Oscillatory Measurements

This is the response of the material to an osdUating stress or strain [1]. When a sample is constrained in, say, a cone and plate or concentric cylinder assembly, an oscillating strain at a given frequency a (rad s ) (t = 2v r, where v is the frequency in cycles s or Hz) can be appHed to the sample. After an initial start-up period, a stress develops in response of the applied strain that is, it oscillates with the same frequency. The change of the sine waves of the stress and strain with time can be analysed to distinguish between elastic, viscous, and viscoelastic response. An analysis of the resulting sine waves can be used to obtain the various viscoelastic parameters, as discussed below. 

Elastic response This occurs when the maximum of the stress amplitude is at the same position as the maximum of the strain amplitude (no energy dissipation). In this case, there is no time shift between the stress and strain sine waves. Viscous response This occurs when the maximum of the stress is at the point of maximum shear rate (i.e., the inflection point), where there is maximum energy dissipation. In this case, the strain and stress sine waves are shifted by (referred to as the phase angle shift, 5, which in this case is 90°). 

Perfectly elastic solid Perfectly viscos liquid Viscoelastic system 

---

Specific Commercial Rotational Viscometers. Information on selected commercial rotational viscometers can be found ia Table 7. The ATS RheoSystems Stresstech rheometer is an iastmment that combines controlled stress as well as controlled strain (shear rate) and oscillatory measurements. It has a torque range of 10 to 50 mN-m, an angular velocity range of 0 to 300 rad/s, and a frequency range of seven decades. Operation and temperature programming (—30 to 150°C higher temperatures optional) are computer controlled. 

Spccj/jfc Fluids Viscoela.stometers, The ATS RheoSystems Stresstech rheometer can carry out oscillatory measurements over a frequency range of 6.3 x 10 to 630 rad/s. The Bohlin VOR rheometer and the mechanical spectrometer both allow oscillatory measurements. The former has a frequency range of -10 Hz, the latter lO " -100 Hz. The maximum angular ampHtude is 0.02 rad for the VOR and 0.5 rad for the mechanical spectrometer. 

The Weissenbetg Rheogoniometer is well suited to research on homogeneous viscoelastic fluids and elastic melts. For oscillatory shear a second motor-drive mechanism is added. This allows the use of 60 frequencies in the range of 7.6 x 10 to 40 Hz at ampHtudes between 2 x 10 and 3 X 10 rad. An electronic circuit improves the precision of oscillatory measurements, particularly at frequencies neat the natural resonance frequency of the instmment itself (298). 

Knoll, S.K. Prud homme, R.K. "Interpretation of Dynamic Oscillatory Measurements for Characterization of Well Completion Fluids", SPE paper 16283, 1987 SPE International Symposium on Oilfield Chemistry, San Antonio, February 4-6. 

The TA Instruments CSL2 rheometer can perform low frequency oscillatory measurements as well as steady-state viscosity determinations, even though it has a simple mechanical system. The sinusoidal wave form is generated mathematically in the computer rather than with an electromechanical drive system. The stress is controlled, and the resulting strain is determined and stored in memory. The computer analyzes the wave form and calculates the viscosity and elasticity of the specimen at the frequency of the test. As of this writing (1996), the oscillation software covers a frequency range of 10-4 -40 Hz. This range could be increased as faster software and computers become available. 

It is quite clear that experimental evidence in addition to that given by viscometry, will be desirable. In principle, this evidence is obtained from dynamic oscillatory measurements or from measurements of normal... 

The fact that the measured points of Fig. 3.1 lie more closely to the free-draining line, is in accordance with the experience obtained on anionic polystyrenes with other measuring techniques [dynamic oscillatory measurements (115), measurements of normal stresses (776)]. This result is quite surprising since for the description of intrinsic viscosity the non-draining case has clearly been shown to be valid (100). It will be shown below and in Chapter 4 that this inconsistency is in reality a consequence of the fact that the reduction with respect to concentration is less perfect than one would think at a first inspection of Fig. 3.1. 

In dynamic oscillatory measurements, however, higher order relaxation times (i.e. shorter times), which do not noticeably contribute to the zero shear viscosity, can become of importance when the frequency is increased. For this purpose, Ferry and co-operators 123, 14) proposed the following, rather crude approximation of the relaxation times [cf. eq. (3.50)] ... 

Low-strain oscillatory measurements show that PDM-PMAS copolymers with longer side-chains (C e and Cig) form a network structure at temperatures below the side-chain Intermolecular side-chain crystallization may be responsible for this behavior. 

Yoshimura, A. and Prud homme, R. K. 1988b. Wall slip effects on dynamic oscillatory measurements. J. Rheol. 32 575-584. 

By comparing the viscosity of polystyrene samples obtained by oscillatory measurements and in steady-state conditions, Cox and Merz (50) found that... 

Note. The table contains twice. Although we use the same symbol for the interfacial dialtional viscosity (commonly measured at large strain) and the dynamic Interfaclal dilatlonal viscosity (small strain, oscillatory measurements) the values obtciined may differ (as found for instance for some protein monolayers). 

Interfacial shear properties can be determined either by steady state or by oscillatory measurements (see sec. 3.6f). In the latter case dynamic shear moduli are obtained in the former the interfacial shear modulus or the interfacial shear viscosity is obtained. 

Rheology. The rheological properties of the blends and their components were determined on a Rheometrics Mechanical Spectrometer (RMS 800). Three kinds of dynamic oscillatory measurements (i.e. temperature, time, and frequency sweeps) were carried out. All experiments were done by using a parallel plate attachment with a radius of 12.5 mm and a gap setting from 1.2 to 1.8 mm. There was no significant dependence of the experimental results on the gap setting. 

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 ... 

The stability of the latexes was determined using viscoelastic measurements. For this purpose, dynamic (oscillatory) measurements were used to obtain the storage... 

Dynamic (oscillatory) measurements A sinusoidal stress or strain with amphtudes (Tjj and is appHed at a frequency a> (rads ), and the stress and strain are measured simultaneously. For a viscoelastic system, as is the case with most formulations, the stress and strain amplitudes oscillate with the same frequency, but out of phase. The phase angle shift S is measured from the time shift of the strain and stress sine waves. From a, y and S, it is possible to obtain the complex modulus j G, the storage modulus G (the elastic component), and the loss modulus G" (the viscous component). The results are obtained as a function of strain ampHtude and frequency. 

---