The essence of Isocon line and principle for selection of immobile components

Jilin Duan

School of Earth Sciences，East, China University of Technology，Nanchang，330013，China

Yanpeng Liu

State key laboratory of Nuclear Resources and Environment, East China University of Technology，Nanchang，330013，China

Corresponding Author:

## Abstract

Mass balance is of great significance in earth sciences. Isocon method is simple and efficient in mass-transfer calculation. However, problems exist in the identification of immobile components, the choice of the parental sources' compositions, and visualisation. This paper demonstrated that mobility is a relative concept, and the distribution coefficient is the characteristic quantity to describe component mobility. Absolute immobile components are those components with distribution coefficients approaching infinity. The general straight line connecting the origin to the data point of any component carries information on the mass mobility of the component and the evolution degree of the system. Isocon line is a special case of such straight lines. The relationship between final evolved concentrations and the original concentrations is expressed by an equation deduced from mass conservation law and component conservation law, which says the final evolved concentration is determined by the original concentration, distribution coefficient, and the evolution degree. This equation is suitable for all the evolution processes, as long as its mass conserved. Three special Isocon lines were defined, initial Isocon line is the reference line for all the other Isocon lines, absolute Isocon line reflects the evolutionary degree and is formed by absolute immobile components, and relative Isocon line is formed by components having the same/similar distribution coefficients. The components lying on one relative Isocon line are relative immobile to each other, and their ratio equals the original ratio in the initial system. The principle on selection of approximation of absolute immobile components was proposed based on the relationship between the slope and distribution coefficient. A rough knowledge framework on mobility and Isocon analysis was revised and reorganized.08 Jan 2024Submitted to *ESS Open Archive * 02 Feb 2024Published in *ESS Open Archive *