Computational analysis of self-similar capillary-driven thinning and pinch-off dynamics during dripping using the volume-of-fluid method

Abstract

Drop formation and detachment involve large topological changes, including the formation of a fluid neck that thins down due to surface tension-driven flows, and at the neck pinch-off, properties like Laplace pressure display a finite time singularity. Accurately simulating large topological deformations and nonlinearities encountered during drop formation typically makes numerical simulations computationally demanding as resolving small features close to the pinch-off instant requires high resolution and accuracy. In spite of the inherent advantages in tracking interfaces, preserving mass and computational time needed, very few studies utilize the volume-of-fluid (VOF) method for drop formation studies as early practitioners reported convergence problems for fluids with viscosity greater than ten times water viscosity. In this contribution, we utilize the VOF method as implemented in FLOW-3D to simulate the prototypical free surface flow of dripping for Newtonian fluids, including viscosity values four orders of magnitude higher than water viscosity. We benchmark the simulated neck shape, neck evolution rate, and break-up length against experiments carried out as a part of this study. The pinch-off dynamics are determined by a complex interplay of inertial, viscous, and capillary stresses, and self-similar scaling laws that are contrasted here against both experiments and simulations often describe the dynamics. We show that the simulated radius evolution profiles match the pinch-off dynamics that are experimentally observed and theoretically predicted for Newtonian fluids for axisymmetric flows. Furthermore, we determine pre-factors for scaling laws, velocity, and deformation fields within thinning necks, and we show that pre-factors, as well as break-up time and length comparable to experiments can be simulated using the VOF method.