It is widely recognised that the development and optimisation of industrial processes such as extrusion or injection moulding signiﬁcantly beneﬁt from accurate polymer processing simulations. Such simulations can lead to enormous cost savings, time to market and product improvements. The development of suitable constitutive models and a robust numerical algorithm are required for successful application of such tool to these processes. Appropriate material characterisation is also imperative to select the constitutive model parameters.
Despite the importance and maturity of the polymer processing industry, the constitutive modelling of the rheological behaviour of long chain branched polymers presents still fascinating questions that need some answers. A breakthrough in this area was the design of a constitutive equation based on molecular arguments and known as the pom-pom model. The key feature of this model is the presence of separate relaxation times for the orientation and stretch mechanisms. The pompom model has been proved to be very accurate for the modelling of long chain branched polymers in rheometrical ﬂows.
Although very promising, this model suﬀers from numerical and rheological defects that hinder its use in complex ﬂow simulations. To overcome these issues, the Double Convected pom-pom (DCPP) model is proposed. Its predictive capabilities are ﬁrst analysed in various rheometrical ﬂows including reverse multi-step shear strain and large amplitude oscillatory shear experiments. For complex ﬂow simulation, the DCPP model is implemented in the commercial package POLYFLOW™. Model predictions are compared to experimental birefringence data in planar contraction ﬂows. In all cases, a satisfactory agreement is found between numerical simulation and experiments, demonstrating the potential of this model for the simulation of polymer processing operations.
The simulations are then extended to three-dimensional geometries. The inﬂuence of non-perfectly two-dimensional ﬂows on birefringence data is analysed. It is shown that the impact of these imperfections is strongly dependent on the ﬂow rate. Is is commonly believed that increasing the geometry aspect ratio tends to decrease three-dimensional inﬂuence. It is demonstrated that this is veriﬁed only if the zero-order fringe does not disappear at any time during the experiment.
Finally, a pragmatic approach is introduced to reformulate constitutive equations to explicitly express them in terms of orientation and stretch variables. This procedure is applied to the Phan-Thien Tanner and Giesekus models and both models are compared to the DCPP model. Comparing the models in this form, highlights their diﬀerences, and allows one to adopt the best features of each. This almost naturally leads to a proposal of a number of modiﬁcations to each of these models.
The modiﬁed models are then assessed in rheometrical ﬂows by comparing model predictions to experimental data. Signiﬁcant improvements are demonstrated for in particular the Modiﬁed Giesekus model and the Modiﬁed DCPP: both models perform remarkably well in a range of non-linear rheometric ﬂows, and are therefore promising candidates for predicting industrial ﬂow problems.