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Hydrodynamic particle interactions in linear and radial viscosity gradients

Ziegler, Sebastian; Smith, Ana-Sunčana (2022) Hydrodynamic particle interactions in linear and radial viscosity gradients. Journal of Fluid Mechanics, 943 . ISSN 0022-1120

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We present a versatile perturbative calculation scheme to determine the leading-order correction to the mobility matrix for particles in a low-Reynolds-number fluid with spatially variant viscosity. To this end, we exploit the Lorentz reciprocal theorem and the reflection method in the far field approximation. To demonstrate how to apply the framework to a particular choice of a viscosity field, we first study particles in a finite-size, interface-like, linear viscosity gradient. The extent of the latter should be significantly larger than the particle separation. Both situations of symmetrically and asymmetrically placed particles within such an odd symmetric viscosity gradient are considered. As a result, long-range flow fields are identified that decay by one order slower than their constant-viscosity counterparts. Self-mobilities for particle rotations and translations are affected, while for asymmetric placement, additional correction appears for the latter. The mobility terms associated with hydrodynamic interactions between the particles also need to be corrected, in a placement-specific manner. While the results are derived for the system of two particles, they apply also to many-particle systems. Furthermore, we treat the viscosity gradients induced by two particles with temperatures different from that of the surrounding fluid. Assuming a linear relation between fluid temperature and viscosity, we find that both the self-mobilities of the particles as well as the mobility terms for hydrodynamic interactions increase for hot particles and decrease for cold particles.

Item Type: Article
Uncontrolled Keywords: colloids ; general fluid mechanics
Subjects: NATURAL SCIENCES > Physics
NATURAL SCIENCES > Physics > Condensed Matter Physics
Divisions: Division of Physical Chemistry
Depositing User: Ana Sunčana Smith
Date Deposited: 05 Jul 2022 09:19
DOI: 10.1017/jfm.2022.421

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