Isogeometric boundary element formulation to simulate droplets in microchannel confinement

Purpose

This study aims to present an isogeometric boundary element formulation that stably and accurately models the motion of a droplet with arbitrary viscosity in free flows and microchannel confinements.

Design/methodology/approach

Like other numerical methods, isogeometric boundary element formulation also suffers from mesh distortion; therefore, volume correction and mesh relaxation are also required for efficient and stable simulations of deformable particles in Stokes flow with high accuracy. To improve the stability and accuracy of the proposed formulation, (i) volume correction and (ii) mesh relaxation algorithms to prevent mesh distortion are implemented.

Findings

Several test cases for a droplet in free-space shear flow are demonstrated for different Ca and viscosity ratio values which determine the deformability of a droplet. The results reveal that the drift of the enclosed volume inside a droplet and the mesh distortion becomes severe at low viscosity ratios and high Ca values, i.e. in the high deformability regime. The proposed numerical method integrating the stabilization algorithm enables the simulations at low spatiotemporal resolutions, even in extreme cases. The proposed method provides more than 10× speed-up compared to high-fidelity simulations without mesh relaxation. Efficient and accurate 3D simulations of droplets are also presented for simulations in microfluidic confinement.

Practical implications

The current formulation can be applied for many different microfluidic applications, and can be extended to tackle multiphysics simulations of multiple droplets in microchannel confinement.

Originality/value

The paper presents an isogeometric boundary element formulation with volume correction and mesh relaxation to model the motion of a droplet with arbitrary viscosity in free flows and microchannel confinements.