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Capillary Rising in a Tube with Corners
Chen Zhao1,2, Jiajia Zhou3,4, Masao Doi1,5
1Center of Soft Matter Physics and Its Applications, Beihang University, Beijing 100191, China.
Langmuir : the ACS Journal of Surfaces and Colloids
|April 28, 2022
Summary
Fluid dynamics in cornered capillary tubes show distinct bulk and finger regions. The finger part continues rising at late stages, deviating from circular tube behavior and affecting equilibrium height.
Area of Science:
- Fluid dynamics
- Capillary action
- Interfacial phenomena
Background:
- Capillary rise in circular tubes is well-described by Jurin's law.
- Cornered tubes exhibit complex fluid behavior due to geometric confinement.
- Understanding these dynamics is crucial for microfluidics and material science.
Purpose of the Study:
- To investigate the dynamics of fluid rising in a capillary tube with corners.
- To derive and analyze the coupled time-evolution equations for the bulk and finger parts of the fluid.
- To compare the behavior in cornered tubes with that in circular tubes.
Main Methods:
- Application of the Onsager principle to derive fluid dynamics equations.
- Analysis of coupled time-evolution equations for distinct fluid regions.
- Comparison of early-stage and late-stage fluid rising dynamics.
Main Results:
- Fluid rises in two distinct parts: a bulk part and a finger part.
- Early-stage dynamics are dominated by the bulk part, mirroring circular tube behavior.
- Late-stage dynamics show the finger part continuing to rise with a t^(1/3) scaling law, while the bulk part stagnates.
Conclusions:
- The presence of the finger part reduces the equilibrium bulk fluid height compared to Jurin's height.
- Coupling between the bulk and finger regions significantly influences overall capillary rise.
- Corner geometry introduces complex fluid dynamics not observed in simple cylindrical geometries.
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