Homogeneous reference fluid approximation

Minimization of the functional in Eq. (57) gives the local structure in the homogeneous reference fluid approximation (HRFA) (Ramirez and Borgis, 2005)... 

As a first approximation, the analysis in reference [68] uses the well-known model of Davidson and Harrison [65] in which the bubble is assumed to be a spherical cavity without particles and in which the dispersed phase is characterized by uniform concentration < )o everywhere outside the bubble. Relative interstitial fluid velocity, u, and mean particle velocity, w, can then be found on the basis of 1) a simple filtration flow model for a homogeneous porous body containing a spherical cavity, and 2) an ideal fluid model for flow around a sphere. In particular, the vertical components of these velocities along vertical axis z of the coordinate system having its origin at the bubble center are ... 

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