Shear constant rate

C. Above this temperature, the shear stress at constant shear rate increases and the rheological exponent rises from 0.25 toward 0.5 at the final melting point (68). 

Thixotropy and Other Time Effects. In addition to the nonideal behavior described, many fluids exhibit time-dependent effects. Some fluids increase in viscosity (rheopexy) or decrease in viscosity (thixotropy) with time when sheared at a constant shear rate. These effects can occur in fluids with or without yield values. Rheopexy is a rare phenomenon, but thixotropic fluids are common. Examples of thixotropic materials are starch pastes, gelatin, mayoimaise, drilling muds, and latex paints. The thixotropic effect is shown in Figure 5, where the curves are for a specimen exposed first to increasing and then to decreasing shear rates. Because of the decrease in viscosity with time as weU as shear rate, the up-and-down flow curves do not superimpose. Instead, they form a hysteresis loop, often called a thixotropic loop. Because flow curves for thixotropic or rheopectic Hquids depend on the shear history of the sample, different curves for the same material can be obtained, depending on the experimental procedure. 

Time-dependent effects ate measured by determining the decay of shear stress as a function of time at one or more constant shear rates (Fig. 7)... 

Time-dependent fluids are those for which structural rearrangements occur during deformation at a rate too slow to maintain equilibrium configurations. As a result, shear stress changes with duration of shear. Thixotropic fluids, such as mayonnaise, clay suspensions used as drilling muds, and some paints and inks, show decreasing shear stress with time at constant shear rate. A detailed description of thixotropic behavior and a list of thixotropic systems is found in Bauer and Colhns (ibid.). 

Rheopectic behavior is the opposite of thixotropy. Shear stress increases with time at constant shear rate. Rheopeclic behavior has been obsei ved in bentonite sols, vanadium pentoxide sols, and gypsum suspensions in water (Bauer and Colhns, ibid.) as well as in some... 

The rate of mastication, as measured by changes in plasticity or viscosity, is a complex function of temperature (Figure 11.16) with the rate going through a minimum at about 105°C. Below this temperature the increasing viscosity of the rubber causes increased shearing stresses at constant shearing rates and this... 

Describes those fluids whose apparent viscosity decreases with time to an asymptotic value under conditions of constant shear rate. Thixotropic fluids undergo a decrease in apparent viscosity by applying a shearing force such as stirring. If shear is removed, the material s apparent viscosity will increase back to or near its initial value at the onset of applying shear. 

If it is known that a particular form of relation, such as the power-law model, is applicable, it is not necessary to maintain a constant shear rate. Thus, for instance, a capillary tube viscometer can be used for determination of the values of the two parameters in the model. In this case it is usually possible to allow for the effects of wall-slip by making measurements with tubes covering a range of bores and extrapolating the results to a tube of infinite diameter. Details of the method are given by Farooqi and Richardson. 21 ... 

Most pectin solutions behave like Newtonian liquids below a pectin concentration of about 1 % (w/w). Onogi (1966) derived the critical concentration of polymer solutions from plotting the double logarithmic curves of viscosity (ii) against concentration at constant shear rates. Each curve consists of two straight lines intersecting at the critical concentration. At higher... 

Thixotropy is a phenomenon that occurs frequently in dispersed systems. It is defined as a reversible, time-dependent decrease in viscosity at a constant shear rate. Generally, a dispersion that shows an isothermal gel-sol-gel transformation is a thixotropic material. The mechanism of thixotropy is the breakdown and reforming of the gel structure. 

The topological transformations in an incompatible blend can be described by the dynamic phase diagram that is usually determined experimentally at a constant shear rate. For equal viscosities, a bicontinuous morphology is observed within a broad interval of the volume fractions. When the viscosity ratio increases, the bicontinuous region of the phase diagram shrinks. At large viscosity ratios, the droplets of a more viscous component in a continuous matrix of a less viscous component are observed practically for all allowed geometrically volume fractions. 

Rheopexy, a reversible time-dependent effect like thixotropy, is a rare phenomenon in pigmented systems. Rheopectic fluids increase in viscosity t with time when sheared at a constant shear rate D or a constant shear stress t until they approach a viscosity maximum (Fig. 53). 

