Case of The Steady Shear
For this case only two components of the shear stress became non-zero:
and
where is the shear rate.
Thus, the upper-convected Maxwell model predicts for the simple shear that shear stress to be proportional to the shear rate and the first difference of normal stresses is proportional to the square of the shear rate, the second difference of normal stresses is always zero. In other words, UCM predicts appearance of the first difference of normal stresses but does not predict non-Newtonian behavior of the shear viscosity nor the second difference of the normal stresses.
Usually quadratic behavior of the first difference of normal stresses and no second difference of the normal stresses is a realistic behavior of polymer melts at moderated shear rates, but constant viscosity is unrealistic and limits usability of the model.
Read more about this topic: Upper Convected Maxwell Model
Famous quotes containing the words case of, case and/or steady:
“I often used to think myself in the case of the fox-hunter, who, when he had toiled and sweated all day in the chase as if some unheard-of blessing was to crown his success, finds at last all he has got by his labor is a stinking nauseous animal. But my condition was yet worse than his; for he leaves the loathsome wretch to be torn by his hounds, whilst I was obliged to fondle mine, and meanly pretend him to be the object of my love.”
—Sarah Fielding (1710–1768)
“The doctors are all agreed that I am suffering for want of society. Was never a case like it. First, I did not know that I was suffering at all. Secondly, as an Irishman might say, I had thought it was indigestion of the society I got.”
—Henry David Thoreau (1817–1862)
“In all the good Greek of Plato
I lack my roastbeef and potato.
A better man was Aristotle,
Pulling steady on the bottle.”
—John Crowe Ransom (1888–1974)