Numerical simulation of the head-on collision of two equal-sized drops with van der Waals forces

Abstract

The head-on collision of two equal-sized drops in a hyperbolic flow is investigated numerically. An axisymmetric volume-of-fluid (VOF) method is used to simulate the motion of each drop toward a symmetry plane where it interacts and possibly coalesces with its mirror image. The volume-fraction boundary condition on the symmetry plane is manipulated to numerically control coalescence. Two new numerical methods have been developed to incorporate the van der Waals forces in the Navier–Stokes equations. One method employs a body force computed as the negative gradient of the van der Waals potential. The second method employs the van der Waals forces in terms of a disjoining pressure in the film depending on the film thickness. Results are compared to theory of thin-film rupture. Comparisons of the results obtained by the two methods at various values of the Hamaker constant show that the van der Waals forces calculated from the two methods have qualitatively similar effects on coalescence. A study of the influence of the van der Waals forces on the evolution and rupture of the film separating the drops reveals that the film thins faster under stronger van der Waals forces. Strong van der Waals forces lead to nose rupture, and small van der Waals forces lead to rim rupture. Increasing the Reynolds number causes a greater drop deformation and faster film drainage. Increasing the viscosity ratio slows film drainage, although the effect is small for small viscosity ratio.