The current thesis involves a computational study of drop dynamics in microfluidic junctions, at the moderate capillary number of Ca = 0.1. We utilize a three-dimensional Spectral Boundary Element algorithm to determine the drop motion in the presence of intersecting lateral flows in microfluidic, T-junctions and cross-junctions, and analyze the effect on drop deformation and motion with varying shear rates in the channels leading to the junctions, and for viscosity ratios of 0.2 and 20.0 between the drop and the surrounding fluid.

We find that the presence of intersecting flows, drastically affects the transient behavior at the junctions, and the drop reaches steady state further away, both up- stream 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. Drop velocities were found to be a linear function of the effective shear rate in the channel, and length scale fluctuations as high as 30 percent were observed in the junction region for the cases studied in the thesis.

We observed that the excess presure 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 slighly 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. Velocity was found to be a weak, inverse function of the viscosity ratio, the increase in drop surface area was found to be greater in drops with lower viscosity. It was found that the junction bend radius/smoothness had a more significant effect on the dynamics of the drop in a T-junction, compared to that in a cross-junction.