Jinsun Sohn

Dynamics of multicomponent vesicles in a viscous fluid

Jin Sun Sohn, Yu-Hau Tseng, Shuwang Li, Axel Voigt, and John S. Lowengrub

Journal of Computational Physics, Volume 229, Issue 1, pp. 119-144, 2010.

ABSTRACT:

 
We develop and investigate numerically a thermodynamically consistent 
model of two dimensional multicomponent vesicles in an incompressible 
viscous fluid. The model is derived using an energy variation approach 
that accounts for different lipid surface phases, the excess energy 
(line energy) associated with surface phase domain boundaries, bending 
energy, spontaneous curvature, local inextensibility and fluid flow via 
the Stokes equations. The equations are high-order (fourth order) 
nonlinear and nonlocal due to incompressibility of the fluid and the 
local inextensibility of the vesicle membrane. To solve the equations 
numerically, we develop a nonstiff, pseudo-spectral boundary integral 
method that relies on an analysis of the equations at small scales. 
The algorithm is closely related to that developed very recently by 
Veerapaneni et al. [81] for homogeneous vesicles although we use a 
different and more efficient time stepping algorithm and a reformulation 
of the inextensibility equation. We present simulations of multicomponent 
vesicles in an initially quiescent fluid and investigate the effect of 
varying the average surface concentration of an initially unstable 
mixture of lipid phases. The phases then redistribute and alter the 
morphology of the vesicle and its dynamics. When an applied shear is 
introduced, an initially elliptical vesicle tank-treads and attains 
a steady shape and surface phase distribution. A sufficiently elongated 
vesicle tumbles and the presence of different surface phases with 
different bending stiffnesses and spontaneous curvatures yields 
a complex evolution of the vesicle morphology as the vesicle bends in 
regions where the bending stiffness and spontaneous curvature are small.