On the Role Played by the Extensional Behavior of Giesekus Fluids in Plane Stagnation Flow

Abstract

An exact solution has been found in plane stagnation flow for a viscoelastic fluid obeying the Giesekus model. The flow was found to render itself to a local similarity solution in the vicinity of the stagnation point. The solution so obtained could easily enable one to investigate the effects of parameters such as Reynolds number, Weissenberg number and the mobility factor on the velocity and stress fields. Unlike Newtonian and Maxwellian fluids, the thickness of the boundary layer was found to be a decreasing function of the distance from the stagnation point. It will be shown that this effect may have roots in the extensional behavior of the fluid.

Revisiting boundary layer flows of viscoelastic fluids

“…This model is only slightly more complex than the upper-convected Maxwell model, and it should be noted that under the correct limiting choice of constants, the Giesekus model reduces in complexity to UCM. However, upon comparison of both our own UCM results (and those of Phan-Thien [21]) with those presented by Mirzadeh and Sadeghy [23], we note a discrepancy between the reported values for the boundary layer thickness, 𝛥 99 . Again, this is the only tangible reported value that we can make any comparison to.…”

“…In an attempt to extend the study of SHT, Mirzadeh and Sadeghy [23] return to the stagnation point flow problem, and consider a Giesekus governing viscosity law. This model is only slightly more complex than the upper-convected Maxwell model, and it should be noted that under the correct limiting choice of constants, the Giesekus model reduces in complexity to UCM.…”

“…1 Lastly, our solution method benefits from the possibility of evaluating moderate levels of viscoelastic effects. Previous studies [15,[21][22][23] only show results for a relatively low ratio of elastic to viscous effects, in some cases due to the imposition of a boundary condition which restricts the validity of the range of their dimensionless parameters.…”

Effect of non-affine motion on the centrifugal instability of circular Couette flow

“…We consider confined flow between two infinitely-long concentric cylinders of radii 1 R and 2 R as shown in Fig. 1.…”

“…The chance of finding an exact solution becomes less probable when the degree of sophistication of the model is increased. For example, while for Giesekus fluids an exact solution does exist in plane stagnation-point flow [1], no such a solution could be found for the Phan-Thien/Tanner (PTT) fluids. This is rather unfortunate because the PTT model is one of the best rheological models when it comes to representing polymeric melts and concentrated polymer solutions.…”