Oscillatory shear flow measurement

Oscillatory shear flow properties (also referred to as dynamic viscoelastic properties) have long been used to investigate the viscoelastic properties of polymeric materials (Ferry 1980). Oscillatory shear flow measurement requires an instrument that can generate sinusoidal strain as an input to the fluid under test and record the stress resulting from the deformed fluid as an output. For such purposes, a parallel-plates flxture as well as a cone-and-plate flxture can be used the uniform shear rate in the radial direction that is necessary when conducting steady-state shear flow experiments is no longer necessary. 

In the actual experiment, the amplitudes of the oscillation input (y, ) and output (CTq), and the phase angle (p) are measured. Therefore, each oscillatory shear flow 

The components of the complex modulus can be obtained by the inverse relations 

The salient feature of oscillatory shear flow measurement is that it yields information on both the viscous property t] (co) and the elastic property G (o) of a fluid. 

even when the data are obtainable only over one or two decades of the logarithmic frequency scale at any one time, the viscoelastic functions can be traced out over a much larger effective range by making measurements at different temperatures, and by applying time-temperature superposition (TTS) for flexible homopolymers (see Chapter 6). In many instances, the effect of an increase in temperature is nearly equivalent to an increase in time or a decrease in frequency, as molecular viscoelastic theories suggest (see Chapter 4). When properly applied, TTS yields plots in terms of reduced variables that can be used with considerable confldence to deduce the effect of molecular parameters, and also to predict viscoelastic behavior in regions of the time or frequency scale not experimentally readily accessible (see Chapters 4 and 6). 

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Vega, J. F., Santamaria, A. Small-amplitude oscillatory shear flow measurements as a tool to detect very low amounts of long chain branching in polyethylenes. Macromol. (1998) 31, pp.3639-3647... 

Rheological Properties. Rheological studies of the nanocomposites were performed using a Rheometrics Mechanical Spectrometer model 800 on 25mm diameter samples punched from the injection molded plaques. Dynamic oscillatory shear flow measurements of the nanocomposites were made in the linear regime of strain in a frequency range of 0.1 to 100 rad/s under a continuous nitrogen atmosphere. 

Typical for the spectroscopic character of the measurement is the rapid development of a quasi-steady state stress. In the actual experiment, the sample is at rest (equilibrated) until, at t = 0, oscillatory shear flow is started. The shear stress response may be calculated with the general equation of linear viscoelasticity [10] (introducing Eqs. 4-3 and 4-9 into Eq. 3-2)... 

There have been fewer studies in electrochemistry where the flow is known but the boundary-layer approach is inapplicable. One example has been recently analyzed and compared with experiment. In this case, mass transfer to a line electrode or an array of line electrodes in the presence of an oscillatory shear flow was treated. A finite-volume approach was used for the numerical analysis and a ferri/ferrocyanide redox couple was used to measure the mass-transfer rate. The studies show that boundary-... 

Prigogine, Trappeniers, and Mathot pressure-volume-temperature measurements lead zirconate titanate quaternary ammonium salts quasi-two-parameter theory rigid amorphous fraction Rheometrics extensional rheometer Rheometrics elongational rheometer for melts room temperature small-angle neutron scattering small-amplitude oscillatory shear flow small-angle x-ray scattering side-chain LCP... 

Therefore, it is more suitable to measure the shear sensitivity of polypropylene. Capillary rheometers or oscillatory shear flow rheometers are widely used for that purpose. Moreover, an investigation of elongational flow properties of molten PP can be used to check, for example, the presence of long-chain branching in some speciality grades of PP (to study the strain-hardening effect). 

Recent literature has shown that the modified Cox-Merz rule could fit e rimental data very well [20-22], Isayev and Fan [22] of University of Akron investigated both steady and oscillatory shear flow behavior of silicon-polypropylene ceramic compoimd. They reported that steady shear measurement with either parallel plate or capillary rheometers posed a... 

The fluid s relaxation time A is the characteristic time of the fluid and, for oscillatory shearing, cu 1 can be taken as a measure of the characteristic time of the flow process, so De = A to. Thus, viscous behaviour occurs when the Deborah number is low, reflecting the fact that the fluid is able to relax. When the Deborah number is high, elastic behaviour is observed because the fluid is unable to relax sufficiently quickly. 

The phase angle changes with frequency and this is shown in Figure 4.7. As the frequency increases the sample becomes more elastic. Thus the phase difference between the stress and the strain reduces. There is an important feature that we can obtain from the dynamic response of a viscoelastic model and that is the dynamic viscosity. In oscillatory flow there is an analogue to the viscosity measured in continuous shear flow. We can illustrate this by considering the relationship between the stress and the strain. This defines the complex modulus ... 

The Weissenbeig Rheogoniometer (49) is a complex dynamic viscometer that can measure elastic behavior as well as viscosity. It was the first rheometer designed to measure both shear and normal stresses and can be used for complete characterization of viscoelastic materials. Its capabilities include measurement of steady-state rotational shear within a viscosity range of 10-1 —13 mPa-s at shear rates of 10-4 — 104 s-1, of normal forces (elastic effect) exhibited by the material being sheared, and of an oscillatory shear range of 5 x 10-6 to 50 Hz, from which the elastic modulus and dynamic viscosity can be determined. A unique feature is its ability to superimpose oscillation on steady shear to provide dynamic measurements under flow conditions all measurements can be made over a wide range of temperatures (—50 to 400°C). 

Fig. 2.5. Steady-state and dynamic oscillatory flow measurements on a 2 wt. per cent solution of polystyrene S 111 in Aroclor 1248 according to Philippoff (57). ( ) steady shear viscosity (a) dynamic viscosity tj, ( ) cot 1% from flow birefringence, (A) cot <5 from dynamic measurements, all at 25° C. (o) cot 8 from dynamic measurements at 5° C. Steady-state flow properties as functions of shear rate q, dynamic properties as functions of angular frequency m. Shift factor aT which is equal to unity for 25° C, is explained in the text, cot 2 % and cot 8 are expressed in terms of shear (see eqs. 2.11 and 2.22)...

Both strain- and stress-controlled rotational rheometers are widely employed to study the flow properties of non-Newtonian fluids. Different measuring geometries can be used, but coaxial cylinder, cone-plate and plate-plate are the most common choices. Using rotational rheometers, two experimental modes are mostly used to study the behavior of semi-dilute pectin solutions steady shear measurements and dynamic measurements. In the former, samples are sheared at a constant direction of shear, whereas in the latter, an oscillatory shear is used. 

Steady shear flow measnrements, however, can measure only viscosity and the first normal stress difference, and it is difficult to derive information abont fluid structure from such measurements. Instead, dynamic oscillatory rheological measurements are nsed to characterize both enhanced oil recovery polymer solutions and polymer crosslinker gel systems (Prud Homme et al., 1983 Knoll and Pmd Homme, 1987). Dynamic oscillatory measurements differ from steady shear viscosity measnrements in that a sinusoidal movement is imposed on the fluid system rather than a continnons, nnidirectional movement. In other words, the following displacement is imposed ... 

In marked contrast to measurements of shear rheological properties, such as apparent viscosity in steady shear, or of complex viscosity in small amplitude oscillatory shear, extensional viscosity measurements are far from straightforward. This is particularly so in the case of mobile elastic liquids whose rheology can mitigate against the generation of well-defined extensional flow fields. 

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