Premium
A theory of roll coating of viscous and viscoelastic fluids
Author(s) -
Greener Yehuda,
Middleman Stanley
Publication year - 1975
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.760150102
Subject(s) - viscoelasticity , deborah number , newtonian fluid , generalized newtonian fluid , herschel–bulkley fluid , materials science , power law fluid , non newtonian fluid , mechanics , elasticity (physics) , shear stress , perturbation (astronomy) , coating , shear rate , classical mechanics , rheology , composite material , physics , quantum mechanics
A theory for roll coating of a fluid onto a moving sheet is developed utilizing the usual “lubrication approximations.” The effects of fluid and operating parameters on coating thickness and pressure distribution are determined for a Newtonian fluid, and for a purely viscous non‐Newtonian fluid obeying the Power Law. The results for these cases are obtained analytically, and are rather straightforward. A viscoelastic fluid is considered, of a type which shows typical non‐Newtonian shear behavior observed in polymer melts and solutions and which also exhibits normal stress behavior. Analytical solutions are not possible, but a perturbation method, using a viscoelastic perturbation parameter related to a Deborah number, yields an approximate solution. Only terms to first order in the perturbation parameter are given. Subject to that degree of approximation, the following conclusions are drawn: 1 Non‐Newtonian shear behavior reduces the pressure distribution, and increases the coating thickness. 1 Elasticity of the type usually observed in polymer solutions makes only a minor contribution to the roll‐separating (load‐carrying) force. The contribution is positive, but smaller than the corresponding negative contribution due to the non‐Newtonian shear effects. 1 An increase in load‐carrying capacity would require a different viscoelastic fluid than the type considered here—one that is essentially Newtonian in shear but, independently, capable of developing significant normal stresses.