A suspended particle in a temperature gradient experiences a force known as thermophoresis. Hot gas molecules collide with one side of the particle on average with greater force than cold gas molecules collide with the opposite side. This creates a net force on the particle towards the cold gas region and away from the hot (Bott, 1995).
This effect can be exploited in industrial gas cleaning operations, in the form of a ‘thermoprecipitator’ or ‘thermopositor’. Like an electrostatic precipitator, thermophoresis creates a force on the particle towards a cold surface, eventually the particles collide with and deposit on the surface (Davis and Schweiger, 2002).
Ansys Fluent allows the user to include thermophoretic force on particles in DPM simulations, through a tickbox option in the GUI. A closer look at the Fluent Theory Guide shows this is (unless otherwise specified by the user) calculated using an equation from Talbot:
Equation: Talbot equation for thermophoretic force. Where: dp = particle diameter; µ = fluid viscosity; Cs = 1.17; K = k/kp (k = fluid thermal conductivity based on translational energy only k = 15/4 µR; kp = particle thermal conductivity); Cm =1.14; Ct = 2.18; Kn = Knudsen number = 2λ/dp; λ = mean free path of fluid; mp = particle mass. The equation assumes a spherical particle & ideal gas behaviour.
The referenced paper by Talbot (1981) consists of a comprehensive literature review with some experimental work. This expression is actually attributed to JR Brock, and Talbot simply suggests adjustments to the C constants. Division by mp is due to the fact Fluent accepts F in units of acceleration not force.
Talbot explains that this equation is theoretically applicable for Kn < 0.1 as this is the limit of the Basset drag formula that forms part of Brock’s derivation. But Talbot also shows the expression (with the revised constants) reduces to the Waldmann formula for Kn tending to infinity. In the appendix Talbot also provides a rough discussion of the applicability of the formula in the intermediate range of Kn.
Bott, TR. (1995). Fouling of Heat exchangers. Amsterdam: Elsevier. pp.67
Davis, J. Schweiger, G. (2002). The Airborne Microparticle. Berlin: Springer. pp. 756
Talbot, L. et al. (1981). Thermophoresis of Particles in a Heated Boundary Layer. Journal of Fluid Mechanics. 101(4). pp737-758.
