Viscoelastic simulations using the closed-form Adaptive Length Scale (ALS-C) model

In this paper we employ the closed-form of the Adaptive Length Scale Model (ALS-C) [Ghosh et al., "A new model for dilute polymer solutions in flows with strong extensional components", J. Rheol. 46, 1057–1089 (2002)] and we investigate its characteristics and potential to more accurately capture pressure-drop in contraction flows of viscoelastic fluids. The ALS-C model was originally derived based on purely homogeneous elongational flows in order to model coil-stretch hysteresis. However, in its originally proposed form we reveal a number of numerical issues which have not been analysed previously and are reported here considering both standard rheological flows, simple channel flows and complex flows within a 4:1 contraction. We demonstrate a new approach for evaluating the instantaneous change in the adaptive length scale as a result of instantaneous changes in the flow field, overcoming the need to employ other root-finding approaches. Guidelines are provided for the correct use of the employed local Weissenberg number and a modified approach is considered for the evolution equation of the actual extensibility, allowing its efficient use in complex numerical simulations. We illustrate that a suitable combination of the model parameters can produce behaviours that are found experimentally in viscoelastic fluids and we find that pressure-drop enhancements in flows within 4:1 contractions observed experimentally are achievable.