Shear transient

The orientation angle can be obtained from the Gaussian equation by fitting the scattering data  

The dependence of the ER effect on the dispersed particle conductivity has been comprehensively investigated. As shown earlier, the strongest ER effect was found to occur at the conductivity about 10 S/m for the polyaceneqiiinones/cereclor suspension fllS], and tliere was no detectable ER activity observed once the conductivity shifts far away from this value. A similar result was obtained in oxidized polyacrylonitrilc/siliconc oil suspension and interpreted in view of Maxwell-Wagner polarization [119, 120]. The effect of the particle conductivity on the ER activity was also theoretically analyzed [121-123]. A conduction model was presented for understanding ER phenomena and ER mechanism [124]. The current density of an ER fluid is obviously a very important parameter that scales energy consumption in practical devices. Both the current density and ER activity 

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Many other techniques of measuring viscoelastic parameters, such as transient shear, creep and sinusoidally-varying shear, are available. A good description, together with the merits and demerits of each of these techniques, is available in Whorlow(19. ... 

Lele AK, Mashelkar R A. Energetically crosslinked transient network (ECTN) model implications in transient shear and elongation flows. J Non-Newtonian Eluid Mech 1998 75 99-115. 

As discussed in section 7.1.6.4, semidilute solutions of rodlike polymers can be expected to follow the stress-optical rule as long as the concentration is sufficiently below the onset of the isotropic to nematic transition. Certainly, once such a system becomes nematic and anisotropic, the stress-optical rule cannot be expected to apply. This problem was studied in detail using an instrument capable of combined stress and birefringence measurements by Mead and Larson [109] on solutions of poly(y benzyl L-glutamate) in m-cresol. A pretransitional increase in the stress-optical coefficient was observed as the concentration approached the transition to a nematic state, in agreement of calculations based on the Doi model of polymer liquid crystals [63]. In addition to a dependence on concentration, the stress-optical coefficient was also seen to be dependent on shear rate, and on time for transient shear flows. 

Transient shear stresses following either a flow reversal or a step-up in shear rate show pronounced oscillations, and the period of these oscillations scales with the shear rate [161]. 

Applications of optical methods to study dilute colloidal dispersions subject to flow were pioneered by Mason and coworkers. These authors used simple turbidity measurements to follow the orientation dynamics of ellipsoidal particles during transient shear flow experiments [175,176], In addition, the superposition of shear and electric fields were studied. The goal of this work was to verify the predictions of theories predicting the orientation distributions of prolate and oblate particles, such as that discussed in section 7.2.I.2. This simple technique clearly demonstrated the phenomena of particle rotations within Jeffery orbits, as well as the effects of Brownian motion and particle size distributions. The method employed a parallel plate flow cell with the light sent down the velocity gradient axis. 

S. J. Johnson, P. L. Frattini and G. G. Fuller, Simultaneous dichroism and birefringence measurements of dilute colloidal suspensions in transient shear flow, J. Colloid Interface Sci., 104,440 (1985) S. J. Johnson and G. G. Fuller, Flowing colloidal suspensions in non-Newtonian suspending fluids decoupling the composite birefringence, Rheol. Acta, 25, 405 (1986). 

A.W. Chow, and G.G. Fuller, The rheo-optical response of rod-like chains subject to transient shear flow. Part I Model calculations on the effects of polydispersity, Macromolecules 18, 786 (1985) A.W. Chow, G.G. Fuller, D.G. Wallace and J.A. Madri, The rheo-optical response of rod-like chains subject to transient shear flow. Part II. Two-color flow birefringence measurements, Macromolecules 18,793 (1985) A.W. Chow, G.G. Fuller, D.G. Wallace and J.A. Madri, The rheo-optical response of rod-like shortened collagen protein to transient shear flow, Macromolecules, 18, 805 (1985). 

In Fig. 15.26 an example is given of Eq. (15.97) for a Maxwell element with G = 1000 N/m2 and t = 1 s. For small extensional rates of strain, the extensional viscosity is constant and equal to 3000 N s/m2. For higher extensional rates of strain, the viscosity increases. At the extensional rate of strain of 0.5 s-1 there is a transition to infinite extensional viscosities. The dotted line is the transient shear viscosity r)+(t) at low shear rates and equal to 14 of the transient extensional viscosity r)+ (f) at low extensional rates of strain. 

