Rheological viscosity-shear rate curve

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. 

Polymers are used for mobility control in chemical flooding processes such as micellar-polymer and caustic-polymer flooding and in polymer augmented waterflooding. Selection of a polymer for mobility control is a complex process because it is not possible to predict the behavior of a polymer in porous rock from rheological measurements such as viscosity/ shear rate curves. Polymers used for mobility control are non-Newtonian fluids. Flow characteristics are controlled by the shear field to which the polymer is subjected. Properties of polymers can be measured under steady shear in rheometers. However, in porous rock, it is difficult to define the shear environment a polymer experiences as it flows through tortuous pores. 

Lot to lot variations in polymer properties were observed. Because of this, there were differences in rheological properties between fluids which had the same nominal concentration. It was necessary to determine viscosity-shear rate curves for several concentrations in order to match polymer solution characteristics of previous runs. 

In simple geometries the shear rate—and hence the shear stress—are the same ever)rwhere in the liquid, and cone-and-plate and narrow-gap concentric-cylinder geometries are examples of this situation used in viscometers, see chapter 6. In some other situations, either the shear rate or the shear stress varies in a known manner independently of the rheology of the test liquid, and this information can be used to reduce the measured data to viscosity/shear-rate or viscosity/shear-stress, however we must make some assumption about the form of the viscosity/shear-rate curve, for example that it approximately obeys a power-law relationship. Examples of this known relationship are found in... 

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. 

Rheological measurements Two instruments were used to investigate the rheology of the suspensions. The first was a Haake Rotovisko model RV2(MSE Scientific Instruments, Crawley, Sussex, England) fitted with an MK50 measuring head. This instrument was used to obtain steady state shear stress-shear rate curves. From these curves information can be obtained on the viscosity as a function of shear rate. The yield value may be obtained by extrapolation of the linear portion of the shear stress-shear rate curve to zero shear rate. The procedure has been described before (3). 

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),... 

The effect of overall molecular weight or the number of blocks on rheological properties for the samples from the second fractionation can be illustrated as a plot of reduced viscosity vs. a function proportional to the principal molecular relaxation time (Figure 2). This function includes the variables of zero shear viscosity, shear rate, y, and absolute temperature, T, in addition to molecular weight, and allows the data to be expressed as a single master curve (10). All but one of the fractions from the copolymer containing 50% polystyrene fall on this... 

In non-Newtonian fluids K a also depends on their physical and rheoiogical properties. The contribution of the latter has been normally expressed in terms of the apparent viscosity, and there is general agreement that this dependence is of the form Kj a 0(11 ) % where z can take values between 0.4 to 0.7. In the case of viscoelastic materials, inclusion of the fluid rheology is less straightforward. Several authors have tried to include the effect of elasticity via the Deborah number, which for stirred tanks is defined as the product of a characteristic time of the fluid and impeller speed. However, determination of the former is not an easy task because it is not always possible to characterize experimentally the viscoelastic properties of the fluid. Determination of the characteristic time of the fluid from experimental shear viscosity vs. shear rate curves [29] and from interpolation of published experimental data on viscoelastic properties [30] has been tried in the past. However, values thus obtained are not necessarily representative of the actual behavior of the liquid. At present, inclusion of the Deborah number in dimensional or dimensionless correlations has not been completely successful. 

Figure 2.16 lypical viscosity versus shear rate curve depicting the method for determining the parameters of the General Rheological ModeL rom Re 87.)... 

The General Rheological Model [87] was basically developed for master curves of viscosity versus shear rate for polymer melts using the melt-flow index (MFI) as a normalizing parameter. It can be written in a general form applicable to any viscosity versus shear rate curve of a polymer melt simply by putting MFI as unity to give... 

The presented command sequences in Chapter 7 for developing the spreadsheet program are given only for viscosity versus shear rate curves. The step-by-step procedure is very simple and needs to be extended for other rheological parameters once master curves are established for a long list of polymers. 

The reasons why rheology is selected as a separate chapter is as follows the capillary rheometer and the rotational rheometer, which had originally been designed for the rheological measurements of liquids have been used for the observation of gum rubber and compound behaviour. The question is what these measurements really mean, because gum rubbers as well as compounds are not liquids but they are in the rubbery state. However, in this chapter, the conventional practice of treating the material as if it were liquid is followed. Not only is the viscosity-shear rate relationship discussed but also the melt fracture, extrudate swell and slip. Shown in Figure 8.1 are flow curves of NBR samples. A, B, C, and D at 100 °C [1]. 

Figure 1. 7 mode PTT model fit to the bulk steady-state viscosity vs. shear rate curve of a short glass fiber filled PP. Rheological tests were performed at 200 C. 

Viscosity is equal to the slope of the flow curve, Tf = dr/dj. The quantity r/y is the viscosity Tj for a Newtonian Hquid and the apparent viscosity Tj for a non-Newtonian Hquid. The kinematic viscosity is the viscosity coefficient divided by the density, ly = tj/p. The fluidity is the reciprocal of the viscosity, (j) = 1/rj. The common units for viscosity, dyne seconds per square centimeter ((dyn-s)/cm ) or grams per centimeter second ((g/(cm-s)), called poise, which is usually expressed as centipoise (cP), have been replaced by the SI units of pascal seconds, ie, Pa-s and mPa-s, where 1 mPa-s = 1 cP. In the same manner the shear stress units of dynes per square centimeter, dyn/cmhave been replaced by Pascals, where 10 dyn/cm = 1 Pa, and newtons per square meter, where 1 N/m = 1 Pa. Shear rate is AH/AX, or length /time/length, so that values are given as per second (s ) in both systems. The SI units for kinematic viscosity are square centimeters per second, cm /s, ie, Stokes (St), and square millimeters per second, mm /s, ie, centistokes (cSt). Information is available for the official Society of Rheology nomenclature and units for a wide range of rheological parameters (11). 

The measurements are carried out at preselected shear rates. The resulting curves are plotted in form of flow-curves t (D) or viscosity-curves ti (D) and give information about the viscosity of a substance at certain shear rates and their rheological character dividing the substances in Newtonian and Non-Newtonian fluids. 

Rheology concerns the study of the deformation and flow of soft materials when they respond to external stress or strain. If the ratio of its shear stress and shear rate is a straight line, the material is termed Newtonian otherwise, it is termed non-Newtonian (Figure 4.3.2(a)). As the slope of the curve is the viscosity rj, a shear-thinning fluid exhibits a reduced viscosity as the shear stress increases, whereas a shear-... 

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