Yield stress —> Rheology

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. 

One simple rheological model that is often used to describe the behavior of foams is that of a Bingham plastic. This appHes for flows over length scales sufficiently large that the foam can be reasonably considered as a continuous medium. The Bingham plastic model combines the properties of a yield stress like that of a soHd with the viscous flow of a Hquid. In simple Newtonian fluids, the shear stress T is proportional to the strain rate y, with the constant of proportionaHty being the fluid viscosity. In Bingham plastics, by contrast, the relation between stress and strain rate is r = where is... 

Foams have a wide variety of appHcations that exploit their different physical properties. The low density, or high volume fraction of gas, enable foams to float on top of other fluids and to fiU large volumes with relatively Httle fluid material. These features are of particular importance in their use for fire fighting. The very high internal surface area of foams makes them useful in many separation processes. The unique rheology of foams also results in a wide variety of uses, as a foam can behave as a soHd, while stiH being able to flow once its yield stress is exceeded. 

The square root of viscosity is plotted against the reciprocal of the square root of shear rate (Fig. 3). The square of the slope is Tq, the yield stress the square of the intercept is, the viscosity at infinite shear rate. No material actually experiences an infinite shear rate, but is a good representation of the condition where all rheological stmcture has been broken down. The Casson yield stress Tq is somewhat different from the yield stress discussed earlier in that there may or may not be an intercept on the shear stress—shear rate curve for the material. If there is an intercept, then the Casson yield stress is quite close to that value. If there is no intercept, but the material is shear thinning, a Casson plot gives a value for Tq that is indicative of the degree of shear thinning. 

The existence of yield stress Y at shear strains seems to be the most typical feature of rheological properties of highly filled polymers. A formal meaing of this term is quite obvious. It means that at stresses lower than Y the material behaves like a solid, i.e. it deforms only elastically, while at stresses higher than Y, like a liquid, i.e. it can flow. At a first approximation it may be assumed that the material is not deformed at all, if stresses are lower than Y. In this sense, filled polymers behave as visco-plastic media with a low-molecular and low-viscosity dispersion medium. This analogy is not random as will be stressed below when the values of the yield stress are compared for the systems with different dispersion media. The existence of yield stress in its physical meaning must be correlated with the strength of a structure formed by the interaction between the particles of a filler. 

Generally speaking, to obtain, reliable rheological characteristics of disperse systems with fibre-like filler turned out to be a difficult methodological problem. Therefore, the question on the effect of the shape of a filler particles on the value of yield stress is left open at present. In the papers published we can encounter only individual examples and qualitative considerations concerning this question, which do not enable us to formulate general conclusions. 

Appearance of rheological effects — yield stress, non-Newtonian viscosity, thixotropy... 

The rheological properties of a particular suspension may be approximated reasonably well by either a power-law or a Bingham-plastic model over the shear rate range of 10 to 50 s. If the consistency coefficient k is 10 N s, /m-2 and the flow behaviour index n is 0.2 in the power law model, what will be the approximate values of the yield stress and of the plastic viscosity in the Bingham-plastic model ... 

The rheological characteristics of AB cements are complex. Mostly, the unset cement paste behaves as a plastic or plastoelastic body, rather than as a Newtonian or viscoelastic substance. In other words, it does not flow unless the applied stress exceeds a certain value known as the yield point. Below the yield point a plastoelastic body behaves as an elastic solid and above the yield point it behaves as a viscoelastic one (Andrade, 1947). This makes a mathematical treatment complicated, and although the theories of viscoelasticity are well developed, as are those of an ideal plastic (Bingham body), plastoelasticity has received much less attention. In many AB cements, yield stress appears to be more important than viscosity in determining the stiffness of a paste. 

Galgali and his colleagues [46] have also shown that the typical rheological response in nanocomposites arises from frictional interactions between the silicate layers and not from the immobilization of confined polymer chains between the silicate layers. They have also shown a dramatic decrease in the creep compliance for the PP-based nanocomposite with 9 wt% MMT. They showed a dramatic three orders of magnitude drop in the zero shear viscosity beyond the apparent yield stress, suggesting that the solid-like behavior in the quiescent state is a result of the percolated structure of the layered silicate. 

