Two-dimensional phoretic swimmers: the singular weak-advection limits
Two-dimensional phoretic swimmers: the singular weak-advection limits
复制标题
二维泳动游泳者：奇异的弱平流极限
DOI：
10.1017/jfm.2017.126
复制
发表时间：
2017
影响因子：
3.7
通讯作者：
E. Yariv
中科院分区：
文献类型：
--
作者：
E. Yariv
Because of the associated far-field logarithmic divergence, the transport problem governing two-dimensional phoretic self-propulsion lacks a steady solution when the Péclet number $\mathit{Pe}$ vanishes. This indeterminacy, which has no counterpart in three dimensions, is remedied by introducing a non-zero value of $\mathit{Pe}$ , however small. We consider that problem employing a first-order kinetic model of solute absorption, where the ratio of the characteristic magnitudes of reaction and diffusion is quantified by the Damköhler number $\mathit{Da}$ . As $\mathit{Pe}\rightarrow 0$ the dominance of diffusion breaks down at distances that scale inversely with $\mathit{Pe}$ ; at these distances, the leading-order transport represents a two-dimensional point source in a uniform stream. Asymptotic matching between the latter region and the diffusion-dominated near-particle region provides the leading-order particle velocity as an implicit function of $\log \mathit{Pe}$ . Another scenario involving weak advection takes place under strong reactions, where $\mathit{Pe}$ and $\mathit{Da}$ are large and comparable. In that limit, the breakdown of diffusive dominance occurs at distances that scale as $\mathit{Da}^{2}/\mathit{Pe}$ .
Because of the associated far-field logarithmic divergence, the transport problem governing two-dimensional phoretic self-propulsion lacks a steady solution when the Péclet number $\mathit{Pe}$ vanishes. This indeterminacy, which has no counterpart in three dimensions, is remedied by introducing a non-zero value of $\mathit{Pe}$ , however small. We consider that problem employing a first-order kinetic model of solute absorption, where the ratio of the characteristic magnitudes of reaction and diffusion is quantified by the Damköhler number $\mathit{Da}$ . As $\mathit{Pe}\rightarrow 0$ the dominance of diffusion breaks down at distances that scale inversely with $\mathit{Pe}$ ; at these distances, the leading-order transport represents a two-dimensional point source in a uniform stream. Asymptotic matching between the latter region and the diffusion-dominated near-particle region provides the leading-order particle velocity as an implicit function of $\log \mathit{Pe}$ . Another scenario involving weak advection takes place under strong reactions, where $\mathit{Pe}$ and $\mathit{Da}$ are large and comparable. In that limit, the breakdown of diffusive dominance occurs at distances that scale as $\mathit{Da}^{2}/\mathit{Pe}$ .
登录
查看更多内容
DOI：
10.1088/0953-8984/28/25/253001
发表时间：
2016-01
期刊：
Journal of Physics: Condensed Matter
影响因子：
--
作者：
A. Zöttl;H. Stark
通讯作者：
A. Zöttl;H. Stark
跑步游泳运动员在二维角附近的应力渐进：流体动力学束缚态
DOI：
10.1098/rspa.2012.0237
发表时间：
2012
期刊：
Mathematical, Physical and Engineering Sciences
影响因子：
--
作者：
Davis A
通讯作者：
Davis A
影响因子：
2.4
作者：
Ebbens, Stephen;Tu, Mei-Hsien;Golestanian, Ramin
通讯作者：
Golestanian, Ramin
影响因子：
44.1
作者：
Bechinger, Clemens;Di Leonardo, Roberto;Volpe, Giovanni
通讯作者：
Volpe, Giovanni