Inclusion of viscous fingering in the macroscopic flow equations

1 Inclusion of viscous fingering in the macroscopic flow equations 

Recently, Vossoughi et al (1984) have incorporated Koval s central idea into a generalised convection-dispersion equation to describe both ordinary dispersive transport and viscous fingering. The form of their equation as it 

This model has been generalised even further by the inclusion of physical non-equilibrium effects in addition to viscous fingering by Sorbie et al (1987d) but this is not considered further here. 

Equation 7.38 is non-linear in the general case and analytic solutions are available only under the conditions of linear adsorption and no viscous fingering as discussed above. Numerical solutions must be used in the general case. 

It can be shown (Vossoughi et al, 1984) that the fractional flow of polymer is given by an expression of the following form. 

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