Drainage in thin planar non‐newtonian fluid films

Equations for the radial and linear drainage of non‐Newtonian fluids in horizontal and inclined films are presented. For a power law fluid with index m, the variation in dimensionless film thickness Δ with dimensionless time T is given by:\documentclass{article}\pagestyle{empty}\begin{document}$$ T = \frac{{\left( {2m + 1} \right)}}{{\left( {m + 1} \right)}} \cdot \frac{1}{{\Delta ^{\left( {m + 1} \right)/m} }} $$\end{document}where Δ and T are appropriately defined for drainage in radial horizontal and linear inclined films. The corresponding approximate expression for a Bingham plastic fluid is:\documentclass{article}\pagestyle{empty}\begin{document}$$ T = \frac{2}{{A^2 }}\left\{ { - \ell n\left( {1 - \frac{A}{\Delta }} \right) - \frac{A}{\Delta }} \right\} $$\end{document}in which A is the minimum film thickness defined appropriately at the asymptotic limits when Δ » A and Δ ⋍ A.