Casteel-Amis equation: Its extension from univariate to multivariate and its use as a two-parameter function

The report describes the background of the empirical Casteel-Amis equation and its application to fitting experimental data of conductivity as a function of salt content in electrolytes. It further summarizes the attempts since its publication to extend the equation from a univariate to a multivariate function to include additional variables such as temperature and solvent composition, focusing on that to extend it to a bivariate function of salt content and solvent composition with examples from the solutions of LiPF6, LiBF4, LiBOB, Et4NPF6, and Et4NBF4 in propylene carbonate (PC) + diethyl carbonate and in PC + ethylene carbonate and LiClO4 in PC + acetonitrile. In addition, I discuss, along with experimental data and functional analysis, the validity of using this equation as a two-parameter function in relation to the range of salt content.