Break-up of drops in microfluidic T-junction

We propose a mechanism of droplet break-up in a symmetric microfluidic T-junction driven by pressure decrement in a narrow gap between the droplet and channel wall. This mechanism works in a two-dimensional setting where the capillary (Rayleigh- Plateau) instability of a cylindrical liquid thread suggested earlier [Phys. Rev. Lett. 92, 054503 (2004)] as the cause of break-up is not operative, but is likely to be responsible for the breakup also in three dimensions. We derive a dependence of the critical droplet extension on the capillary number Ca by combining a simple geometric construction for the interface shape with lubrication analysis in a narrow gap where the surface tension competes with viscous drag. The theory, formally valid for Ca$^{1/5}<<1$, shows a very good agreement with numerical results when it is extrapolated to moderate values of Ca.