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

Developments in the Flow of Complex Fluids in Tubes

“…2.5a) and corresponding to the viscoelastic fluid (Eq. 2.6) of the K-BKZ type, the Papanastasiou model [21] of the same zero shear viscosity μ 0 , are quite different, thereby affirming that elasticity plays a significant role in determining the longitudinal flow field along the lines of the findings of Siginer and Letelier [15].…”

“…The work of Siginer and Letelier [15] as well as of Ahmeda et al [20] clearly demonstrates the effect of elasticity in computing the longitudinal field and the related components of the stress tensor. The conjecture that the longitudinal fields of viscoelastic fluids and purely viscous fluids of the power-law type are one and the same in tubes of arbitrary cross sections and can be predicted with good accuracy, if a modified Reynolds number of the Kozicki (Eq.…”

“…But on the basis of the evidence available for rectangular cross sections, it makes sense to extend the findings for rectangular cross sections to arbitrary cross sections and assume that unless future experimental evidence proves the contrary pressure drop in the fully established laminar flow of viscoelastic fluids in tubes of arbitrary but constant cross section in the longitudinal direction is well predicted by the generalized Newtonian model. However, recent research by Siginer and Letelier [15] provides evidence that elastic effects clearly contribute to the longitudinal velocity field, and thus predicting the longitudinal velocity field with power-law type of constitutive equations that does not account for elastic effects, reasonably good that the predictions may be, would give only approximately correct results. Siginer and Letelier [15] have studied the fully developed steady pressure-gradient-driven laminar flow of a class of non-linear and non-affine, single mode, quasilinear viscoelastic fluids with instantaneous elasticity in straight tubes of arbitrary cross section.…”

“…However, recent research by Siginer and Letelier [15] provides evidence that elastic effects clearly contribute to the longitudinal velocity field, and thus predicting the longitudinal velocity field with power-law type of constitutive equations that does not account for elastic effects, reasonably good that the predictions may be, would give only approximately correct results. Siginer and Letelier [15] have studied the fully developed steady pressure-gradient-driven laminar flow of a class of non-linear and non-affine, single mode, quasilinear viscoelastic fluids with instantaneous elasticity in straight tubes of arbitrary cross section. The class of viscoelastic fluids investigated includes the non-affine Johnson-Segalman [16] and Phan-Thien [18] models and the affine Phan-Thien-Tanner [17] model as special cases (see Sect.…”

“…3.6.1 for details). A continuous oneto-one mapping is used to obtain arbitrary tube contours from a base tube contour ∂D o , Siginer and Letelier [15]. The analytical method presented is capable of predicting the velocity field in tubes with arbitrary cross section.…”