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Measurements of Local Instantaneous Convective Heat Transfer in a Pipe - Single and Two-phase Flow
Published on: April 30, 2018
Potential flow inside an evaporating cylindrical line
1Institute of Chemical Engineering and High Temperature Chemical Processes, Foundation for Research and Technology, Hellas, Greece.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
Summary
Researchers analyzed potential flow in an evaporating line shaped as a half-cylinder. The study reveals outward liquid flow for pinned contact lines, explaining the coffee-stain phenomenon.
Area of Science:
- Fluid dynamics
- Mathematical modeling
Background:
- Understanding liquid evaporation from surfaces is crucial in various scientific and industrial applications.
- The coffee-stain phenomenon, characterized by solute deposition at the receding contact line, is a common observation during droplet evaporation.
Purpose of the Study:
- To derive an analytical solution for potential flow within an evaporating half-cylindrical line.
- To investigate the influence of pinned versus depinned contact lines on the evaporation dynamics.
- To elucidate the underlying fluid mechanics contributing to the coffee-stain effect.
Main Methods:
- Employing the separation of variables technique in both velocity potential and stream function formulations.
- Calculating the flow field within the evaporating liquid.
- Analyzing the vertically averaged velocity for different contact line conditions.
Main Results:
- An analytical solution for potential flow in an evaporating half-cylinder was obtained.
- The coffee-stain phenomenon is predicted even with uniform evaporation flux if contact lines are pinned.
- A simple velocity potential expression accurately reproduces the local velocity vector.
- Pinned contact lines result in outward liquid flow, while depinned lines show inward flow.
Conclusions:
- The study provides a theoretical framework for understanding liquid evaporation in confined geometries.
- Contact line behavior (pinned vs. depinned) significantly dictates the internal flow patterns and potential for solute accumulation.
- The findings offer insights into controlling or predicting deposition patterns in evaporating systems.
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