Similarity solutions of radially symmetric two-phase flow (Q1804268)

When both the diffusivity \(D\) and fractional flow function \(f\) have a power law dependence on the water content \(\theta\), i.e. \(D= D_ 0 \theta^ \alpha\) and \(f= \theta^{\alpha+1}\), the nonlinear transport equation for radially symmetric two-phase flow can, in certain circumstances, be reduced to a weakly coupled system of two first order nonlinear ordinary differential equations. Numerical solutions of these equations for a constant flux boundary condition and comparison with experimental data are given. We show that the existence of some exact solutions is due to the presence of a Lagrangian symmetry.