Capillary rise between parallel plates under dynamic conditions

A Lattice-Boltzmann method based on field mediators is proposed to simulate the capillary rise between parallel plates by considering the effect of long-range interactions between the fluids and the solid walls. As a starting point, a liquid-vapor system was employed, which was modeled using a known model described in the literature. The simulations were compared with theoretical solutions of the Bosanquet equation. The results obtained are in good agreement with theoretical predictions, particularly when the dependence between the dynamic contact angle and the capillary number is taken into account. This dependence shows that on smooth and homogeneous solid surfaces, where pinning effects in the contact line are weak, the dynamic contact angle is linearly dependent on the capillary number, in good agreement with theoretical and experimental results available in the literature. Some discrepancies were observed in the first stages of the capillary rise when the distance between the parallel plates is large, considering the high complexity involved in predicting the initial meniscus formation. The results presented in this work appear to indicate that the inclusion of long-range forces does not change significantly the fluid flow dynamics at the mesoscopic level, at least, when ideally flat and homogeneous solid surfaces are used in the simulations.