Mathematical approach to zone boundary of isotachophoresis system

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Abstract
A mathematical approach to the behavior of isotachophoretic and counter ion components in the steady state of isotachophoresis of weak acids was developed. In steady state, the partial time derivative can be replaced by the ‐ν times χ derivative, where ν is the velocity of isotachophoresis. Application of this relation to mass balance equations of the components gave the expression of concentration gradients as functions of concentrations of the components, conductance and the H+ ion concentration gradient. The results were inserted into the χ derivative of the electric neutrality equation and the electric current equation, including both electrophoretic and diffusional currents. These equations were solved for conductance and H+ ion concentration gradients and the latter quantities could be expressed as functions of concentrations of the components. Thus, concentration gradients of the components were calculable from the concentrations. Given proper initial or boundary conditions for the concentrations of the components, numerical integration gave pH, conductance and concentration profiles of the components. The results were in agreement with those of capillary isotachophoresis experiments.