Some model problems are considered in order to investigate wetting failure in liquid–liquid systems. Three geometries are considered, two-dimensional two-phase shear flow, two-dimensional driven capillary rise, and both two- and three-dimensional two-phase driven cavity flow. In the first two cases, the two fluids are made equiviscous. The driven cavity flow is investigated for both equi- and non-equiviscous fluids. Three methods of analysis are used for the equiviscous case, an essentially exact Fourier series method, a quasi-parallel approximation and a phase-field model. The Fourier series validates the phase-field method in that they both give nearly identical results for onset of instability. At relatively large slip length divided by channel width ($10^{-2}$), the capillary number at which onset of wetting failure (entrainment of the receding fluid in the advancing) occurs is highly dependent on the type of flow. This dependence, however, appears to diminish rapidly as the slip length becomes smaller. The capillary number for the onset of instability is moderately dependent on gravity level.

Three-dimensional phase-field calculations are then discussed that show wetting failure through tipstreaming and splitting instabilities. Spot checks indicate that the onset points of two- and three-dimensional instabilities are very close. It is hypothesized that tipstreaming can be understood in part as a quasi-two-dimensional phenomenon.