Journal of Fluid Mechanics

Thermophoresis of particles in a heated boundary layer

L.  Talbot a1, R. K.  Cheng a2, R. W.  Schefer a2 and D. R.  Willis a3
a1 Mechanical Engineering Department and Lawrence Berkeley Laboratory, University of California
a2 Lawrence Berkeley Laboratory
a3 Mechanical Engineering Department, University of California

Article author query
talbot l   [Google Scholar] 
cheng rk   [Google Scholar] 
schefer rw   [Google Scholar] 
willis dr   [Google Scholar] 


A laser-Doppler velocimeter (LDV) study of velocity profiles in the laminar boundary layer adjacent to a heated flat plate revealed that the seed particles used for the LDV measurements were driven away from the plate surface by thermophoretic forces, causing a particle-free region within the boundary layer of approximately one half the boundary-layer thickness. Measurements of the thickness of this region were compared with particle trajectories calculated according to several theories for the thermophoretic force. It was found that the theory of Brock, with an improved value for the thermal slip coefficient, gave the best agreement with experiment for low Knudsen numbers, λ/R = O(10−1), where λ is the mean free path and R the particle radius.

Data obtained by other experimenters over a wider range of Knudsen numbers are compared, and a fitting formula for the thermophoretic force useful over the entire range 0 [less-than-or-eq, slant] λ/R [less-than-or-eq, slant] [infty infinity] is proposed which agrees within 20% or less with the majority of the available data.

(Published Online April 19 2006)
(Received October 15 1979)