Acrivos number expression

Lighthill-Acrivos Generalized Expression Acrivos Number.312... 

Acrivos and Taylor actually evaluated two additional terms in the inner expansion. Their expression for the correlation between Nusselt number and Peclet number is... 

O Brien (Ola) applied the Acrivos-Taylor analysis to the case where the Reynolds number, though small, is not identically zero as in the Stokes flow case. The analysis is vastly more complicated because, to any order in the Reynolds number, the velocity field v appearing in Eq. (298) is now expressed in terms of two, locally valid expansions [the inner and outer expansions of v given by the Proudman-Pearson analysis (PI 1)], rather than the single Stokes velocity field. For a solid spherical particle she obtains for small Pe and Re... 

Taylor and Acrivos (1964) found an approximate expression for applicable for small valnes of the Reynolds nnmbCT (= l/ap /fi ) and capillary number (= U]4gly). They first obtained the creeping flow solution that satisfied all boundary conditions, those at the drop-flnid intaface being satisfied at r = a. The normal stress balance (Equation 7.19), which was not used in this initial proce-dnre, was then applied, with evaluated at r = a to obtain a first approximation... 

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