Viscosity Yield stress

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... 

The two main rheological properties of a suspension are the yield stress and the viscosity. Yield stress determines when the system becomes a fluid state and when is in a solid state, whereas viscosity determines the ability to flow. In this section, we start with the viscosity measurement. Although one can extract the yield stress from the complete viscosity-shear rate curve, it is helpful to measure the yield stress directly as well. The dynamic and transient measurements are also important for concentrated suspensions. However, because these two types of measurements can be blended into the measurements of the two main rheological properties with some modifications to the measuring instrument, we refer to their measurements only briefly when it is relevant to the discussion. 

Hanehara and Yamada [360] studied the effect of PA admixture addition on the flow diameter and found an exact lelationship in the case of w/c = 0.4 however the results are not always good for w/c = 0.3 because of the effect of cement with water mixing procedure. This problem was resolved by addition of limestone powder. According to these authors there is no general method of cement-admixture compatibility establishment, but it is possible to settlement certain experimental conditions, which permit to determine it. It is moderate fineness of cement and suitable w/c. Moreover, the proper conformity criteria should be selected, because the plastic viscosity, yield stress value and flow diameter can give various results [400]. In Fig. 6.105 the effect of SP on the relative flow area, chosen as cement-SP compatibility determining parameter, after Yamada [400] is shown. SP does not affect the relative flow area below the threshold value, above this value the flow area is increasing proportionally with admixture, but above the saturation level this parameter is not influenced by an admixture content. 

Colloidal dispersions often display non-Newtonian behaviour, where the proportionality in equation (02.6.2) does not hold. This is particularly important for concentrated dispersions, which tend to be used in practice. Equation (02.6.2) can be used to define an apparent viscosity, happ, at a given shear rate. If q pp decreases witli increasing shear rate, tire dispersion is called shear tliinning (pseudoplastic) if it increases, tliis is known as shear tliickening (dilatant). The latter behaviour is typical of concentrated suspensions. If a finite shear stress has to be applied before tire suspension begins to flow, tliis is known as tire yield stress. The apparent viscosity may also change as a function of time, upon application of a fixed shear rate, related to tire fonnation or breakup of particle networks. Thixotropic dispersions show a decrease in q, pp with time, whereas an increase witli time is called rheopexy. 

The apparent viscosity, defined as du/dj) drops with increased rate of strain. Dilatant fluids foUow a constitutive relation similar to that for pseudoplastics except that the viscosities increase with increased rate of strain, ie, n > 1 in equation 22. Dilatancy is observed in highly concentrated suspensions of very small particles such as titanium oxide in a sucrose solution. Bingham fluids display a linear stress—strain curve similar to Newtonian fluids, but have a nonzero intercept termed the yield stress (eq. 23) ... 

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... 

Apparent viscosity of a grease at low shear rates, eg, below about 10, is approximately equal to the yield stress divided by the shear rate. This... 

For a Hquid under shear the rate of deformation or shear rate is a function of the shearing stress. The original exposition of this relationship is Newton s law, which states that the ratio of the stress to the shear rate is a constant, ie, the viscosity. Under Newton s law, viscosity is independent of shear rate. This is tme for ideal or Newtonian Hquids, but the viscosities of many Hquids, particularly a number of those of interest to industry, are not independent of shear rate. These non-Newtonian Hquids may be classified according to their viscosity behavior as a function of shear rate. Many exhibit shear thinning, whereas others give shear thickening. Some Hquids at rest appear to behave like soHds until the shear stress exceeds a certain value, called the yield stress, after which they flow readily. 

Of the models Hsted in Table 1, the Newtonian is the simplest. It fits water, solvents, and many polymer solutions over a wide strain rate range. The plastic or Bingham body model predicts constant plastic viscosity above a yield stress. This model works for a number of dispersions, including some pigment pastes. Yield stress, Tq, and plastic (Bingham) viscosity, = (t — Tq )/7, may be determined from the intercept and the slope beyond the intercept, respectively, of a shear stress vs shear rate plot. 

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. 

When an electric field is appHed to an ER fluid, it responds by forming fibrous or chain stmctures parallel to the appHed field. These stmctures greatly increase the viscosity of the fluid, by a factor of 10 in some cases. At low shear stress the material behaves like a soHd. The material has a yield stress, above which it will flow, but with a high viscosity. The force necessary to shear the fluid is proportional to the square of the electric field (116). 

Controlled stress viscometers are useful for determining the presence and the value of a yield stress. The stmcture can be estabUshed from creep measurements, and the elasticity from the amount of recovery after creep. The viscosity can be determined at very low shear rates, often ia a Newtonian region. This 2ero-shear viscosity, T q, is related directly to the molecular weight of polymer melts and concentrated polymer solutions. 

