Breakup of drops in a microfluidic T junction

We propose a mechanism of droplet breakup in a symmetric microfluidic T junction driven by pressure decrement in a narrow gap between the droplet and the channel wall. This mechanism works in a two-dimensional setting where the capillary (Rayleigh–Plateau) instability of a cylindrical liquid thread, suggested earlier [D. Link, S. Anna, D. Weitz, and H. Stone, Phys. Rev. Lett. 92, 054503 (2004)] as the cause of breakup, is not operative, but it 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 the viscous drag. The theory, formally valid for Ca1/5⪡1, shows a very good agreement with numerical results when it is extrapolated to moderate values of Ca.