Shear flow phenomenon

In their milestone work, Melander and Hussain found that the method of complex helical wave decomposition was instrumental in modeling both laminar as well as turbulent shear flows associated with coherent vortical structures, and revealed much new important data about this phenomenon than had ever been known before through standard statistical procedures. In particular, this approach plays a crucial role in the description of the resulting intermittent fine-scale structures that accompany the core vortex. Specifically, the large-scale coherent central structure is responsible for organizing nearby fine-scale turbulence into a family of highly polarized vortex threads spun azimuthally around the coherent structure. 

The sine form of the damping function leads to another major problem, which lays in the occurrence of undesirable oscillations in transient shear flows (Figure 11). This phenomenon may be misleading for example when modelling instabilities in complex flows, since it is then hardly possible to distinguish between real phenomena and those generated by the model itself. 

D.S. Malkus, J.A. Nohel and B.J. Plohr, Analysis of a new phenomenon in shear flow of non-Newtonian fluids, SIAM J. Appl. Math., 51 (1991) 899-929. 

In stress growth at inception of steady shearing flow, the rigid dumbbells give a stress expression which is dependent on the steady-state shear rate however, elastic dumbbells do not. Also the rigid dumbbell model predicts stress overshoot, a phenomenon which the elastic dumbbell model cannot describe. 

Turbulent flow consists of a mass of eddies of various sizes coexisting in the flowing stream. Large eddies are continually formed. They break down into smaller eddies, which in turn evolve still smaller ones. Finally, the smallest eddies disappear. At a given time and in a given volume, a wide spectrum of eddy sizes exists. The size of the largest eddy is comparable with the smallest dimension of the turbulent stream the diameter of the smallest eddies is 10 to 100 pim. Smaller eddies than this are rapidly destroyed by viscous shear. Flow within an eddy is laminar. Since even the smallest eddies contain about 10 molecules, all eddies are of macroscopic size, and turbulent flow is not a molecular phenomenon. 

Small amplitude dynamic viscoelastic properties of apple butter, mustard, table margarine, and mayonnaise were compared to their respective properties in steady shear flow in the range of shear rates and frequencies of 0.1 to 100 sec" (Bistany and Kokini, 1983). Comparisons of dynamic and steady viscosities showed that dynamic viscosities (tj ) are much greater than steady viscosities (17). Consequently, the Cox-Merz rule is not obeyed (Bistany and Kokini, 1983). This phenomenon can be explained by a signifi-... 

The phenomenon of hydrodynamic diffusion in a shear flow, and also its possible applications are discussed in [70]. 

Fig. 8.8 An ensemble-average extensional equivalent stress-strain curve of amorphous polypropylene, derived from axial extension and shear-flow ensembles of separate simulations. The smoothed broken line, average curve, drawn-in by eye, shows clear elasto-plastic behavior and a beginning yield phenomenon (from Mott et al. (1993) courtesy of Taylor and Francis).

When there is a prominent dilatancy effect in the flow phenomenon arising from the interaction of the shear-induced dilatation, with a prevailing mean normal stress (Tin, this is often considered to make the critical threshold resistance in shear T dependent on through a friction coefficient... 

The molecular dynamics theories need to make a proper combination to describe the rheological behaviors of polymer melt in various regions of shear rates (Bent et al. 2003). Above 1/t the convective constraint release dominates the rheological behaviors of polymers in shear flow, and thus explains the shear-thinning phenomenon. Beyond 1/t, the extensional deformation reaches saturation, and the shear flow becomes stable, entering the second Newtonian-fluid region, as demonstrated in Fig. 7.6. 

In the year 1949, Toms (1) observed that the pressure drop in a turbulent pipe flow becomes substantially smaller when a minute amount of a polymer is added to the flow medium. One has since attempted to understand this effect. Known as Toms phenomenon, this effect is found in all wall-bounded turbulent shear flows. 

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