Jonathan Lester Brockwell

A numerical study of parameters affecting gas bubble dissolution

Abstract The mass transfer driven dissolution of a gas bubble containing either a single component or a multicomponent mixture, and which can include the presence of a nonsoluble gas, is analyzed by a finite difference procedure. Various effects including surface tension, gas expansion, and the presence of solvent vapor are examined. The predicted results with inclusion of these effects compare favorably with available experimental data and are compared with the results obtained using approximate solutions. For multicomponent gas bubble dissolution, it is found that the conventional assumption that neglects the gas expansion effect inside the bubble may lead to an erroneous prediction of the time-dependent bubble radius and concentration. The dissolution process is initially governed by solubility. However, at large times, the diffusivity and the concentration difference in the liquid are important. For a bubble containing a nonsoluble gas, the results show that even a small amount of this species will alter the behavior of bubble shrinkage. The final radius is dependent upon the content of the nonsoluble gas and the saturation condition of the liquid.

The transient motion of a spherical fluid droplet

Abstract A numerical method is developed for investigation of the unsteady motion of a spherical fluid droplet under the influence of gravity. This study extends previous work valid for creeping flow to moderate Reynolds number. The unsteady flow fields inside and outside of the fluid sphere are described by the two-dimensional, axisymmetric Navier-Stokes equations in the form of vorticity and stream function, along with the equation of motion of the droplet. The governing equations are approximated by a central difference and a second-order upwind difference, and are solved iteratively using the Gauss-Siedel and secant methods. Numerical results of the time-dependent vorticity, stream function and drop velocity are presented for a water droplet moving through air and for an air bubble rising in water. The steady state drop velocity and the drag coefficient at various Reynolds numbers are examined, and they are shown to agree very well with previous results.

Mass transport phenomena between bubbles and dissolved gases in liquids under reduced gravity conditions

This paper will describe the experimental and analytical work that has been done to establish justification and feasibility for a Shuttle mid-deck experiment involving mass transfer between a gas bubble and a liquid. The experiment involves the observation and measurement of the dissolution of an isolated, immobile gas bubble of specified size and composition in a thermostatted solvent liquid of known concentration in the reduced gravity environment of earth orbit. Methods to generate and deploy the bubble have been successful both in normal gravity using mutually buoyant fluids and under reduced gravity conditions in the NASA Lear Jet. Initialization of the experiment with a bubble of a prescribed size and composition in a liquid of known concentration has been accomplished using the concept of unstable equilibrium. Subsequent bubble dissolution or growth is obtained by a step increase or decrease in the liquid pressure. A numerical model has been developed which simulates the bubble dynamics and can be used to determine molecular parameters by comparison with the experimental data. The primary objective of the experiment is the elimination of convective effects that occur in normal gravity. The results will yield information on transport under conditions of pure diffusion.