Converging flow

Extensional Viscosity. AH three types of extensional viscosity can be measured (101,103) uniaxial, biaxial, and pure shear. Only a few commercial instmments are available, however, and most measurements are made with improvised equipment. Extensional viscosity of polymer melts can be estimated from converging flow (entrance pressure) or from a melt strength drawdown test (208). 

Flow through a convergent channel, either two-dimensional or axisymmetric, are probably the most investigated geometries (due to their connection with the technical die entry flow problem). Most of the other convergent flows could be derived from the abrupt contraction flow which is depicted schematically in Fig. 25. 

By using a tapered inlet instead of an abrupt constriction, different variations of convergent flow could be envisioned axisymmetric flow in a conical channel... 

The residence time of a fluid element entering the region of high strain rate, along any streamline, is typically of the order of r0/v0 or 2-10 (is under present flow conditions. These converging flows are termed transient due to this short residence time. 

Fig. 56. Schematic representation of the convergent flow apparatus < > = 180° (abrupt contraction), 14° or 5° (conical inlet)

Elongation flow fields are likely to be present whenever streamlines cease to be parallel and in particular converging flow typical of that at the entrance of, for example, a capillary flow device is known to develop strong stretching flow The strength of elongational flow at the entrance of a capillary can be determined by one of several equations [106]. In the case of capillary flow, an estimate of the normal (tensile) stress at the entrance can be obtained from ... 

Rupture of fractal (flocculated) aggregates of polystyrene latices in simple shear flow and converging flow was studied by Sonntag and Russel (1986, 1987b). For simple shear flow and low electrolyte concentrations, the critical fragmentation number decreases sharply with agglomerate radius (R) as... 

Pipe number Length / (ft) Diameter d (in.) Estimated flow rate 4° (gpm) Converged flow rate 4 (gpm)... 

For a Newtonian liquid, there is negligible frictional loss due to the converging flow. However, a vena contracta forms in the smaller pipe and the expansion and reattachment downstream of it are similar to the flow in the sudden expansion. The difference is that it takes place from dc to dl2. The momentum equation cannot be applied over the whole flow because... 

Harrison PJ, Newton JM, Rowe RC. Convergent flow analysis in the extrusion of wet powder masses. J Pharm Pharmacol 1984 36 796-798. 

Trial Estimates and Converged Flow Rates and Compositions in All Stages id an Extraction Battery Cor a Emu-Component Mixture... 

The gas flow toward the pinhole is a converging flow. The ratio of the flow cross-sectional area to the area in the pinhole, for isentropic flow of an ideal gas is... 

D.M. Binding, An Approximate Analysis for Contraction and Converging Flows, J. Non-Newt. Fluid Mech., 27 173-189 (1988). 

For the ideal case of frictionless flow, every term in the brackets is zero, resulting in a coefficient of unity. The same result may be produced in a real flow if the sum of all the terms in the brackets is zero. The friction hf is always positive, but in converging flow the sum of the other two terms can be negative. 

Reactions r-j dwniitry l Reactions Convergence Flows heeling Cptlons... 

Fig. 12.4, the melt is forced into a converging flow pattern and undergoes a large axial acceleration, that is, it stretches. As the flow rate is increased, the axial acceleration also increases, and as a result the polymer melt exhibits stronger elastic response, with the possibility of rupturing, much like silly putty would, when stretched fast. Barring any such instability phenomena, a fully developed velocity profile is reached a few diameters after the geometrical entrance to the capillary. 

The opposite behavior as sketched before was detected for solutions of PS in DOP [112], Again, the critical temperature (an UCST at Tc = 12 °C in the quiescent state) turned out to be a function of the shear rate to which the solution is subjected. But, in contrast to solutions of PS and PB in DOP, here enhancements of the UCST as large as 28 °C were recorded at a shear rate of 220 s-1. Similar results have been found for PS solutions in di(2-ethyl hexyl)phthalate or in a mixture of cis- and frans-decalin [113], The solutions demixed in a converging flow from a reservoir into a capillary tube. It has been observed that an increase in the deformation rate raised the UCST or reduced the region of miscibility. In both of these studies an increase of the cloud point temperature of the polymer solutions was used as an indication of phase separation. 

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