Premium
Drainage in thin planar non‐newtonian fluid films
Author(s) -
Hartland Stanley,
Jeelani A. K.
Publication year - 1987
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450650305
Subject(s) - dimensionless quantity , non newtonian fluid , newtonian fluid , drainage , mechanics , planar , bingham plastic , power law fluid , materials science , geology , mathematics , physics , rheology , composite material , computer science , ecology , biology , computer graphics (images)
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.