Steady shear

Shear, steady and dynamic, transient elongational rheology... 

LCPs exhibit in simple shear steady-flow several rheological effects, uncommon to polymers with long flexible chains. The first is negative normal stresses observed in some LCPs. The second is the effect of three-region viscosity shown schematically in Figure 11.1. 

Figure A3.1.5. Steady state shear flow, illustrating the flow of momentum aeross a plane at a height z.

Koelman J M V A and P J Hoogerbrugge 1993. Dynamic Simulations of Hard-sphere Suspensio Under Steady Shear. Europhysics Letters 21 363-368. 

Theoretically the apparent viscosity of generalized Newtonian fluids can be found using a simple shear flow (i.e. steady state, one-dimensional, constant shear stress). The rate of deformation tensor in a simple shear flow is given as... 

Figure 5,16. It is assumed that by using an exactly symmetric cone a shear rate distribution, which is very nearly uniform, within the equilibrium (i.e. steady state) flow held can be generated (Tanner, 1985). Therefore in this type of viscometry the applied torque required for the steady rotation of the cone is related to the uniform shearing stress on its surface by a simplihed theoretical equation given as...

Kaye, A., Lodge, A. S. and Vale, D. G., 1968. Determination of normal stress difference in steady shear flow. Rheol. Acta 7, 368-379. 

Atomization. A gas or Hquid may be dispersed into another Hquid by the action of shearing or turbulent impact forces that are present in the flow field. The steady-state drop si2e represents a balance between the fluid forces tending to dismpt the drop and the forces of interfacial tension tending to oppose distortion and breakup. When the flow field is laminar the abiHty to disperse is strongly affected by the ratio of viscosities of the two phases. Dispersion, in the sense of droplet formation, does not occur when the viscosity of the dispersed phase significantly exceeds that of the dispersing medium (13). 

High molecular weight components, which can be important in extmsion processes, can be accurately measured in steady shear experiments (34). 

Fig. 7. Decay of shear stress during steady shear at various shear rates. Determination of zero-time shear stresses or yield stresses and equiUbrium shear...

Normal Stress (Weissenberg Effect). Many viscoelastic fluids flow in a direction normal (perpendicular) to the direction of shear stress in steady-state shear (21,90). Examples of the effect include flour dough climbing up a beater, polymer solutions climbing up the inner cylinder in a concentric cylinder viscometer, and paints forcing apart the cone and plate of a cone—plate viscometer. The normal stress effect has been put to practical use in certain screwless extmders designed in a cone—plate or plate—plate configuration, where the polymer enters at the periphery and exits at the axis. 

Rotational viscometers often were not considered for highly accurate measurements because of problems with gap and end effects. However, corrections can be made, and very accurate measurements are possible. Operating under steady-state conditions, they can closely approximate industrial process conditions such as stirring, dispersing, pumping, and metering. They are widely used for routine evaluations and quahty control measurements. The commercial instmments are effective over a wide range of viscosities and shear rates (Table 7). 

Dyna.mic Viscometer. A dynamic viscometer is a special type of rotational viscometer used for characterising viscoelastic fluids. It measures elastic as weU as viscous behavior by determining the response to both steady-state and oscillatory shear. The geometry may be cone—plate, parallel plates, or concentric cylinders parallel plates have several advantages, as noted above. 

The Weissenberg Rheogoniometer (49) is a complex dynamic viscometer that can measure elastic behavior as well as viscosity. It was the first rheometer designed to measure both shear and normal stresses and can be used for complete characteri2ation of viscoelastic materials. Its capabiUties include measurement of steady-state rotational shear within a viscosity range of 10 — mPa-s at shear rates of, of normal forces (elastic... 

The RMS-800 provides steady-shear rotational rates from 10 to 100 rad/s and oscillatory frequencies from 10 to 100 rad/s. An autotension device compensates for expansion or contraction. With the standard 25- and 50-mm parallel plates, the viscosity range is 50-10 mPa-s, and the shear modulus range is 8 x 10 to 10 N/m. These ranges can be expanded with nonstandard plates, cones, and a Couette system. The temperature range is 20-350°C (-150 0 optional). 

Open-loop systems have inherently long residence times which may be detrimental if the retentate is susceptible to degradation by shear or microbiological contamination. A feed-bleed or closed-loop configuration is a one-stage continuous membrane system. At steady state, the upstream... 

For steady-state laminar flow of any time-independent viscous fluid, at average velocity V in a pipe of diameter D, the Rabinowitsch-Mooney relations give a general relationship for the shear rate at the pipe wall. 

Steady-propagating plastic waves [20]-[22] also give some useful information on the micromechanics of high-rate plastic deformation. Of particular interest is the universality of the dependence of total strain rate on peak longitudinal stress [21]. This can also be expressed in terms of a relationship between maximum shear stress and average plastic shear strain rate in the plastic wave... 

The flow in the diffuser is usually assumed to be of a steady nature to obtain the overall geometric configuration of the diffuser. In a channel-type diffuser the viscous shearing forces create a boundary layer with reduced kinetic energy. If the kinetic energy is reduced below a certain limit, the flow in this layer becomes stagnant and then reverses. This flow reversal causes... 

Figure 10 Relaxation of shear stress with time upon cessation of steady flow. (O) Resin A, ( ) Resin B, (O) Resin C, (A) Resin D, (A) Resin E. (Refer to Table 2 for symbol code.) Source Ref. 56.

The purpose of our study was to model the steady-state (capillary) flow behavior of TP-TLCP blends by a generalized mathematical function based on some of the shear-induced morphological features. Our attention was primarily confined to incompatible systems. 

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