Dynamic Oscillatory Measurements

These are by far the most commonly used method to obtain information on the flocculation of a suspension. A strain is applied in a sinusoidal manner, with an amplitude and a frequency v (cycles s or Hz) or m (rad s ). This is usually carried out by moving one of the platens say the cup (in a concentric cylinder geometry) or the plate (in a cone-and-plate geometry) back and forth in a sinusoidal manner. The stress on the other platen, the bob or the cone is simultaneously measured. These platens are usually connected to interchangeable torque bars, whereby the stress can be directly measured. The stress amplitude uq is simultaneously measured. 

In a viscoelastic system (such as the case with a flocculated suspension), the stress oscillates with the same frequency, but out-of-phase from the strain. From measurement of the time shift between strain and stress amplitudes (At) one can obtain the phase angle shift 3, 

From the amplitudes of stress and strain and the phase-angle shift one can obtain the various viscoelastic parameters The complex modulus G, the storage modulus (the elastic component of the complex modulus) G, the loss modulus (the viscous component of the complex modulus) G , tan 3 and the dynamic viscosity t].  

G is a measure of the energy stored in a cycle of oscillation G is a measure of the energy dissipated as viscous flow in a cycle of oscillation tan (5 is a measure of the relative magnitudes of the viscous and elastic components. Clearly, the smaller tan 3 is the more elastic the system is and vice versa. 

In oscillatory measurements one carries out two sets of experiments, strain sweep and oscillatory sweep, which are detailed below. 

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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. 

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)] ... 

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

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. 

The viscoelastic parameters are generally measured by dynamic oscillatory measurements. Apparatus of three different configurations can be used cone and plate, parallel plates, or concentric cylinders. In the case of cone and plate geometry, the test material is contained between a cone and a plate with the angle between cone and plate being small (<4°). The bottom member undergoes forced harmonic oscillations about its axis and this motion is transmitted through the test material to the top member, the motion of which is constrained by a torsion bar. The relevant measurements are the amplitude ratio of the motions of the two members and the associated phase lag. From this information it is relatively simple to determine G and G". 

FIGURE 5.9 Illustration of dynamic (oscillatory) measurement of rheological properties. In (a) the applied shear strain (y) is shown as a function of time t oscillation frequency. In (b d) the resulting shear stress a is given for an elastic, a viscous, and a viscoelastic response. 5 is the phase or loss angle. See text. 

Dynamic rheometry was not (and, apparently, cannot be) employed for studying melt fracture of neat plastics and composite materials. This has been done so far only using capillary rheometry. However, dynamic oscillatory measurements can produce the most reliable rheological data on filled polymers [2,4]. It should be noted that measurements at dynamic oscillatory conditions bellow frequency of 0.1 rad/s likely produce erroneous results due to the increased time for reaching steady state at low frequencies [4]. 

The linear viscoelastic properties in the melt state of highly grafted polymers on spherical silica nanoparticles are probed using linear dynamic oscillatory measurements and linear stress relaxation measurements. While the pure silica tethered polymer nanocomposite exhibits solid-like response, the addition of a matched molecular weight free matrix homopolymer chains to this hybrid material, initially lowers the modulus and later changes the viscoelastic response to that of a liquid. These results are consistent with the breakdown of the ordered mesoscale structure, characteristic of the pure hybrid and the high hybrid concentration blends, by the addition of homopolymers with matched molecular weights. 

Figure 4. A cross-plot of the complex modulus (G ) and the complex viscosity (Tj ) from linear dynamic oscillatory measurements for the blends of the PBA50K homopolymer with the SiO2-PBA50K hybrid material. The samples with liquid like behavior (pure homopolymer and the blend with 20 % hybrid) demonstrate Newtonian behavior with the viscosity being well behaved down to the lowest value of the complex modulus. On the other hand, for the blends with higher levels of hybrid material, the viscosity diverges at significant values of the complex modulus, a feature characteristic of materials with a yield stress.

In practice, dynamic oscillatory measurements are sensitive probes of molecular structure and interactions, for example, in emulsions and dispersions. Oscillatory measurements probe emulsion structure without destroying it. This is accomplished by applying very small sinusoidal displacements or strains to the emulsion at controlled amplitude and frequency. In general, there are two mechanisms for a material to respond to a deformation ... 

The objective of this study was to make sure that degradation of PE was prevented during the conditioning process. Different techniques were used to examine the stability of PE in the melt blender. Small-strain dynamic oscillatory measurements of viscoelastic properties (r] ) in a mechanical spectrometer as well as and molecular weight distribution from GPC analysis were used to assess the stability of samples of linear low-density polyethylene (LLDPE) and LDPE in the melt blender. 

The viscoelastic properties of concentrated o/w and w/o emulsions were investigated using dynamic (oscillatory) measurements. For that purpose a Bohlin VOR (Bohlin Reologie, Lund, Sweden) instrument was used. Concentric cylinder platens were used and the measurements were carried out at 25 0.1 °C. In oscillatory measurements, the response in stress of a viscoelastic material subjected to a sinusoidally varying strain is monitored as a function of strain amplitude and frequency. The stress amplitude is also a sinusoidally varying function in time, but for a viscoelastic material it is shifted out of phase with the strain. The phase angle shift between stress and strain, 5, is given by... 

Table 10.7 provides some of the current instrumentation for rheological measurements. Note that some of them are designed for flow, while others are designed for dynamic oscillatory measurements, while still others are basically uniaxial extension or creep instrumentation. 

Dynamic (oscillatory) measurements (preferably carried out using a constant... 

A third technique to investigate the viscoelastic properties of semi-solids is to apply dynamic (oscillatory) measurements. A sinusoidal strain or stress (with amplitudes 7o or To) is applied on the system at a frequency e/rad s and the resulting stress or strain is measured simultaneously. For a viscoelastic system, the strain... 

In dynamic (oscillatory) measurements, one applies a sinusoidal strain or stress (with amplitudes yo or < o and frequency co in rad s ) and the stress or strain is measured simultaneously. For a viscoelastic system, the stress oscillates with the same frequency as the strain, but out of phase. From the time shift of stress and strain, one can calculate the phase angle shift <5. This allows one to obtain the various viscoelastic parameters G (the complex modulus), G (the storage modulus, i.e. the elastic component of the complex modulus) and G" (the loss modulus or the viscous component of the complex modulus). These viscoelastic parameters are measured as a function of strain amplitude (at constant frequency) to obtain the linear viscoelastic region, whereby G, G and G" are independent of the applied strain until a critical strain above which G and G begin to decrease with further increase of strain, whereas G" shows an increase. Below y the structure of the system is not broken down, whereas above y the structure begins to break. From G and one can obtain the cohesive energy density of the structure... 

Nakajima et al. [101] studied the viscoelastic behavior of butadiene-acrylonitrile copol)rmer filled with carbon black. Capillary extrusion measurements with an Instron and dynamic oscillatory measurements with a Rheovibron suggested the occurrence of strain hardening in filled elastomer due to tensile extension causing structural changes in the carbon black filled elastomer. It is possible fliat the structure built by the carbon black in the elastomer increasingly jams against... 

D. DYNAMIC (OSCILLATORY) MEASUREMENTS WITHOUT SAMPLE INERTIA EFFECTS ( GAP LOADING )... 

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