Solid-like behaviour

The rapid stopping may be due merely to the higher apparent viscosity but the recoil is a manifestation of solid-like behaviour a purely viscous material cannot recoil. 

Where (pm is the maximum concentration at which flow is possible -above this solid-like behaviour will occur. q>/(pm is the volume effectively occupied by particles in unit volume of the suspension and therefore is not just the geometric volume but is the excluded volume. This is an important point that will have increasing relevance later. Now integration of Equation (3.53) with the boundary condition that as... 

The results of Equation (3.56) are plotted in Figure 3.14. It can be seen that shear thinning will become apparent experimentally at (p > 0.3 and that at values of q> > 0.5 no zero shear viscosity will be accessible. This means that solid-like behaviour should be observed with shear melting of the structure once the yield stress has been exceeded with a stress controlled instrument, or a critical strain if the instrumentation is a controlled strain rheometer. The most recent data24,25 on model systems of nearly hard spheres gives values of maximum packing close to those used in Equation (3.56). 

Figure 5.14 The dimensionless internal energy versus volume fraction, indicating empirically defined zones of liquid-like and solid-like behaviour...

In a rheomety experiment the two plates or cylinders are moved back and forth relative to one another in an oscillating fashion. The elastic storage modulus (G - The contribution of elastic, i.e. solid-like behaviour to the complex dynamic modulus) and elastic loss modulus (G" - The contribution of viscous, i.e. liquid-like behaviour to the complex modulus) which have units of Pascals are measured as a function of applied stress or oscillation frequency. For purely elastic materials the stress and strain are in phase and hence there is an immediate stress response to the applied strain. In contrast, for purely viscous materials, the strain follows stress by a 90 degree phase lag. For viscoelastic materials the behaviour is somewhere in between and the strain lag is not zero but less than 90 degrees. The complex dynamic modulus ( ) is used to describe the stress-strain relationship (equation 14.1 i is the imaginary number square root of-1). 

Polyester BB1 was run twice in steady mode at 290°C (Figure 10), and shows that the orientational effect of the first run has a drastic effect on steady shear viscosity. In the first run the log viscosity vs. log shear rate had a slope of -0.92 (solid like behaviour, yield stress), but in the second run a pseudo-Newtonian plateau was reached from approx. 1 sec 1. Capillary viscosity values corresponded reasonably well with the second run steady shear data. The slope at high shear rates was close to -0.91 which corresponds nicely to the first-run steady shear run. All this could suggest, that this system is not completely melted, but still has some solid like regions incorporated. At 300°C capillary viscosity data showed an almost pseudo-Newtonian plateau. This corresponds quite well to the fact that fiber spinning as mentioned earlier was difficult and almost impossible below 290°C, but easy at 300°C. At an apparent shear rate of 100 sec 1, a die-swell was found to be approximately 0.95. 

Chronakis IS, Doublier J-L, Piculell L (2000) Viscoelastic properties for kappa- and iota-carrageenan in aqueous Nal from the liquid-like to the solid-like behaviour. Int J Biol Macromol 28 1-14... 

When NR was the rubber, a NR latex was mixed with Na-bentonite and Na-fluorohectorite, varying the concentration of clays from 1 to 2.5 phr and determining rheological properties with a coaxial cylinder viscometer. Viscosity increased with clay loading. Pseudo solid-like behaviour was observed in bentonite-filled composites at the loading of 2.5 phr, whereas a behaviour close to that of the Newtonian fluid was shown by unfilled NR. Stronger rubber bentonite interaction was revealed by the higher viscosity, the lower power-law indexes and the slope of the Kraus plot. ... 

At very low frequencies, G" is much larger than G, and hence liquid-Kke behaviour predominates. However as the testing frequency is increased, G takes over and solid-like behaviour prevails. The determinant of which kind of behaviour is most significant is the value of the test frequency co relative to the relaxation time x. This is a simple way to define a Deborah number, De—the ratio of the relaxation time to the test time—and a measure of De in this case is cox. Hence, low Deborah numbers always indicate liquid-like behaviour, whereas high Deborah numbers means solid-like response. At the midpoint, where G" goes through a maximum G = G", and this takes place at a critical crossover frequency of co = 1/x. 

Figure 25 shows that the viscoelastic behaviour strongly depends on nanotube dispersion. When the nanotubes are supposed to be well dispersed in an isotropic configuration, the variation of the complex shear modulus (under 5 % strain) shows a rheological behaviour close to the viscoelastic behaviour of the PDMS matrix, i.e. a liquid viscoelastic behaviour. After the aggregation process, the viscoelastic behaviour of the composite shows a solid-like behaviour, at least in the frequency window used in the present study, due to the formation of the CNT network from dynamic CNT aggregation. 

To aid the process plant engineer, information must be available in terms of bulk powder behaviour under specific conditions. Powders should therefore be treated as a biphasic assembly and handled with knowledge of the interactions between a fluid and the solid external and internal surfaces. In this way, powder behaviour can be visualised as behaving in two separate manners either in terms of fluid-like behaviour or compacted solid-like behaviour. Both of these conceptual viewpoints will be considered in this section, but the emphasis will be on the fluid-like (flow) behaviour of powders. 

If the Deborah number is large, solid-like behaviour results. However, a small Deborah number results in fluid-like behaviour and the fluid can act as if it were purely viscous. 

In chabazite, a zeolite with a 3-dimensional array of ellipsoidal cavities (0.37 x 0.42 nm), Stockmeyer followed the variation with q of the elastic intensity in the temperature range 40 K to 300 K and several loadings of H2 [59]. He found a continuous change in the spectrum, going from a solid-like behaviour at 25 K to an encapsulated gas-like motion at room temperature he interpreted the data with a model considering the motions of the orthohydrogen molecule in a potential well (depth U = 153 meV - size 1 = 0.08 nm) located inside a potential box of size L = 0.4 nm with infinite high barriers. 

Motion in Solids - The boundary between liquid-like and solid-like behaviour in magnetic resonance has been described. ... 

Values of De that approach zero indicate liquid behaviour, while values that approach infinity have solid-like behaviour. It was coined by Israeli scientist Markus Reiner (1886-1976) from the Bible (Judges 5 5) as The mountains melted from before the Lord.... ... 

OMLS nanocomposites. In its most basic form it involves dispersion of OMLS in an organic monomer, followed by polymerization of the monomer. The corresponding chemical shifts in H NMR spectra clearly demonstrate conversion from CL to PCL. Complete conversion of CL to PCL was assumed because residual CL was not detected in the NMR spectra of any of the composites. The peak broadening effect seen in XRD pattern of PCLC2 is believed to be due to the strong attachment of PCL chains to the silicate layers, resulting in partial solid-like behaviour. 

The terminal regions slope of the master curves for G and G" are presented in Table 3.7. The slope of and in the terminal region of the master curves of PLA matrix was 1.85 and 1, respectively, and these values are in the range expected for polydisperse polymers. On the other hand, the slopes of G and G" were considerably lower for all PLACNs compared to those of pure PLA. In fact, for PLACNs with high C18MMT content, G becomes nearly independent at low atut and exceeds G", characteristic of materials exhibiting a pseudo-solid-like behaviour. 

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