Effective Viscosity of a Suspension of Hot Particles

TL;DR

This paper develops a theoretical framework to calculate the effective viscosity of suspensions containing hot particles with temperature gradients, revealing anisotropic and non-symmetric stress behaviors under certain conditions.

Contribution

It introduces a method using energy dissipation and Lorentz Reciprocal Theorem to determine the global viscosity of hot particle suspensions, including effects of particle orientation and heat distribution.

Findings

Effective viscosity depends on particle heat distribution and orientation.

Viscosity becomes anisotropic when particles are aligned.

Stress tensor can be non-symmetric with external field orientation.

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.