| Summary: | 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, non-invasive 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 behaviour 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 towards 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.
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