Showing papers on "Second-order fluid published in 1988"

Flow singularity and slip velocity in plane extrudate swell computations

Abstract: It is common knowledge that flows of viscoelastic liquids with stress singularities, like the extrudate swell flow, pose formidable obstacles to numerical computations at relatively low Weissenberg number. This paper describes an effort toward alleviating the stress singularity by means of a slip boundary condition at the die wall. The Oldoyd-B and the upper-convected Maxwell differential constitutive equations were used for simplicity and computational efficiency. With a no-slip boundary condition it was found that for Newtonian, upper-convected Maxwell and Oldroyd-B liquids the global solution was always mesh-dependent until the Newton iteration diverged at very fine tessellations in the vicinity of the static contact line. With a natural slip boundary condition the global solution became mesh-independent at the same tessellations. Moreover, the macroscopic predictions became independent of the amount of slip in a relatively broad region of slip coefficient. The Newton iteration converged up to Weissenberg number 0.6 with a no-slip boundary condition and up to 1.7 with a lip boundary condition for the upper-convected Maxwell liquid. For the Oldroyd-B liquid the maximum Weissenberg number was 0.85 without slip and 1.866 with slip. Although slip velocity, surface tension and Newtonian viscosity (or retardation time) enhanced some numerical stability in general, it appears unlikely that they could advance viscoelastic computations significantly. In the limiting case of no swelling, at infinitely large surface tension, the analytical solution for Newtonian and, a second order fluid showed: (a) elasticity increases the strength of the singularity that exists for Newtonian liquid at the contact line, and thus Newton iteration is expected to diverge at coarser and coarser tessellations as the elasticity increases in agreement with the finite element findings. (b) Finite element predictions for the same flow agreed with the analytical solution in the vicinity of the singularity only when a slip boundary condition was employed. (c) Slip boundary condition in the vicinity of the contact line alleviates the stress singularity. However, it forces the stress to go through a maximum which is equally catastrophic of the Newton iteration convergence.

Stagnation Point Flow of a Non-Newtonian Second Order Fluid

Abstract: In this paper the flow near a two-dimensional stagnation point for a particular non-Newtonian fluid has been studied. For a second order fluid the equation of motion for the stream function has bee...

Experimental estimation of elongational stresses of dilute polymer solutions and a related examination of some constitutive equations

Abstract: Elongational stresses of dilute polymer solutions have been estimated by utilizing the flow through small orifices under the condition of no vortex upstream of the orifice plane. The flow was approximated with a linearly converging flow towards an apex of a cone, its validity being partially confirmed by the measured center velocities, and the elongational stresses are determined from the measured thrusts of dilute polymer solutions. On the other hand, elongational stresses were theoretically obtained with the modified Maxwell model and the second order fluid. A comparison was made between the experimental and the theoretical results and the following points were clarified; below an elongational rate of 2 × 104 s−1 the modified Maxwell model gives elongational stresses close to the experimentally determined ones, but above that elongational rate it deviates from the experimental results. The second order fluid is not sufficient to describe the stresses in this kind of elongational flow and an acceleration term such as δ2eij/δt2 may be necessary in this case.