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The confined stresslet for suspensions in a spherical cavity. Part 1. Traceless elements

Published online by Cambridge University Press:  14 November 2024

Emma Gonzalez Open the ORCID record for Emma Gonzalez [Opens in a new window]  and
Roseanna N. Zia Open the ORCID record for Roseanna N. Zia [Opens in a new window]
Emma Gonzalez
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA
Roseanna N. Zia*
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305, USA Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65203, USA
*
†Email address for correspondence: [email protected]
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Abstract

The confined Stokesian dynamics (CSD) algorithm recently reported equilibrium properties but was missing hydrodynamic functions required for suspension stress and non-equilibrium properties. In this first of a two-part series, we expand the CSD algorithm to model the traceless part of the stress tensor. To obtain quantities needed to solve the integral expressions for the stress, we developed a general method to solve Stokes’ equations in bispherical coordinates. We calculate the traceless stress tensor for arbitrary particle-to-enclosure size ratio. We next compute rheology of a confined suspension by implementing the stresslet hydrodynamic coefficients into CSD, yielding the deviatoric part of the many-body hydrodynamic stresslet. We employed energy methods to relate this stresslet to the high-frequency viscosity of the confined suspension, finding an increase in viscous dissipation with crowding and confinement well beyond the unconfined value. We show that confinement effects on viscosity are dominated by near-field interactions between the particles that reside very near the cavity wall (rather than particle–wall interactions). Surprisingly, this near-field effect is stronger than the viscosity of an unconfined suspension, showing that entropic exclusion driven by the wall sets up many lubrication interactions that then generate strong viscous dissipation. The limiting case of a particle near a flat wall reveals a correction to prior literature. The theory presented in this work can be expanded to study the Brownian contribution to the viscosity of confined suspensions in and away from equilibrium. In part 2, we report the osmotic pressure, via the trace of the stress tensor.

JFM classification

Complex Fluids: Colloids Low-Reynolds-number flows: Lubrication theory Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 999 , 25 November 2024 , A38
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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