Isotropically active particle closely fitting in a cylindrical channel: spontaneous motion at small Péclet numbers
Isotropically active particle closely fitting in a cylindrical channel: spontaneous motion at small Péclet numbers
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紧密贴合在圆柱形通道中的各向同性活性粒子：小佩克莱数下的自发运动
DOI：
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发表时间：
2023
影响因子：
3.7
通讯作者：
Rodolfo Brandão
中科院分区：
文献类型：
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作者：
Rodolfo Brandão
本文从理论上预言了无界流体域中的活性液滴和各向同性活性粒子由于对称性破缺而产生的自发运动，只要它们的内禀Péclet数Pe超过一个临界值。然而，由于其固有的小$Pe$，这种现象还没有被观察到的活性粒子的实验。在本文中，我们从理论上证明，自发运动的一个活跃的球形粒子紧密配合在一个圆柱形通道是可能的在任意小的Pe$。尺度参数的限制，其中的无量纲清除是1$揭示，当Pe=O（ε ^{1/2}）$，封闭的颗粒达到的速度相当于在一个无界流体在中等（超临界）Pe$值。我们在该特殊极限中使用匹配的渐进展开式，其中流体域分解为几个渐进区域：间隙区域，适用润滑近似;颗粒尺度区域，浓度均匀;和远场区域，其中溶质传输是一维的。我们导出了粒子速度的渐近公式，它是一个单调递减的函数$overline {Pe}=Pe/ε ^{1/2}$，并在$overline {Pe}searrow 0$时接近一个有限极限。我们的结果为实验实现活性粒子的破缺自发运动铺平了道路。
Abstract Spontaneous motion due to symmetry breaking has been predicted theoretically for both active droplets and isotropically active particles in an unbounded fluid domain, provided that their intrinsic Péclet number $Pe$ exceeds a critical value. However, due to their inherently small $Pe$, this phenomenon has yet to be observed experimentally for active particles. In this paper, we demonstrate theoretically that spontaneous motion for an active spherical particle closely fitting in a cylindrical channel is possible at arbitrarily small $Pe$. Scaling arguments in the limit where the dimensionless clearance is $epsilon ll 1$ reveal that when $Pe=O(epsilon ^{1/2})$, the confined particle reaches speeds comparable to those achieved in an unbounded fluid at moderate (supercritical) $Pe$ values. We use matched asymptotic expansions in that distinguished limit, where the fluid domain decomposes into several asymptotic regions: a gap region, where the lubrication approximation applies; particle-scale regions, where the concentration is uniform; and far-field regions, where solute transport is one-dimensional. We derive an asymptotic formula for the particle speed, which is a monotonically decreasing function of $overline {Pe}=Pe/epsilon ^{1/2}$ and approaches a finite limit as $overline {Pe}searrow 0$. Our results could pave the way for experimental realisations of symmetry-breaking spontaneous motion in active particles.