Fig. 4.

Semilog plot showing the relationship between the generalized capillary number Ca* and λ. The solid line indicates the analytically predicted critical value of the generalized capillary number, which is a solution of the stability criterion derived from linear stability analysis. The symbols are the results obtained by the direct numerical simulations, where filled, half-filled, and open symbols represent the stable front, critical value of the generalized capillary number, and unstable front, respectively. Yellow and red regions mark analytically predicted stable and unstable regions, respectively, separated by the solid line predicted by Eq. 4. Insets illustrate the displacement front morphology at Ca = 3.2 × 10⁻⁶ computed by the direct numerical simulation.