Computational studies of nonlinear elastic dumbbell models of Boger fluids in a cross-slot flow

On extensibility effects in the cross-slot flow bifurcation

“…Table 2a. L 2 = 100 is a typical extensibility value which has been used in many other studies (Bird et al [13]; Remmelgas et al [3]; Oliveira [18]) and so here we are doubling and halving that base extensibility. It is also useful to keep in mind that the UCM and Oldroyd-B models correspond to L 2 = ∞ and the critical Deborah number for the occurrence of a bifurcated solution was found to be De cr ≈ 0.31 by Poole et al [11] for the UCM model.…”

“…5 and 6 for increasing De: these evolve from the centrally symmetrical situation of Newtonian flow -in the absence of convective terms, since Re = 0, the equations of motion are linear and symmetry about both x and y axis must be satisfied (and also about the two diagonals, y = ±x) -to the compressive stresses for the viscoelastic cases along the horizontal channels, and the typical "birefringent strands" due to the strong and localised extensional flow along the centrelines of the vertical channels. These birefringence strands (Harlen et al [1]) have been the focus of much research in previous studies concerned with the cross-slot geometry, in particular researchers have used constant-viscosity models, and modifications to existing ones, in order to predict the longer strands observed in experiments (Remmelgas et al [3]). However, the birefringent strands do not appear to be related to the origin of the bifurcation, which is rather linked to the compressive flow in the inlet channels (Poole et al [11]).…”

“…It is possible to define a polymer concentration parameter c in terms of the solvent viscosity ratioˇ, as was done most notably by Leal and co-workers (Singh and Leal [2]; Remmelgas et al [3] and [7]; and Feng and Leal [8]); thus c = Á p /Á s which implies the relation c = (1/ˇ) − 1. Therefore Boger fluids, whose shear-thinning in shear viscosity is masked by the dominant solvent viscosity, should have values ofˇclose to 1 and hence a small concentration parameter c, while by decreasingˇfrom the Newtonian value of unity, the concentration parameter increases up to infinity.…”

“…Sharp corners are well known to be troublesome in the numerical solution of viscoelastic flow equations (Owens and Philips [22]) and in many of the early simulations of the cross-slot, in which only one quarter of the full geometry was simulated, the corner was artificially rounded by a slight amount (e.g. Remmelgas et al [3]) in order to enable solutions at high Deborah numbers to be obtained. Even experimental studies (Schoonen et al [5]) have followed the route of rounding the corners to avoid extreme stress concentration and allow easier interpretation of the birefringence visualizations.…”

“…Harlen et al [1]; Singh and Leal [2]; Remmelgas et al [3]) because it offers a number of interesting advantages over similar flows. Most significantly it is a geometry that, due to the existence of an interior stagnation point, can generate a high degree of accumulated Hencky strain, much higher than in comparable contraction flows and flow around cylinders, see for instance Peters et al [4].…”