Viscosity flow curve

The viscosity flow curves for these materials are shown in Fig. 5.17. To obtain similar data at other temperatures then a shift factor of the type given in equation (5.27) would have to be used. The temperature effect for polypropylene is shown in Fig. 5.2. 

Viscosity Analysis. Rheological analyses of the unground spray dried resins in dioctyl phthalate (DOP) plastisols gave the viscosity flow curves in Figures V-VIII. Characteristic data are presented in Tables II and III. 

Fig. 4. Viscosity flow curves of PP copolymer (with ethylene monomer) and PP homopolymer obtained using a twin screw extruder...

The fact that the Trouton ratio eventually approaches a constant value means that the shear and extensional viscosity flow curves are paraUeT in that range, and if the behaviour is power-law, then the power-law index is the same in both cases. (Notice this from the polymer melt examples shown later in the figures 13 - 20.)... 

Rapid yield stress determination and viscosity flow curves with built-in temperature control... 

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) or grams per centimeter second ((g/(cm-s)), called poise, which is usually expressed as centipoise (cP), have been replaced by the SI units of pascal seconds, ie, Pa-s and mPa-s, where 1 mPa-s = 1 cP. In the same manner the shear stress units of dynes per square centimeter, dyn/cmhave been replaced by Pascals, where 10 dyn/cm = 1 Pa, and newtons per square meter, where 1 N/m = 1 Pa.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). 

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. 

A plot of apparent viscosity against shear rate produces a unique flow curve for the melt is shown in Fig. 5.3. Occasionally this information may be based on the true shear rate. As shown in Section 5.4(a) this is given by... 

Other factors such as the use of additives also have an effect on the shape of the flow curves. Flame retardants, if used, tend to decrease viscosity whereas pigments tend to increase viscosity. Fig. 5.17 shows flow curves for a range of plastics. 

For scaly fillers the increase of relative viscosity with filler concentration is not as pronounced as in case of fibrous fillers [177,178]. Owing to filler orientation, the flow curves for systems with different concentrations of a fibrous and a scaly filler may merge together at high shear rates [181]. In composites with a dispersed filler the decrease of the effective viscosity of the melt with increasing strain rate is much weaker. 

In a number of works (e.g. [339-341]) the authors sought to superimpose graphically the flow curves of filled melts and polymer solutions with different filler concentrations however, it was only possible to do so at high shear stresses (rates). More often than not it was impossible to obtain a generalized viscosity characteristic at low shear rates, the obvious reason being the structurization of the system. 

Third. Points in Fig. 1 show only a part of a flow curve. In reality if we take very low stresses t, it turns out that in this field a flow is also possible and in fact such a flow curve in the field of low rates looks like it is shown in Fig. 3, i.e. at low stresses x the flow takes place, though viscosity in this range of stressesT]c turns out to be very high amounting to 109-1010 Pa s and, moreover, (and this is of fundamental importance)... 

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...

During dynamic measurements frequency dependences of the components of a complex modulus G or dynamic viscosity T (r = G"/es) are determined. Due to the existence of a well-known analogy between the functions r(y) or G"(co) as well as between G and normal stresses at shear flow a, seemingly, we may expect that dynamic measurements in principle will give the same information as measurements of the flow curve [1],... 

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]. 

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. 

According to the structure of this equation the quantity cp indicates the influence of the filler on yield stress, and t r on Newtonian (more exactly, quasi-Newtonian due to yield stress) viscosity. Both these dependences Y(cp) andr r(cp) were discussed above. Non-Newtonian behavior of the dispersion medium in (10) is reflected through characteristic time of relaxation X, i.e. in the absence of a filler the flow curve of a melt is described by the formula ... 

