Numerical simulation used either finite element method (FEM) [16-19] or finite volume method combined with volume of fluid [20] to analyze dip coating for Newtonian and non-Newtonian fluids.
(To avoid further misunderstanding, we use a for external field instead of the letter g, which is reserved for a self-similar solution.) The [E.sub.i]j is the Newtonian linear stress tensor, where x(x,y) are the Cartesian coordinates.
The constitutive equation of Newtonian fluids was determined by Newton, using flows between parallel plains--one plain was steady, one was moving at a constant velocity--and hound thee the flow velocity profile was linear, thus shear rate and shear stress are proportional and the proportionality factor between them is the absolute viscosity.
The Newtonian fluid constitutive approximation is not a satisfactory engineering approach to most of the lubrication problems, because the modern lubricants are non-Newtonian in their character.
Through these studies, QCM measurements have shown that viscoelastic fluids containing macromolecules exhibit different behavior from that of Newtonian fluids.