Enhanced imbibition from the cooperation between wetting and inertia via pulsatile forcing

Abstract

We study the dynamics of microfluidic interfaces driven by pulsatile pressures in the presence of neutral and hydrophilic walls. For this, we propose a new phase field model that takes inertia into account. For neutral wetting, the interface dynamics is characterized by a response function that depends on a non-dimensional frequency, which involves the time scale associated with inertia. We have found a regime, for large values of this non-dimensional frequency, in which inertia is relevant, and our model is necessary for a correct description of the dynamics. For hydrophilic walls, the dynamics of the contact line with pulsatile forcing is basically undistinguishable to the dynamics of imbibition solely due to wetting. However, we observe that the presence of inertia causes the interface to advance faster than in the absence of pulsatile forcing. This is because pulsatile forcing induces inertia at the bulk to cooperate with wetting creating an enhancement of the imbibition process. We characterize this complex dynamics with transitory exponents that, at early times, are larger than the Washburn ones, and tend to the Washburn exponent at long times, when the interface feels less and less the driving force applied at the entrance of the microchannel, and the dynamics is dominated solely by wetting.