Preliminary Study of the Effects of a Reversible Chemical Reaction on Gas Bubble Dissolution
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Inc. OF SPACE
301
PRELIMINARY STUDY OF THE EFFECTS OF A REVERSIBLE CHEMICAL REACTION ON GAS BUBBLE DISSOLUTION MICHAEL C. WEINBERG Jet Propulsion Laboratory, 4800 Oak Grove Drive, Pasadena, California 91109 ABSTRACT A preliminary investigation of the effects of a reversible chemical reaction upon the dissolution of an isolated, stationary gas bubble in a glassmelt is presented. The exact governing equations, for the model system, are formulated and discussed. The approximate quasi-steady state version of these equations are solved analytically and bubble dissolution rates are computed. These results are compared with numerical solutions obtained from the finite difference form of the exact governing equations. INTRODUCTION Refining, or bubble removal from glassmelts is a topic of considerable practical interest to the glass industry. Rapid elimination of bubbles from melts could result in appreciable cost and energy savings. Thus, significant effort has been expended in an attempt to shorten refining times. A long standing technique which has been utilized for hastening bubble removal consists of the use of refining agents. Although the detailed mechanisms of refining agent action is not understood, it is clear that in most instances refining agents participate in chemical reactions with gases dissolved in
the melt.
Cable and coworkers [1,2] and Nemec [3,4] have
performed detailed experimental studies of the refining of soda lime melts using As2 03 and As2 03 in combination with NaNO 3 . In addition, numerous experimental studies have been performed which examined gas bubble behavior in glassmelts [5-10]. In order to fully describe chemical refining action it will not only be required to determine the relevant reaction kinetics, but also to elucidate the influence of these reactions upon gas bubble dissolution (growth). The effects of chemical reactions upon the mass transfer of gas to and from rising bubbles has been examined quite extensively [11-13]. Ruckenstein, Dang and Gill [13] for example, have studied two component bubbles and droplets as well as single component gas bubbles in reactive systems. In the latter case they obtained analytical solutions by invoking a thin boundary layer approximation and finding a similarity solution for this problem. In the case of the former problem identical techniques were used, but numerical methods were employed to solve the resulting integral equations. In the microgravity condition of space the buoyant rise of a gas bubble in a glass melt will be negligible on the timescale of most experiments. Hence, the determination of the behavior of a stationary gas bubble in a melt is
302 relevant for the understanding of glass refining in space. investigations have dealt with this topic.
However, few
Subramanian and Chi [14] have presented a detailed investigation of the dissolution of a stationary, isolated gas bubble enhanced by a first order irreversible chemical reaction. They considered the accuracy of various approximate solutions to the exact governing equations of
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