# Asymptotic reductions of the diffuse-interface model, with applications to contact lines in fluids

## TL;DR

This paper examines the diffuse-interface model's assumptions for contact line dynamics, revealing that the common isothermality assumption fails for some fluids like water, which impacts the model's applicability.

## Contribution

It provides an asymptotic reduction of the diffuse-interface model and tests the isothermality assumption for fluids where contact line models typically fail.

## Key findings

- Isothermality assumption does not hold for water and one other fluid.
- The work offers a refined understanding of contact line modeling.
- Implications for the validity of diffuse-interface models in fluid dynamics.

## Abstract

The diffuse-interface model (DIM) is a tool for studying interfacial dynamics. In particular, it is used for modeling contact lines, i.e., curves where a liquid, gas, and solid are in simultaneous contact. As well as all other models of contact lines, the DIM implies an additional assumption: that the flow near the liquid/gas interface is isothermal. In this work, this assumption is checked for the four fluids for which all common models of contact lines fail. It is shown that, for two of these fluids (including water), the assumption of isothermality does not hold.