FIG. 16.35 Transient shear stress vs. time upon starting steady shear flow at three different shear rates for a 20% (w/w) solution of PpPTA in concentrated sulphuric acid. Reproduced with permission from Doppert HL and Picken SJ (1987) Mol Cryst Liq Cryst 153,109. Copyright Taylor and Francis Ltd., http //www.informaworld.com. 

The experimental ranges of strain rates (or strains) are summarized in Table 2 for the various types of experiments. Time-temperatiire superposition was successfully applied on the various steady shear flow and transient shear flow data. The shift factors were foimd to be exactly the same as those obtained for the dynamic data in the linear viscoelastic domain. Moreover, these were found to be also applicable in the case of entrance pressure losses leading to an implicit appUcation to elongational values. 

Figures 7 and 8 show the predictions of the Wagner model compared to experimental data for transient shear viscosity and first normal stress coefficient of LD. These have been calculated according to ...

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. 

R.Fulchiron, V.Verney, G.Marin, Determination of the elongational behavior of polypropylene melts from transient shear experiments using Wagner s model, J. Non-Newt. Fluid Mech. 45 (1993), 49-61. 

Mason, P. L., Bistany, K. L., Puoti, M. G., and Kokini, J. L. 1982. A new empirical model to simulate transient shear stress growth in semi-solid foods. J. Food Process Eng. 6 219-233. 

Several studies were conducted on the stress overshoot and/or decay at a constant shear rate. Kokini and Dickie (1981) obtained stress growth and decay data on mayonnaise and other foods at 0.1, 1.0, lO.Oand 100 s . As expected from studies on polymers, shear stresses for mayonnaise and other food materials displayed increasing degrees of overshoot with increasing shear rates. The Bird-Leider empirical equation was used to model the transient shear stresses. 

Figure 1.10 Transient shear stress a and first normal stress difference A i after start-up of steady shearing for a low-density polyethylene melt, Melt I, at a shear rate y = 1 sec . (From Laun 1978, reprinted with permission from Steinkopff Publishers.)...

In transient shear flows starting from an isotropic distribution of fiber orientations, considerably higher viscosities will be initially observed, until the fibers become oriented. In Bibbo s experiments, t]r for isotropically oriented fibers is around 3.5 for v = 75. These viscosities can also be predicted reasonably well by semidilute theory and by simulations (Mackaplow and Shaqfeh 1996). Figure 6-25 shows the shear stress as a function of strain for a polyamide 6 melt with 30% by weight glass fibers of various aspect ratios, where the fibers were initially oriented in the flow-gradient direction. Notice the occurrence of a stress overshoot (presumably due to polymer viscoelasticity), followed by a decrease in viscosity, as the fibers are reoriented into the flow direction. 

Figure 11.18 Predictions of the tumbling parameter A as a function of reduced concentration C/C2 from the Smoluchowski equation for hard rods with the Onsager potential. The exact result from the spherical-harmonic expansion is shown, compared to approximate results from an analytic formula and from the perturbation expansion of Kuzuu and Doi. The open circles (O) are estimates from the periods of shear stress oscillations in transient shearing flows for PEG solutions (see Walker et al. 1995), and the closed circle ( ) is from a direct conoscopic measurement of Muller et al. (1994).

Suto, S. Tateyama, S. Transient shear response of liquid crystal-forming hydroxypropyl cellulose solution in dimethylacetamide. I. Stress growth and relaxation behavior. J. Appl. Polym. Sci. 1994, 53 (2), 161-168. 

Figure 12 shows the transient shear modulus g(f,y) of the ISHSM from (27c), which determines the viscosity via ri = It is the time derivative of the... 

Transient shear flows involve examining the shear stress and viscosity response to a time-dependent shear. The stress build up at the start of steady flow (<7+) and at the cessation of steady flow (a ) and the stress decay (ff(0) after a dynamic instantaneous impulse of deformation strain (y) can be used to characterize transient rheological behaviour. 

Shear rheology itself can be further subdivided into cases of steady shear, dynamic shear and transient shear. 

Transient shear is defined as when a material is subject to an instantaneous change in deformation and the response as a function of time is measured. For example. Figure 3.72 shows an instantaneously applied step-strain test. 

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