Analytical, experimental, and numerical study of capillary rise dynamics from inertial to viscous flow

Fundamental understanding of capillary rise dynamics and precise evaluation of imbibition processes should be considered in many natural and industrial phenomena. In the presence of the capillary rise dynamics, it is obligatory to know the dominant forces. The assumptions considered to solve the capillary rise motion usually neglect specific forces, which limit the reliability of the derived solutions. In the present study, the dominant forces and regimes involved in the initial moments of the capillary rise imbibition process in a tube were investigated analytically, experimentally, and numerically. Analytical solutions available in the literature were discussed, and then, their validity was verified by comparing them to experimental observations and numerical results. Comparing the capillary rise behavior at the initial stages revealed significant differences between the theoretical models and the numerical lattice Boltzmann method. This behavior is attributed to simplify assumptions and ignore the entrance effect, dynamic contact angle, and the inertial term in the theoretical model. By removing these assumptions in numerical formulations, closer results to the experimental records were observed. In the present study, for the first time, capillary rise dynamics were divided into five steps: (1) a transition regime with h ∼ t 2 , (2) purely inertial (stage one) with h ∼ t, (3) viscous-inertial or crossover (stage two) with h ∼ log 10 (t), (4) purely viscous (stage three) with h ∼ t 1 /2 , and (5) gravitational-viscous with constant h. It was known that stage one was purely dominated by the inertial forces, then the influence of viscosity increased (viscous-inertial flow), and finally, the effect of inertia faded and the flow became purely viscous and approached the Lucas–Washburn law.