Reports: AC947610-AC9: Dynamics of Three-Dimensional Droplets Sliding on Solid Substrates

Panagiotis Dimitrakopoulos, University of Maryland (College Park)

With the support of this award we have investigated computationally the dynamics of droplets and bubbles in confined solid geometries in the presence of viscous flows. During the period of the award we have investigated the following projects: (a) droplet motion in porous media or microfluidic channels with constrictions, (b) droplet dynamics at intersecting flows in cross-junctions, and (c) droplet motion at the intersecting flows in T-junctions. Our work has already resulted in a number of significant publications and conference talks. In particular, a paper describing our results from the first year of the award (on the migration and deformation of droplets and bubbles rising in wall bounded shear flows) has been published in the top-rated Journal of Fluid Mechanics. In addition, currently we are writing three papers on the projects mentioned previously. Furthermore, our work has already resulted in ten conference talks and proceedings at national and international meetings.

In the following, I highlight our major accomplishments/findings supported by this award.

(a) Droplet motion in porous media or microfluidic channels with constrictions

The study of droplet motion through a three-dimensional constriction in a circular or rectangular channel is a problem encountered in a broad range of applications including the enhance oil recovery and microfluidic devices. Utilizing our three-dimensional spectral boundary element algorithm, we investigated the squeezing motion of a single droplet in a square cross-sectional microfluidic channel with a rectangular constriction filled with another immiscible fluid. We started by investigating the differences between a square and a rectangular constriction in a square microchannel. Then we considered the influences of the capillary number, fluids' viscosities and the geometric size on the droplet interfacial shape, droplet velocity and the minimum gap between the droplet and the solid wall. As the flow rate is increased, we found higher droplet deformation and a thicker lubrication film between the droplet and solid surface. As the viscosity ratio is increased, the droplet acts as a more rigid droplet and deforms slower. However, due to the non-symmetric geometry of our constriction, different dynamics and droplet motion was identified compared to that in the axisymmetric geometry. In our problem, the droplet forms a flat disk shape and the overall deformation of the droplet is smaller. At least in the range of parameters studied here, no sign of snap-off of the droplet was found since owing to the rectangular constriction, the droplet does not show a neck.

(b) Droplet dynamics at intersecting flows in cross-junctions

The dynamics of droplets in confined microfluidic junctions is a problem of fundamental interest as such flow conditions occur in multiphase flows in porous media, biological systems, microfluidics and material science applications. Thus, we have investigated computationally the dynamics of naturally buoyant droplets, with constant surface tension, in cross-junctions and T-junctions constructed from square microfluidic channels. A three-dimensional fully-implicit interfacial spectral boundary element method is employed to compute the interfacial dynamics of the droplets in the junctions and investigate the problem physics for a wide range of flow rates, viscosity ratios and droplet sizes.

In microfluidic cross-junctions, we have considered droplets with similar size as the cross-section of the square channels comprising the cross-junction. Our work shows that droplet dynamics in the cross-junction depends strongly on the flow rate in the channels, the droplet size and the viscosity ratio. As the flow rate or the droplet size increases, the droplets show a rich deformation behavior as it moves inside the microfluidic device. After obtaining a bullet-like shape before the cross-junction, the droplet become very slender inside the junction (to accommodate the intersecting flows), then it obtains an inverse-bullet shape as it exits the cross-junction which reverts to a more pointed bullet-like shape far downstream the cross-junction (due to the combined flow rates of all intersecting channels). The viscosity ratio has also strong effects on the droplet deformation and motion with different dynamics at low or high droplet viscosity.

(c) Droplet dynamics at intersecting flows in T-junctions

We have also investigated computationally the dynamics of a naturally buoyant droplet with constant surface tension in the intersecting flows of a microfluidic T-junction device. After obtaining a bullet-like shape before the T-junction, the droplet takes the shape of a bullet skewed to one side (to accommodate the intersecting flow), and then it obtains a slipper shape with a very pointed rear (skewed to one side) as it exits the flow intersection of the T-junction. Further downstream, the T-junction the droplet tries to regain its shape and the rear of the slipper shaped droplet becomes less pointed and finally exits the junction. Our results are in agreement with experimental findings, and provide physical insight on the confined droplet deformation. In addition, we have found that the presence of intersecting flows, drastically affects the transient behavior at the junctions, and the drop reaches steady state further away, both upstream and downstream of these junctions. The time taken to reach steady state in the T-junctions was found to be significantly greater than that in the cross-junction, under identical conditions. We observed that the excess pressure drop with respect to the flow of a single phase fluid was strongly related to the length of the droplet at a given spatial coordinate. The peak surface area of the drop in the junction was found to be a slightly non-linear function of the flow rates in the lateral channels, and almost all the surface area increase was occurring at the head of the drop, in the direction of the flow.