Shear oscillatory

In an oscillatory shear experiment, the sample is subjected to a homogeneous deformation at a sinusoidally varying shear strain or shear stress. In a controlled strain experiment, one generates a strain that is as close as possible to a sine wave. 

If the strain amplitude is sufficiently small that the response is linear, the resulting stress is also sinusoidal and can be written in terms of the stress amplitude, Oq, and the phase shift, 5, usually called the loss angle, as follows  

As is the case for any linear system in the frequency domain, the results of an oscillatory shear test can be represented in terms of an amplitude ratio G = 0(JYq and a phase shift 5 which are functions of frequency. While the function S(0)) is sometimes used to characterize the linear behavior of a melt, dynamic test results are usually reported in terms of the storr e and loss moduli G and G as functions of frequency  

It is sometimes useful in deriving equations to consider the storage and loss moduli to be the real and imaginary components of the complex modulus, G (o ), which is defined as follows  

In this interpretation, we see that the parameter defined above as Gj is the absolute magnitude of the complex modulus G, and the loss angle is the angle between the store e and loss moduli in the complex plane. An alternative representation of dynamic data is in terms of the complex viscosity, i], defined as follows  

A simple linear viscoelastic measurement that has become very easy to implement with the advent of modern electronics is oscillatory shear. A sinusoidal strain with angular frequency oj is applied to a sample in simple 

The principal advantage of this technique is that the viscoelastic response of any material can be probed directly on different time scales (l/cu) of interest by simply varying the angular frequency u. If the material studied Ts a perfectly elastic solid, then the stress in the sample will be related to the strain through Hooke s law [Eq. (7.98)]  

The stress is perfectly in-phase with the strain for a Hookean solid, as shown in Fig. 7.26, At times t = 7v/(2uj), 57r/(2ca), 9tv/(2uj),. .. the strain has a maximum and the stress also has a maximum. Similarly, at times t = 0, tt/uj, livjuj. both the strain and the stress are simultaneously zero. 

On the other hand, if the material being studied is a Newtonian liquid, the stress in the liquid will be related to the shear rate through Newton s law [Hq. (7.100)] ---------------------------------------------------- 

Oscillatory strain (solid curve and left axis) and oscillatory stress (dashed curve and right axis) are in-phase for a Hookean solid. 

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Dyna.mic Viscometer. A dynamic viscometer is a special type of rotational viscometer used for characterising viscoelastic fluids. It measures elastic as weU as viscous behavior by determining the response to both steady-state and oscillatory shear. The geometry may be cone—plate, parallel plates, or concentric cylinders parallel plates have several advantages, as noted above. 

Rheometric Scientific markets several devices designed for characterizing viscoelastic fluids. These instmments measure the response of a Hquid to sinusoidal oscillatory motion to determine dynamic viscosity as well as storage and loss moduH. The Rheometric Scientific line includes a fluids spectrometer (RFS-II), a dynamic spectrometer (RDS-7700 series II), and a mechanical spectrometer (RMS-800). The fluids spectrometer is designed for fairly low viscosity materials. The dynamic spectrometer can be used to test soHds, melts, and Hquids at frequencies from 10 to 500 rad/s and as a function of strain ampHtude and temperature. It is a stripped down version of the extremely versatile mechanical spectrometer, which is both a dynamic viscometer and a dynamic mechanical testing device. The RMS-800 can carry out measurements under rotational shear, oscillatory shear, torsional motion, and tension compression, as well as normal stress measurements. Step strain, creep, and creep recovery modes are also available. It is used on a wide range of materials, including adhesives, pastes, mbber, and plastics. 

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). 

Brown, W Schillen, K Hvidt, S, Triblock Copolymers in Aqueous Solution Studied by Static and Dynamic Light Scattering and Oscillatory Shear Measurements. Influence of Relative Block Sizes, Journal of Physical Chemistry 96, 038, 1992. 

