Anomalous water slippage in pulsatile microfluidics caused by nanoscale emergent viscoelasticity

A theoretical model is proposed to study fluid dynamics in microchannels under pulsatile external forcing. This model incorporates the fluid/wall interaction considering that a rough interface consists of an array of parallel nanometric channels coupled with the bulk flow generated in the main microfluidic channel. Consequently, a theoretical technique is developed to compute an exact analytical solution. This solution is fundamental for the study of the multiscale flow dynamics involved in the interaction between adjacent flows with confining dimensions and properties that differ by orders of magnitude. This is particularly relevant for the case of confined water, as recent evidence suggests a confinement-dependent viscoelastic behavior. Under these conditions, considerable flow slippage is predicted at the interface between nanoconfined water and larger confinements. This finding is understood in terms of the propagation of elastic waves that are generated in the nanometric channels and propagated and magnified in the microchannel. Finally, the stability and robustness of the solution for all ranges of channel dimensions and relaxation times is exploited to carry out a comprehensive exploration of the key physical conditions that determine the arising and persistence of anomalous flow slippage due to size-dependent viscoelasticity. The results of this model are of interest for a better understanding of the impact of fluid/wall interactions in dynamic situations, as for a reassessment of typical assumptions of no-slippage at the fluid/wall interface, widely employed in microfluidics of high-polarity channels.