Bubble buoyancy driven motion

Ryskin, G., and Leal, L. G., Numerical solution of ffee-boundary problems in fluid mechanics. Part II, Buoyancy-driven motion of a gas bubble through a quiescent liquid. J. Fluid Mech. 148, 19 (1984b). 

A second problem, closely related to Stokes problem, is the steady, buoyancy-driven motion of a bubble or drop through a quiescent fluid. There are many circumstances in which the buoyancy-driven motions of bubbles or drops are of special concern to chemical engineers. Of course, bubble and drop motions may occur over a broad spectrum of Reynolds numbers, not only the creeping-flow limit that is the focus of this chapter. Nevertheless, many problems involving small bubbles or drops in viscous fluids do fall into this class.23... 

In this section, we begin by considering the buoyancy-driven motion of a single gas bubble or drop through an otherwise stationary viscous fluid under the assumption that the bubble or drop shape is nearly spherical. We denote the viscosities and densities of the two fluids as /x, /x, p, and p with the variables with carets corresponding to the fluid inside the drop. In this section, we also assume that the interfacial tension, which we denote as y, is uniform at the drop surface, and that the Reynolds numbers for both the interior and exterior flows are sufficiently small that the creeping-motion approximation can be applied for both fluids. Under these circumstances, experimental evidence shows (and we will assume) that the drop or bubble will translate with a constant velocity U. In addition, though we must consider the shape of the drop to be unknown, we may also anticipate that it will be axisymmetric about an axis that is collinear with the velocity vector U. 

A qualitative explanation for this observation was discovered many years ago by Frumkin and Levich,30 who carried out experiments on buoyancy-driven motion of gas bubbles in... 

M. Hemmat and A. Borhan, Buoyancy-Driven Motion of Drops and Bubbles in a Periodically Constricted Capillary, Chem. Eng. Commun., 150 (1996). 

Surface active agents (surfactant) are either present as impurities that are difficult to remove from a system or they are deliberately added to fluid mixtures to manipulate interfacial flows. It has been well known that the presence of surfactant in a fluid mixture can critically alter the motion and deformation of bubbles moving through a continuous liquid phase. Probably, the best-known example is the retardation effect of surfactant on the buoyancy-driven motion of small bubbles. Numerous experimental studies have shown that the terminal velocity of a contaminated spherical bubble is significantly smaller than the classical Hadamard-Rybczynski prediction... 

S. Tasoglu, U. Demirci and M. Muradoglu, The Effect of Soluble Surfactant on the Transient Motion of a Buoyancy-Driven Bubble, Phys. Fluids, 20, 040805 (2008). 

Reviews of thermocapillary migration may be found in Refs. 24 and 25. The book by Subramanian and Balasubramaniam [26] provides discussions of both thermocapillary migration and buoyancy-driven bubble motion. 

Sankaranarayanan et al. [116] reported LBM results for the motion of buoyancy-driven bubbles in a quiescent liquid. Periodic boundary conditions... 

Yuan and Prosperetti [140] used a hybrid spectral-finite difference method to simulate the motion of two identical buoyancy-driven bubbles that were... 

Li et al. 48) studied how 1.0 pm particles of polystyrene and poly(methyl methacrylate) interacted when they were melt processed at 180 °C. They observed by confocal microscopy on a hot stage that there was a preferential motion for particles, which they attributed to a buoyancy-driven flow because of the 10% density difference between the polymers. Jang et al. had made a similar observation 49), Li et al. did not consider possible surface-tension induced convection or that droplets could migrate in a temperature gradient, as has been observed by Balasubramaniam et al. for the thermocapillary migration of bubbles 50),... 

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