Viscosity shear time

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 rotational viscometer connected to a recorder is used. After the sample is loaded and allowed to come to mechanical and thermal equiUbtium, the viscometer is turned on and the rotational speed is increased in steps, starting from the lowest speed. The resultant shear stress is recorded with time. On each speed change the shear stress reaches a maximum value and then decreases exponentially toward an equiUbrium level. The peak shear stress, which is obtained by extrapolating the curve to zero time, and the equiUbrium shear stress are indicative of the viscosity—shear behavior of unsheared and sheared material, respectively. The stress-decay curves are indicative of the time-dependent behavior. A rate constant for the relaxation process can be deterrnined at each shear rate. In addition, zero-time and equiUbrium shear stress values can be used to constmct a hysteresis loop that is similar to that shown in Figure 5, but unlike that plot, is independent of acceleration and time of shear. 

If there is particle—particle interaction, as is the case for flocculated systems, the viscosity is higher than in the absence of flocculation. Furthermore, a flocculated dispersion is shear thinning and possibly thixotropic because the floccules break down to the individual particles when shear stress is appHed. Considered in terms of the Mooney equation, at low shear rates in a flocculated system some continuous phase is trapped between the particles in the floccules. This effectively increases the internal phase volume and hence the viscosity of the system. Under sufficiently high stress, the floccules break up, reducing the effective internal phase volume and the viscosity. If, as is commonly the case, the extent of floccule separation increases with shearing time, the system is thixotropic as well as shear thinning. 

The solidity of gel electrolytes results from chain entanglements. At high temperatures they flow like liquids, but on cooling they show a small increase in the shear modulus at temperatures well above T. This is the liquid-to-rubber transition. The values of shear modulus and viscosity for rubbery solids are considerably lower than those for glass forming liquids at an equivalent structural relaxation time. The local or microscopic viscosity relaxation time of the rubbery material, which is reflected in the 7], obeys a VTF equation with a pre-exponential factor equivalent to that for small-molecule liquids. Above the liquid-to-rubber transition, the VTF equation is also obeyed but the pre-exponential term for viscosity is much larger than is typical for small-molecule liquids and is dependent on the polymer molecular weight. 

Figure 3.34. Effect of sudden change of shear rate on apparent viscosity of time-dependent fluid...

FIGURE 3.21 Plots of shear viscosity versus time for (a) acrylic rubber (ACM)-silica and (b) epoxidized natural mbber (ENR)-silica hybrid nanocomposites in solution at different tetraethoxysilane (TEOS) concentrations, continuously for five days. The numbers in the legends indicate wt% TEOS concentration. (From Bandyopadhyay, A., De Sarkar, M., and Bhowmick, A.K., J. Polym. Sci., Part B Polym. Phys., 43, 2399, 2005. Courtesy of Wiley InterScience.)... 

This model contains four rheological parameters the low shear limiting viscosity (rj0), the high shear limiting viscosity a time constant (X),... 

Now when we apply a shear rate to the sample, as t - oo the viscosity tends to rj(0). At short times the elasticity can be obtained by differentiating the viscosity versus time curve ... 

VISCOSITY. The internal resistance to flow exhibited by a fluid the ratio of shearing stress to rate of shear. A liquid has a viscosity of one poise if a force of 1 dyne/sqnare centimeter causes two parallel liquid surfaces one square centimeter in area and one centimeter apart to move past one another at a velocity of 1 cm/second. One poise equals 100 centipoises divided by the liquid density at the same temperature gives kinematic viscosity in centistokes (cs). One hundred centistokes equal on e stoke. To determine kinematic viscosity, the time is measured tor an exact quantity of liquid to flow by gravity ilirough a standard capillary. See also Rheology. 

The use of Brabender torque rheometer enabled us to evaluate the behavior of melt viscosity vs. time at low shear stresses the usual operating conditions were adopted—i.e., granules (28 grams) were introduced in the bowl, the temperature was fixed at 187 °C, and each run was started after 5 minutes of conditioning. 

For the laminar flow region of Newtonian fluid, shear stress r is equal to the viscosity /t times the velocity gradient du/dy as... 

In general, the viscosity will be a function of the physical-chemical nature of the dispersion or substance, its temperature (usually t] drops as T increases), its pressure (usually increasing P compresses and increases the intermolecular resistance, increasing t]), the applied shear rate (as seen above this can either increase or decrease viscosity), and time (for many dispersions their recent history influences the present viscosity). An important consequence is that if one wishes to determine viscosity as a function of one of these parameters then the other four must be kept well defined (usually constant). 

The exponential decrease in the thread diameter and the highly time-dependent increase in extensional viscosity is clearly visible in the case of the PEO solution. However, the silicone oil displays a linear drop in the diameter of the thread (Newtonian fluid) and no increase of the extensional viscosity over time the extensional viscosity corresponds to approximately three times the shear viscosity. 

In order to elucidate the correlation method it may be recalled that the viscosity 77 approaches asymptotically to the constant value r c with decreasing shear rate q. Similarly, the characteristic time t approaches a constant value xQ and the shear modulus G has a limiting value G0 at low shear rates. Bueche already proposed that the relationship between 77 and q be expressed in a dimensionless form by plotting 77/r]0 as a function of qx. According to Vinogradov, also the ratio t/tq is a function of qxQ. If the zero shear rate viscosity and first normal stress are determined, then a time constant x0 may be calculated with the aid of Eqs. (15.60). This time constant is sometimes used as relaxation time, in order to be able to produce general correlations between viscosity, shear modulus and recoverable shear strain as functions of shear rate. 

At a viscosity range exceeding 600 mN-sec-m-2 (cP) methylcellulose solutions are pseudoplastic which means that the apparent viscosity decreases with increasing shear rate. Solutions of low viscosities again tend to be thixotropic, resulting in a decreased viscosity with increasing shear times. 

Melt Viscosity Equation of Sulfui>-DCP Solutions. An assumption is made that the sulfur-DCP solution is a Newtonian fluid, i.e., the viscosity measured by the Brookfield viscometer is independent of the spindle speed, which is related to shear rate. The linear plots of log (viscosity) vs. time as in Figures 8, 9, and 10 give the following equation for a given sulfur-DCP composition at a given temperature ... 

In view of the fact that fluid elasticity develops as the curing reaction progresses (i.e., as the size of the molecules becomes larger due to polymerization) and that the fluid elasticity increases with shear rate, the deviation of the viscosity-cure time curve from the vertical line at t

flow instability due to fluid elasticity. 

There is not complete agreement on how to mathematically describe the mode of change of shear viscosity with time for thermosets. However, an expression which is basic to the approach of a number of authors is (1,3.15-17)... 

Polymeric (and other) solids and liquids are intermediate in behavior between Hookean, elastic solids, and Newtonian, purely viscous fluids. They often exhibit elements of both types of response, depending on the time scale of the experiment. Application of stresses for relatively long times may cause some flow and permanent deformation in solid polymers while rapid shearing will induce elastic behavior in some macromolecular liquids. It is also frequently observed that the value of a measured modulus or viscosity is time dependent and reflects the manner in which the measuring experiment was performed. Tliese phenomena are examples of viscoelastic behavior. 

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