Air entrainment driven by a converging rotational field in a viscous liquid

Abstract

A thorough physical understanding of gas entrainment within a liquid pool is established using a pair of fully submerged cylinders with an opposite but symmetric rotational field. An asymmetric version of such entrainment of gaseous filaments inside a liquid has been demonstrated in our earlier work [P. Kumar, A. K. Das and S. K. Mitra, Phys. Fluids 29, 022101 (2017)]. Here, our efforts focus on revealing the governing factors and understanding the stages of alteration from a stratified to an undulating interface for a wide range of symmetric cylinder rotations. Interfacial configurations such as an upper rounded crest, a bubble-ejecting jet, and a non-collapsible jet with an air pocket in the stagnant zone are obtained as the cylinder rotation increases. Near the critical capillary number, air pinch-off into a filament and subsequent stable collapse of this filament into bubbles were observed. As the rotation-driven capillary number increased, we noted the formation of an entrained jet of gaseous-phase forming air pockets in the region, which resulted in a diverging rotational field. Our analysis of the fluid stream explains the interfacial configurations and corresponding entrainment patterns based on fundamental physics. The power-law fit (Y = KXm) of the cusp profiles revealed close agreement with numerically obtained interfaces. We propose correlation coefficients as a function of the capillary number. We also assess the dependence of the entrainment pattern on cylinder submergence and spacing.