Rheology shear modulus

Other characteristics of elasticity, such as the shear modulus G, the volume compression coefficient the coefficients p and X used in mathematical elasticity theory, the c modulus, and the compliance 5 used in crystallography can be expressed via E and v. To illustrate this, let us use the rheological shear modulus G as an example. 

Rheology. The rheology of foam is striking it simultaneously shares the hallmark rheological properties of soHds, Hquids, and gases. Like an ordinary soHd, foams have a finite shear modulus and respond elastically to a small shear stress. However, if the appHed stress is increased beyond the yield stress, the foam flows like a viscous Hquid. In addition, because they contain a large volume fraction of gas, foams are quite compressible, like gases. Thus foams defy classification as soHd, Hquid, or vapor, and their mechanical response to external forces can be very complex. 

Although aH these models provide a description of the rheological behavior of very dry foams, they do not adequately describe the behavior of foams that have more fluid in them. The shear modulus of wet foams must ultimately go to zero as the volume fraction of the bubbles decreases. The foam only attains a solid-like behavior when the bubbles are packed at a sufficiently large volume fraction that they begin to deform. In fact, it is the additional energy of the bubbles caused by their deformation that must lead to the development of a shear modulus. However, exactly how this modulus develops, and its dependence on the volume fraction of gas, is not fuHy understood. 

Rheological parameters, such as relaxation time, shear modulus, and stored elastic energy, are determined from the extrudate swell and stress-strain data as previously described. Representative examples of the variation of these parameters with blend ratios for both blends are shown in Figs. 16-18. Figure 16 shows that relaxation time for both preblends without heating and... 

The plot of the rheological parameters (relaxation time, shear modulus, and stored elastic energy) are shown in Figs. 22-24. The relaxation time increases as the ACM content is increased to attain a maximum at 60 40 = ACM XNBR blend ratio for the preblends. For lower shear rate the rise is sharp and after 60 40 blend ratio, // remains almost constant, whereas for the higher shear rate region the rise is not sharp and after 60 40 blend ratio ty decreases as ACM percent increased in the blend. In the case of the preheated blends the /y increases up to 50 50 blend ratio and then decreases with the addition of ACM in the blend. The preheating increases the ty in both shear rate regions. 

The plot of the rheological parameters (relaxation time, /r shear modulus, G and stored elastic energy, W ) are given in Figs. 28-30. The relaxation time of both preblends and preheated blends remains almost constant up to 50 50 blend ratio and then shoots up drastically at both shear rates. Up to 50 50 blend ratio it is observed that the relaxation time is more at lower shear rate. Preheating of blends lowers the values. 

In case of copper some rheological experiments carried out at a given polymer concentration and increasing amoimt of cations indicates that copper/pectin systems in the one-phase domain behave as a viscoelastic liquid rather than a viscoelastic solid referred to as true gel (G (co) = G, when to—>0 with Gg the equilibrium shear modulus)[35]. Despite the lack of experimental data the range in cation and polymer concentration in which true gels may be observed seemed very limited. These results corroborate the strength of the binding of copper by pectins evidenced by the properties of the phase separation curves. 

The major difficulty in predicting the viscosity of these systems is due to the interplay between hydrodynamics, the colloid pair interaction energy and the particle microstructure. Whilst predictions for atomic fluids exist for the contribution of the microstructural properties of the system to the rheology, they obviously will not take account of the role of the solvent medium in colloidal systems. Many of these models depend upon the notion that the applied shear field distorts the local microstructure. The mathematical consequence of this is that they rely on the rate of change of the pair distribution function with distance over longer length scales than is the case for the shear modulus. Thus... 

H.M. Princen and A.D. Kiss Rheology of Foams and Highly Concentrated Emulsions III. Static Shear Modulus. I. Colloid Interface Sci. 112, 427 (1986). 

The rheology of the sol-gel transition was undertaken with special care in order to avoid gel disruption. A critical behaviour for the shear modulus with respect to the helix amount, is noticed. A simple relation between the rheological parameters and the degree of helix formation is pointed out in a limited range of helix amounts (X<15%). These experiments will continue on the fully matured gels. 

