# Mesoscale Models

### Mesoscale ('Latin: intermediate') models capture phenomena that are right on the edge between where matter is considered a collection of atoms, and where it can be considered a smooth, continuous medium. An important example of this are interfaces between phases, and the associated energy and effects.

### These models are typically derived from considering the total energy of the system, and can naturally incorporate thermodynamic (CALPHAD-type) potentials. By applying the theory of irreversible processes, a robust mathematical approach, a thermodynamically consistent model of the system's evolution can be derived in such a way to capture multiphysics effects.

## Integrating thermodynamics with phase-field and transport models

Phase changes and transport processes like heat balance and diffusion are driven by thermodynamic forces. In this work models are developed which integrate equilibrium thermodynamic data into phase-field and transport models. A central issue is how to understand and control the interfacial energy contributions.

The image below to the left is a typical free energy diagram for a binary two-phase system. The green line shows how the components are distributed between phases at equilibrium. The images to the right are different ways to extend the curves to the left into a continuous free energy surface with a trough along the equilibrium.

## The included phase model

A commonly encountered situation is a phase on sitting on the boundary between two other phases, like water beading on the hood of a car. This new model simplifies this 3D problem into a 2D one by projecting the 'included' phase onto the boundary, resulting in substantial computational efficiency.

## Lithium-oxygen electrodes reactions for a advanced battery type

The Lithium-oxygen reaction is interesting for advanced batteries since oxygen is available in the air, which could mean weight and size reduction. This work looks at couple reaction-diffusion and growth of particles on the cathode surface.

The image to the right is the schematic for the reaction, and below is the predicted chemistry in the electrolyte as particles nucleate and grow.