Shear strain phase behavior

Rheological properties of food materials over a wide range of phase behavior can be expressed in terms of viscous (viscometric), elastic and viscoelastic functions which relate some components of flie stress tensor to specific components of the strain or shear rate response. In terms of fluid and solid phases, viscometric... 

The most popular dynamic test procedure for viscoelastic behavior is the application of an oscillatory stress of small amplitude. This shear stress applied produces a corresponding strain in the material. If the material were an ideal Hookean body, the shear stress and shear strain rate waves would be in phase (Fig. 14A), whereas for an ideal Newtonian sample, there would be a phase shift of 90° (Fig. 14B), because for Newtonian bodies the shear strain is at a maximum, when a maximum of stress is present. The shear strain, when assuming an oscillating sine fimction, is at a maximum in the middle of the slope, because there is the steepest increase in shear strain due to the change in direction. For a typical viscoelastic material, the phase shift will have a value between >0° and <90° (Fig. 14C). 

As wc pointed out in S tion 4.3.1, the confiiKHl fluid < an be cxj)osed to a nonvanisliiug shear strain by misaligning the two chemically striped surfaces. Misaligmnent is specified quantitatively in terms of the parameter a in Eq. (4.48a). On account of the discrete nature of our model, a can only be varied discretely iu increments of Aa = l/n. This section is devoted to a discussion of both structure and phase behavior of a confined lattice fluid exposed to a shear strain. 

Because of the similarity between the lattice fluid calculations and the MC simulations for the continuous model, it seems instructive to study the phase behavior in the latter if the confined fluid is exposed to a shear strain. This may be done quantitatively by calculating p as a function of p and as -For sufficiently low p, one expects a gas-like phase to exist along a subcritical isotherm (see Fig. 4.13) defined as the set of points (T = const)... 

Rheological behavior can be determined with small-amplitude sinusoidal shear, using the cone-and-plate steady-shear test to determine the linear viscoelastic shear strain. A sinusoidal curve is charted to represent the viscous (loss) modulus (out-of-phase segment) and the elastic (storage) modulus (in-phase segment) [2]. 

Another important class of experiments involves periodic tensile or shear strains of the type e(t) = e cos cot = Re(soe ). In a linear elastic solid deformed in tension, a oscillates in phase with s with amplitude Ee . In a linear viscous liquid, cr = t/de/dt and hence varies as —rjSoCO sin cot = t]s oj cos(ot + njl). In a linear viscoelastic material, however, intermediate behavior is observed [Eqs. (34), where 0 < d < 7i/2],... 

The rheological behavior of the lAL formed between a nonpolar phase (HL, FL) and an aqueous solution of a surfactant (HS, FS) was studied by the rotation suspension ( torque pendulum ) method [13-15]. Its principle is illustrated in Figure 3.1. As a rule, the conditions of constant rate of revolution Q of the cylindrical vessel were used, that is, the constant shear strain rate. Both the revolution rate and the surfactant concentrations were varied over a broad range. 

Acoustic cavitation (AC), formation of pulsating cavities in a fluid, occurs when a powerful ultrasound is applied to a non-viscous fluid. The cavities are formed when the variable acoustic pressure in the rarefaction phase exceeds the cohesive strength of the fluid. Under acoustic treatment (AT), cavities grow to resonance dimensions conditioned by frequency, amplitude of oscillations, stiffness properties and external conditions, and start to pulsate synchronously (self-consistently) with acoustic pressure in the medium. The cavities undergo significant strains (compared to their dimensions) and their size decreases under compression up to collapsing. This nonlinear behavior determines the active, destructional character of the cavities near which significant shear velocities, local pressure and temperature bursts occur in the fluid. Cavitation determines the specific character of acoustic treatment of the fluid and effects upon objects resident in the fluid, as well as all consequences of these effects. 

Dynamic or oscillatory rheometers measure viscous and elastic modulus in shear or tension. Energy dissipation produces a phase difference, so stress, strain, and phase angle can be used to characterize complex viscosity behavior. 

These rheological parameters have been successfully correlated to textural attributes of hardness and spreadabUity and provide information pertaining to the fat crystal network (69). The value of G is useful in assessing the solid-like stmcture of the fat crystal network. Increases in the value of G typically correspond to a stronger network and a harder fat (66). Alternatively, G" represents the fluid-like behavior of the fat system. This value can be related to the spreadability of a fat system, because increases in G" indicate more fluid-like behavior under an applied shear stress. The tan 8 is the ratio of these two values. As the value of 5 approaches 0° (stress wave in phase with stress wave), the G" value approaches zero, and therefore, the sample behaves like an ideal solid and is referred to as perfectly elastic (68). As 8 approaches 90° (stress is completely out of phase relative to the strain). 

LDPE, and with polypropylene, PP, was studied In steady state shear, dynamic shear and uniaxial extenslonal fields. Interrelations between diverse rheological functions are discussed In terms of the linear viscoelastic behavior and Its modification by phase separation Into complex morphology. One of the more Important observations Is the difference In elongational flow behavior of LLDPE/PP blends from that of the other blends the strain hardening (Important for e.g. fllm blowing and wire coating) occurs In the latter ones but not In the former. 

Viscosity curves obtained with constant-shear viscosimetry are shown in Figure 11. In this land of measurement, phase separation is monitored, but the same behavior is obtained with the three types of phase separation. As in the high-strain dynamic measurements, the constant shear applied during phase separation forbids the formation of a continuous (3-phase, which would normally exist in type 2 and 3 blends. On the contrary, because it is liquid, the a-phase can be continuous, and in all cases the viscosity of this phase governs the viscosity of the blend. The fast increase in viscosity is therefore characteristic of the gelation of the a-phase. 

Oscillatory measurements using the cone-and-plate viscometer are sometimes carried out to demonstrate the elastic behavior of a viscoelastic fluid [10]. The fluid in the viscometer is subjected to an oscillatory strain imposed on the bottom surface while the response of the shearing stress is measured on the top surface. If the phase shift between the input strain and the output stress is 90°, the sample is purely viscous if it is 0°, the sample is completely elastic. A measured phase shift between 0° and 90° demonstrates that the fluid is viscoelastic. 

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