First Passage Times and Breakthrough Curves Associated with Interfacial Phenomena

TL;DR

This paper develops a mathematical framework to analyze first passage times and breakthrough curves in heterogeneous environments with interfacial discontinuities, relevant to physical and biological sciences.

Contribution

It introduces a novel mathematical approach to model empirical phenomena involving interfacial effects on advection and dispersion.

Findings

Framework successfully models interfacial phenomena

Provides insights into first passage time behaviors

Applicable to diverse physical and biological systems

Abstract

Advection and dispersion in highly heterogeneous environments involving interfacial discontinuities in the corresponding drift and dispersion rates are described through disparate examples from the physical and biological sciences. A mathematical framework is formulated to address specific empirical phenomena involving first passage time and occupation time functionals observed in relation to the interfacial parameters.