Three-dimensional numerical simulation of vesicle dynamics using a front-tracking method

Three-dimensional numerical simulation using the front-tracking method is presented on the dynamics of a vesicle in a linear shear flow. The focus here is to elucidate the parametric dependence and the self-similarity of the vesicle dynamics, quantification of vesicle deformation, and the analysis of shape dynamics. A detailed comparison of the numerical results is made with various theoretical models and experiments. It is found that the applicability of the theoretical models is limited despite some general agreement with the simulations and experiments. The deviations between the perturbative results and the simulation results occur even in the absence of thermal noise. Specifically, we find that the vesicle dynamics does not follow a self-similar behavior in a two-parameter phase space, as proposed in a theoretical model. Rather, the dynamics is governed by three controlling parameters, namely, the excess area, viscosity ratio, and dimensionless shear rate. Additionally, we find that a linear scaling of the tank-treading angle, as proposed in the theoretical model, is possible only for nearly spherical vesicles. The breakdown of the scaling occurs at higher values of the excess area even in the absence of thermal noise. We find that the vesicle deformation saturates at large shear rates, and the asymptotic deformation matches well with a theoretical prediction for nearly spherical vesicles. The dependence of the critical viscosity ratio associated with the onset of unsteady dynamics on the vesicle excess area is in excellent agreement with the experimental observation. We show that near the transition between the tank-treading and tumbling dynamics, both the vacillating-breathing-like motion characterized by a smooth ellipsoidal shape and the trembling-like motion characterized by a highly deformed shape are possible. For the trembling-like motion, the shape is highly three-dimensional with concavities and lobes, and the vesicle deforms more in the vorticity direction than in the shear plane. A Fourier spectral analysis of the vesicle shape shows the presence of the odd harmonics and higher order modes beyond fourth order.