Experimental and simulation studies of the shape and motion of an air bubble contained in a highly viscous liquid flowing through an orifice constriction

This paper reports an experimental and computational study on the shape and motion of an air bubble, contained in a highly viscous Newtonian liquid, as it passes through a rectangular channel having a constriction orifice. The magnitude of the viscosity ratios, $\lambda$, and capillary numbers, CA, explored is high: 5.5 x 10$^{5}$ < $\lambda$ < 3.9 x 10$^{6}$ and 2.9 < Ca < 35.9 respectively. A multipass rheometer is used for the experimental work: air bubbles are suspended in 10 Pa s and 70 Pa s polybutene viscosity standards and passed through an orifice-plate geometry constructed within an optical flow-cell. High levels of bubble distortion are observed, including bubbles that resemble ‘crescent moons’. Simulation work is carried out using an implementation of the volume of fluid method in the freely-available finite-volume computational fluid dynamics code OpenFOAM. Quantitative data pertaining to the motion and shape of the bubble was extracted from both the experimental and simulation work. Initially, a good match between numerical simulation and experimental work could not be obtained: this problem was alleviated by changing the viscosity averaging method from an arithmetic mean to a logarithmically-weighted arithmetic mean. Medium- and high-resolution simulations using this new viscosity averaging method were able to match experimental data with coefficients of determination, R$^{2}$, typically 0.898 < R$^{2}$ < 0.985.Funding is gratefully acknowledged from the EPSRC, grant EP/N00230X/1