Fluid displacement by high Reynolds number bubble motion in a thin gap

Abstract

The fluid displacement associated with the injection and subsequent translation of high Reynolds number bubbles in a thin gap is examined experimentally, and compared with a theoretical model based on a two-dimensional inviscid flow calculation. In the experiments, air bubbles are injected and rise through an aqueous solution bound in a thin gap. Particular attention is given to the parameter regime characterised by the steady rectilinear motion of oblate elliptical or elliptical cap bubbles which transport a closed volume of fluid which trails the bubble in the form of a stable primary wake, and by laminar flow in the suspending fluid. The fluid displacement is measured by digitally tracking either particles suspended in the fluid, or the distortion of an initially horizontal fluid–fluid interface. While the fluid transport associated with the narrow region of viscous influence, or secondary wake, trailing the bubble is observed to contribute to the total fluid displacement over long times, its contribution is minimized by the influence of the channel walls. We thus focus on the fluid displacement associated with the irrotational component of the flow, which is described in terms of two components: a positive “drift” component which is localized near the point of crossing, and a negative “reflux” component required by continuity in a bounded domain. The experimental observations confirm a number of theoretical predictions concerning the fluid displacement accompanying high Reynolds number bubble motion. At distances greater than half the channel width from the point of injection, both the injection-induced displacement and the reflux are spread uniformly across the channel width. The reflux amplitude depends on the size of the primary wake, the drift volume and the channel width. The drift volume does not depend on the detailed shape of the bubble and wake or on the channel width, but is uniquely set by the cross-sectional area of the compound body composed of bubble plus wake. The shape of a distorted material surface depends weakly on the compound body shape, and becomes more peaked as the compound body becomes more oblate. This indicates that the presence of a primary wake adjoining a bubble will influence the longitudinal dispersion rather than the total drift volume. The relevance of this study for the analogous three-dimensional problem is discussed, and a heuristic model of mixing by high Reynolds number bubbles in a bounded domain is developed. The importance of fluid transport in the secondary wake, which was neglected in the theoretical model, is discussed in detail.