Wall shear stress, critical

Fig. 8 shows DR vs. of a typical DR cationic surfactant with counterion solution, Ci7H35N(CH3)3Cl/ 3,4-Cl-benzoate (5mM/12.5mM). Drag reduction reaches a maximum of 65%. In the effective temperature range (15-85°C), DR first increases with Arc until a critical Arc (critical wall shear stress) is reached above which it begins to lose its DR ability because of the... 

The amount, flexibility, and strength of the threadlike micelles determine the temperature range, critical wall-shear stress, and maximum DR ability of surfactant solutions. 

Micelle growth is favored by an increase in f, as is critical wall shear stress for drag reduction [Rose and Foster, 1989 Chou, 1991 Lu, 1997 Lu et al., 1998b Lin et al., 2001]. However, at high values of f, some systems become insoluble [Qi, 2002]. The effect of I on TLM formation is complex, depending on both molecular structures... 

Zhang et al. [2005b] studied the effects of various percents of ethylene glycol in water (15,20, and 28%) on cationic surfactant solution properties. Using commercial cationics from Akzo Nobel (Ethoquad 012 and 013), they observed that the cosolvent reduced the upper temperature limit for drag reduction, maximum percent drag reduction, maximum critical wall shear stress, and relative shear viscosity. The formation of TLMs was hampered, but the addition of excess sodium salicylate promoted TLM... 

Many authors have studied the melt fracture of polypropylene. Bartos [97] found for a variety of polypropylene resins that the critical wall shear stress for melt fracture ranged from... 

However, there is relatively uniform agreement that melt fracture is triggered when a critical wall shear stress Is exceeded in the die. This critical stress is in the order of 0.1 to 0.4 MPa (15 to 60 psi). A number of mechanisms have been proposed to explain melt fracture. Some of the more popular ones are ... 

Streamlining the flow channel geometry has been found to reduce the tendency for melt fracture in branched polymers. Increased temperatures, particularly at the wall of the die land, enable higher extrusion rates before melt fracture appears. The critical wall shear stress appears to be relatively independent of the die length, radius, and temperature. The critical stress seems to vary inversely with molecular weight, but seems to be independent of MWD. Certain polymers exhibit a superextrusion region, above the melt fracture range, where the extrudate is not distorted... 

A statistical fit of the data for LDPE leads to the following empirical expression for the critical wall shear stress for fracture (Middleman, 1977) ... 

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