Chemical-reactor theory recognizes three ideal reactor types: batch reactors, which are filled with reactants, continuously stirred during the reaction, and then emptied of products after a given reaction period; plug-flow reactors (PFR's), in which reactants continuously enter and products continuously exit with no mixing along the flow path; and continuous-flow, stirred-tank reactors (CSTR's), in which reactants continuously enter and products continuously leave a stirred vessel. Performance equations for these reactors, together with kinetic models for simple enzymatic catalysis and microbially mediated (autocatalytic) digestive fermentation, reveal necessary functional relationships among initial concentrations of the limiting food component, gut volume, throughout time or gut holding time, and digestive reaction kinetics. We use these models to suggest optimization constraints for digestion, analogous to those of optimal foraging theory. Two general predictions are possible. To sustain the greatest digestive production rate in minima of throughout time and gut volume, an animal dependent on its own digestive enzymes should function as a PFR. Animals fermenting refractory materials should combine a CSTR and a PFR in series at all but the slowest throughput rates, when a PFR will suffice.
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