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• W2038441431 abstract "The failure of some careful attemps to provide numerical solutions of the equations for non-Newtonian flow suggests to us some inadequacies of the constitutive equations. (After all no one would doubt the validity of the conservation of mass and momentum.) To understand the physics in the constitutive equation, and thence to correct its undesirable features, it is helpful to look at a micro-structural model which leads to the constitutive equation. The bead-and-spring dumbbell model for a dilute polymer solution leads to an Oldroyd-like equation. The simplest version of the bead-and-spring model has a linear spring and a constant friction coefficient for the beads. While this model is simple and usefully combines viscous and elastic behaviour, it has the very unphysical feature of blowing up in strong straining flows (i.e. at a Deborah number in excess of unity), with the spring lengthening indefinitely in time and the steady extensional viscosity becoming unbounded at a critical flow strength. The hope that the corresponding large stresses would not occur in a flow calculation seems to have been misguided: some simple examples show that the large stresses may not act through the momentum equation to inhibit the flow. To cure this unphysical behaviour one clearly needs to use a non-linear spring force which gives a finite limit to the extension. Incorporating this modification into the constitutive equation enables the numerical solution of (some) flow problems to proceed to large Deborah numbers. Care is of course still needed in the numerical calculations, for example in resolving thin layers of high stress. (A boundary layer theory needs to be developed for the nonlinearity introduced by the non-Newtonianness.) A further modification of the bead-and-spring model may be necessary if argument is sought between numerical calculations and experiments. Many flows of interest subject the fluid to a sudden strong strain. In such circumstances the polymer chains will not be in thermodynamic equilibrium and so will not give the standard entropic spring. It may be possible to model this behaviour by a large temporary internal viscosity." @default.
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• W2038441431 date "1988-01-01" @default.
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• W2038441431 title "Do we understand the physics in the constitutive equation?" @default.
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• W2038441431 doi "https://doi.org/10.1016/0377-0257(88)85049-3" @default.
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