Phase boundary layer, volume related

Reactions carried in aqueous multiphase catalysis are accompanied by mass transport steps at the L/L- as well as at the G/L-interface followed by chemical reaction, presumably within the bulk of the catalyst phase. Therefore an evaluation of mass transport rates in relation to the reaction rate is an essential task in order to gain a realistic mathematic expression for the overall reaction rate. Since the volume hold-ups of the liquid phases are the same and water exhibits a higher surface tension, it is obvious that the organic and gas phases are dispersed in the aqueous phase. In terms of the film model there are laminar boundary layers on both sides of an interphase where transport of the substrates takes place due to concentration gradients by diffusion. The overall transport coefficient /cl can then be calculated based on the resistances on both sides of the interphase (Eq. 1) ... 

Equations relating x and t have been derived for simple geometrical systems assuming (1) the reaction rate is phase-boundary controlled, (2) the reaction rate is proportional to the surface area of the fraction of unreacted material, and (3) the nucleation step occurs virtually instantaneously so that the surface of each particle is covered with a layer of product. The models developed from the foregoing boundary conditions are termed phase boundary or contracting volume kinetic models. For a sphere reacting from the surface inward ( ) the relationship between x and t is... 

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