In this thesis we conduct an investigation into the transient deformation of a droplet flowing through a sudden expansion in a microfluidic device. The dynamics of droplets in confined microfluidic geometries is a problem of fundamental interest as such flow conditions occur in multiphase flows in porous media, biological sys- tems, microfluidics and material science applications. We computationally simulate naturally buoyant droplets possessing constant surface tension and of a size smaller than the cross-section of the rectangular channels in the expansion geometry. Our investigation presents cases in which the flow rate ranges from weak-to-strong and the fluids viscosity ratio ranges from low-to-high. The geometry of the expanding channel causes the droplet to display an interesting deformation behavior as it passes through the point of expansion. Our investigation draws attention to the effects of the asymmetric microchannel geometry on the droplet deformation and the different effects of the strength of the surrounding fluid flow rate, the fluid viscosity ratio, the initial displacement of the droplet, and the size of the droplet on the deformation of the droplet edges. In addition, our study highlights the multi-length nature of the current interfacial investigation.

Our investigation reveals that as the flow rate or the droplet size increases, the droplets show a rich deformation behavior as they moved inside the microfluidic channel. The viscosity ratio also has strong effects on the droplet deformation especially for high-viscosity droplets which do not have the time to accommodate the much slower deformation rate while they move through the channel. Our results

provide insight into the physical deformation of droplets flowing through microfluidic expansions.