An analytic solution of capillary rise restrained by gravity

The transition from inertial to viscous flow in capillary rise

“…Fries and Dreyer [16] show that for h > 0.1 h eq gravity has to be considered. h eq is the equilibrium height where the hydrostatic pressure balances the capillary pressure (see Eq.…”

“…Thus, to have a clear separation of inertia and gravity we can state the following: h 3 , the height below which inertia has to be taken into account, has to be smaller that the height from which on gravity has to be considered. Using the criterion given in [16] we can write…”

“…Some publications focus on the effect of the dynamic contact angle [12][13][14]. Subsequent time stages (t 0) with influence of gravity are discussed in [15,16]. In this paper we now want to shed some light on the different stages of capillary rise and the transitions between them.…”

Dimensionless scaling methods for capillary rise

“…However, in favor of readability, we will not continue to explicate the Darcy version in the further text. Please note that the parameters a, b and c are not identical to those applied in [18,19]. Using the introduced dimensional parameters one can rearrange Eqs.…”

“…There also exist studies involving gravity, thus leading to different scaling approaches e.g. by Quéré et al [13,14], Marmur and Cohen [15], Zhmud et al [16], Lee and Lee [17] or Fries and Dreyer [18,19]. McKinley [20] investigates dimensionless groups for free surface flows with a focus on complex fluids.…”