(465c) Dynamics of Deformable Droplets in 3D Channels of Different Geometries: An Experimental and Numerical Study

Motion of deformable droplets is relevant to several application areas including lab-on-a-chip devices, droplet sorting, micro-reactors, and transport of cells. As drop microfluidic applications become more advanced, it is crucial to have a fundamental understanding of the physics behind droplet motion in confined domains to design such systems effectively. Microfluidic systems usually have a very low Reynolds number owing to their small dimensions or high fluid viscosity. In this work, we study the motion of liquid droplets of size comparable to the channel height suspended in viscous flow through straight rectangular microchannels and microchannels with constrictions. We use a moving-frame boundary-integral (MFBI) method [1] to analyze the dynamics of a 3D, deformable droplet inside a finite-depth channel [2]. To simulate the motion of a drop in a channel, contributions from all the channel walls need to be included, which can be computationally expensive. Instead, a computational cell that is much larger than the drop yet significantly smaller than the whole domain is dynamically constructed around the drop in this method, resulting in considerable acceleration of the code.

Furthermore, we experimentally inspect the motion of aqueous glycerol or PDMS drops subjected to a background flow consisting of viscous castor oil in a flow cell. Along its course through a straight channel, the drop deforms due to the viscous forces until it finally reaches a steady state due to the counteracting surface tension forces. In this work, we primarily focus on investigating this steady-state velocity of the drop and how it is affected by changes in important parameters such as the drop diameter relative to the channel width, viscosity ratio of the droplet fluid to the bulk fluid, capillary number, and aspect ratio of the rectangular channel. The experimental results are then compared with numerical results simulated using our MFBI solver for the Stokes equations. Interestingly, it was found that although the steady-state velocity of a drop usually decreases with increasing drop diameter at a fixed viscosity ratio and capillary number due to increased interaction with the walls, this phenomenon is reversed at very low viscosity ratios. Experiments are also done in straight rectangular channels with constrictions. Three kinds of constrictions are investigated: a short-abrupt constriction, a long-abrupt constriction, and a long-gradual constriction. A deformable drop moving through a channel with a constriction can give interesting outcomes such as passing through without breakup, breakup due to significant stretching while passing through the narrow constriction and subsequent pinch off as it relaxes while leaving the constriction, and drop-trapping at the channel-constriction junction. The outcomes are compared with numerical results with the help of phase maps. A quantitative comparison is also done for the transit time of a drop, which is the extra time that it takes the drop to travel through the channel with the restriction in place; this extra time becomes large as trapping conditions are approached.

[1] Zinchenko, Alexander Z., John F. Ashley, and Robert H. Davis. "A moving-frame boundary-integral method for particle transport in microchannels of complex shape." Physics of Fluids 24.4 (2012).

[2] Roure, Gesse, Alexander Z. Zinchenko, and Robert H. Davis. "Numerical simulation of deformable droplets in three-dimensional, complex-shaped microchannels." Physics of Fluids 35.10 (2023).