Migration of magnetic microparticles through a liquid–liquid interface under an external magnetic field

Liquid–liquid interfaces play a pivotal role in various microfluidic processes involving microparticles, including coating, dissolution, controlled release of polyelectrolytes or drugs, and self-assembly processes. In all of these cases, noninvasive techniques to manipulate the microparticle transport are essential. Magnetic manipulation offers an accessible and straightforward means of controlling the motion of magnetic particles within microfluidic devices. Magnetic microparticles are commonly used for conformal polyelectrolyte coating and drug encapsulation by passing them through a liquid–liquid interface due to their high saturation magnetization, stability, and low toxicity. In this work, we draw inspiration from the lack of studies on the behavior of magnetic particles near a liquid–liquid interface under conditions of low Reynolds numbers and high capillary action, despite its engineering relevance in microfluidic systems. We consider a canonical flow configuration in which particle motion is driven by the stagnation-point flow that is generated when two different liquids flow toward one another. We show how the operating conditions dictate whether the particle will pierce the interface and become coated or not and illustrate this via parameter-space plots. We use the results of this analysis to understand how the operating conditions influence the fraction of particles that pass through the liquid–liquid interface and are conformally coated, which may be used to guide a variety of industrial processes.