Effect of the meniscus contact angle during early regimes of spontaneous imbibition in nanochannels

Nanoscale capillarity has been extensively investigated; nevertheless, many fundamental questions remain open. In spontaneous imbibition, the classical Lucas-Washburn equation predicts a singularity as the fluid enters the channel consisting of an anomalous infinite velocity of the capillary meniscus. Bosanquet's equation overcomes this problem by taking into account fluid inertia predicting an initial imbibition regime with constant velocity. Nevertheless, the initial constant velocity as predicted by Bosanquet's equation is much greater than those observed experimentally. In the present study, large scale atomistic simulations are conducted to investigate capillary imbibition of water in slit silica nanochannels with heights between 4 and 18 nm. We find that the meniscus contact angle remains constant during the inertial regime and its value depends on the height of the channel. We also find that the meniscus velocity computed at the channel entrance is related to the particular value of the meniscus contact angle. Moreover, during the subsequent visco-inertial regime, as the influence of viscosity increases, the meniscus contact angle is found to be time dependent for all the channels under study. Furthermore, we propose an expression for the time evolution of the dynamic contact angle in nanochannels which, when incorporated into Bosanquet's equation, satisfactorily explains the initial capillary rise.