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Liquid withdrawal from capillary tubes: explicit and implicit analytical solution for constant and dynamic contact

Markus Hilpert¹

¹Johns Hopkins University, Department of Geography and Environmental Engineering, Baltimore, MD 21218, USA. markus_hilpert@jhu.edu

Journal of Colloid and Interface Science

|August 10, 2010

Summary

This study presents analytical solutions for gas-liquid displacement in capillary tubes, identifying five flow scenarios. New diagrams predict these scenarios based on capillary number and dynamic contact angle, aiding in understanding liquid withdrawal and infiltration dynamics.

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Area of Science:

Fluid dynamics
Capillary phenomena
Interface dynamics

Background:

Previous work derived analytical solutions for gas-liquid displacement in capillary tubes with general dynamic contact angle models.
These solutions identified five distinct flow scenarios for liquid withdrawal based on interface velocity and acceleration.

Purpose of the Study:

To derive explicit and implicit analytical solutions for gas-liquid interface position and velocity in capillary tubes.
To develop predictive diagrams for flow scenarios based on a specific dynamic contact angle model (linear dependence on capillary number).
To map the entire parameter space for liquid withdrawal, infiltration, and equilibrium states.

Main Methods:

Analytical derivation of solutions for gas-liquid interface motion.
Modeling dynamic contact angle with a nonequilibrium Young force linearly dependent on capillary number.
Construction of phase diagrams to predict flow regimes.

Main Results:

Explicit and implicit analytical solutions for interface position and velocity were obtained.
Predictive diagrams were constructed, categorizing five flow scenarios based on nondimensional parameters.
The parameter space was comprehensively mapped, distinguishing between liquid withdrawal, infiltration, and equilibrium states.

Conclusions:

The derived solutions are valid for a linear dynamic contact angle model and the constant contact angle limit.
The developed diagrams provide a robust tool for predicting gas-liquid displacement behavior in capillary tubes.
This work unifies understanding of liquid withdrawal and infiltration under various dynamic contact angle conditions.