A phenomenological model is proposed for the rates of bubble coalescence and bubble break-up in turbulent gas-liquid dispersions. Bubble coalescence is modeled by considering bubble collisions due to turbulence, buoyancy, and laminar shear, and by analysis of the coalescence efficiency of collisions. Bubble break-up is analyzed in terms of bubble interactions with turbulent eddies. A method for the measurement of coalescence and break-up events in turbulent systems is described and used to test the validity of the proposed model. The measurement technique relies on the mixing of tracer gases within bubbles upon coalescence, in conjunction with Monte-Carlo simulations of coalescence events. Both distilled water and salt solutions are examined. Favorable agreement is found between the model and the individual coalescence and breakage rates, as well as with data obtained for the average bubble size and bubble size distribution. Michael J. Prince Harvey W. Blanch Department of Chemical EngineeringUniversity of California Berkeley, CA 94720Introduction Gas-liquid contactors find broad application as reactors and separation units in the chemical, mining, pharmaceutical and biochemical industries. In these systems the rate of transport of the gas to the liquid phase often limits productivity and is therefore a critical design criterion. Current design methods rely on empirical correlations which may not be confidently applied beyond the narrow range of operating conditions and geometries over which they were determined.The uncertainty in bubble column design arises from a lack of fundamental understanding of the hydrodynamics and rate processes which govern bubble size and thus interfacial area. Bubble size depends on a balance of coalescence and break-up rates in the vessel. No broadly applicable model for these rate processes in turbulent systems has yet been presented. This has been due to the inability to measure bubble coalescence and break-up in systems where high gas flow rates prevent direct visual observation.The objective of this study is to measure bubble coalescence and break-up rates in turbulent gas-liquid dispersions and to develop a model for these rate processes based on physicochemical and hydrodynamic principles. The ability of the model to adequately predict the individual experimental rate of coales- cence and break-up is used to judge its validity. In addition, the model is tested against its ability to'predict bubble size and bubble size distributions.The coalescence process is analyzed by examination of bubble collision events and the likelihood of collisions resulting in coalescence. Bubble break-up is examined in terms of bubble interactions with turbulent eddies. In addition to the theoretical development, an experimental method for the measurement of bubble coalescence and break-up rates in turbulent systems is described.The effect of inorganic electrolytes on coalescence and break-up rates is also examined. Much of the current interest in the prediction of bubble size stems from the desire t...

With the aim of understanding the contribution of enzymes to the cost of lignocellulosic biofuels, we constructed a techno-economic model for the production of fungal cellulases. We found that the cost of producing enzymes was much higher than that commonly assumed in the literature. For example, the cost contribution of enzymes to ethanol produced by the conversion of corn stover was found to be $0.68/gal if the sugars in the biomass could be converted at maximum theoretical yields, and $1.47/gal if the yields were based on saccharification and fermentation yields that have been previously reported in the scientific literature. We performed a sensitivity analysis to study the effect of feedstock prices and fermentation times on the cost contribution of enzymes to ethanol price. We conclude that a significant effort is still required to lower the contribution of enzymes to biofuel production costs.

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