Non-Newtonian fluids include those for which a finite stress 1,. is reqjiired before continuous deformation occurs these are c ailed yield-stress materials. The Bingbam plastic fluid is the simplest yield-stress material its rheogram has a constant slope [L, called the infinite shear viscosity. 

Viscosity has been replaced by a generahzed form of plastic deformation controlled by a yield stress which may be determined by compression e)meriments. Compare with Eq. (20-48). The critical shear rate describing complete granule rupture defines St , whereas the onset of deformation and the beginning of granule breakdown defines an additional critical value SVh... 

For viscosity or sag control. When the rubber base adhesive is applied on a vertical surface, addition of a filler prevents the adhesive from running down the wall. In solvent-borne formulations, fumed silica can be used as anti-sag filler. In water-borne systems, clays impart yield stress and excellent sag control. 

If the extruder is to be used to process polymer melts with a maximum melt viscosity of 500 Ns/m, calculate a suitable wall thickness for the extruder barrel based on the von Mises yield criterion. The tensile yield stress for the barrel metal is 925 MN/m and a factor of safety of 2.5 should be used. 

For Newtonian fluids the dynamic viscosity is constant (Equation 2-57), for power-law fluids the dynamic viscosity varies with shear rate (Equation 2-58), and for Bingham plastic fluids flow occurs only after some minimum shear stress, called the yield stress, is imposed (Equation 2-59). 

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. 

Fig. 3. A complete flow curve of plastic disperse system with a field of flow (with a very high viscosity tic) at stresses smaller than the yield stress...

The problem of the influence of molecular parameters of a polymer (i.e. of an average molecular weight and molecular-weight distribution) on yield stress is related with the problem of the role of viscosity of a dispersion medium. 

In essence, it follows from Fig. 7 that the viscosity of a dispersion medium does not affect yield stress, since with the variation in temperature (as in Fig. 7), the viscosity of a polymer melt changes by a hundred times, while yield stress remains unchanged. 

A comparison of values of yield stress for filled polymers of the same nature but of different molecular weights is of fundamental interest. An example of experimental results very clearly answering the question about the role of molecular weight is given in Fig. 9, where the concentration dependences of yield stress are presented for two filled poly(isobutilene)s with the viscosity differing by more than 103 times. As is seen, a difference between molecular weights and, as a result, a vast difference in the viscosity of a polymer, do not affect the values of yield stress. 

Data of Figs 8-10 give a simple pattern of yield stress being independent of the viscosity of monodisperse polymers, indicating that yield stress is determined only by the structure of a filler. However, it turned out that if we go over from mono- to poly-disperse polymers of one row, yield stress estimated by a flow curve, changes by tens of times [7]. This result is quite unexpected and can be explained only presumably by some qualitative considerations. Since in case of both mono- and polydisperse polymers yield stress is independent of viscosity, probably, the decisive role is played by more fine effects. Here, possibly, the same qualitative differences of relaxation properties of mono- and polydisperse polymers, which are known as regards their viscosity properties [1]. 

The situation becomes most complicated in multicomponent systems, for example, if we speak about filling of plasticized polymers and solutions. The viscosity of a dispersion medium may vary here due to different reasons, namely a change in the nature of the solvent, concentration of the solution, molecular weight of the polymer. Naturally, here the interaction between the liquid and the filler changes, for one, a distinct adsorption layer, which modifies the surface and hence the activity (net-formation ability) of the filler, arises. Therefore in such multicomponent systems in the general case we can hardly expect universal values of yield stress, depending only on the concentration of the filler. Experimental data also confirm this conclusion [13],... 

How does yield stress depend on a filler concentration It is shown in Fig. 9 that appreciable values of Y appear beginning from a certain critical concentration cp and then increase rather sharply. Though the existence of cp seems to be quite obvious from the view point of the possibility of contacts of the filler, i.e. the beginning of a netformation in the system, practically the problem turns on the accuracy of measuring small stresses in high-viscosity media. It is quite possible to represent the Y(cp) dependence by exponential law, as follows from Fig. 10, for example, leaving aside the problem of the behavior of this function at very low concentrations of the filler, all the more the small values of are measured with a significant part of uncertainty. 

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

First, it is necessary to take into account a yield stress, which at once makes the problem on universality of the r (q>) dependence to be doubtful since it is unclear what viscosity is spoken about. 

Since non-Newtonian flow is typical for polymer melts, the discussion of a filler s role must explicitly take into account this fundamental fact. Here, spoken above, the total flow curve includes the field of yield stress (the field of creeping flow at x < Y may not be taken into account in the majority of applications). Therefore the total equation for the dependence of efficient viscosity on concentration must take into account the indicated effects. 

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