Numerical Simulation of Flows of Drops and Bubbles

An unsteady viscous incompressible two-phase flow is directly simulated using a commercial CFD package (FLUENT). Thereby, the interface between gas and the fluid is captured with the Volume-of-Fluid (VOF) method. In the case of very small Weber numbers, where the capillary forces prevail over the inertial forces, the VOF method encounters severe numerical difficulties. With the vanishingly small inertia terms, the otherwise negligible numerical inaccuracies in the discretized representation of the gas-liquid interface lead to unphysical currents. Using the standard VOF-method as implemented in the employed CFD-code the numerical instabilities induced by these "parasitic" currents impeded the simulation of the slow formation of a single air bubble in water, where the Weber number is small due to the small volumetric air feed stream. The velocities associated with the spurious currents finally distorted the bubble surface thoroughly. Alternatively, the formation of a bubble in the limit of a vanishing Weber number can be handled appropriately assuming a quasi-static behaviour. Thereby, neglecting inertial forces, the equations of motion can be reduced to the Young-Laplace equations, whose solution allows to evaluate the temporal evolution of the bubble's volume for varying the capillarity at the liquid-air-solid contact point. The obtained quasi-steady results could be compared with the corresponding experimental data.