Effective Viscosity and Force Moments of a Hot Particles Suspension

Active particles with a temperature distribution ('hot particles') have a distinct effect on viscous fluids. The temperature gradients deems the viscosity spatially dependent, therefore violating the linearity of the problem making a full description of velocity and pressure fields challenging. Using energy dissipation analysis we show that it is still possible to study global properties of such hot suspensions.  We calculate the effective viscosity of a dilute hot suspension, correcting Einstein’s formula to include contributions from the particles themselves and from their effect on their vicinity. We go on to present corrections for Faxen's Laws for hot spheres in the case of a linear external flow and discover non-trivial coupling due to the temperature distribution.