An objective rotation tensor applied to non-Newtonian fluid mechanics |
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Authors: | Lewis E Wedgewood |
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Institution: | (1) University of Illinois at Chicago Department of Chemical Engineering Chicago, IL 60607-7000, USA, US |
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Abstract: | To develop objective constitutive equations, local frames which translate and rotate with the fluid particle can be used.
For example, the corotating frame rotates such that the curl of the velocity calculated in this frame vanishes. From the corotating frame, the Jaumann derivative
can be derived. In this paper, a new local frame is developed which causes the cross product of the velocity and acceleration
to vanish and is designated as the rigid-rotating frame. The corotating and rigid-rotating frames rotate identically for a rigid-body rotation of the fluid, but rotate differently
in flows that contain shearing. This difference in rotation can be used to develop an objective rotation tensor that can be
applied to constitutive equations for viscoelastic liquids. The rigid-rotating frame can also be used to develop a rheological
time derivative which has been designated the rigid-rotating derivative. These new quantities expand the traditional set of kinematical variables and invariants available for use in constitutive
equations. Use of this expanded set of kinematic variables is demonstrated in limiting constitutive equations.
Received: 1 March 1999 Accepted: 5 March 1999 |
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Keywords: | Flow kinematics Objectivity Vorticity decomposition Viscoelastic fluids Flow characterization |
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