Enhanced pressure drop, planar contraction flows and continuous spectrum models

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 [1]. 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 [2], [3]. 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 [3]. 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 [1], absent in tubular flows, are also predicted under the associated regime of high deformation-rates where enhanced pressure-drop arise

Hyperbolic contraction measuring systems for extensional flow

In this paper an experimental method for extensional measurements on medium viscosity fluids in contraction flow is evaluated through numerical simulations and experimental measurements. This measuring technique measures the pressure drop over a hyperbolic contraction, caused by fluid extension and fluid shear, where the extensional component is assumed to dominate. The present evaluative work advances our previous studies on this experimental method by introducing several contraction ratios and addressing different constitutive models of varying shear and extensional response. The constitutive models included are those of the constant viscosity Oldroyd-B and FENE-CR models, and the shear-thinning LPTT model. Examining the results, the impact of shear and first normal stress difference on the measured pressure drop are studied through numerical pressure drop predictions. In addition, stream function patterns are investigated to detect vortex development and influence of contraction ratio. The numerical predictions are further related to experimental measurements for the flow through a 15:1 contraction ratio with three different test fluids. The measured pressure drops are observed to exhibit the same trends as predicted in the numerical simulations, offering close correlation and tight predictive windows for experimental data capture. This result has demonstrated that the hyperbolic contraction flow is well able to detect such elastic fluid properties and that this is matched by numerical predictions in evaluation of their flow response. The hyperbolical contraction flow technique is commended for its distinct benefits: it is straightforward and simple to perform, the Hencky strain can be set by changing contraction ratio, non-homogeneous fluids can be tested, and one can directly determine the degree of elastic fluid behaviour. Based on matching of viscometric extensional viscosity response for FENE-CR and LPTT models, a decline is predicted in pressure drop for the shear-thinning LPTT model. This would indicate a modest impact of shear in the flow since such a pressure drop decline is relatively small. It is particularly noteworthy that the increase in pressure drop gathered from the experimental measurements is relatively high despite the low Deborah number range explored

Hermeneutic musings on learning: the dialogical nature of teaching interpretively

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Modelling of Industrial Processes for Polymer Melts: Extrusion and Injection Moulding

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