Viscoelasticity viscosity shear dependence

Frequently used single-point viscosity tests in the starch plant are orifice pipettes,56 orifice funnels,57 the Hot Scott viscometer, and various methods to determine alkaline fluidity.58 For absolute measurements of the rheological properties, rotating viscometers with coaxial cylinders are used.59 The paper industry uses mainly the Brookfield viscometer and the Hercules viscometer for determining shear-dependent viscosity, pseudoplasticity, and thixotropy. Oscillatory and capillary viscometers are used for more detailed viscosity characterization, such as yield value, elastic properties, and viscoelasticity.60... 

In the case of fluids without yield stress, viscous and viscoelastic fluids can be distinguished. The properties of viscoelastic fluids lie between those of elastic solids and those of Newtonian fluids. There are some viscous fluids whose viscosity does not change in relation to the stress (Newtonian fluids) and some whose shear viscosity T] depends on the shear rate y (non-Newtonian fluids). If the viscosity increases when a deformation is imposed, we define the material as a shear-thickening (dilatant) fluid. If viscosity decreases, we define it as a shear-thinning fluid. 

The major characteristic of a polymeric reactor that is different from most other types of reactors discussed earlier is the viscous and often non-Newtonian behavior of the fluid. Shear-dependent rheological properties cause difficulties in the estimation of the design parameters, particularly when the viscosity is also time-dependent. While significant literature on the design parameters for a mechanically agitated vessel containing power-law fluid is available, similar information for viscoelastic fluid is lacking. 

Flow behavior also depends on the solids loading, which is the volume percent of the particles in the solution. The flow of a system can be categorized into two types viscous and viscoelastic. Viscous solutions are solutions where viscosity (t ) depends on the shear stress (x) and the shear rate (y) ... 

Influence of the Strain Rate on Viscoelastic Response. In high-shear-strain experiments, we observe significant differences only with type 2 and type 3 blends (Figures 9b and 9c). The complex viscosity still depends on frequency, but it decreases as phase separation begins. Moreover, a crossover of the tan 8 curves appears at this moment. The differences reported in this land of experiment can be found at two levels ... 

For infinitely diluted viscoelastic emulsions, the shear dependence of inherent viscosity was derived as [Barthes-Biesel and Acrivos, 1973] ... 

Most fluids exhibit non-Newtonian behavior—blood, household products like toothpaste, mayonnaise, ketchup, paint, and molten polymers. As shown in Figure 7.9, shear stress, t, increases linearly with strain rate, y, for Newtonian fluids. Non-Newtonian fluids may be classified into those that are time dependent or time independent and include viscoelastic fluids. Shear thinning (pseudoplastic) and shear thickening (dilatant) fluids are time independent while rheopectic and thixotropic are time dependent. The shear stress (viscosity) of shear thinning fluids decreases with increasing shear rate and examples include blood and syrup. The viscosity of dilatant fluids increases with shear rate. The viscosity of rheopectic fluids—whipping cream, egg whites—increases with time while thixotropic fluids— paints (other than latex) and drilling muds— decrease their viscosity with the duration of the shear. 

Polymer melts are in most cases viscoelastic, meaning the viscosity is dependent oti measurement conditions, like frequency or shear rate. Most polymer melts show a viscosity plateau at low shear rates, called Newtonian plateau and the viscosity drops with increasing shear rate. 

Very dilute solutions of axisymmetric rigid molecules exhibit not only frequency-dependent viscoelastic properties but also an apparent viscosity which depends on shear rate. This non-Newtonian flow is predicted by theory for elongated ellipsoids and rigid dumbbells,and the theoretical results have been widely applied for certain biological macromolecules. The shear-rate dependent viscosity r) is defined as the ratio of shear stress a to shear rate 7, and the intrinsic viscosity as defined by equation 5 with 77 substituted for rjo is then in general a function of 7. At low shear rates, the shear-dependent intrinsic viscosity has the form... 

