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Stokes flow inside an evaporating liquid line for any contact angle
1Institute of Chemical Engineering and High Temperature Chemical Processes-Foundation for Research and Technology, Hellas and Department of Chemical Engineering, University of Patras, 26504 Patras, Greece.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2008
Summary
Internal viscous flow during droplet evaporation drives particle transport and deposit patterns. This study models Stokes flow in evaporating liquid lines, revealing flow direction depends on substrate properties and contact line behavior, influencing the "coffee stain" effect.
Area of Science:
- Fluid dynamics
- Surface science
- Particle transport
Background:
- Evaporation of liquid droplets or films on substrates causes internal viscous flow.
- This flow significantly impacts suspended particle transport and the final deposit morphology.
- Understanding this phenomenon is crucial for applications involving liquid deposition.
Purpose of the Study:
- To analyze Stokes flow within a 2D evaporating liquid line on a substrate.
- To derive a closed-form solution for internal flow dynamics.
- To investigate the influence of contact angle and evaporation mechanisms on flow patterns.
Main Methods:
- Stream function formulation leading to the biharmonic equation in bipolar coordinates.
- Application of Navier slip boundary condition for compatible contact line conditions.
- Numerical analysis for kinetically and diffusion-controlled evaporation modes.
Main Results:
- A closed-form solution for Stokes flow is obtained, valid for all contact angles (0, pi).
- Pinned contact lines result in outward flow towards edges, promoting the coffee stain effect.
- Depinned contact lines show inward flow for hydrophilic surfaces (contact angle < pi/2) and outward flow for hydrophobic surfaces.
Conclusions:
- The derived solution accurately models internal viscous flow in evaporating liquid lines.
- Contact line behavior (pinned vs. depinned) and substrate wettability dictate particle transport and deposit patterns.
- The findings provide insights into controlling deposition in various scientific and industrial applications.
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