From Homogeneous to Heterogeneous Flow

Gezork, KM., Bujalski, W., Cooke, M., and Nienow, A.W. (2000), The transition from homogeneous to heterogeneous flow in a gassed, stirred vessel, Chemical Engineering Research Design, 78(3) 363-370. 

Fig. 10.3 Photographs of a homogenous, saturated sand pack with seven dye tracer point injections being transported, under a constant flow of 53 mL/min, from left to right times at (a) t=20, (b) t= 105, (c) t= 172, (d) t=255 min after injection. Internal dimensions of the flow cell are 86 cm (length), 45cm (height), and 10cm (width). Reprinted from Levy M, Berkowitz B (2003) Measurement and analysis of non-Fickian dispersion in heterogeneous porous media. J Contam Hydrol 64 203-226. Copyright 2003 with permission of Elsevier...

A careful analysis of the current portfolio of one major pharmaceutical company indicates that about 60% of the chemistry is suitable for continuous processing. About 50% of this chemistry is homogeneous and therefore readily transferable to existing continuous processing technology. The remaining 50% is heterogeneous and will therefore require implementation of some of the current advances in continuous flow equipment such as oscillatory flow reactors [13]. Technically, the transfer of these processes from batch to continuous could happen within... 

The mathematical difficulty increases from homogeneous reactions, to mass transfer, and to heterogeneous reactions. To quantify the kinetics of homogeneous reactions, ordinary differential equations must be solved. To quantify diffusion, the diffusion equation (a partial differential equation) must be solved. To quantify mass transport including both convection and diffusion, the combined equation of flow and diffusion (a more complicated partial differential equation than the simple diffusion equation) must be solved. To understand kinetics of heterogeneous reactions, the equations for mass or heat transfer must be solved under other constraints (such as interface equilibrium or reaction), often with very complicated boundary conditions because of many particles. 

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