Weakly nonlinear analysis on radially growing interface with the effect of viscous normal stress

Two-phase Hele-Shaw problem is studied as a model for a two-dimensional radially growing interface. Instead of the Young-Laplace equation, which has been employed in almost all previous studies concerning Hele-Shaw problem, we apply the normal stress balance and derive the new mode coupling equation for perturbation of the interface. In the present research, weakly nonlinear analysis is carried out and time evolution of the interfaces is numerically calculated. These numerical results suggest that our model reflects more exactly the nonlinear features of a radially growing interface, rather than the previous ones based on the Young-Laplace equation.