us to associate (map) each time-sequence to a point in the zero-temperature (shape) phase diagram. Changing the laboratory temperature…
Nuclear pores have an approximately uniform distribution in the nuclear envelope of most living cells. Hence, the morphology of the nuclear envelope is a spherical stomatocyte with a high genus. We have investigated the morphology of high-genus vesicles under pore-size constraint using dynamically triangulated membrane simulations. Bending-energy minimization without volume or other constraints produces a circular-cage stomatocyte, where the pores are aligned in a circular line on an oblate bud. As the pore radius is reduced, the circular-pore alignment is more stabilized than a random pore di…
We consider a new class of model systems to study systematically the role of molecular shape in the transport properties of dense liquids. Our model is a liquid binary mixture where both the molecules are non-spherical and characterized by a collection of parameters. Although in the real world most of the molecules are non-spherical, only a limited number of theoretical studies exist on the effects of molecular shapes and hardly any have addressed the validity of the hydrodynamic predictions of rotational and translational diffusion of these shapes in liquids. In this work, we study a model li…
