Biological systems, chemical equilibrium active transport

In the case of the fast binary reaction we could eliminate the reaction term from the reaction-diffusion-advection equation. But in general this is not possible. In this chapter we consider another class of chemical and biological activity for which some explicit analysis is still feasible. We consider the case in which the local-reaction dynamics has a unique stable steady state at every point in space. If this steady state concentration was the same everywhere, then it would be a trivial spatially uniform solution of the full reaction-diffusion-advection problem. However, when the local chemical equilibrium is not uniform in space, due to an imposed external inhomogeneity, the competition between the chemical and transport dynamics may lead to a complex spatial structure of the concentration field. As we will see in this chapter, for this class of chemical or biological systems the dominant processes that determine the main characteristics of the solutions are the advection and the reaction dynamics, while diffusion does not play a major role in the large Peclet number limit considered here. Thus diffusion can be neglected in a first approximation. 

The principle of Le ChStelier asserts that in general a system will react to lessen the effect of a stress on an intensive variable, if it can do so. This effect was illustrated by considering the shift in equilibrium by changing the temperature or the pressure on a system and by adding a reactant or product to the system. The application of the thermodynamics of chemical equilibrium to biological processes was illustrated through a discussion of the coupling of chemical reactions and active transport. 

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