Effect of the Wetting Layer on the Fingering Pattern in a Hele-Shaw Cell

摘要

The pattern formation of a radially growing interface in a Hele-Shaw cell is studied. In contrast to the previous studies based on the Young-Laplace equation, a boundary condition is employed that included the effect of the wetting layer of the displacing fluid in the cell. Under this boundary condition, a weakly nonlinear analysis is carried out and the time evolution of the interface is numerically calculated. These results, compared to those obtained in the previous studies, suggest that our model reflects the nonlinear features of the viscous fingering phenomena more precisely.