Hydrodynamic mobility of a solid particle near a spherical elastic membrane. II. Asymmetric motion

Daddi-Moussa-Ider, Abdallah; Lisicki, Mmaciej and Gekle, Stephan (2017). Hydrodynamic mobility of a solid particle near a spherical elastic membrane. II. Asymmetric motion. Physical Review E, 95(5), article no. 053117.

DOI: https://doi.org/10.1103/PhysRevE.95.053117


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 toward shearing and bending. Together with the results obtained in the first part [Daddi-Moussa-Ider and Gekle, Phys. Rev. E 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 nonvanishing resistance toward shearing. We further compute the 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.

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