二维泡在无界Poiffille流中的侧向迁移
Lateral migration of a 2D vesicle in unbounded Poiseuille flow
摘要：
在低雷诺数限制下，数值研究了悬浮液泡在无界Poiffille流中的迁移。我们考虑囊泡内部和外部之间没有粘度差异的情况。使用边界积分方法，我们解决了相应的流体力学流动方程和明确的跟踪囊泡动力学在二维。我们发现，Poiffille流的非线性特征和囊泡变形之间的相互作用导致了囊泡向Poiffille流中心的跨流线迁移。这与[L.G. Leal，Ann.Rev.Fluid Mech.12，435（1980）]，根据该方法，液滴从中心移开（假设内部和外部流体之间没有粘度对比）。发现的迁移速度增加与当地的毛细管数（定义的时间尺度的囊泡松弛朝向其平衡形状倍的当地剪切速率），但达到一个平台以上的毛细管数的某个值。该平台值随着抛物线流动剖面的曲率而增加。我们提出了迁移速度的标度律。
英文摘要：
The migration of a suspended vesicle in an unbounded Poiseuille flow is investigated numerically in the low Reynolds number limit. We consider the situation without viscosity contrast between the interior of the vesicle and the exterior. Using the boundary integral method we solve the corresponding hydrodynamic flow equations and track explicitly the vesicle dynamics in two dimensions. We find that the interplay between the nonlinear character of the Poiseuille flow and the vesicle deformation causes a cross-streamline migration of vesicles towards the center of the Poiseuille flow. This is in a marked contrast with a result [L.G. Leal, Ann. Rev. Fluid Mech. 12, 435(1980)]according to which the droplet moves away from the center (provided there is no viscosity contrast between the internal and the external fluids). The migration velocity is found to increase with the local capillary number (defined by the time scale of the vesicle relaxation towards its equilibrium shape times the local shear rate), but reaches a plateau above a certain value of the capillary number. This plateau value increases with the curvature of the parabolic flow profile. We present scaling laws for the migration velocity.
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