Solidlike behavior

Here U is the velocity of the drop and u0 is the velocity at the interface with respect to the center of the drop for 9 = n/2. For solidlike behavior, which occurs in the presence of surface active agents, ua becomes zero, while u 0 in systems in which the surface active agents are either absent or present in extremely small amounts [5,40]. When the interface has a solidlike behavior [5,40]... 

A characteristic feature during network formation is the presence of a critical transition called gelation, which involves an abrupt change from a liquidlike to a solidlike behavior. Figure 3.3 illustrates the evolution of (zero-shear) viscosity, elastic modulus and fraction of soluble material (sol fraction), as a function of the conversion of reactive groups (x). At x = xgel, the (zero-shear) viscosity becomes infinite, there is a buildup of the elastic modulus, and an insoluble fraction (gel fraction) suddenly appears. 

All the preceding particulate handling steps are affected by the unique properties of all particulates, including polymeric particulates while they may behave in a fluidlike fashion when they are dry, fluidized and above 100 pm, they also exhibit solidlike behavior, because of the solid-solid interparticle and particle-vessel friction coefficients. The simplest and most common example of the hermaphroditic solid/ fluidlike nature of particulates is the pouring of particulates out of a container (fluidlike behavior) onto a flat surface, whereupon they assume a stable-mount, solidlike behavior, shown in Fig. 4.2. This particulate mount supports shear stresses without flowing and, thus by definition, it is a solid. The angle of repose, shown below, reflects the static equilibrium between unconfined loose particulates. 

Solidlike behavior abounds when the surface-to-volume ratio is very high,1 that is, when the particulates are even mildly compacted, surface-charged, or wet all contribute to large frictional forces and to nonuniform, often unstable stress fields in both flowing and compacted particulate assemblies, as we discuss later in this chapter. We begin by discussing some of the unique properties of polymer particulates relevant to processing. Comprehensive reviews can be found in the literature f 1 —4). 

Figure 5-7 shows the frequency dependences of the storage and loss moduli at various times during the reaction, from 6 minutes before G to 6 minutes after it. Note that at tc (labeled Gel Point in Fig. 5-7), G and G" follow power laws over the entire frequency range For times less than this (labeled —2 and —6 in Fig. 5-7), the curves slope downward at low frequencies, which is indicative of fluid-like behavior, while at times after the gel point (labeled -t-2 and - -6), G flattens at low frequency—a characteristic of solidlike behavior. Thus, the intermediate state with a power-law frequency dependence over the whole frequency range is the transitional state between liquid-like and solid-like behavior, and therefore it defines the gel point. This rheologically determined gel point coincides with the conventional value, namely the maximum degree of cure at which...

As stated above,/(u) has two contributions/o(t>) and/i(n), and the latter depends sensitively on the nature of the cell s immediate environment. This dependence is not so crucial for smaller expansions, u < in the quadratic range, but in the linear range v>v it must be taken into account. We therefore decompose f into two corresponding parts fo and f, leave Cg as a constant, and introduce the environment dependence into f,. The system clearly becomes more rigid as the volume decreases is maximal when the system is entirely solidlike. We can characterize the deviation from solidlike behavior through the mean free volume within the liquidlike fraction of the material ... 

Figure 1 shows the dynamic moduli as a function of frequency for an HPG-borate gel (0.48 wt % HPG, 3 wt % sodium tetraborate, 2 wt % KGl) at ambient temperature. The moduli show solidlike behavior the storage modulus is independent of frequency and higher than the loss modulus. At 65 G, in Figure 2, the moduli show fiuidlike behavior, and both moduli decrease at low frequency. This thermal melting is characteristic of borate gels and limits their application in high-temperature environments. 

Rheological studies of PET nanocomposites are not ample, but show very interesting features. In the low frequency range, the nanocomposites display a more elastic behavior than that of PET. It appears that there are some physical network structures formed due to filler interactions, collapsed by shear force, and after all the interactions have collapsed, the melt state becomes isotropic and homogeneous. Linear viscoelastic properties of polycaprolactone and Nylon-6 [51] with MMT display a pseudo-solidlike behavior in the low frequency range of... 

Another example of network formation is found in PEO (poly(ethylene oxide))-silica systems [58, 59]. At relatively small-particle concentrations, the elastic modulus increases at low frequencies, suggesting that stress relaxation of these hybrids is effectively arrested by the presence of silica nanoparticles. This is indicative of a transition from liquidlike to solidlike behavior. At high frequencies, the effect of particles is weak, indicating that the influence of particles on stress relaxation dynamics is much stronger than their influence on the plateau modulus. 

A physical insight into the viscoelastic character of a material can be obtained by examining the material response time. This can be illustrated by defining a characteristic time for the material — for example, the relaxation time for a Maxwell element, which is the time required for the stress in a stress relaxation experiment to decay to e (0.368) of its initial value. Materials that have low relaxation times flow easily and as such show relatively rapid stress decay. This, of course, is indicative of liquidlike behavior. On the other hand, those materials with long relaxation times can sustain relatively higher stress values. This indicates solidlike behavior. Thus, whether a viscoelastic material behaves as an elastic solid or a viscous liquid depends on the material response time and its relation to the time scale of the experiment or observation. This was first proposed by Marcus Reiner, who defined the ratio of the material response time to the experimental time scale as the Deborah number, D . That is. 

The word vixt oeUislic encompasses many fluids that exhibit both elasticity (solidlike behavior) and flow (liquid-like behavior) when sheared. Most concentrated pastes, emulsions, and gels are viscoelastic. Under small deformations, viscoelastic fluids literally behave as elastic solids under higher deformations they flow as liquids. 

Usually this criterion allows us to unambiguously classify a phase as either a solid or a fluid. Over a sufficiently long time period, however, detectable flow occurs in any material under shear stress of any magnitude. Thus, the distinction between solid and fluid actually depends on the time scale of observation. This fact is obvious when we observe the behavior of certain materials (such as Silly Putty, or a paste of water and cornstarch) that exhibit solidlike behavior over a short time period and fluid-like behavior over a longer period. Such materials, that resist deformation by a suddenly-applied shear stress but undergo flow over a longer time period, are called viscoelastic solids. 

Cui, S. T., Cummings, P. T. and Cochran, H. D. Molecular simulation of the transition from frquidhke to solidlike behavior in complex fluids confined to nanoscale gaps. 2001.7. Chem. Phys.114 7189. 

Shear-rate-dependent viscosities in certain shear rate ranges with or without the presence of an accompanying elastic solidlike behavior. 

Note that the form for G is the same as that for a Maxwell model, eq. 3.3.31, while that for G" shows liquid rather than solidlike behavior at high frequency. Figure 10.3.9 shows good agreement between [G /j ] and [G ] and measurements on tobacco mosaic virus. DuPauw (1968) gives the virus dimensions as 2n = 300 nm and 2b = 18 nm (DuPauw, 1968). 

The DP of fats corresponds to an SFC of 3-5%. Studies of water-in-oil emulsions have shown that coalescence of the aqueous phase does not occur with as little as 3-4% SFC (29). Structurally, fats can form a network even at very low SFCs. This behavior was evident in all blends before and after interesterification. This would seem to indicate that a continuous fat crystal network is present and is responsible for much of the solidlike behavior of plastic fats. Without the presence of such a network, DPs would be expected to be much lower. 

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