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Gibbsian Thermodynamic Study of Capillary Meniscus Depth
Fatemeh Eslami1, Janet A W Elliott2
1Department of Process Engineering, Faculty of Chemical Engineering, Tarbiat Modares University, Tehran, Iran. f_eslami@modares.ac.ir.
Scientific Reports
|January 26, 2019
Summary
This study introduces a new method for analyzing liquid meniscus shapes by integrating the Young-Laplace equation from the three-phase contact line (TPCL). This approach accurately models capillary phenomena in systems with high Bond numbers, enabling precise surface tension measurements.
Area of Science:
- Fluid dynamics
- Surface science
- Physical chemistry
Background:
- Liquid surface curvature deviates from spherical shape due to external fields like gravity.
- The Young-Laplace equation is typically solved numerically, starting integration from the interface apex.
- This apex-initial point method fails for large Bond number systems where the interface is flattened.
Purpose of the Study:
- To develop a numerical method for determining capillary meniscus depth in high Bond number systems.
- To evaluate the curvature at the three-phase contact line (TPCL) using free energy analysis.
- To introduce and analyze a new parameter (SR) quantifying the deviation from spherical curvature at the TPCL.
Main Methods:
- Numerical integration of the Young-Laplace equation with the TPCL as the initial integration point.
- Free energy analysis to determine the equilibrium curvature at the TPCL.
- Systematic variation of parameters to study their effect on interface shape.
Main Results:
- A novel method successfully determines meniscus depth by integrating from the TPCL.
- The deviation of equilibrium curvature at the TPCL from spherical shape (SR) was introduced and analyzed.
- Maximum deviation (SR ≈ 0.8) occurs at a Bond number of 13; SR approaches 1 for larger Bond numbers.
Conclusions:
- Integrating the Young-Laplace equation from the TPCL provides an effective method for analyzing capillary menisci, especially in high Bond number systems.
- The SR parameter quantifies deviations from spherical curvature at the TPCL.
- This approach offers a potential method for measuring surface tension in systems with low surface/interfacial tensions via capillary rise at the TPCL.
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