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On Unsteady Non-homogenous Flows of Incompressible Fluids
Mehrdad Massoudi
U. S. Department of Energy
National Energy Technology Laboratory (NETL), Pittsburgh, 15236, US
Phone: 412-386-4975, Email: MASSOUDI@NETL.DOE.GOV
Ashwin Vaidya
Montclair State University, Montclair, NJ
Abstract:
Researchers investigating flows of non-Newtonian fluids often use the power-law constitutive relation.
Although the power-law model adequately fits the shear stress and the shear rate measurements for
many non-Newtonian fluids, it cannot be used to accurately describe phenomena such as ‘die-swelling’
and ‘rod-climbing’ which are manifestations of the stresses that develop orthogonal to planes of shear
in the flow of these complex fluids. In general non-Newtonian fluids differ from Newtonian fluids in at
least two ways: (1) they exhibit normal stress effects, such as rod-climbing and die-swell; and (2) they
exhibit shear-thinning or shear-thickening which is the decrease or increase in viscosity with increasing
shear rate, respectively. Both of these phenomena introduce non-linearities into the equations.
The non-linear time-dependent response of complex fluids (such as drilling fluids, coal-water
slurries, electro-rheological fluids, polymers) constitutes an important area of mathematical modeling
of non-Newtonian fluids. For many practical engineering cases, where non-linear fluids such as paints,
slurries, etc. are used, the shear viscosity can be a function of one or all of the following: Time; shear
rate; concentration; temperature; pressure; electric field; magnetic field. Thus in general, where t is the
time, à is some measure of the shear rate, á the temperature, Ö the concentration, p the pressure, the
electric field, and the magnetic field. Of course, in certain materials or under certain conditions, the
dependence of one or more of these can be ignored. In general, one can classify these fluids as nonhomogenous
fluids where the viscosity is given by an equation of the type .
In this presentation we will discuss a simple constitutive relation for a non-homogenous fluid
and attempt to provide numerical solutions to the unsteady flow of such a fluid between two flat plates.
227 ABSTRACTS