Thermophoresis

:: Section 2

Thermophoretic Force and Velocity

I. Small Particles

For particles whose diameters are smaller than the gas mean free path (0.066 μm), the thermophoretic force depends on the temperature gradient in the surrounding gas molecules. As shown in the animation below, the gas molecules coming from the right hand side (the hot side) have a greater velocity than those coming from the left hand side (a high temperature means a larger kinetic energy of the molecule). Therefore, the greater momentum received from the right hand side causes a net force — the thermophoretic force — to the left, in the direction of decreasing temperature, leading to the overall movement of the aerosol to the cooler side.

The thermophoretic force (F_th) for the small particles can be expressed as:

where p is the gas pressure, λ is the gas mean free path, d_p is the particle diameter,▽T is the temperature gradient, and T is the absolute temperature of the particle.

The velocity resulting from the thermophoretic force is called the thermophoretic velocity (V_th). For small particles (d_p << λ), it is independent of particle size and directly proportional to the temperature gradient. The thermophoretic velocity in this regime can be expressed as:

where η is the gas viscosity and ρ_g is the gas density.

How can we make a "small particle" of a given size move faster (i.e., higher velocity) through thermophoresis?