An analytic solution of capillary rise restrained by gravity
1Center of Applied Space Technology and Microgravity ZARM, University of Bremen, Am Fallturm, 28359 Bremen, Germany.
Journal of Colloid and Interface Science
|February 8, 2008
Summary
We present an analytic solution for capillary rise, extending the Lucas-Washburn equation to include gravity for longer-term liquid behavior in tubes and porous media.
Area of Science:
- Fluid dynamics
- Physical chemistry
- Materials science
Background:
- The Lucas-Washburn equation describes capillary rise but neglects gravity.
- Accurate modeling of liquid transport in porous media and tubes is crucial for various applications.
Purpose of the Study:
- To derive an analytic height(time) solution for capillary rise, incorporating hydrostatic pressure.
- To extend the applicability of capillary rise models to longer timescales.
Main Methods:
- Rearrangement of the Washburn equation using the Lambert W function.
- Derivation from the 1D momentum conservation equation, including viscous and gravity terms.
Main Results:
- An explicit analytic solution for capillary rise height as a function of time (h(t)).
- The solution accurately models liquid rise behavior over extended periods by including the gravity term.
- Analysis of steady-state time and the validity limits of the classical Lucas-Washburn equation.
Conclusions:
- The derived analytic solution provides a more comprehensive model for capillary rise, especially for longer durations.
- This extended model allows for better prediction of liquid behavior in cylindrical tubes and porous media.
- The study offers insights into the interplay of viscous, gravity, and capillary forces in fluid transport phenomena.
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