Basset, Boussinesq, and Oseen BBO 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] 

It is suggested that the pressure gradient may be estimated from the Navier-Stokes equation of a single-phase fluid by [Corrsin and Lumley, 1956] 

In gas-solid flows well beyond the Stokes regime, the effect of convective acceleration of the gas surrounding the particle is important. To incorporate this effect into the preceding formulation, modifications of the expressions for the Stokes drag, carried mass, and Basset force in the BBO equation are necessary [Odar and Hamilton, 1964]. The modified BBO equation takes the form [Hansell et al., 1992] 

For a simple harmonic motion at Rep 62, correlations of Ci and Cb are suggested as [Odar and Hamilton, 1964] 

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