Nonlinear simulations of vesicle wrinkling

Abstract

In this paper, we study nonlinear wrinkling dynamics of a vesicle in an extensional flow. Motivated by the recent experiments and linear theory on wrinkles of a quasi‐spherical membrane, we are interested in examining the linear theory and exploring wrinkling dynamics in a nonlinear regime. We focus on a quasi‐circular vesicle in two dimensions and show that the linear analytical results are qualitatively independent of the number of dimensions. Hence, the two‐dimensional studies can provide insights into the full three‐dimensional problem. We develop a spectral accurate boundary integral method to simulate the nonlinear evolution of surface tension and the nonlinear interactions between flow and membrane morphology. We demonstrate that for a quasi‐circular vesicle, the linear theory well predicts the characteristic wavenumber during the wrinkling dynamics. Nonlinear results of an elongated vesicle show that there exist dumbbell‐like stationary shapes in weak flows. For strong flows, wrinkles with pronounced amplitudes will form during the evolution. As far as the shape transition is concerned, our simulations are able to capture the main features of wrinkles observed in the experiments. Interestingly, numerical results reveal that, in addition to wrinkling, asymmetric rotation can occur for slightly tilted vesicles. The mathematical theory and numerical results are expected to lead to a better understanding of related problems in biology such as cell wrinkling. Copyright © 2013 John Wiley & Sons, Ltd.