A Numerical Study of Two-Phase Stokes Flow in an Axisymmetric Flow-Focusing Device
Physics of Fluids, 18 (7):
077103+ (2006)DOI: 10.1063/1.2214461
Abstract
We present a numerical investigation of the time-dependent dynamics of the creation of gas bubbles in an axisymmetric flow-focusing device. The liquid motion is treated as a Stokes flow, and using a generic framework we implement a second-order time-integration scheme and a free-surface model in MATLAB, which interfaces with the finite-element software FEMLAB. We derive scaling laws for the volume of a created bubble and for the gas flow rate, and confirm them numerically. Our results are consistent with existing experimental results by Garstecki et al. Phys. Rev. Lett. 94, 164501 (2005) , and predict a scaling yet to be observed: the bubble volume scales with the outlet channel radius to the power of 4 and the surface tension. Our axisymmetric simulations further show that the collapse of the gas thread before bubble snap-off is different from the recent experimental results. We suggest that this difference is caused by differences in geometry between experiments and the simulations.