Laminar jets of Bingham‐plastic liquids

Abstract

The steady and transient behavior of jets generated by circular and slit nozzles are analyzed by the Galerkin finite-element method with free-surface parametrization and Newton iteration. A novel constitutive equation is used to approximate Bingham liquids that is valid uniformly in yielded and unyielded domains and which approximates the ideal Bingham model and the Newtonian liquid in its two limiting behaviors. At steady state the influence of yield stress on the die swell is equivalent to that of surface tension; that is, suppression of jet diameter at low Reynolds numbers and necking at high Reynolds number. The predictions at high Reynolds numbers agree with the asymptotic behavior at infinite Reynolds number of the jet far downstream. In the transient analysis, surface tension destabilizes round jets and increases the size of satellite drops. Yield stress was found to retard jet breakup times in addition to producing smaller satellites. Shear thinning was found to result in shorter collapse times than those for Newtonian fluid; furthermore, the satellite drop size increased with increasing shear thinning. The nonlinear analysis predicts that, although round jet breakup may occur spontaneously by surface tension, an external factor, commonly air shear, must be applied to break a planar jet at Reynolds numbers below its transition to a turbulent jet.

Simulation of viscoelastic and viscoelastoplastic die-swell flows

“…Subsequently, such a modified model has found wide appeal and been applied to several types of flow problems, as in: one-dimensional channel flow, two-dimensional boundary layer flow, and two-dimensional extrusion flow [10]. Ellwood et al [11] used the Papanastasiou model to study steady and transient jets from circular and slit nozzles, noting the influence of yield stress on the resulting extrudate. Likewise, Abdali et al [12] solved entry and exit flows of Bingham plastics through planar and axisymmetric 4:1 contractions to determine extrudate swell factors.…”

Effect of colloidal aggregation on the sedimentation and rheological properties of tank waste

“…Many empirical expressions have been developed to fit the viscometric data of non-Newtonian fluids. Models for pseudoplastic fluids include the power law or Ostwald-DeWaele (Bird et al 1960), Cross (1965), Caneau (Ellwood et al 1990), and Biviscous (Kalyon et al 1993) expressions. Models for viscoelastic materials include the Bingham plastic (Bird et al 1960), Casson (Bird et al 1983), Herschel-Bulkley (Bird et al 1983), and Gay @ab& and Yucel 1987) expressions.…”

Yield behavior of commercial Al-Si alloys in the semisolid state

“…The ideal Bingham-plastic behavior can be approximated by relatively large values of m. The accuracy and effectiveness of the Papanastasiou model have been discussed by several researchers. [26][27][28][29][30][31] Dimensional analysis shows that filling depends on two dimensionless parameters, the Reynolds number and the Bingham number, given by [13] where is the density, U 0 is the average inlet velocity, and H is the inlet height.…”