Abstract for Mass Action and Conservation of Current February 23-2 2015 .docx


Electronic technology has remade our world in fifty years, increasing capability by factors of billions, unprecedented in human history. Electronics depends on models that precisely represent its devices and circuits. Circuit models are robust and work well over a wide range of conditions without changing parameters. Circuit models are based on the laws of electricity, conservation of charge, and Kirchoff's current law: current flow is exactly the same everywhere in a series of devices (with two terminals, like diodes or ionic channels). Interruptions anywhere stop current everywhere, even far away. Electrical forces and potentials change automatically to ensure the same current flows everywhere (in a series system). Succinctly, for steady flows the divergence of the vector field of current is zero. Chemical and biochemical models have been built on conservation of matter, expressed as the law of mass action, with constant rate constants. Chemical and biochemical technology has made striking progress by making compounds, not so much by making devices.
Device design in the chemical world is difficult because the rate constants of the law of mass action are found experimentally to change from one set of conditions to another. The law is not robust in most cases and cannot serve the same role that circuit models do in our electrical technology. The law of mass action does not automatically conserve current, as is clear from the mathematics of a simple case, chosen to illustrate the issues involved: Consider the flux from A to B and from B to C in the simple series reaction A ====> B ====>C.   They are not equal in general. Of course, there are some series of reactions in which current is conserved and thus the same everywhere. The Appendix identifies special symmetrical cases in which charge flow is conserved. The law of mass action, however, does not seem to 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 (analyzed with law of mass action), and so does not obey Kirchoff's current law. The Appendix also evaluates consequences when current flow is not conserved. I fear classical models of many reactions will be in peril, when current flow is examined. 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 developed by Chun Liu, more than anyone else, should allow the development of successful models of chemical, biochemical, and biological systems. 
I believe robust models and device designs in the chemical world will not be possible until the law of mass action and Kirchoff's current law are embedded together in a consistent variational model of energy and dissipation.