Department of Aerospace Engineering, Tohoku University, Sendai 980-8579, Japan.
Department of Physics, Tohoku University, Sendai 980-8578, Japan.
J Chem Phys. 2018 Mar 21;148(11):114905. doi: 10.1063/1.4999049.
We propose a systematic formulation of the migration behaviors of a vesicle in a Poiseuille flow based on Onsager's variational principle, which can be used to determine the most stable steady state. Our model is described by a combination of the phase field theory for the vesicle and the hydrodynamics for the flow field. The dynamics is governed by the bending elastic energy and the dissipation functional, the latter being composed of viscous dissipation of the flow field, dissipation of the bending energy of the vesicle, and the friction between the vesicle and the flow field. We performed a series of simulations on 2-dimensional systems by changing the bending elasticity of the membrane and observed 3 types of steady states, i.e., those with slipper shape, bullet shape, and snaking motion, and a quasi-steady state with zig-zag motion. We show that the transitions among these steady states can be quantitatively explained by evaluating the dissipation functional, which is determined by the competition between the friction on the vesicle surface and the viscous dissipation in the bulk flow.
我们基于 Onsager 的变分原理，提出了一种对囊泡在泊肃叶流中迁移行为的系统表述，该表述可用于确定最稳定的稳态。我们的模型由囊泡的相场理论和流场的流体力学描述。动力学由弯曲弹性能和耗散泛函控制，后者由流场的粘性耗散、囊泡弯曲能的耗散和囊泡与流场之间的摩擦组成。我们通过改变膜的弯曲弹性，在二维系统上进行了一系列模拟，观察到了 3 种稳态，即滑靴状、子弹状和蛇形运动，以及准稳态的锯齿状运动。我们表明，通过评估耗散泛函可以定量解释这些稳态之间的转变，该泛函由囊泡表面上的摩擦力和体相流动中的粘性耗散之间的竞争决定。
