Hydrodynamic mobility of a solid particle nearby a spherical elastic membrane. II. Asymmetric motion
Abstract
In this paper, we derive analytical expressions for the leading-order hydrodynamic mobility of a small solid particle undergoing motion tangential to a nearby large spherical capsule whose membrane possesses resistance towards shearing and bending. Together with the results obtained in the first part (Daddi-Moussa-Ider and Gekle, Phys. Rev. E {\bfseries 95}, 013108 (2017)) where the axisymmetric motion perpendicular to the capsule membrane is considered, the solution of the general mobility problem is thus determined. We find that shearing resistance induces a low-frequency peak in the particle self-mobility, resulting from the membrane normal displacement in the same way, although less pronounced, to what has been observed for the axisymmetric motion. In the zero frequency limit, the self-mobility correction near a hard sphere is recovered only if the membrane has a non-vanishing resistance towards shearing. We further compute the particle in-plane mean-square displacement of a nearby diffusing particle, finding that the membrane induces a long-lasting subdiffusive regime. Considering capsule motion, we find that the correction to the pair-mobility function is solely determined by membrane shearing properties. Our analytical calculations are compared and validated with fully resolved boundary integral simulations where a very good agreement is obtained.
Keywords
Cite
@article{arxiv.1705.02626,
title = {Hydrodynamic mobility of a solid particle nearby a spherical elastic membrane. II. Asymmetric motion},
author = {Abdallah Daddi-Moussa-Ider and Maciej Lisicki and Stephan Gekle},
journal= {arXiv preprint arXiv:1705.02626},
year = {2017}
}
Comments
17 pages, 9 figures and 64 references. Manuscript accepted for publication in Phys. Rev. E