Rotne-Prager mobilities

Close to a planar surface with no-slip boundary condition, the traditional Rotne-Prager mobilities can no longer be employed. The velocity and pressure fields of a point force for this boundary condition were first derived by Lorentz more than 100 years ago [86]. Blake put these results into a modem form replacing the Oseen tensor by the appropriate Green function, now called Blake tensor [87]. The condition of a... 

This condition is guaranteed for the correct mobility matrix. However, the mobility matrix given by eqn (4.40) is an approximate one, and does not satisfy the inequality (4.1 ) in a certain configuration in which the beads are too close to each other. An improved formula which guarantees the inequality is proposed by Rotne and Prager. However, this correction is irrelevant for the asymptotic behaviour of N 1, which is determined by the hydrodynamic interaction between beads far apart from each other. Thus we shdl use eqn (4.40) for H, . 

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