Common geometries used to make viscosity measurements over a range of shear rates are Couette, concentric cylinder, or cup and bob systems. The gap between the two cylinders is usually small so that a constant shear rate can be assumed at all points in the gap. When the liquid is in laminar flow, any small element of the liquid moves along lines of constant velocity known as streamlines. The translational velocity of the element is the same as that of the streamline at its centre. There is of course a velocity difference across the element equal to the shear rate and this shearing action means that there is a rotational or vorticity component to the flow field which is numerically equal to the shear rate/2. The geometry is shown in Figure 1.7. 

The Mooney arrangement of a bob with a conical base is an attractive design as it is relatively easy to fill and uses the base area to enhance the measurement sensitivity. However the cone angle must be such that the shear rates in both the cone and plate and concentric cylinder sections are the same. This means that the gap between the cylinders must be very slightly larger than the gap at the edge of the cone and plate if a constant shear rate is required. Unfortunately the DIN standard bob is poor in this respect. 

An important and sometimes overlooked feature of all linear viscoelastic liquids that follow a Maxwell response is that they exhibit anti-thixo-tropic behaviour. That is if a constant shear rate is applied to a material that behaves as a Maxwell model the viscosity increases with time up to a constant value. We have seen in the previous examples that as the shear rate is applied the stress progressively increases to a maximum value. The approach we should adopt is to use the Boltzmann Superposition Principle. Initially we apply a continuous shear rate until a steady state... 

Whilst the flow curves of materials have received widespread consideration, with the development of many models, the same cannot be said of the temporal changes seen with constant shear rate or stress. Moreover we could argue that after the apparent complexity of linear viscoeleastic systems the non-linear models developed above are very poor cousins. However, it is possible to introduce a little more phenomenological rigour by starting with the Boltzmann superposition integral given in Chapter 4, Equation (4.60). This represents the stress at time t for an applied strain history ... 

Now a shear rate represents the rate of change of strain so for the application of a constant shear rate to the sample the strain is the product of the rate and the time ... 

The 3 1 LDAO/SDS mixture becomes viscoelastic and rheo-pectic when a small amount of NaCl Is added. Its viscosity shows a reversible Increase with time of shearing at constant shear rate. The rheopectic behavior Is probably due to long thread-like micelles that are aligned parallel to the flow In weakly bound clusters, as In the case of cetyltrlmethyl ammonium bromide and monosubstituted phenol mixed solutions (21). 

Inverted W/O emulsion. The premixed emulsion was composed of aqueous droplets dispersed in an oil phase containing a lipophilic surfactant. The droplet mass fraction (/>, was set to 80%. This crude emulsion was sheared into the Couette-type cell [159] at constant shear rate V = 10000 s and a... 

Note 3 fy t)=yt, where is a constant, then the flow has a constant shear rate and is known as steady (simple) shear flow. 

Figure 4.6 Thixotropic behavior, in which time at constant shear rate affects viscosity. From J. S. Reed, Principles of Ceramics Processing, 2nd ed. Copyright 1995 by John Wiley Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

Mechanical synthesis by cold mastication of rubber and monomers depends on the reaction condition (monomer concentration, temperature, solvent concentration, atmosphere, presence of transfer agents, or catalyst) and on the physical and chemical properties of the rubbers, the monomers and the product interpolymers. A critical factor is the shear stress developed in the system rather than instrumentally-defined shear rates. The degree of reaction of polymer and consequently also the concentration of free macroradicals depends on stress. As a consequence, the influence of the above parameters may be connected to their influence on the viscosity of the reaction medium since an increase in viscosity causes an increase in stress at constant shear rate. 

Another often used representation of the viscoelastic flow behavior utilizes normal stress coefficients P/ = Ni/y. Figure 10 depicts flow curves of a family of PAA/water solutions differing in concentrations and therefore in their viscosities. Normalized by the zero-shear viscosity fiQ and by a constant shear rate /q shear stress value of to= 1 N/m they produce master curves for viscosity and the normal stress coefficient. The preparation... 

These time-of-shear-dependent non-Newtonians may be divided into two groups, depending on whether the shear stress increases or decreases with time of shear at a constant shearing rate. The former are termed rheopectic the latter thixotropic Quids (P3). 

At sufficiently low shear rates the viscosity is constant. If a constant shear rate in this range is imposed, the shear stress should grow monotonically to its steady state value c(oo) according to the equation from linear viscoelasticity ... 

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