A Kinetic Approach to Active Rods Dynamics in Confined Domains
A Kinetic Approach to Active Rods Dynamics in Confined Domains
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DOI：
10.1137/19m1263510
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发表时间：
2019-03
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影响因子：
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通讯作者：
L. Berlyand;P. Jabin;M. Potomkin;Elżbieta Ratajczyk
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作者：
L. Berlyand;P. Jabin;M. Potomkin;Elżbieta Ratajczyk
对由强加流中的许多自驱动（主动）游泳者组成的活性物质的研究对于许多应用都很重要。自推进游泳器可以代表活体和人造物体，例如细菌和化学驱动的双金属纳米颗粒。在这项工作中，我们重点关注以在壁限制的粘性流体中游动的自推进杆为代表的活性物质的动力学描述。众所周知，与无界或周期性容器相比，墙壁可能会显着影响活动杆的轨迹。这些效应包括壁上的积累和上游运动（也称为负流变性）。我们的第一个主要结果是在惯性消失极限下严格推导主动杆概率分布函数的边界条件。找到这样的极限很重要，因为（i）事实上，在许多例子中，活性物质惯性可以忽略不计，因为游泳发生在低雷诺数范围内，（ii）这个极限允许我们减少动力学描述的维度，从而减少计算复杂性。对于最终的模型，我们在平移扩散消失的极限下推导出系统，这对于活性粒子来说通常也可以忽略不计。该系统允许单独跟踪聚集在壁上的活性颗粒和在大量流体中游动的活性颗粒。
The study of active matter consisting of many self-propelled (active) swimmers in an imposed flow is important for many applications. Self-propelled swimmers may represent both living and artificial ones such as bacteria and chemically driven bi-metallic nano-particles. In this work we focus on a kinetic description of active matter represented by self-propelled rods swimming in a viscous fluid confined by a wall. It is well-known that walls may significantly affect the trajectories of active rods in contrast to unbounded or periodic containers. Among such effects are accumulation at walls and upstream motion (also known as negative rheotaxis). Our first main result is the rigorous derivation of boundary conditions for the active rods' probability distribution function in the limit of vanishing inertia. Finding such a limit is important due to (i) the fact that in many examples of active matter inertia is negligible, since swimming occurs in a low Reynolds number regime, and (ii) this limit allows us to reduce the dimension - and so computational complexity - of the kinetic description. For the resulting model, we derive the system in the limit of vanishing translational diffusion which is also typically negligible for active particles. This system allows for tracking separately active particles accumulated at walls and active particles swimming in the bulk of the fluid.