Though the accuracy of description of flow curves of real polymer melts, attained by means of Eq. (10), is not always sufficient, but doubtless the equation of such a structure based on the idea of relaxation mechanism of non-Newtonian polymer flow, correctly reflects the main peculiarities of viscous properties. Therefore while discussing the effect a filler has on the viscosity properties of polymer melts, besides the dependences Y(filler modifies the characteristic time of relaxation. According to [19], a possible form of the X versus

[Pg.86]

Concrete calculations carried out via formula (10) for different values of constant have shown that it reflects the behavior of flow curves quite really. However, a series doubt remains for such a system (with a yield stress) it is not obvious how to determine the initial Newtonian viscosity (is it necessary to determine it and does it exist ). 

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. 

Figure 3 gives an example of a typical force profile. The force is increased continuously and reaches the point - at the end of the first part of the force profile - where the pectin preparations start to flow. The so-called yield point is reached. The further increase leads to the continuous destruction of the internal structure and the proceeding shear thinning. The applied stress in part 3 of the stress profile destroys the structure of the fruit preparations completely. Now the stress is reduced linearly, see part 4 and 5, down to zero stress. The resulting flow curves 2, 3 and 4 and the enclosed calculated area from the hysteresis loop give important evidence about the time-dependent decrease of viscosity and a relative measure of its thixotropy. 

The viscosity level in the range of the Newtonian viscosity r 0 of the flow curve can be determined on the basis of molecular models. For this, just a single point measurement in the zero-shear viscosity range is necessary, when applying the Mark-Houwink relationship. This zero-shear viscosity, q0, depends on the concentration and molar mass of the dissolved polymer for a given solvent, pressure, temperature, molar mass distribution Mw/Mn, i.e. 

In order to evaluate the viscosity of a polymeric liquid at finite rates of deformation, two parameters must be determined, i.e. (i) the critical shear rate y (y=l/7.) at which T) becomes a function of the of deformation, and (ii) the slope in the linear range of the flow curve. 

Polymers in solution or as melts exhibit a shear rate dependent viscosity above a critical shear rate, ycrit. The region in which the viscosity is a decreasing function of shear rate is called the non-Newtonian or power-law region. As the concentration increases, for constant molar mass, the value of ycrit is shifted to lower shear rates. Below ycrit the solution viscosity is independent of shear rate and is called the zero-shear viscosity, q0. Flow curves (plots of log q vs. log y) for a very high molar mass polystyrene in toluene at various concentrations are presented in Fig. 9. The transition from the shear-rate independent to the shear-rate dependent viscosity occurs over a relatively small region due to the narrow molar mass distribution of the PS sample. 

A plot of Tvs. G yields a rheogram or a flow curve. Flow curves are usually plotted on a log-log scale to include the many decades of shear rate and the measured shear stress or viscosity. The higher the viscosity of a liquid, the greater the shearing stress required to produce a certain rate of shear. Dividing the shear stress by the shear rate at each point results in a viscosity curve (or a viscosity profile), which describes the relationship between the viscosity and shear rate. The... 

From such a flow curve, the apparent viscosity can be calculated at any... 

The apparent viscosity becomes infinite as the shear stress is reduced to the yield value because below the non-zero yield stress there is no flow. As the shear rate is increased, the apparent viscosity tends to the value /3, which is equal to the gradient of the flow curve. 

Under conditions of steady fully developed flow, molten polymers are shear thinning over many orders of magnitude of the shear rate. Like many other materials, they exhibit Newtonian behaviour at very low shear rates however, they also have Newtonian behaviour at very high shear rates as shown in Figure 1.20. The term pseudoplastic is used to describe this type of behaviour. Unfortunately, the same term is frequently used for shear thinning behaviour, that is the falling viscosity part of the full curve for a pseudoplastic material. The whole flow curve can be represented by the Cross model [Cross (1965)] ... 

The second category, time-dependent behaviour, is common but difficult to deal with. The best known type is the thixotropic fluid, the characteristic of which is that when sheared at a constant rate (or at a constant shear stress) the apparent viscosity decreases with the duration of shearing. Figure 1.21 shows the type of flow curve that is found. The apparent viscosity continues to fall during shearing so that if measurements are made for a series of increasing shear rates and then the series is reversed, a hysteresis loop is observed. On repeating the measurements, similar behaviour is seen but at lower values of shear stress because the apparent viscosity continues to fall. 

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