Obstructed Breakup of Slender Drops in a Microfluidic T Junction

In this Letter we present a theoretical analysis of the droplet breakup with permanent obstruction in a microfluidic T junction [M.-C. Jullien et al., Phys. Fluids 21, 072001 (2009)]. The proposed theory is based on a simple geometric construction for the interface shape combined with Tanner's law for the local contact angle. The resulting scaling of the droplet deformation with time and capillary number is in excellent agreement with the results of direct numerical simulations and prior experiments. More rigorous analysis based on the lubrication approximation reveals a self-similar behavior analogous to the classical problem of a droplet spreading over a preexisting liquid film.