Spontaneous autophoretic motion of isotropic disks
Spontaneous autophoretic motion of isotropic disks
复制标题
各向同性盘的自发自泳运动
DOI：
10.1017/jfm.2023.740
复制
发表时间：
2023
影响因子：
3.7
通讯作者：
E. Yariv
中科院分区：
文献类型：
--
作者：
Rodolfo Brandão;E. Yariv
Abstract It is theoretically known that an isotropic chemically active particle in an unbounded solution undergoes symmetry breaking when the intrinsic Péclet number ${{Pe}}$ exceeds a finite critical value (Michelin et al., Phys. Fluids, vol. 25, 2013, 061701). At that value, a transition takes place from a stationary state to spontaneous motion. In two dimensions, where no stationary state is possible in an unbounded domain, a linear stability analysis in a large bounded domain (Hu et al., Phys. Rev. Lett., vol. 123, 2019, 238004) reveals that the critical ${{Pe}}$ value slowly diminishes as the domain size increases. Motivated by these findings, we here consider an unbounded domain from the outset, addressing the two-dimensional problem of steady self-propulsion with a focus on the limit ${{Pe}}\ll 1$. This singular limit is handled using matched asymptotic expansions, conceptually decomposing the fluid domain into a particle-scale region, where the leading-order solute transport is diffusive, and a remote region, where diffusion and advection are comparable. The expansion parameter is provided by the product of ${{Pe}}$ and $U$, the unknown particle speed (normalised by the standard autophoretic scale). The problem is unconventional in that the scaling of $U$ with ${{Pe}}$ must be determined in the course of the perturbation analysis. The resulting approximation, $U=4\exp ({-2/{Pe}-\gamma _{E}-1})/{{Pe}}$ ($\gamma _{E}$ being the Euler–Mascheroni constant), is in remarkable agreement with the numerical predictions of Hu et al. in the common interval of validity.
Abstract It is theoretically known that an isotropic chemically active particle in an unbounded solution undergoes symmetry breaking when the intrinsic Péclet number ${{Pe}}$ exceeds a finite critical value (Michelin et al., Phys. Fluids, vol. 25, 2013, 061701). At that value, a transition takes place from a stationary state to spontaneous motion. In two dimensions, where no stationary state is possible in an unbounded domain, a linear stability analysis in a large bounded domain (Hu et al., Phys. Rev. Lett., vol. 123, 2019, 238004) reveals that the critical ${{Pe}}$ value slowly diminishes as the domain size increases. Motivated by these findings, we here consider an unbounded domain from the outset, addressing the two-dimensional problem of steady self-propulsion with a focus on the limit ${{Pe}}\ll 1$. This singular limit is handled using matched asymptotic expansions, conceptually decomposing the fluid domain into a particle-scale region, where the leading-order solute transport is diffusive, and a remote region, where diffusion and advection are comparable. The expansion parameter is provided by the product of ${{Pe}}$ and $U$, the unknown particle speed (normalised by the standard autophoretic scale). The problem is unconventional in that the scaling of $U$ with ${{Pe}}$ must be determined in the course of the perturbation analysis. The resulting approximation, $U=4\exp ({-2/{Pe}-\gamma _{E}-1})/{{Pe}}$ ($\gamma _{E}$ being the Euler–Mascheroni constant), is in remarkable agreement with the numerical predictions of Hu et al. in the common interval of validity.
影响因子：
2.4
作者：
Ebbens, Stephen;Tu, Mei-Hsien;Golestanian, Ramin
通讯作者：
Golestanian, Ramin