A Procedure for the Motion of Particle-Encapsulated Droplets in Microchannels

A fixed-grid approach for modeling the motion of a particle-encapsulated droplet carried by a pressure-driven immiscible carrier fluid in a microchannel is presented. Three phases (the carrier fluid, the droplet, and the particle) and two different moving boundaries (the droplet–carrier fluid and droplet–particle interfaces) are involved. This is a moving-boundaries problem with the motion of the three phases strongly coupled. In the present article, the particle is assumed to be a fluid of high viscosity and constrained to move with rigid body motion. A combined formulation using one set of governing equations to treat the three phases is employed. The droplet–carrier fluid interface is represented and evolved using a level-set method with a mass-correction scheme. Surface tension is modeled using the continuum surface force model. An additional signed distance function is employed to define the droplet–particle interface. Its evolution is determined from the particle motion governed by the Newton-Euler equations. The governing equations are solved numerically using a finite-volume method on a fixed Cartesian grid. For demonstration purposes, the flows of particle-encapsulated droplets through a constricted microchannel and through a microchannel system are presented