Transport of wetting liquid plugs in bifurcating microfluidic channels

A plug of wetting liquid is driven at constant pressure through a bifurcation in a microchannel. For a plug advancing in a straight channel, we find that the viscous dissipation in the bulk may be estimated using Poiseuille's law while Bretherton and Tanner's laws model the additional dissipation occurring at the rear and front interfaces. At a second stage, we focus on the behavior of the plug flowing through a T-junction. Experiments show the existence of a threshold pressure, below which the plug remains blocked at the entrance of the junction. Above this required pressure, the plug enters the bifurcation and either ruptures or splits into two daughter plugs, depending on the applied pressure and on the initial length of the plug. By means of geometrical arguments and the previously cited laws, we propose a global model to predict the transitions between the three observed behaviors.