On the use of continuous spectrum and discrete-mode differential models to predict contraction-flow pressure drops for Boger fluids

Over recent years, there has been slow but steady progress towards the qualitative numerical prediction of observed behaviour when highly elastic Boger fluids flow in contraction geometries. This has led to an obvious desire to seek quantitative agreement between prediction and experiment, a subject which is addressed in the current paper. We conclude that constitutive models of non-trivial complexity are required to make headway in this regard. However, we suggest that the desire to move from qualitative to quantitative agreement between theory and experiment is making real progress. In the present case with differential models, this has involved the introduction of a generalized continuous spectrum model. This is based on direct data input from material functions and rheometrical measurements. The class of such models assumes functional separability across shear and extensional deformation, through two master functions, governing independently material-time and viscous-response. The consequences of such a continuous spectrum representation are compared and contrasted against discrete-mode alternatives, via an averaged single-mode approximation and a multi-modal approximation. The effectiveness of each chosen form is gauged by the quality of match to complex flow response and experimental measurement. Here, this is interpreted in circular contraction-type flows with Boger fluids, where large experimental pressure-drop data are available and wide disparity between different fluid responses has been recorded in the past. Findings are then back-correlated to base-material response from ideal viscometric flow.