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Extended lubrication theory: improved estimates of flow in channels with variable geometry
Behrouz Tavakol1,2, Guillaume Froehlicher3, Douglas P Holmes4
1Wellman Center for Photomedicine, Massachusetts General Hospital, Harvard Medical School, Cambridge, MA 02139, USA.
Proceedings. Mathematical, Physical, and Engineering Sciences
|November 10, 2017
Summary
This study extends lubrication theory using Stokes equations to accurately model fluid flow and pressure drop in channels with geometric changes. The enhanced model shows strong agreement with experimental and numerical results.
Area of Science:
- Fluid dynamics
- Continuum mechanics
- Applied mathematics
Background:
- Lubrication theory is essential for analyzing thin fluid films and particle motion near surfaces.
- Existing models may not fully capture flow dynamics in channels with complex geometries.
- Stokes equations provide a fundamental basis for fluid flow analysis.
Purpose of the Study:
- To extend lubrication theory by incorporating higher-order terms from Stokes equations.
- To accurately characterize fluid flow and pressure drop in channels with modest aspect ratios and geometric variations.
- To validate the extended theory against experimental and numerical data.
Main Methods:
- Systematic perturbation expansion of Stokes equations.
- Analytical solution development for fluid flow in channels with geometric features.
- Comparison of analytical results with experimental measurements and numerical simulations.
Main Results:
- Higher-order analytical solutions were derived for fluid flow in channels.
- Experimental data qualitatively confirmed the analytical solutions.
- Numerical results demonstrated excellent agreement with the higher-order analytical findings.
- The extended lubrication theory accurately estimates pressure drop for channels with smooth and sharp geometric changes.
Conclusions:
- The extended lubrication theory provides a robust and accurate method for analyzing fluid flow in channels with geometric variations.
- This approach enhances the predictive capability of lubrication theory for complex channel geometries.
- The findings are valuable for applications requiring precise fluid flow characterization in microfluidic devices and other systems.
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