Small an jlitude oscillatory shear measurements have been widely used to follow the gelation process of biopolymers [9] because of their non-destroying character and the great variability of procedures, which allow simultaneous investigations of various features of a single sample. 

Oscillatory shear experiments are the preferred method to study the rheological behavior due to particle interactions because they directly probe these interactions without the influence of the external flow field as encountered in steady shear experiments. However, phenomena that arise due to the external flow, such as shear thickening, can only be investigated in steady shear experiments. Additionally, the analysis is complicated by the different response of the material to shear and extensional flow. For example, very strong deviations from Trouton s ratio (extensional viscosity is three times the shear viscosity) were found for suspensions [113]. 

Small amplitude oscillatory shear is the method of choice for materials with very broad distributions of relaxation modes, such as materials near LST, and for materials which undergo change during the measurement. The dynamic moduli in Eq. 4-10 are defined by [10]... 

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)... 

Dynamic oscillatory shear measurements of polymeric materials are generally performed by applying a time dependent strain of y(t) = y0sin(cot) and the resultant shear stress is a(t) = y0[G sin(a)t) + G"cos(cot)], with G and G" being the storage and loss modulus, respectively. 

To date, the melt state linear dynamic oscillatory shear properties of various kinds of nanocomposites have been examined for a wide range of polymer matrices including Nylon 6 with various matrix molecular weights [34], polystyrene (PS) [35], PS-polyisoprene (PI) block copolymers [36,37], poly(e-caprolactone) (PCL) [38], PLA [39,40], PBS [30,41], and so on [42],... 

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. 

Oscillatory shearing is used to characterize viscoelastic fluids using coaxial cylinders or cone and plate instruments. 

The complex viscosity, i.e., the viscosity observed in the presence of an oscillatory shear rate, is a dynamic property that can be straightforwardly obtained from the Rouse, or Rouse-Zimm theory as the Fourier transform of the stress time-correlation function. Thus, these theories give [15]... 

Rheological observations of the UHMWPE pseudo-gels of different concentrations under oscillatory shear conditions at different temperatures showed that these systems exhibit considerable drawability at temperatures above ambient. The deformation of the crystalline phase of the gel-like system is not reversible and, as shown in the sequence of photographs Figure 2, for a pseudo-gel of 4% concentration, it was greater when the sample was sheared under the same oscillatory conditions at higher temperatures. The displaced crystals of the UHMWPE pseudo-gel showed remarkable dimensional stability after shear cessation and removal of any compression load in the optical rotary stage. 

Figure 2. Deformability of 4% w/w UHMWPE pseudo-gel sample under oscillatory shear force at different temperatures (a) 25 C, (b) 30 C, and (c)...

The rheological properties, during the sol-gel transition, are investigated with a Weissenberg rheogoniometer in oscillatory shear (linear behaviour). 

Makinen R, Ruokolainen J, Ikkala O, De Moel K, ten Brinke G, De Odorico W, Stamm M. Orientation of supramolecular self-organized polymeric nanostructures by oscillatory shear flow. Macromolecules 2000 33 3441-3446. 

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). 

Using model concentrated suspensions of polyvinyl chloride and titanium dioxide particles in a Newtonian polybutene fluid, small amplitude oscillatory shear and creep experiments were described [2]. It was shown that the gel-like behaviour at very small strain, and strain hardening at a critical strain, are caused by particle interactions and the state of particle dispersion. 

NAD(P)H oxidase can also be activated by fluid shear stresses. This is one reason why branched and curved arteries tend to develop atherosclerotic plaques earlier than straight arteries. Using a spin probe to detect 02 , Hwang et al. have demonstrated that monolayer cultures of EC exposed to oscillatory (but not laminar) shear stresses produce the radical using NAD(P)H oxidase.292 A subsequent study showed that XO also responds to oscillatory shear stress.293 Other workers, using BMPO, have detected the flow-induced production of 02 by mitochondria.294... 

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