# An efficient mass-preserving interface-correction level set/ghost fluid method for droplet suspensions under depletion forces

## TL;DR

This paper introduces a novel, efficient numerical method for simulating colloidal droplet suspensions in microfluidic devices, incorporating mass conservation, accurate interface curvature, and depletion force interactions.

## Contribution

It presents a new interface-correction level set method combined with ghost fluid and pressure-correction techniques for improved two-phase flow simulation.

## Key findings

- Achieved global mass conservation with an interface correction technique.
- Developed a second-order accurate curvature estimation method.
- Enabled fast, accurate simulations of droplet interactions under depletion forces.

## Abstract

Aiming for the simulation of colloidal droplets in microfluidic devices, we present here a numerical method for two-fluid systems subject to surface tension and depletion forces among the suspended droplets. The algorithm is based on an efficient solver for the incompressible two-phase Navier-Stokes equations, and uses a mass-conserving level set method to capture the fluid interface. The four novel ingredients proposed here are, firstly, an interface-correction level set (ICLS) method; global mass conservation is achieved by performing an additional advection near the interface, with a correction velocity obtained by locally solving an algebraic equation, which is easy to implement in both 2D and 3D. Secondly, we report a second-order accurate geometric estimation of the curvature at the interface and, thirdly, the combination of the ghost fluid method with the fast pressure-correction approach enabling an accurate and fast computation even for large density contrasts. Finally, we derive a hydrodynamic model for the interaction forces induced by depletion of surfactant micelles and combine it with a multiple level set approach to study short-range interactions among droplets in the presence of attracting forces.