Energy exchange in a dual flow diffusion process that consists of particles of the same nature divided into two different microstates

TL;DR

This paper introduces a novel model for particle systems with two microstates, incorporating energy exchange and a new potential, governed by a fourth order PDE, ensuring mass conservation in the dynamics.

Contribution

It presents a new theoretical framework for dual microstate diffusion with energy exchange, including a fourth order PDE with time-dependent parameters.

Findings

The model avoids violations of mass conservation.

Solutions are governed by a fourth order PDE with novel parameters.

The approach extends classical diffusion to include microstate energy dynamics.

Abstract

This article presents a new approach to the dynamics of a particle system, divided into two distinct microstates spreading out in a homogeneous medium. The particles belonging to the main microstate spread according to classical Fick's law and the complementary set moves excitedly by a new potential. Each set is associated with a certain energy level. The particles can move between the two sets, introducing a third flow that is internal to the system. The governing equation is a fourth order PDE containing two new parameters, which can be time-dependent functions, in addition to the classical diffusion constant. It is shown that the solutions can avoid violations of the mass conservation requirements.