In wet grinding the power consumption is generally about 30 per cent lower than that for dry grinding and, additionally, the continuous removal of product as it is formed is facilitated. The rheological properties of the slurry are important and the performance tends to improve as the apparent viscosity increases, reaching an optimum at about 0.2 Pa.s. At very high volumetric concentrations (ca. 50 volume per cent), the fluid may exhibit shear-thickening behaviour or have a yield stress, and the behaviour may then be adversely affected. 

Much less is known about the settling of particles in fluids exhibiting a yield stress. Barnes (39) suggests that this is partly due to the fact that considerable confusion exists in the literature as to whether or not the fluids used in the experiments do have a true yield stress 39. Irrespective of this uncertainty, which usually arises from the inappropriateness of the rheological techniques used for their characterisation, many industrially important materials, notably particulate suspensions, have rheological properties closely approximating to viscoelastic behaviour. 

H.M. Princen Rheology of Foams and Highly Concentrated Emulsions I. Elastic Properties and Yield Stress of a Cyhndrical Model System. J. Colloid Interface Sci. 91, 160 (1983). 

Flow and self-leveling characteristics of these products are governed by the rheological behavior of the slurrylike materials. At the low water-cement ratios required to ensure proper suspension of the solids, most selfleveling compositions are characterized by a yield stress and thixotropic behavior [75]. To obtain self-leveling properties, the yield stress has to be reduced and this is achieved by the selection and combination of suitable mix ingredients at... 

Fernandez et al. (2007) have characterized the rheological behavior of the mashed potatoes with added biopolymers using steady shear measurements. Fresh and frozen/thawed mashed potatoes present shear thinning with yield stress (Canet et al., 2005a), and dynamic shear data reveal weak gel-like behavior in potato purees (Alvarez et al., 2004). The effects are strongly... 

Perhaps the most important and striking features of high internal phase emulsions are their rheological properties. Their viscosities are high, relative to the bulk liquid phases, and they are characterised by a yield stress, which is the shear stress required to induce flow. At stress values below the yield stress, HIPEs behave as viscoelastic solids above the yield stress, they are shear-thinning liquids, i.e. the viscosity varies inversely with shear rate. In other words, HIPEs (and high gas-fraction foams) behave as non-Newtonian fluids. 

Princen [57, 64, 82] and others [84] also noted the presence of wall-slip in rheological experiments on HIPEs and foams. However, instead of attempting to eliminate this phenomenon, Princen [64] employed it to examine the flow properties of the boundary layer between the bulk emulsion and the container walls, and demonstrated the existence of a wall-slip yield stress, below that of the bulk emulsion. This was attributed to roughness of the viscometer walls. Princen and Kiss [57], and others [85], have also showed that wall-slip could be eliminated, up to a certain finite stress value, by roughening the walls of the viscometer. Alternatively [82, 86], it was demonstrated that wall-slip can be corrected for and effectively removed from calculations. Thus, viscometers with smooth walls can be used. This is preferable, as the degree of roughness required to completely eradicate wall-slip is difficult to determine. 

Pons et al. have studied the effects of temperature, volume fraction, oil-to-surfactant ratio and salt concentration of the aqueous phase of w/o HIPEs on a number of rheological properties. The yield stress [10] was found to increase with increasing NaCl concentration, at room temperature. This was attributed to an increase in rigidity of films between adjacent droplets. For salt-free emulsions, the yield stress increases with increasing temperature, due to the increase in interfacial tension. However, for emulsions containing salt, the yield stress more or less reaches a plateau at higher temperatures, after addition of only 1.5% NaCl. 

The non-aqueous HIPEs showed similar properties to their water-containing counterparts. Examination by optical microscopy revealed a polyhedral, poly-disperse microstructure. Rheological experiments indicated typical shear rate vs. shear stress behaviour for a pseudo-plastic material, with a yield stress in evidence. The yield value was seen to increase sharply with increasing dispersed phase volume fraction, above about 96%. Finally, addition of water to the continuous phase was studied. This caused a decrease in the rate of decay of the emulsion yield stress over a period of time, and an increase in stability. The added water increased the strength of the interfacial film, providing a more efficient barrier to coalescence. 

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