Capillary rise between parallel plates under dynamic conditions

Abstract

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.

A universal law for capillary rise in corners

“…The major assumption used in (1.2) is the constancy of the contact angle θ. The studies of dynamical wetting (Hoffman 1974;Tanner 1979;de Gennes 1985) later showed that this is generally not the case, so that the Lucas-Washburn law must be corrected in the first steps of the rise (Siebold 2000;Wolf 2010). Another assumption in this law is that inertia is negligible.…”

Spontaneous Imbibition in Disordered Porous Solids: A Theoretical Study of Helium in Silica Aerogels

“…In spite of the diversity of actual porous media, the √ t scaling law, which results macroscopically from the balance between a constant driving capillary force and an increasing viscous drag, is ubiquitously observed. In fact, it appears that the LW relationship holds down to the nanoscopic scale, as shown by recent experimental 10,11 and theoretical studies [13][14][15][16][17][18] . This of course is an important indication for the development of nanofluidic devices.…”

Wetting boundary condition for the color-gradient lattice Boltzmann method: Validation with analytical and experimental data

“…In the literature, capillary rise simulations using the lattice Boltzmann method have been performed ( Latva-Kokko and Rothman, 2005b;Raiskinmäki et al, 2002;Wolf et al, 2010 ). These simulations considered Bond numbers = 10 −1 − 10 0 based on the definition of Eq.…”