Volume 26, Issue 1, February 1982
Index of content:
Lubrication Flows in Viscoelastic Liquids. I. Squeezing Flow between Approaching Parallel Rigid Planes26(1982); http://dx.doi.org/10.1122/1.549657View Description Hide Description
The problem of squeezing flow of a viscoelastic fluid between two parallel disks approaching each other at constant speed is examined theoretically and experimentally. Theory treats a nonlinear viscoelasticconstitutive equation due to Wagner. Experiments are performed with aqueous polyacrylamide solutions. The data exhibit significant deviations from purely viscous but non‐Newtonian performance, and the Wagner model shows good agreement with several features of the data.
26(1982); http://dx.doi.org/10.1122/1.549658View Description Hide Description
The problem of flow of an elasticoviscous fluid characterized by a four‐constant Oldroyd model is treated when such a fluid is confined between a pair of infinite coaxial parallel disks. The governing system of nonlinear coupled differential equations for the stresses and the velocity field is expressed by the corresponding finite difference analogs and solved by using the SOR method. For the case of one disk held at rest, the solutions are provided for Reynolds numbers 10 and 100, while for the case of counterrotations of the disks, they are also provided for the intermediate value of 20. The graphical representations of the velocity functions bring out some very interesting differences in the behavior of a Newtonian, slightly elastic and an elastic liquid.
26(1982); http://dx.doi.org/10.1122/1.549659View Description Hide Description
For any incompressible fluid whose stress is a frame indifferent function of the velocity gradient and the material time derivative of the velocity gradient, i.e., for any Rivlin‐Ericksen fluid of complexity 2, we show that thermodynamics implies that the first normal stress difference of viscometric flows must be nonpositive for small enough shearings unless a certain very special degeneracy occurs. More precisely, we show that the Clausius‐Duhem inequality, together with the postulate that the Helmholtz free energy has a minimum in equilibrium, suffices to ensure that, except for a very special subclass, every Rivlin‐Ericksen fluid of complexity 2 has a negative first normal stress difference for all small enough shearings in any viscometric flow. Our results significantly extend a similar analysis given by Dunn and Fosdick in 1974 for those special Rivlin‐Ericksen fluids of complexity 2 known as second grade fluids. In addition, they direct attention at a new class of complexity 2 fluids that have been little explored by theorists or experimenters. Furthermore, we study in detail the implications of our thermodynamic postulates for a certain subclass of these complexity 2 fluids that is more general than either second grade fluids or generalized Newtonian fluids. We find that for the fluids in this class the first normal stress difference may change sign as the shearing changes, and we find an interesting linkage between such sign alterations and potential local instabilities in the flow field. Finally, we examine the global stability of the rest state for our fluids and show that if the free energy has a strict, gobal minimum in equilibrium, then our fluids are better behaved than any Navier‐Stokes fluid, since not only does the kinetic energy of any disturbance decay in mean but so too does a certain positive definite function of the stretching tensor.
26(1982); http://dx.doi.org/10.1122/1.549689View Description Hide Description
26(1982); http://dx.doi.org/10.1122/1.549690View Description Hide Description