WIAS Preprint No. 1215, (2007)

On the Landau--Levich problem for non-Newtonian liquids


  • Afanasiev, Konstantin
  • Münch, Andreas
  • Wagner, Barbara

2010 Mathematics Subject Classification

  • 34B15 35G25 35K55 35Q35

2008 Physics and Astronomy Classification Scheme

  • 68.15.+e


  • Lubrication models, non-Newtonian flow, fluid dynamics, phase plane analysis




In this paper the drag-out problem for shear-thinning liquids at variable inclination angle is considered. For this free boundary problem dimension-reduced lubrication equations are derived for the most commonly used viscosity models, namely, the power-law, Ellis and Carreau model. For the resulting lubrication models a system of ordinary differential equation governing the steady state solutions is obtained. Phase plane analysis is used to characterize the type of possible steady state solutions and their dependence on the rheological parameters.

Appeared in

  • Phys. Rev. E, 76 (2007) pp. 036307/1--036307/12.

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