Flow Around a Rising Clean Microbubble in a Vertical Square Tube

Flow structure around a rising clean microbubble in a vertical square tube is investigated on a fixed nonstaggered Cartesian grid system. A single set of three dimensional governing equations over the entire physical domain including the liquid, the air, and the bubble surface (the liquid-air interface) is formulated without smearing the bubble surface. There are three step functions in the problem, namely, the density jump, the viscosity jump, and the pressure jump across the bubble surface. A modified NAPPLE algorithm is proposed to handle the pressure jump on a fixed nonstaggered Cartesian grid system, while the density and viscosity jumps appearing in the momentum equations are solved with the extended weighting function scheme. This strategy prevents the occurrence of “parasitic current” on the bubble surface. Solutions of flow structure (velocity and pressure) are obtained for bubble diameters of less than 500 micrometers rising in quiescent pure water. The numerical result evidences that the distorted microbubble under study is of the oblate spheroid type. The distortion parameter is only 1.0006 when the bubble diameter is 250 micrometers. However, the surface tension force due to bubble distortion generates a large pressure jump across the bubble surface that dominates the flow around the bubble. It plays a role similar to the non-transpiration condition on a solid surface. The resulting terminal velocity of the bubble agrees excellently with the existing analytical solutions and numerical results.