The thermophoretic forces acting on a bispherical system

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Abstract
The thermophoretic forces acting on two spheres rigidly joined at their point of contact has been calculated and also the thermophoretic velocity which the particle acquires when moving unrestrained. The problem divides into two distinct parts: (i) calculation of the temperature distribution in and around the bispherical system due to the imposed temperature gradient and (ii) the solution of the viscous flow problem when the creep effect is included in the fluid boundary conditions at the surface of the body. The author obtains explicit expressions for the force and velocity which depend only on the solution of a second-order differential equation. Two special cases can be solved exactly: namely when the thermal conductivity of the particle and the gas are the same and also when the gas thermal conductivity is very much less than that of the body. A simple approximation to the differential equation is also derived, which leads to accurate results over a range of conductivities of practical interest. The accuracy of the equivalent-sphere approximation is assessed and found to be accurate to better than 10%.