Boussinesq-Basset force

In summary, the Boussinesq-Basset, Brownian, and thermophoretic forces are rarely used in disperse multiphase flow simulations for different reasons. The Boussinesq-Basset force is neglected because it is needed only for rapidly accelerating particles and because its form makes its simulation difficult to implement. The Brownian and thermophoretic forces are important for very small particles, which usually implies that the particle Stokes number is near zero. For such particles, it is not necessary to solve transport equations for the disperse-phase momentum density. Instead, the Brownian and thermophoretic forces generate real-space diffusion terms in the particle-concentration transport equation (which is coupled to the fluid-phase momentum equation). 

The BBO equation delineates a sphere in linear motion at low Reynolds numbers [Basset, 1888 Boussinesq, 1903 Oseen, 1927], For a spherical particle, the BBO equation, based upon Eq. (3.37) with the replacement of the buoyancy force with the pressure gradient force, can be expressed as [Soo, 1990]... 

The history force was discovered independently by Boussinesq [18] and Basset [10] in their study of the oscillations of a rigid sphere in a viscous flow. 

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