Jinsun Sohn

Axisymmetric multicomponent vesicles: A comparison of hydrodynamic and geometric models

Jin Sun Sohn, Shuwang Li, Xiaofan Li and John S. Lowengrub

International Journal for Numerical Methods in Biomedical Engineering, Vol. 28, issue 3, pp. 346-368. 2012.

ABSTRACT:

 
Using a mathematical model, we investigate the role of hydrodynamic 
forces on three-dimensional axisymmetric multicomponent vesicles. 
The equations are derived using an energy variation approach that 
accounts for different surface phases, the excess energy associated 
with surface domain boundaries, bending energy and inextensibility. 
The equations are high-order (fourth order) nonlinear and nonlocal. 
To solve the equations numerically, we use a nonstiff, 
pseudo-spectral boundary integral method that relies on an analysis
of the equations at small scales. We also derive equations governing 
the dynamics of inextensible vesicles evolving in the absence of 
hydrodynamic forces and simulate numerically the evolution of this 
geometric model. We find that compared with the geometric model, 
hydrodynamic forces provide additional paths for relaxing inextensible 
vesicles. The presence of hydrodynamic forces may enable the dynamics 
to overcome local energy barriers and reach lower energy states than 
those accessible by geometric motion or energy minimization algorithms. 
Because of the intimate connection between morphology, surface phase 
distribution and biological function, these results have important 
consequences in understanding the role vesicles play in biological 
processes.