Phoretic self-propulsion at large Péclet numbers
Phoretic self-propulsion at large Péclet numbers
复制标题
大佩克莱数下的泳动自推进
DOI：
10.1017/jfm.2015.78
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发表时间：
2015
影响因子：
3.7
通讯作者：
S. Michelin
中科院分区：
文献类型：
--
作者：
E. Yariv;S. Michelin
我们分析了由边界不均匀化学反应激发的球形颗粒的自扩散泳动。我们考虑两种模型的溶质吸收，一个具有指定的分布的界面溶质通量和一个在此通量是由一阶动力学与指定的分布速率常数。我们采用了一个宏观模型，其中的溶质与颗粒边界的短程相互作用是由一个有效的滑移条件。溶质运移受对流扩散方程控制。我们专注于大Péclet数的奇异极限，$\mathit{Pe}\gg 1$。在固定通量模型中，过剩溶质浓度被限制在一个狭窄的边界层。与该极限有关的缩放允许将溶质浓度问题与流场解耦。由此产生的非线性边界层问题的处理使用的变换流函数坐标和随后的应用傅立叶变换，从而减少到一个非线性积分方程的界面浓度。它的解提供了粒子速度的必要近似，其标度为$\mathit{Pe}^{-1/3}$。在固定速率模型中，大的Péclet数可以在不同的极限过程中实现。我们考虑大型游泳者或强烈反应的情况，其中Damköhler数$\mathit{Da}$也很大，缩放为$\mathit{Pe}$。在没有边界层形成的双重极限中，我们得到了粒子速度的封闭形式近似，表示为速率常数分布的非线性泛函;这个速度标度为$\mathit{Pe}^{-2}$。固定流量和固定速率的渐近预测同意提供的数值计算解决方案的非线性传输问题。
We analyse the self-diffusiophoresis of a spherical particle animated by a non-uniform chemical reaction at its boundary. We consider two models of solute absorption, one with a specified distribution of interfacial solute flux and one where this flux is governed by first-order kinetics with a specified distribution of rate constant. We employ a macroscale model where the short-range interaction of the solute with the particle boundary is represented by an effective slip condition. The solute transport is governed by an advection–diffusion equation. We focus upon the singular limit of large Péclet numbers, $\mathit{Pe}\gg 1$ . In the fixed-flux model, the excess-solute concentration is confined to a narrow boundary layer. The scaling pertinent to that limit allows the problem governing the solute concentration to be decoupled from the flow field. The resulting nonlinear boundary-layer problem is handled using a transformation to stream-function coordinates and a subsequent application of Fourier transforms, and is thereby reduced to a nonlinear integral equation governing the interfacial concentration. Its solution provides the requisite approximation for the particle velocity, which scales as $\mathit{Pe}^{-1/3}$ . In the fixed-rate model, large Péclet numbers may be realized in different limit processes. We consider the case of large swimmers or strong reaction, where the Damköhler number $\mathit{Da}$ is large as well, scaling as $\mathit{Pe}$ . In that double limit, where no boundary layer is formed, we obtain a closed-form approximation for the particle velocity, expressed as a nonlinear functional of the rate-constant distribution; this velocity scales as $\mathit{Pe}^{-2}$ . Both the fixed-flux and fixed-rate asymptotic predictions agree with the numerical values provided by computational solutions of the nonlinear transport problem.