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Enhanced pressure drop, planar contraction flows and continuous spectrum models
Journal of Non-Newtonian Fluid Mechanics, Volume: 273, Start page: 104184
Swansea University Authors: Michael Webster , Hamid Tamaddon-Jahromi
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DOI (Published version): 10.1016/j.jnnfm.2019.104184
This study addresses a rheological problem that has been outstanding now for the past few decades, raised by the experimental findings of Binding and Walters . There, it was established experimentally that planar contraction flows for some Boger fluids could display enhanced pressure-drops above...
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This study addresses a rheological problem that has been outstanding now for the past few decades, raised by the experimental findings of Binding and Walters . There, it was established experimentally that planar contraction flows for some Boger fluids could display enhanced pressure-drops above Newtonian flows, as was the case for their tubular counterparts. Nevertheless, flow-structures to achieve this result were reported to be markedly different, planar to circular. In this article, it is shown how predictive differential-viscoelastic solutions with continuum models can replicate these observations. Key to this success has been the derivation of a new definition for the third-invariant of the rate-of-deformation tensor in planar flows, mimicking that of the circular case , . This provides a mechanism to successfully incorporate dissipation within planar flows, as performed earlier for tubular flows. Still, to reach the necessary large deformation-rates to achieve planar enhanced pressure-drops, and whilst maintaining steady flow-conditions, it has been found crucial to invoke a continuous-spectrum relaxation-time model . The rheological power and flexibility of such a model is clearly demonstrated, over its counterpart Maxwellian single-averaged relaxation-time approximation; the latter transcending the boundaries of steady-to-unsteady flow to manifest equivalent levels of enhanced pressure-drops. Then, the role of extensional viscosity and first normal-stress difference, each play their part to achieve such planar enhanced pressure-drops. As a by-product, the distinctive planar ‘bulb-flow’ structures discovered by Binding and Walters , absent in tubular flows, are also predicted under the associated regime of high deformation-rates where enhanced pressure-drop arise.
Boger fluids, Planar contraction flow, Pressure-drop enhancement, SwAM model