Dynamics of liquid rise in a vertical capillary tube

The governing equation for capillary rise in a vertical tube is derived using energy balance. The derived governing equation includes kinetic, gravity, and viscous effects. Through normalizing different terms in the governing equation, a form of nonlinear ordinary differential equation (ODE) with a positive dimensionless parameter was obtained. The ODE equation was solved numerically and the numerical results were compared with some published experimental data. The derived governing equation was found to be quite accurate for predicting the liquid rise and oscillation in a capillary tube. The effect of a dimensionless parameter on the behavior of the liquid rise was explored numerically. A simple critical condition, which leads to the oscillation of the liquid column in the capillary tube, was found in the form of a dimensionless parameter in the governing equation.

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► A new method of deriving governing equation for capillary flow was presented.
► A simple dimensionless governing equation with just one parameter was proposed.
► The parameter in the governing equation was related to dimensionless numbers.
► The proposed equation was verified using experimental data.
► A criterion which leads to the oscillation of liquid column was found.