Creeping motion of a solid particle inside a spherical elastic cavity. II. Asymmetric motion
Abstract
An analytical method is proposed for computing the lowReynoldsnumber hydrodynamic mobility function of a small colloidal particle asymmetrically moving inside a large spherical elastic cavity, the membrane of which is endowed with resistance toward shear and bending. In conjunction with the results obtained in the first part [DaddiMoussaIder, Löwen, and Gekle, Eur. Phys. J. E 41, 104 (2018)], in which the axisymmetric motion normal to the surface of an elastic cavity is investigated, the general motion for an arbitrary force direction can be addressed. The elastohydrodynamic problem is formulated and solved using the classic method of images through expressing the hydrodynamic flow fields as a multipole expansion involving higherorder derivatives of the freespace Green's function. In the quasisteady limit, we demonstrate that the particle selfmobility function of a particle moving tangent to the surface of the cavity is larger than that predicted inside a rigid stationary cavity of equal size. This difference is justified by the fact that a stationary rigid cavity introduces additional hindrance to the translational motion of the encapsulated particle, resulting in a reduction of its hydrodynamic mobility. Furthermore, the motion of the cavity is investigated, revealing that the translational pair (composite) mobility, which linearly couples the velocity of the elastic cavity to the force exerted on the solid particle, is solely determined by membrane shear properties. Our analytical predictions are favorably compared with fullyresolved computer simulations based on a completeddoublelayer boundary integral method.
 Publication:

arXiv eprints
 Pub Date:
 March 2019
 arXiv:
 arXiv:1903.04464
 Bibcode:
 2019arXiv190304464H
 Keywords:

 Physics  Fluid Dynamics;
 Condensed Matter  Soft Condensed Matter;
 Physics  Biological Physics
 EPrint:
 14 pages, 4 figures. This is a preprint of an article published in The European Physical Journal E. The final authenticated version is available online at: https://doi.org/10.1140/epje/i2019118534