Mass Action and Conservation of Current

Abstract

The law of mass action is used widely. The law of mass action does not automatically conserve current, as is clear from mathematics of a simple case, chosen to illustrate the issues. The law of mass action does not force a series of chemical reactions to have the same current flow everywhere. Interruption of far-away current does not stop current everywhere in a series of chemical reactions, and so does not obey Maxwell equations. An additional constraint and equation is needed to enforce the global continuity of current flow. The additional constraint is introduced in this paper in the special case that the chemical reaction describes spatial movement through narrow channels. In that case, a fully consistent treatment is possible using a variety of models of charge movement. The general case must be dealt with by variational methods that enforce consistency of all the physical laws involved. Variational methods have only recently been developed to ensure that charge flow is conserved globally, along with mass, in dissipative systems like ions in solution or proteins. The Energy Variational Approach EnVarA should allow the development of more robust models of chemical, biochemical, and biological systems, making practical devices more easy to design and build. These difficulties arise away from equilibrium, when current flows, and the law of mass action is applied to a non-equilibrium situation, different from the systems considered when the law was originally derived. Non-equilibrium systems are important. Almost all of biology occurs away from equilibrium. Almost all devices of our technology function away from equilibrium. I believe robust models and device designs in the chemical world will not be possible until continuity of current is embedded in a generalization of the law of mass action using a consistent variational model of energy and dissipation.