transport mechanisms, the slip velocity (velocity between gas and particle) caused by thermophoresis can be found from [Talbot et al., 1980; Friedlander, 2000]: UTP = mol k (17+ C,(2) k₁ P -2C,V = V k (1+6C Kn) 1+2 +4C, Kn where d is the particle diameter, kp is the thermal conductivity of the particle, all properties without a subscript represent the gas, and C, 1.17; C = 2.18; C = 1.14. Kn₁ = 2/d πΜ 2R T u VT T +C, (2Kn) C- 1/2 P (Knudsen number) (1.5.10) (Gas molecular mean free path) C=1+2Kn [1.257 +0.4cxp(-0.55/ Kn)] (Cunningham correction factor) Consider a flat and horizontal surface that is at a temperature of 398 K, and is cooled by a parallel air flow. The air has a pressure of 0.1 bar and a temperature of 253 K, and flows with a far-field velocity of 20 m/s with respect to the surface. At a distance of 0.5 m downstream from the leading edge of the surface, calculate the thermophoretic velocity in the vertical (y) direction of a metallic spherical particle that is 0.5 µm in diameter and has the thermophysical properties of cupper, when it is 1 mm away from the surface. How does this velocity compare with the fluid velocity in the y direction?
Fig: 1