平面泊肃叶流中内部驱动弹性粒子的动力学
Dynamics of an internally actuated elastic particle in a plane Poiseuille flow
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中文总结 AI 辅助
该研究在斯托克斯极限下解析分析平面泊肃叶流中内部驱动弹性粒子的动力学，推导外力外力矩至O(α²)阶，发现其侧向迁移方向与液滴、胶囊等不同，存在远离中心线的稳定平衡位置。
中文摘要 AI 辅助
我们在斯托克斯极限下，解析分析了一种内部驱动粒子的动力学：该粒子被建模为可压缩弹性球，其未变形中心嵌入有一个磁珠，在平面泊肃叶流中运动。通过在粒子未变形中心施加外部点力和外部点力矩，可约束粒子以规定速度运动，同时保持在流场中的任意位置。流体和粒子的控制方程分别为斯托克斯方程和纳维弹性方程。我们利用控制方程的级数解和域扰动法来捕捉粒子的变形形状，假设α远小于1，其中α量化了流体粘性应力在粒子中诱导的弹性应变。我们得到了直到O(α²)阶的外力和外力矩。沿通道长度运动的粒子会受到弹性诱导的流体升力以及流体力矩，两者均出现在O(α)和O(α²)阶。主导阶升力线性依赖于局部剪切率，以及滑移速度和流曲率的综合效应，其中滑移速度定义为粒子速度相对于局部环境流的速度。粒子会到达远离中心线的稳定平衡位置，此处净升力为零。我们表明，内部驱动粒子的变形诱导侧向迁移方向，在定性上不同于斯托克斯极限下的液滴、胶囊和囊泡，也不同于经历惯性迁移的刚性球。
英文摘要
We analytically analyse the dynamics of an internally actuated particle, modelled as a compressible elastic sphere embedded with a magnetic bead at its undeformed centre, translating in a plane Poiseuille flow in the Stokes limit. The particle is constrained to translate with a prescribed velocity while remaining at an arbitrary position within the flow by applying an external point force and external point torque at its undeformed centre. The governing equations for the fluid and particle are the Stokes and Navier elasticity equations, respectively. We use the series solutions to the governing equations and the domain perturbation method to capture the deformed shape of the particle, assuming $α\ll 1$. Here, $α$ quantifies the elastic strain induced in the particle due to the viscous stress from the fluid. The external force and external torque are obtained until O($α^2$). The particle translating along the channel length experiences an elastic-induced hydrodynamic lift as well as hydrodynamic torque both at O($α$) and O($α^2$). The leading-order lift depends linearly on the local shear rate and on the combined effects of slip velocity and flow curvature, where the slip velocity is defined as the particle velocity relative to the local ambient flow. The particle reaches a stable equilibrium position away from the centreline, where the net lift vanishes. We show that the direction of deformation-induced lateral migration of the internally actuated particle is qualitatively distinct from that of drops, capsules, and vesicles in the Stokes limit and from that of rigid spheres undergoing inertial migration.
