On flows of viscoelastic liquids in long channels and dies

Numerical investigation of the velocity overshoots in the flow of viscoelastic fluids inside a smooth contraction

“…The patterns of the secondary flow are symmetric about the diagonal and the two mid-planes in the inlet square duct (x/h = −70), whereas increasing aspect ratio expands the vortices near the top and bottom walls while squeezing them near the side walls (x/h = 120). Nevertheless, in all cases there are eight vortices as expected [18,36,37].…”

“…For square ducts, the secondary motion in fully developed laminar flow of viscoelastic fluids was first investigated numerically by Wheeler and Whissler [32] and Townsend et al [33], both numerically and experimentally. More recently, Gervang and Larsen [34], Debbaut et al [35] and Siline and Leonov [36] showed that the magnitude of the secondary-flow velocities are typically two orders of magnitude lower than that of the streamwise velocity (the secondary motion actually varies with the fourth power of the axial velocity at low shear rates and linearly with the axial velocity at high shear rates according to Refs. [35,36]).…”

Fully-developed pipe and planar flows of multimode viscoelastic fluids

“…It is the case of Hulsen [12] and Siline and Leonov [13] for the Giesekus and Leonov models, but also of Georgiou [14] for the Oldroyd-B model and of Georgiou and Vlassopoulos [15] for the model of Johnson and Segalman [16] in steady flow and of Fyrillas et al [17] for unsteady flows. Many other analytical contributions can be found in the specialized journals, such as the Journal of Non-Newtonian Fluid Mechanics and Rheologica Acta, or earlier in the Quaterly Journal of Mechanics and Applied Mathematics, among others.…”

Laminar flow of non-linear viscoelastic fluids in straight tubes of arbitrary contour

“…Similarly as e ? 0 the limit of the elastic non-linearity and shear-thinning contributed velocities (16) and (17) It is worthwhile to note that the exact analytical solution for the longitudinal velocity field of the MPPT fluid in round tubes in pressure gradient driven flows is given by (Eq. (15)), Letelier and Siginer [19], when both e o -0 -n. The expression equivalent to the longitudinal field up to and including O(Wi 2 )…”

“…In the ensuing years the field evoked little interest among researchers in non-Newtonian fluid mechanics until the fundamental and industrial importance of secondary flows regained the attention of researchers starting from the early nineties on, Gervang and Larsen [12], Xue et al [13], Debbaut et al [14], Debbaut and Dooley [15] and Siline and Leonov [16]. In all these investigations the flow is assumed to be steady.…”