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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 second year of the award we investigated two projects: (a) droplet motion in porous media or microfluidic channels with constrictions, and (b) droplet dynamics at intersecting flows in T- and cross-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 two papers on the two projects investigated during the second year of the award. Furthermore, our work has already resulted in six conference talks and proceedings at national and international meetings.

In the following, I highlight our major accomplishments/findings during the second year of the 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 influence of the capillary number, fluids' viscosities and the geometric size on the droplet interfacial shape, droplet velocity and the lubrication film 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 object 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 T- and cross-junctions

Junctions are very common in both microfluidic devices and porous media.  In this work we investigated the drop dynamics in junctions at moderate flow rates utilizing our three-dimensional Spectral Boundary Element algorithm. We considered both T-junctions and cross-junctions, and analyzed the effect on drop deformation and motion with varying shear rates in the channels leading to the junctions, and for different viscosity ratios between the drop and the surrounding fluid.

We 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.