Head-on Collision Of Two Equal-sized Drops With Van Der Waals Forces

Abstract

Drop collision is significant not only in natural processes, such as raindrop formation, but also in various engineering applications, such as chemical separation, spray coating, encapsulation, and drug delivery. In this study, head on collision of two equal-sized drops in a hyperbolic flow is investigated numerically. It is well known that van der Waals forces become important and govern coalescence when the thickness of the fluid film between the two drops falls into the range of several hundreds of Angstroms, 100-1000 A. We have developed two new numerical methods to introduce non-retarded van der Waals forces into the Navier-Stokes equations. An axisymmetric volume of fluid (VOF) method is used to simulate the motion of a drop toward a symmetry plane where it interacts with, and possibly coalesces with, its mirror image. A hyperbolic flow imposed initially and at the domain boundaries drives the motion. In the absence of van der Waals forces, the VOF boundary condition on the symmetry plane determines whether the two drops coalesce or bounce. One method used to include van der Waals forces is to apply the force on the drop as the negative gradient of van der Waals potential between the drops. The other method computes the force in terms of a disjoining pressure in the film which depends on the film thickness. A cut-off is used as the thickness of the film approaches zero to avoid singularity. Comparisons of the results of the two methods at various values of the Hamaker constant are presented. A comparison to results without van der Waals forces is also reported. In future work mesh adaptivity will be used to better resolve the film between the two drops. Transactions on Engineering Sciences vol 42, © 2003 WIT Press, www.witpress.com, ISSN 1743-3533