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Mechanical approach to chemical transport

Significance It is useful to have a systematic and simple framework to describe transport and equilibrium in chemical systems. Here, we present a general Lagrangian-based approach to describe transport phenomena, while remaining consistent with chemical thermodynamics. Although we neglect heat flow independent of transport, the ease with which transport and equilibrium relations can be derived for any type of driving factors (electromagnetic, thermal, pressure, surface tension, etc.) should make this approach useful in physics, chemistry, biophysics, engineering, and even economics and social sciences. Nonequilibrium thermodynamics describes the rates of transport phenomena with the aid of various thermodynamic forces, but often the phenomenological transport coefficients are not known, and the description is not easily connected with equilibrium relations. We present a simple and intuitive model to address these issues. Our model is based on Lagrangian dynamics for chemical systems with dissipation, so one may think of the model as physicochemical mechanics. Using one main equation, the model allows a systematic derivation of all transport and equilibrium equations, subject to the limitation that heat generated or absorbed in the system must be small for the model to be valid. A table with all major examples of transport and equilibrium processes described using physicochemical mechanics is given. In equilibrium, physicochemical mechanics reduces to standard thermodynamics and the Gibbs–Duhem relation, and we show that the First and Second Laws of thermodynamics are satisfied for our system plus bath model. Out of equilibrium, our model provides relationships between transport coefficients and describes system evolution in the presence of several simultaneous external fields. The model also leads to an extension of the Onsager–Casimir reciprocal relations for properties simultaneously transported by many components.