Landau-Levich problem for non-Newtonian liquids
Konstantin Afanasiev1, Andreas Münch, Barbara Wagner
1Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany. afanasie@wias-berlin.de
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
Summary
This study analyzes liquid film behavior for shear-thinning fluids on inclined surfaces. We derived simplified equations and used phase plane analysis to understand fluid flow and predict steady states.
Area of Science:
- Fluid dynamics
- Rheology
- Mathematical modeling
Background:
- The drag-out phenomenon is crucial in industrial coating processes.
- Understanding non-Newtonian fluid behavior, specifically shear-thinning liquids, is complex.
- Variable inclination angles add further complexity to fluid flow analysis.
Purpose of the Study:
- To investigate the drag-out problem for shear-thinning liquids under varying inclination angles.
- To develop dimension-reduced lubrication equations for common non-Newtonian viscosity models.
- To analyze the steady-state solutions and their dependence on rheological parameters.
Main Methods:
- Derivation of dimension-reduced lubrication equations for power-law, Ellis, and Carreau viscosity models.
- Formulation of a system of ordinary differential equations for steady-state analysis.
- Application of phase plane analysis to characterize solution types.
Main Results:
- Successfully derived lubrication models for shear-thinning fluids.
- Obtained ordinary differential equations governing steady-state solutions.
- Characterized steady-state solutions and their dependence on rheological parameters through phase plane analysis.
Conclusions:
- The derived models provide a simplified yet accurate approach to studying shear-thinning liquid drag-out.
- Phase plane analysis effectively reveals the behavior of steady-state solutions.
- This work contributes to a better understanding of free boundary problems in non-Newtonian fluid dynamics.
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