Dynamics of Membrane-Bound Particles: Capsules and Vesicles

Abstract

This chapter provides a tutorial on the analytical modeling of the nonequilibrium dynamics of particles enclosed by viscoelastic membranes, such as vesicles and capsules. A particular challenge for this kind of problem stems from asphericity and membrane inextensibility, which engenders nonlinearity that gives rise to unexpected behavior, such as multiple dynamical states of vesicles in shear flow (tank-treading, tumbling, trembling, swinging), asymmetric slipper-like shapes in Poiseuille flow, and pearling and asymmetric dumbbell shapes in straining flows or uniform electric fields. We derive solutions for the deformation and motion of a nearly spherical particle, which illustrates the use of a formalism based on spherical harmonics. In particular, we show how a theoretical analysis of the motion and deformation of a freely suspended capsule (referring to both vesicles and polymer capsules) subject to forces arising from applied flows, electric fields, or actively generated surface tractions explains some of the experimentally observed responses. The results are applied to the analysis of blood flow in the microcirculation, and microorganism swimming.

Numerical and asymptotic analysis of the three-dimensional electrohydrodynamic interactions of drop pairs

“…Let us consider the transient drop dynamics after the electric field is applied in the limit of small deformations Ca 1. At leading order in Ca, the shape is described by r s = 1 + f 2 (t)(−1 + 3 cos 2 θ), and the velocity field outside the drop at distance r from the drop centre and an angle θ with the applied field direction is given by Vlahovska (2011Vlahovska ( , 2016a…”

Fluctuation spectroscopy of giant unilamellar vesicles using confocal and phase contrast microscopy

“…Here we summarize the main results for the dynamics of a quasi-spherical vesicle [33,34,[55][56][57][58][59][60]. Mean Squared Magnitude of the Fourier Modes: The dynamics of the spherical harmonics modes is governed by the following Langevin equation,…”

A robust method for quantification of surface elasticity in soft solids

“…At linear perturbation order [39], interfacial elastic stresses following from Equation (4) may be written as…”