The viscoelastic properties in the terminal zone are dominated by the characteristic constants rjo, J% Ac, and i,o (equation 74 of Chapter 3) and if the molecular weight distribution is sharp, additional constants are the terminal relaxation time r I (or or tj) and a related characteristic time constant r, which sets the scale for the shear dependence of non-Newtonian viscosity. Here the entanglements have their maximum effect in influencing the properties which reflect the longest-range molecular motions. 

Most adsorbed surfactant and polymer coils at the oil-water (0/W) interface show non-Newtonian rheological behavior. The surface shear viscosity Pg depends on the applied shear rate, showing shear thinning at high shear rates. Some films also show Bingham plastic behavior with a measurable yield stress. Many adsorbed polymers and proteins show viscoelastic behavior and one can measure viscous and elastic components using sinusoidally oscillating surface dilation. For example the complex dilational modulus c obtained can be split into an in-phase (the elastic component e ) and an out-of-phase (the viscous component e") components. Creep and stress relaxation methods can be applied to study viscoelasticity. 

The first of these relationships, eq. 4.2.4, follows from little more than the definitions of rj and t], while eq. 4.2.5 is less obvious (Coleman and Markovitz, 1964). Both relationships are of limited usefulness because they are relevant only for low shear rate properties. However, an empirical relationship, called the Cox-Merz rule, often holds fairly well at high shear rates. This rule states that the shear rate dependence of the steady state viscosity ij is equal to the frequency dependence of the linear viscoelastic viscosity ri that is. 

The classical viscoelastic properties are the dynamic shear moduli, written in the frequency domain as the storage modulus G ( y) and the loss modulus G a>), the shear stress relaxation function G t), and the shear-dependent viscosity j (k). Optical flow birefringence and analogous methods determine related solution properties. Nonlinear viscoelastic phenomena are treated briefly in Chapter 14. 

In order to make satisfactory predictions, it was necessary to take a step that prior chapters did not. Rather than using the classical storage and loss moduli G co) and G" co), a novel pair of viscoelastic moduli are here introduced. The ansatz makes predictions for the novel functions. The new functions are actually not very radical indeed, there is a sense in which they are more consistent with prior chapters than are G (co) and G"(co). The previous chapter described the zero-shear viscosity as the low-shear limit t](c, M) of the experimentally accessible viscosity. To describe shear thinning, rj is extended to the shear-dependent For oscillatory motion, one might by analogy have expected rj to become r cd) with complications arising because at nonzero co the displacement and applied force shift in relative phase. The orthodox loss function is G", with... 

For some materials the linear constitutive relation of Newtonian fluids is not accurate. Either stress depends on strain in a more complex way, or variables other than the instantaneous rate of strain must be taken into account. Such fluids are known collectively as non-Newtonian. Many different types of behavior have been observed, ranging from fluids for which the viscosity in the Navier-Stokes equation is a simple function of the shear rate to the so-called viscoelastic fluids, for which the constitutive equation is so different that the normal stresses can cause the fluid to flow in a manner opposite to that predicted for a Newtonian fluid. 

Viscous Hquids are classified based on their rheological behavior characterized by the relationship of shear stress with shear rate. Eor Newtonian Hquids, the viscosity represented by the ratio of shear stress to shear rate is independent of shear rate, whereas non-Newtonian Hquid viscosity changes with shear rate. Non-Newtonian Hquids are further divided into three categories time-independent, time-dependent, and viscoelastic. A detailed discussion of these rheologically complex Hquids is given elsewhere (see Rheological measurements). 

Taking into account the relevance of the range of semi-dilute solutions (in which intermolecular interactions and entanglements are of increasing importance) for industrial applications, a more detailed picture of the interrelationships between the solution structure and the rheological properties of these solutions was needed. The nature of entanglements at concentrations above the critical value c leads to the viscoelastic properties observable in shear flow experiments. The viscous part of the flow behaviour of a polymer in solution is usually represented by the zero-shear viscosity, rj0, which depends on the con-... 

The coordinates (x, y, z) define the (velocity, gradient, vorticity) axes, respectively. For non-Newtonian viscoelastic liquids, such flow results not only in shear stress, but in anisotropic normal stresses, describable by the first and second normal stress differences (oxx-Oyy) and (o - ozz). The shear-rate dependent viscosity and normal stress coefficients are then [1]... 

---