The Brownian dynamics of a lipid vesicle

We propose a Brownian dynamics simulation method to study the motion of a lipid vesicle in a suspending fluid. The lipid bilayer of the vesicle is modeled as a two-dimensional fluidic membrane with bending resistance and a high local area dilatational modulus. Using a Stokes flow boundary integral equation method, we calculate the grand mobility tensor of the deformable membrane at arbitrary viscosity ratio between the fluid inside and outside the vesicle. The fluctuation--dissipation theorem, as well as the drifting due to the configuration dependence of the diffusivity tensor, are rigorously accounted for. The flow transitions (tank-treading, tumbling and trembling) and the particle stresslet for an athermal vesicle in a simple shear flow calculated by the present method are in good agreement with existing results by a spectral boundary integral equation method. We demonstrate that the effect of Brownian motion is most significant for a tumbling vesicle. The thermal fluctuation tilts the vesicle off the shear plane, and the disruption of the originally two-dimensional tumbling orbit results in a qualitatively different three-dimensional ``wobbling'' motion. The change to the suspension rheology due to the altered dynamics is discussed.