The application of enzyme reaction, nonlinear diffusion models to the malting process

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We extend the classic Michaelis–Menten kinetics model of the enzyme-mediated conversion of substrate to product to situations in which the enzymes need to diffuse through the underlying structure to reach unconverted substrate and in which the diffusivity is greatly increased by the conversion. The work was prompted by the study of the germination and modification of barley grain that occurs during malting, but is broadly applicable. A nonlinear diffusion, enzyme reaction model of the modification process is proposed and some accurate approximate analytic solutions are derived. We find that a sharp modification front is set up between the modified and the unmodified regions of the barley grain. This front propagates with an almost constant speed through the medium and our findings are consistent with the available experimental observations.