Effective Viscosity of a Suspension of Hot Particles

Osher Arbib; Naomi Oppenheimer

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arXiv · 2408.02579

Effective Viscosity of a Suspension of Hot Particles

Osher Arbib·Naomi Oppenheimer

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Abstract

Active particles with a temperature distribution, "hot particles", have a distinct effect on the fluid that surrounds them. The temperature gradients they create deem the fluid's viscosity spatially dependent, therefore violating the linearity of the problem, making a full description of velocity and pressure fields challenging. Using energy dissipation analysis and Lorentz Reciprocal Theorem, we show that it is still possible to study global properties of such hot suspensions. Namely, we calculate the effective viscosity of a dilute hot suspension, adding a correction that includes contributions from the bulk fluid and the particles themselves. As examples of this method, we derive the effective viscosity of a suspension of spherical particles with different heat distributions. We show that when the particles are non-Brownian and are all oriented in the same direction, the viscosity is no longer isotropic and depends on the direction of the shear relative to the orientation of the particles. If the particles' orientation is fixed due to an external field, the stress tensor is no longer symmetric, and the viscosity has odd components.

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Osher Arbib, Naomi Oppenheimer. 2024-08-25. Effective Viscosity of a Suspension of Hot Particles. https://arxiv.org/abs/2408.02579

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