Shear rate modified

The influence of shear rate on membrane structure is illustrated in Figures 31.4 (Ren et al., 2002) and 31.5 (Chung et al., 2002). Figure 31.4 exhibits the cross-section morphology of hollow-fiber membranes spun at shear rates of 812 and 2436 s. Some macrovoids can be observed near the inner skin of fibers spun at a low shear rate (812 s ), while these macrovoids are apparently eliminated or suppressed when the shear rate increases to 2436 s Clearly, high shear rates modify the precipitation path and retard the formation of macrovoids. In addition, with an increase in shear rate, the membrane structure becomes... 

The data structure organization described above has been implemented in the BFM as well as in a very efficient off-lattice Monte Carlo algorithm, discussed in detail in the next chapter, which was modified to handle EP and used to study shear rate effects on GM [57]. 

A Newtonian liquid of viscosity 0.1 N s/m2 is flowing through a pipe of 25 mm diameter and 20 m in lenglh, and the pressure drop is 105 N/m2. As a result of a process change a small quantity of polymer is added to the liquid and this causes the liquid to exhibit non-Newtonian characteristics its rheology is described adequately by the power-law model and the flow index is 0.33. The apparent viscosity of the modified fluid is equal to ihc viscosity of the original liquid at a shear rate of 1000 s L... 

Modify the dependence of viscosity on shear rate, producing low viscosity at high rates, and vice versa. 

The usual approach for non-Newtonian fluids is to start with known results for Newtonian fluids and modify them to account for the non-Newtonian properties. For example, the definition of the Reynolds number for a power law fluid can be obtained by replacing the viscosity in the Newtonian definition by an appropriate shear rate dependent viscosity function. If the characteristic shear rate for flow over a sphere is taken to be V/d, for example, then the power law viscosity function becomes... 

If the ideas of Marrucci [69] are correct and the non-monotonic predictions of the simple Doi-Edwards theory need to be modified in the case of polymer melts (for a recent development see [78]), then an explanation will be required for the apparent difference at high shear rates between melts and wormlike micelle solutions. There is also evidence that ordinary entangled polymer solutions do exhibit non-monotonic shear-stress behaviour [79]. As in the field of linear deformations, it may be that a study of the apparently more complex branched polymers in strong flows may shed light on their deceptively simple linear cous-... 

Shear enhancement effects in foam formation can be understood through the modified cavity model. Shear force behaves as catalyst to reduce energy barrier to allow a quik path from stable gas cavity to unstable bubble phase. It can be concluded that both shear rate and viscosity contribute to foam nucleation in the continuous foam extrusion process. Therefore, proper die opening and process conditions will help to optimise the foam product. 11 refs. 

In the in situ consolidation model of Liu [26], the Lee-Springer intimate contact model was modified to account for the effects of shear rate-dependent viscosity of the non-Newtonian matrix resin and included a contact model to estimate the size of the contact area between the roller and the composite. The authors also considered lateral expansion of the composite tow, which can lead to gaps and/or laps between adjacent tows. For constant temperature and loading conditions, their analysis can be integrated exactly to give the expression developed by Wang and Gutowski [27]. In fact, the expression for lateral expansion was used to fit tow compression data to determine the temperature dependent non-Newtonian viscosity and the power law exponent of the fiber-matrix mixture. 

The lowering of die swell values has a direct consequence on the improvement of processability. It is apparent that the processability improves with the incorporation of the unmodified and the modified nanofillers. Figure lOa-c show the SEM micrographs of the surface of the extrudates at a particular shear rate of 61.2 s 1 for the unfilled and the nanoclay-filled 23SBR systems. The surface smoothness increases on addition of the unmodified filler, and further improves with the incorporation of the modified filler. This has been again attributed to the improved rubber-clay interaction in the exfoliated nanocomposites. 

Ibrahin (II) has published an addition to the Navier-Stokes equations which was intended to modify them for use with non-Newtonian fluids. The modification was only for the purpose of taking fluid elasticity into account, a factor which does not appear to be necessary for the majority of materials showing non-Newtonian behavior. Instead, a redevelopment of the original equations to allow for variations in viscosity with shear rate is required, an approach that would appear to be very complex but perhaps rewarding. 

The unsuitable nature of many commercial instruments which are in common use clearly illustrates the confusion prevalent in the field of viscometric measurements. Many instruments measure some combination of properties which depend only partly on the fluid consistency since the flow is not laminar. In others the shear rates are indeterminate and the data cannot be interpreted completely. Examples of such units include rotational viscometers with inserted baffles, as in the modified Stormer instruments in which the fluid flows through an orifice, as in the Saybolt or Engler viscometers instruments in which a ball, disk, or cylinder falls through the fluid, as in the Gardiner mobilometer. Recently even the use of a vibrating reed has been claimed to be useful for measurement of non-Newtonian viscosities (M14, W10), although theoretical studies (R6, W10) show that true physical properties are obviously not obtainable in these instruments for such fluids. These various instru-... 

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