Another important rheological property of dry foams and highly concentrated emulsions is G, the shear modulus. Princen and Kiss [57] demonstrated that this property was dependent on < >, the volume fraction of the system. Previously, Stamenovic et al. [58] and, much earlier, Derjaguin and coworker [59], had derived an expression for the shear modulus of foams of volume fraction very close to unity. The value was found to depend on the surface tension of the liquid phase (in foams), for the particular case of (Jja 1. However, Princen demonstrated that the values of G obtained were overestimated by a factor of two. This error was attributed to the model used by Stamenovic and coworker, which failed to maintain the equilibrium condition that three films always meet at angles of 120° during deformation. 

The results obtained by the present mechanical measurements are also consistent with the previous experimental results of the dynamic light scattering studies of the collective diffusion coefficient of gels and the rheological studies of the shear modulus of gels. The studies published by different researchers indicate that the concentration dependence of the collective diffusion constant of the polymer networks of gel and that of the elastic modulus are well represented by the following power law relationships [2, 3, 5]... 

Electrorheological (ER) fluids are materials whose rheological properties (viscosity, yield stress, shear modulus, etc.) can be readily controlled using an external electric field. For example, in some cases, they can switch from a liquid-like material to a solid-like material within a millisecond with the aid of an electric field, by means of the so-called ER effect.1617 The unique feature of the ER effect is that ER fluids can reversibly and continuously change from a liquid state to a solid state. ER fluid research is focused mainly on the automotive and robotics industry as electrical and mechanical interfaces for applications such as clutches, brakes, damping devices, fuel injection, and hydraulic valves. However, more recently, there is growing... 

A variety of rheological tests can be used to evaluate the nature and properties of different network structures in foods. The strength of bonds in a fat crystal network can be evaluated by stress relaxation and by the decrease in elastic recovery in creep tests as a function of loading time (deMan et al. 1985). Van Kleef et al. (1978) have reported on the determination of the number of crosslinks in a protein gel from its mechanical and swelling properties. Oakenfull (1984) used shear modulus measurements to estimate the size and thermodynamic stability of junction zones in noncovalently cross-linked gels. 

For a viscoelastic solid (like an organogel), any rheological description should give a constant finite elastic modulus and infinite viscosity at zero frequency or long times. The situation is somewhat comparable to that of a cross-linked network [2. The equilibrium shear modulus for small deformations is proportional... 

The influence of addition of sodium bentonite (a commonly used antisettling system) on the rheological behaviour of a pesticide suspension concentrate (250 g dm ) has been investigated. Steady state shear stress-shear rate curves were carried out to obtain the yield value and viscosity as a function of shear rate. The shear modulus was also measured using a pulse shearometer, and the residual viscosity was obtained in afew cases from creep measurements. The rheological parameters Tg (Bingham yield value),... 

Gg (instantaneous modulus), Hg (residual viscosity) and G (shear modulus) all showed a rapid increase above 30g dm bentonite. This was attributed to the formation of a gel network structure in the continuous medium and the strength of such a gel increased with increase in bentonite concentration. The results could be qualitatively described in terms of the elastic floe model of Hunter and co-workers. Moreover, the settling characteristics of the structured suspensions were found to be consistent with the predictions from the rheological measurements. This demonstrates the value of rheological studies in predicting the longterm physical stability of suspension concentrates. 

A particularly useful expression for the complex dynamic moduli was introduced using operators and fractional derivatives for the viscoelastic constitutive equations ( ). For a rheologically simple system the complex shear modulus is... 

Extending the analogy with bulk rheology, for linear shear deformation of an interface it is possible to define a surface (or interfacial) shear viscosity rj° and a surface (or interfacial) shear modulus G°. In a Cartesian co-ordinate system, with again the z-axis normal to the interface... 

Keywords Colloidal dispersion Flow curve Glass transition Integration through transients approach Linear viscoelasticity Mode coupling theory Nonlinear rheology Non-equilibrium stationary state Shear modulus Steady shear... 

Rheological and elastic properties under flow and deformations are highly characteristic for many soft materials like complex fluids, pastes, sands, and gels, viz. soft (often metastable) solids of dissolved macromolecular constituents [1]. Shear deformations, which conserve volume but stretch material elements, often provide the simplest experimental route to investigate the materials. Moreover, solids and fluids respond in a characteristically different way to shear, the former elastically, the latter by flow. The former are characterized by a shear modulus Go, corresponding to a Hookian spring constant, the latter by a Newtonian viscosity r]o, which quantifies the dissipation. 

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