Response to oscillatory shear

Buzza et al. (105) have presented a qualitative discussion of the various dissipative mechanisms that may be involved in the small-strain linear response to oscillatory shear. These include viscous flow in the films. Plateau borders, and dispersed-phase droplets (in the case of emulsions) the intrinsic viscosity of the surfactant monolayers, and diffusion resistance. Marangoni-type and marginal regeneration mechanisms were considered for surfactant transport. They predict that the zero-shear viscosity is usually dominated by the intrinsic dilatational viscosity of the surfactant mono-layers. As in most other studies, the discussion is limited to small-strain oscillations, and the rapid events associated with T1 processes in steady shear are not considered, even though these may be extremely important. 

Hsiai TC, SK Wong P, Ing M, Salazar A, Hama S, Navab M, Demer L, Ho CM (2003) Monocyte recruitment to endothelial cells in response to oscillatory shear stress. FASEB J 17 1648-1657... 

Stainback PC, Nagabushana KA (1996) Review of Hot-Wire Anemometry Techniques and the Range of their Applicability for Various Hows. Electron J Huids Eng, Transaction of the ASME King LV (1914) Phil. Trans R Soc, London 4. Liu CJ, Huang J, Zhu Z, Jiang F, Tung S, Tai YC, Ho CM (1999) A Micromachined How Shear-stress Sensor Based on Thermal Transfer Principles. J MEMS 8(l) 90-99 Sheplak M, et al (2002) Characterization of a silicon-micro-machined thermal shear-stress sensor. AIAA J 40(6) 1099-1104 Hsiai TC, SK Wong P, Ing M, Salazar A, Hama S, Navab M, Demer L, Ho CM (2003) Monocyte Recruitment to Endothelial Cells in Response to Oscillatory Shear Stress. EASED J 17 1648-1657... 

Response to oscillatory shear. Figure 6 shows the response of a glassy film to an oscillatory shear force. To mimic the SFA experiments, the top wall was pulled by a spring (k/A =7.94E/a ) coupled to a translational stage. The stage was displaced sinusoidally, and its position is shown by dashed lines in panels (a) and (c). A solid line shows the position of the top wall. The force fx on the wall is just the difference in wall and stage positions multiplied by the spring constant (panels (b) and (d)). 

To develop the tube theory of polymer motion, we consider the response of the melt to a step deformation. This is an idealized deformation that is so rapid that during the step no polymer relaxation can occur, and the polymer is forced to deform affinely, that is, to the same degree as the macroscopic sample is deformed. The total deformation, though rapid, is small, so that the chains deform only slightly this is called a small amplitude step strain. Because the deformation is very small, the distribution of chain configurations remains nearly Gaussian, and linear viscoelastic behavior is expected. In Chapter 4 we saw that the assumption of linear behavior makes it possible to use the response to a small step strain experiment to calculate the response to oscillatory shear or any other prescribed deformation. 

An example of the linear viscoelastic response in oscillatory shear for a nearly monodisperse linear polybutadiene melt is shown in Fig. 1.2%. Extrapolation of the limiting power laws oiG uP and G" u (the dashed lines in Fig. 7.28) to the point where they cross has special significance. The intersection of the power laws G = J qrj uP and G = t]uj using the above two equations allows us to solve for the frequency where they cross uj= l/(/)/eq), which is the reciprocal of the relaxation time r [Eq. (7.132)]. The modulus level where the two extrapolations cross, obtained by setting a = 1/r = 1 /(/ /eq) iti either equation, is simply the reciprocal of the steady... 

A reversible crosslinked system forms a transient network that when placed under a macrodeformation shear rate exhibited shear flow. The properties depended on disruption and recombination of the reversible network. The linear response to oscillatory deformations has been determined for the reversible network with uniform chains with reversible crosslinking at end groups. Where molar mass (M) was less than the critical M for entanglements the dynamic moduli were related to temperature, M and crosslink bond... 

On the other hand, the Maxwell fluid model explains the response of complex fluids to an oscillatory shear rate. The frequency-dependent behavior of this model, displayed into linear responses to applied shear rates has been found to be applicable to a variety of complex fluid systems. Although the linear viscoelasticity is useful for understanding the relationship between the microstructure and the rheological properties of complex fluids, it is important to bear in mind that the linear viscoelasticity theory is only valid when the total deformation is quite small. Therefore, its ability to distinguish complex fluids with similar micro- and nanostructure or molecular structures (e.g. linear or branched polymer topology) is limited. However, complex fluids with similar linear viscoelastic properties may show different non-linear viscoelastic properties [31]. 

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. 

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]. 

Due to the viscoelastic nature of the material the stress response, after the application of the oscillatory shear strain, is also a sinusoidal but out of phase relative to the strain what can be represented by equation (2.7) as... 

In the first part of this chapter we studied the radial vibrations of a solid or hollow sphere. This problem was considered an extension to the dynamic situation of the quasi-static problem of the response of a viscoelastic sphere under a step input in pressure. Let us consider now the simple case of a transverse harmonic excitation in which separation of variables can be used to solve the motion equation. Let us assume a slab of a viscoelastic material between two parallel rigid plates separated by a distance h, in which a sinusoidal motion is imposed on the lower plate. In this case we deal with a transverse wave, and the viscoelastic modulus to be used is, of course, the shear modulus. As shown in Figure 16.7, let us consider a Cartesian coordinate system associated with the material, with its X2 axis perpendicular to the shearing plane, its xx axis parallel to the direction of the shearing displacement, and its origin in the center of the lower plate. Under steady-state conditions, each part of the viscoelastic slab will undergo an oscillatory motion with a displacement i(x2, t) in the direction of the Xx axis whose amplitude depends on the distance from the origin X2-... 

Diblock copolymers with roughly equal block lengths can microphase— separate into a lamellar phase, with alternating layers of mostly A monomer and mostly B monomer. When quenched into the lamellar phase from the isotropic phase, these layers form roughly parallel to each other locally. A polydomain texture is created from this quenching, with a typical grain size of order 0.1 pm. The oscillatory shear response of such a quenched sample is observed to have at the lowest measurable frequencies. Can this observed response be the real terminal response of the sample Is this sample a viscoelastic solid or a viscoelastic liquid ... 

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