Conservation of Charge and Conservation of Current

TL;DR

This paper discusses the relationship between charge and current conservation, emphasizing the importance of explicitly enforcing current conservation in models of complex fluids and environments to improve accuracy and numerical stability.

Contribution

It provides a universal derivation of current conservation and advocates for its explicit inclusion in models of charge movement in non-ideal materials.

Findings

Classical models often fail to conserve current.

Enforcing current conservation can prevent numerical artifacts.

Explicit conservation laws improve modeling accuracy.

Abstract

Conservation of current and conservation of charge are nearly the same thing: when enough is known about charge movement, conservation of current can be derived from conservation of charge, in ideal dielectrics, for example. Conservation of current is enforced implicitly in ideal dielectrics by theories that conserve charge. But charge movement in real materials like semiconductors or ionic solutions is never ideal. We present an apparently universal derivation of conservation of current and advocate using that conservation law explicitly as a distinct part of theories and calculations of charge movement in complex fluids and environments. Classical models using ordinary differential equations rarely satisfy conservation of current, including the chemical kinetic models implementing the law of mass action and Markov models. These models must be amended if they are to conserve current. Strict enforcement of conservation of current is likely to aid numerical analysis by preventing artifactual accumulation of charge.