Rheogram

Typical rheograms representing the behaviour of various types of generalized Newtonian fluids are shown in Figure 1.2. 

Stress relaxation time, obtained from rheograms based on viscometric flows, is used to define a dimensionless parameter called the Deborah number , which quantifies the elastic character of a fluid... 

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. 

The branch of science which is concerned with the flow of both simple (Newtonian) and complex (non-Newtonian) fluids is known as rheology. The flow characteristics are represented by a rheogram, which is a plot of shear stress against rate of shear, and normally consists of a collection of experimentally determined points through which a curve may be drawn. If an equation can be fitted to the curve, it facilitates calculation of the behaviour of the fluid. It must be borne in mind, however, that such equations are approximations to the actual behaviour of the fluid and should not be used outside the range of conditions (particularly shear rates) for which they were determined. 

Reynolds apparatus for tracing flow patterns 59 Rheogram 105, 197 Rheological equation (Cross) 110 Rheology 105, 195... 

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... 

Fig. 86 Rheograms of publication gravure printing inks containing 15% pigment.

Systematic measurements of stress and strain can be made and the results plotted as a rheogram. If our material behaves in a simple manner - and it is surprising how many materials do, especially if the strains (or stresses) are not too large - we find a linear dependence of stress on strain and we say our material obeys Hooke s law, i. e. our material is Hookean. This statement implies that the material is isotropic and that the pressure in the material is uniform. This latter point will not worry us if our material is incompressible but can be important if this is not the case. 

As an example, let us consider a typical response produced by stretching a sample of a vulcanised rubber. The components of the stress that we have to consider are the normal stresses axx, [Pg.15]

If we work at small strains so that we are in the linear (Hooke s law) region of the rheogram, then Equation (2.2) reduces to... 

Figure 3.2 Rheogram for water at 25 °C. The slope gives a value for the viscosity of 8.85 x 0 4 Pas...

Figure 3.5 Calculated rheograms for a Bingham plastic with rj(oo) = 5 x 10 3 Pas and aB — 0.8 Pa. Note how the nominal shear rate is significantly lower than the actual value resulting from a given applied stress...

Figure 1.22. Rheograms of a newtonian (4) N and two shear-thinning STl and ST2 emulsions obtained by adding 1.5 wt% ( ) and 1.9 wt% (A) of a nonadsorbing polymer in the continuous phase. (Adapted from [150].)...

Fig. 33 Cure-rheograms of the SBR/EPDM blends cured with solid line S8 squares PPAS8-1 circles PPAS8-2 triangles PPAS8-3 stars PPAS8-4...

Figure 3 (A) Cooling and (B) heating thermal scanning rheograms for a vaginal cream formulation. The dashed vertical line indicates the 38° C point in both plots. This is clearly the initiation temperature of the phase transition leading to increased apparent viscosity during both heating and cooling.

Figure 6.4. Shear and pipeline flow data of a thixotropic Pembina crude oil at 44.5°F. (a) Rheograms relating shear stress and rate of shear at several constant durations of shear (Ritter and Govier, Can. J. Chem. Eng. 48, 50S (1970)]. (b) Decay of pressure gradient of the fluid flowing from a condition of rest at 15,000 barrels/day in a 12 in. line [Ritter and Batycky, SPE Journal 7, 369 (1967)].

Figure H1.1.2 Rheograms or flow curves for five time-independent fluids. The Newtonian fluid yields a straight line that emanates from the origin. The other four examples are non-Newtonian fluids. o0 represents a yield stress point, which is common for plastic fluids.

Data from viscometers are often presented as a linear plot of shear stress versus shear rate, sometimes called a rheogram (Figure HI.1.2). This type of plot allows the viewer to see directly if there is Newtonian behavior because the plot will take the form of a straight line through the origin. A non-Newtonian response is, by definition, nonlinear and may or may not pass through the origin. If the sample has an apparent yield stress, then the line or curve will... 

Figure H1.1.3 Empirical models commonly used for fitting rheogram data. They all rely on the fact that the data were acquired in a linear fashion. See text for definition of variables.

The apparent viscosity is determined from Eq. 4. The value of shear rate that corresponds to this viscosity is obtained from the known viscosity vs shear rate rheogram for the non-Newtonian fluids generated using the cone-and-plate method. The value of k is determined from Eq. 5. 

Figure 3.33 Dynamic rheogram for a solution of 100mM CPyCI and 60 mM NaSal. The solution behaves like a Maxwell fluid with a single relaxation time.

As pointed out above, small air bubbles in the liquid do not rise. This can be considered as an indication for the existence of a yield stress for a person doing practical work without using highly sophisticated instruments. In Figure 3.36 a dynamic rheogram of this system is depicted. 

Figure 3.36 Oscillatory rheogram of a solution of 90 mM Ci4DMAO, 10 mM C14TMABr and 220 mM C6OH. The moduli are almost independent of the frequency G is one order of magnitude larger than G" and does not vanish for low frequencies. This indicates a yield stress (reproduced with permission [44]).

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