# Phase-field simulation of core-annular pipe flow

## TL;DR

This paper evaluates the accuracy of phase-field methods in simulating core-annular pipe flows, demonstrating their effectiveness in handling complex geometries, high viscosity contrasts, and unsteady conditions.

## Contribution

It provides a quantitative analysis of phase-field simulation convergence to sharp-interface limits in realistic pipe flow scenarios, validating their applicability.

## Key findings

- Phase-field methods accurately simulate non-rectangular geometries.
- They handle strong advection and unsteady fluctuations effectively.
- The methods work well with large viscosity contrasts.

## Abstract

Phase-field methods have long been used to model the flow of immiscible fluids. Their ability to naturally capture interface topological changes is widely recognized, but their accuracy in simulating flows of real fluids in practical geometries is not established. We here quantitatively investigate the convergence of the phase-field method to the sharp-interface limit with simulations of two-phase pipe flow. We focus on core-annular flows, in which a highly viscous fluid is lubricated by a less viscous fluid, and validate our simulations with an analytic laminar solution, a formal linear stability analysis and also in the fully nonlinear regime. We demonstrate the ability of the phase-field method to accurately deal with non-rectangular geometry, strong advection, unsteady fluctuations and large viscosity contrast. We argue that phase-field methods are very promising for quantitatively studying moderately turbulent flows, especially at high concentrations of the disperse phase.