Deformation and breakup of a ferrofluid compound droplet migrating in a microchannel under a magnetic field: A phase-field-based multiple-relaxation time lattice Boltzmann study

TL;DR

This study uses a phase-field lattice Boltzmann method to analyze how magnetic fields influence the deformation and breakup of ferrofluid compound droplets in microchannels, revealing key parameters and regimes affecting droplet stability.

Contribution

It introduces a coupled finite difference and lattice Boltzmann approach to investigate ferrofluid droplet dynamics under magnetic fields, a novel application in confined microfluidic systems.

Findings

UEMF at 0° with ferrofluid shell delays breakup

Strengthening UEMF with ferrofluid core enlarges shell deformation

Identified five regimes based on Bond and Capillary numbers

Abstract

Though ubiquitous in many engineering applications, including drug delivery, the compound droplet hydrodynamics in confined geometries have been barely surveyed. For the first time, this study thoroughly investigates the hydrodynamics of a ferrofluid compound droplet (FCD) during its migration in a microchannel under the presence of a pressure-driven flow and a uniform external magnetic field (UEMF) to manipulate its morphology and retard its breakup. Finite difference and phase-field multiple-relaxation time lattice Boltzmann approaches are coupled to determine the magnetic field and ternary flow system, respectively. Firstly, the influence of the magnetic Bond number (Bo) on the FCD morphology is explored depending on whether the core or shell is ferrofluid when the UEMF is applied along {\alpha}=0{\deg} and {\alpha}=90{\deg} relative to the fluid flow. It is ascertained that imposing the UEMF at {\alpha}=0{\deg} when the shell is ferrofluid can postpone the breakup. Intriguingly, when the core is ferrofluid, strengthening the UEMF enlarges the shell deformation. Afterward, the effects of the Capillary number (Ca), density ratio, viscosity ratio, radius ratio, and surface tension coefficients are scrutinized on the FCD deformation and breakup. The results indicate that augmenting the core-to-shell viscosity and density ratios accelerates the breakup process. Additionally, surface tension between the core and shell suppresses the core deformation. Moreover, increasing the Ca number intensifies the viscous drag force exerted on the shell, flattening its rear side, which causes a triangular-like configuration. Ultimately, by varying Bo and Ca numbers, five distinguished regimes are observed, whose regime map is established.