Faxen theorem

The expressions for e and were obtained by using the generalized Faxen theorem giving the force experienced by a particle of arbitrary shape into a fluid imder non-stationary flow conditions (Mazur Bedeaux, 1974 Santamaria Holek, 2005). For spherical particles at low Reynolds numbers, e = el, e is given by... 

When the oscillatory flow is slow enough, by using Faxen s theorem it was shown that the friction coefficient depends on the frequency (cu) in the form (Mazur Bedeaux, 1974)... 

Mazur, P. Bedeaux, D. (1974). A generalization of faxen s theorem to nonsteady motion of a sphere through an incompressible fluid in arbitrary flow, Physica A 76 235-246. 

Note that Faxen s theorem is valid for any flow field uj(r) satisfying the Stokes equations. Using Eq. (9.23) in Eq. (9.24) and comparing with Eq. (9.21), one obtains... 

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