Inertial focusing in microfluidics has been a promising method for cell sorting in recent years. Despite various experiments and applications in devices implemented for cell sorting, the mechanisms of inertial focusing of deformable particles have yet to be elucidated. Various experiments conducted in inertial focusing demonstrated that the shape and deformation of droplets would affect particle motion and their steady state focusing position. The significance of deformation in inertial focusing inspired this work. In this thesis, we would show the deformation of viscoelastic droplets under different flow rates. Our experimental results show that for dimensionless droplets size 0.2-0.4, an oval shape is formed and a simple two-dimensional measurement has been used to define a deformation of viscoelastic droplets. Analysis shows that the deformation by Taylor measurement could be estimated by the flow and droplet properties and an equation for deformation prediction would be presented. As deformation is an intrinsic factor to any deformable particle in inertial focusing, this connection would provide convenience in assessing deformation contributions in affecting focusing positions. We envision a better understanding of the mechanics of inertial focusing, leading to the improvement of microfluidic devices for cell sorting
