Saffman Force and Other Gradient-Related Forces

3 Saffman Force and Other Gradient-Related Forces 

When a sphere moves in a flow where a velocity gradient, pressure gradient, or temperature gradient exists, additional forces related to these gradients can be as important as the drag force. 

In a shear flow with a constant shear rate, Rss can be estimated by K 

Besides the drag force, Basset force, and Saffman force, another force may act on the particle as a result of the existence of a pressure gradient in the fluid. Using the axisymmetric condition, the force on a differential element of a sphere in a pressure gradient field shown in Fig. 3.2 can be expressed by 

The minus sign indicates that the force is in the opposite direction of the pressure gradient [Tchen, 1947]. The significance of this force is evident, for example, when a shock wave propagates through a gas-solid suspension. 

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