Thermal force thermophoretic velocity

In a discussion of thermal-force theories it is necessary to address the problem of experimental data for the following reason. It has been known for some time that experimental thermal-force data determined by the Millikan-cell method [2.97, 98,137-139] differed from the data obtained by measuring the velocity of particle motion due to the thermal force (thermophoretic velocity) in various flow systems with different configurations [2.121,140,141]. 

To determine the thermophoretic velocity, Stokes law can be utilized by assuming that the Cunningham or slip correction factor (Eq. 5.3) is applicable for cases where Kn > 1. Thermophoretic velocity will be independent of particle diameter since Cc Kn(A + Q) when Kn > 1. Then, equating the thermal force (Eq. 11.8) with the resisting force (Stokes law) and solving for the thermophoretic velocity vT give (Talbot et al., 1980)... 

To determine thermophoretic velocity, the Stokes resisting force is equated with the thermal force. Then... 

DERJAGUIN and co-workers have offered the following explanation for the differences between their experimental data for the measured thermophoretic velocity and Millikan-cell measurements of thermal force. The values of thermophoretic velocity determined by DERJAGUIN and co-workers are usually from two to four times the corresponding values obtained by the Millikan-cell method. DERJAGUIN and coworkers have claimed that there are uncontrolled convection currents in the Millikan cell and cite the experiments of PARANJPE [2.142] who observed convection currents in the central portion between two parallel plates when the ratio of plate diameter to separation between the plates was less than 5 or 6. There are several reasons to discount this explanation. GIESEKE [2.139] has published experimental... 

It is still necessary to explain the large differences between the Millikancell thermal-force data and the thermophoretic-velocity measurements, principally of DERJAGUIN and co-workers. One possible explanation, which might explain some of the difference, lies in the theory and experiment of PHILLIPS [2.128]. PHILLIPS... 

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