Effective viscosity of a suspension of hot particles

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 stress tensor and 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 stress and viscosity of a suspension of spherical particles with different heat distributions. We show that, when the particles are non-Brownian and all oriented along the same direction, the viscosity is no longer isotropic and depends on the direction of shear relative to the orientation of the particles. In such cases, the fluid is also non-Newtonian. If the particles' orientation is fixed due to an external field, the stress tensor is no longer symmetric, and the viscosity has odd components.