Soft viscoelastic solids

Soft viscoelastic solids and liquids of high viscosity, which cover a G region of 105-108 N /m2 in this region the storage and loss moduli have comparable values, so that tan 6 is neither very small nor very large test pieces are softer than the instruments they are confined in. 

A simple example of the relationship between "structure" and "properties" is the effect of increasing molecular weight of a polymer on its physical (mechanical) state a progression from an oily liquid, to a soft viscoelastic solid, to a hard, glassy elastic solid. Even seemingly minor rearrangements of atomic structure can have dramatic effects as, for example, the atactic and syndiotactic stereoisomers of... 

Experimental Methods for Soft Viscoelastic Solids and Liquids of High Viscosity... 

FIG. 6-1. Geometries, coordinates, and dimensions for investigation of soft viscoelastic solids (in addition to those shown in Fig. 5-1). (a) simple shear sandwich (b) simple elongation (c) torsion of bar with rectangular cross-section. 

Once the cubic nature of the blue phase was established, attempts to measure the elastic constants using more sensitive techniques appeared shortly thereafter [25], [96], [97], with those of Kleiman et al. [25] being the most extensive. The latter experiments are very delicate, since the blue phase lattice is both soft (small elastic constants) and weak (small elastic limit). Torsional oscillators configured as cup viscometers were used and the shear distortion was kept to less than 0.02%. Figure 7.12 shows results for both the shear elasticity G and the viscosity rj. These data are taken at various frequencies and must be extrapolated to 0 Hz to obtain the static properties. In the helical phase the extrapolation is somewhat dependent on the model nevertheless, the authors claim that G becomes nearly zero in the helical phase and about 710 dyn cm in BPI. (This figure should be compared to 10" dyn cm 2 in a metal ) However, since BPI also possesses viscosity, its behavior is that of a viscoelastic solid. 

N. Arun, A. Sharma, P. S. G. Pattader, I. Banerjee, H. M. Dixit, and K. S. Narayan, Electric-field-induced patterns in soft viscoelastic films from long waves of viscous liquids to short waves of elastic solids, Phys. Rev. Lett., 102, 254502 [2009]. 

For a viscoelastic liquid with G = 10", the corresponding frequency is about 10 Hz for a soft polymeric solid with G = 10 , 10 Hz for a hard solid with G — 10 , 10 2 Hz. Only in rare cases—possibly for dilute polymer solutions in the megacycle range—would this transition be crossed, since G always increases with frequency. 

It has been also shown that when a thin polymer film is directly coated onto a substrate with a low modulus ( < 10 MPa), if the contact radius to layer thickness ratio is large (afh> 20), the surface layer will make a negligible contribution to the stiffness of the system and the layered solid system acts as a homogeneous half-space of substrate material while the surface and interfacial properties are governed by those of the layer [32,33]. The extension of the JKR theory to such layered bodies has two important implications. Firstly, hard and opaque materials can be coated on soft and clear substrates which deform more readily by small surface forces. Secondly, viscoelastic materials can be coated on soft elastic substrates, thereby reducing their time-dependent effects. 

It is likely that most biomaterials possess non-linear elastic properties. However, in the absence of detailed measurements of the relevant properties it is not necessary to resort to complicated non-linear theories of viscoelasticity. A simple dashpot-and-spring Maxwell model of viscoelasticity will provide a good basis to consider the main features of the behaviour of the soft-solid walls of most biomaterials in the flow field of a typical bioprocess equipment. 

The viscoelastic samples to be tested by this method may be in different forms. The simplest to work with is a soft or liquid-like viscoelastic material such as mayonnaise or other food emulsions. These are easy samples to work with terms of sample loading. More solid-like samples such as cheese or food gels are more difficult to load onto the instrument in a consistent matter. The degree of compression of soft samples should ideally be controlled using a normal force measure or force rebalance system. Slippage is also a concern and roughened plates or even adhesives may be needed if slip is an issue. As this protocol is a general one, it is assumed that the sample is already loaded on the rheometer and has achieved equilibrium in terms of temperature and viscoelastic stmcture (time-dependent behavior). 

Soft glasses are known to exhibit remarkable nonlinear shear rheology. They are yield-stress fluids that respond either like an elastic solid when the applied stress is zero or below the yield stress, or a like a viscoelastic fluid when a stress greater than the yield value of the material is applied [185]. Above their yield stresses, soft glasses are shear thinning fluids and very often the shear stress increases with the shear rate raised to the one-half power. This is well documented for the case of concentrated emulsions [102, 182, 186], microgel suspensions [31], and multilamellar... 

However, most real systems do not comply with the presumptions made in the derivation of Eq. (17.4). Generally, more than one type of interaction force will act, and the structural elements often vary in type or size, which implies a spectrum of interaction forces we will see examples of this in the following sections. The contributions to the modulus of the various forces involved are not additive, primarily because the bonds vary in direction. Moreover, such materials are generally not fully elastic, which implies that the modulus will be complex [see Eq. (5.12)] and depend on deformation rate virtually all soft-solid foods show viscoelastic behavior of some type. Finally, some systems are quite inhomogeneous, which further complicates the relations. 

In practice, large deformation properties are far more useful, and determination of the full relation between stress and strain gives the best information. Materials vary widely in their linear region, i.e., the strain range over which stress and strain remain proportional. Deforming it much farther, the material may eventually break. Relevant parameters then are fracture stress or strength, fracture strain or shortness, and work of fracture or toughness. The correlation between fracture parameters and the modulus is often poor. Since many soft solids exhibit viscoelastic behavior, the values of these parameters can depend, often markedly, on the strain rate. 

For viscoelastic soft solids, the whole test piece shows lasting deformation before and during the event of fracture, making the relations even more complicated. The fracture parameters now are markedly time-scale dependent. The specific work of fracture is increased, since much energy is dissipated during deformation. 

This chapter is an in-depth review on rheology of suspensions. The area covered includes steady shear viscosity, apparent yield stress, viscoelastic behavior, and compression yield stress. The suspensions have been classified by groups hard sphere, soft sphere, monodis-perse, poly disperse, flocculated, and stable systems. The particle shape effects are also discussed. The steady shear rheological behaviors discussed include low- and high-shear limit viscosity, shear thinning, shear thickening, and discontinuity. The steady shear rheology of ternary systems (i.e., oil-water-solid) is also discussed. 

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