The linear stability analysis of Rivlin-Ericksen fluids of second order is investigated for boundary layer flows, where a semi-infinite wedge is placed symmetrically with respect to the flow direction. Second order fluids belong to a larger family of fluids called order fluids, which is one of the first classes proposed to model departures from Newtonian behavior. Second order fluids can model non-zero normal stress differences, which is an essential feature of viscoelastic fluids. The linear stability properties are studied for both signs of the elasticity number K, which characterizes the non-Newtonian response of the fluid. Stabilization is observed for the temporal and spatial evolution of two-dimensional disturbances when K > 0 in terms of increase of critical Reynolds numbers and reduction of growth rates, whereas the flow is less stable when K < 0. By extending the analysis to three-dimensional disturbances, we show that a positive elasticity number K destabilizes streamwise independent waves, while the opposite happens for K < 0. We show that, as for Newtonian fluids, the non-modal amplification of streamwise independent disturbances is the most dangerous mechanism for transient energy growth, which is enhanced when K > 0 and diminished when K < 0.

Smart Separations Limited (SSL) is a UK-based start-up who have developed a ceramic membrane with micron-sized conical pores distinct to the cylindrical pores typically used for filtration. This new technology has the potential to be highly beneficial to many applications. However to realize its potential, a comprehensive analysis of the performance and efficiency of the membrane is vital. We use mathematical modelling to explore and quantify the behaviour and performance of the membrane and its link to the underlying pore structure. We derive a reduced model based on the slenderness of the membrane pores that allows us to predict the flux through the membrane, the optimal pore shape that maximizes the amount of contaminant that is trapped. A full 2D numerical framework allows us to study the flow structure within the pores and the effect of changing the angle of the flow of contaminants as it reaches the membrane. Finally, a probabilistic model based on expectation values provides an analytic prediction for the flux decline with time due to membrane blocking. The outcomes of this work provide a first step to providing the key modelling insight that will allow SSL to take this new technology to market.

This work presents a numerical model for the simulation of package sealing in industrial machines for beverage packaging. The simulations are aimed at the prediction of the temperature field in all the layers of the polylaminate material composing the package. The package sealing is in fact carried out by means of thermal welding. Thus, accurate predictions of the temperatures following the package heating via hot air jet and right before the folding flaps are pressed together is paramount to in turn predict sealing success. The heat equation is solved in the package volume by means of a plate FEM formulation in which arbitrary order Lagrangian shape function are used for both the longitudinal and the normal discretization. The resulting semi-discretized equations are time advanced by means of an Implicit Euler scheme with constant time step. The solution of the system is complemented by forward sensitivity computation to obtain, at each time step, quantitative assessment of the effect of process parameters variations on the temperature output. The numerical results are compared to experimental measurements so as to validate the developed simulation tool. The results obtained suggest that the solver is able to reproduce with satisfactory accuracy the experimental temperature field evolution in the portion of the package interested by the thermal welding.

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