Mass transfer from bubbles and drops suspended in a liquid

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Johns Hopkins University
The objective of this dissertation is the study of different phenomena related to the dissolution of bubbles and drops in liquids and to their influence on the dynamics of buoyant plumes. While the motivation for the work has been the massive oil spill caused by the Deepwater Horizon accident in the Gulf of Mexico in 2010, the results presented are of a fundamental nature and, therefore, of a broader relevance and applicability. The dissertation is divided into two main parts, the first one devoted to the study of single drops and bubbles, the second one to collective phenomena involving drops and bubbles. The first problem considered is that of the dissolution of a single two-component drop. Assuming phase equilibrium at the interface between the drop and the surround- ing ambient liquid, we can accurately capture the dissolution rate of each component despite the difficulty introduced by the mutual interference of the drop components in determining their chemical potential and, therefore, their solubility. In the course of this work, we discovered a new memory term in this type of diffusive processes which arises when the interface concentration is time-dependent. This realization has motivated us to extend the study of this effect to the case of gas bubbles in the chapter that follows. In the second part of the dissertation we broaden the scope of our study by focusing on a larger scale. Instead of single drops or bubbles, we study the collective behavior of buoyant plumes constituted by bubbles or drops. The collective rise of these entities lifts the ambient liquid forming a rising plume. An intrusion layer can form at a certain depth when the ambient liquid density is stratified. The intrusion layer is due to the insufficient buoyancy provided by the discrete phase. As the plume rises, its buoyancy decreases by the entrainment of the ambient liquid. At a certain height above the source, which we term the neutral height, the buoyancy of the plume vanishes while the accumulated momentum does not. Thus, the plume continues to rise to the so-called peel height, before falling back to form an intrusion. An important fact, which does not seem to have been previously recognized in the literature, is that the intrusion height is usually above the neutral height. This fact is due the entrainment of additional ambient liquid during the inertial rise above the neutral level. Once it reaches the peel height, therefore, the mean density of the plume liquid is less than that at the neutral height so that the intrusion forms above the neutral height. This realization explains why the measured intrusion heights are found so often to be significantly above the theoretical predictions. Another interesting effect identified in our study is the importance of the drop or bubble material dissolved in the liquid in maintaining, at least partially, the buoyancy lost with the dissolution of the drops or bubbles. Since, in the modeling of plumes, we have used an averaged form of the balance equations, we have devoted the last chapter of the work to the general problem of averaging in multiphase flow obtaining a general expression for the non-convective fluxes of mass, momentum and energy. The main result is the elucidation of the role played by the total mixture flux in determining the specific fluxes for each phase.
mass transfer, multiphase, drop, bubble