Relaxation dynamics of a compressible bilayer vesicle containing highly viscous fluid

Abstract

We study the relaxation dynamics of a compressible bilayer vesicle with an asymmetry in the viscosity of the inner and outer fluid medium. First we explore the stability of the vesicle free energy which includes a coupling between the membrane curvature and the local density difference between the two monolayers. Two types of instabilities are identified: a small wavelength instability and a larger wavelength instability. Considering the bulk fluid viscosity and the inter-monolayer friction as the dissipation sources, we next employ Onsager's variational principle to derive the coupled equations both for the membrane and the bulk fluid. The three relaxation modes are coupled to each other due to the bilayer and the spherical structure of the vesicle. Most importantly, a higher fluid viscosity inside the vesicle shifts the cross-over mode between the bending and the slipping to a larger value. As the vesicle parameters approach toward the unstable regions, the relaxation dynamics is dramatically slowed down, and the corresponding mode structure changes significantly. In some limiting cases, our general result reduces to the previously obtained relaxation rates.

Onsager's variational principle in active soft matter

“…The above variational principles have been successfully applied to the diffusion in electrolyte solutions by Onsager himself in 1940s, 57 and more recently applied to various soft matter systems such as multiphase flows, 58,69 electrorheological fluids, 70 colloid suspensions, 80 polymer solutions, 53,62,63 polymer gels, 39,63 liquid crystals, 62,74 vesicles, 81 membranes [71][72][73] and so on. This indicates that OVP is an important principle in soft matter dynamics.…”

“…Now we consider the spreading dynamics of thin active droplets on solid substrates. We do not try to solve the thin film eqn (71) directly, but use OVP as an approximation method to solve the scaling laws for the droplet spreading.…”

“…61 In recent years, OVP has been widely used as an indispensable and powerful tool for the study of nonlinear and nonequilibrium phenomena of soft matter. 53,58,[62][63][64][65] OVP can be used to derive many transport equations for soft matter dynamics, 53,62 e.g., the Stokes equation for incompressible low-Reynolds-number flows, 58 the diffusion equation, 53,62 the reaction-diffusion equations for (low molecular weight) multicomponent solutions, 51,64,65 the thin film evolution equations, 63,[66][67][68] the phase field model for two-phase hydrodynamics, 58,69 the electrorheological hydrodynamic equation, 70 the two-fluid model for the phase separation dynamics in colloids and polymers, 53,62,63 the dynamics of polymer gels, 39,63 the dynamic equations of lipid membrane, [71][72][73] etc. Moreover, OVP also provides a very convenient way to derive thermodynamically consistent boundary conditions that supplement the transport equations in the bulk region.…”

Dynamics of a bilayer membrane coupled to a two-dimensional cytoskeleton: Scale transfers of membrane deformations

“…In the presence of tension, their results hold for σ σ c ≡ (2ηk) 2 /(κb 2 ), except at very large scales (see Refs. [19][20][21] and Appendix C). However, for σ σ c the dynamics is dominated at all scales by the inter-monolayer friction, with γ [19].…”

Dynamics of passive and active membrane tubes

“…In this paper, we will focus on the dynamics of membrane tubes, deriving equations of motion from Onsager's variational principle in the manner of Refs. [27][28][29], and analysing the relaxation dynamics in Fourier space. We then consider the case where stochastic forces act on the membrane and derive the statistical properties of the shape undulations, in particular focusing on the case where active noise dominates.…”