Viscoelastic effect

This reaction requires a stoichiometry of FeOOH to Fe2+ of two-to-one. Analysis of the A/in Fig. 12.1, with the Sauerbrey equation (12.1) and the corresponding molar masses of FeOOH and Fe2+ confirms this hypothesis. It is to be noted that this last result could not have been possible should the EQCM had not been used. 

Mason [46] first observed that the viscoelastic properties of a fluid in contact with quartz crystals can affect the resonant properties. However, Mason s work had been forgotten and for a long time there have not been studies of piezoelectric acoustic wave devices in contact with liquids until Nomura and Okuhara [15] found an empirical expression that described the changes in the quartz resonant frequency as a function of the liquid density, its viscosity and the conductivity in which the crystal was immersed. Shortly after the empirical observations of Nomura were described in terms of physical models by Kanazawa [1] and Bruckenstein [2] who derived the equation that describes the changes in resonant frequency of a loss-less quartz crystal in contact with an infinite, non conductive and perfectly Newtonian fluid  

Kinetic applications of the electrochemical quartz crystal microbalance Ch. 12 

More recently the treatment was extended to piezoelectric devices in contact with viscoelastic media (i.e., liquids and polymers). It was then realised that if the deposited mass was not rigidly coupled to the oscillating quartz crystal, separation of inertial mass and energy losses was not possible with the measurement of the resonant frequency alone. Quartz crystal impedance in the acoustic frequencies was introduced in order to study mass and viscoelastic changes and a full electrical characterization of the crystal behaviour near resonance was employed. 

Since the unloaded QCM is an electromechanical transducer, it can be described by the Butterworth-Van Dyke (BVD) equivalent electrical circuit represented in Fig. 12.3 (box) which is formed by a series RLC circuit in parallel with a static capacitance C0. The electrical equivalence to the mechanical model (mass, elastic response and friction losses of the quartz crystal) are represented by the inductance L, the capacitance C and the resistance, R connected in series. The static capacitance in parallel with the series motional RLC arm represents the electrical capacitance of the parallel plate capacitor formed by both metal electrodes that sandwich the thin quartz crystal plus the stray capacitance due to the connectors. However, it is not related with the piezoelectric effect but it influences the QCM resonant frequency. 

Stresses can be either externally applied, which is accounted for at the design step by stress analysis of loading cases, or internally, as a result of processing and part curvature. Reasons for internal stress build-up within a part during processing are  

---

The relaxation and creep experiments that were described in the preceding sections are known as transient experiments. They begin, run their course, and end. A different experimental approach, called a dynamic experiment, involves stresses and strains that vary periodically. Our concern will be with sinusoidal oscillations of frequency v in cycles per second (Hz) or co in radians per second. Remember that there are 2ir radians in a full cycle, so co = 2nv. The reciprocal of CO gives the period of the oscillation and defines the time scale of the experiment. In connection with the relaxation and creep experiments, we observed that the maximum viscoelastic effect was observed when the time scale of the experiment is close to r. At a fixed temperature and for a specific sample, r or the spectrum of r values is fixed. If it does not correspond to the time scale of a transient experiment, we will lose a considerable amount of information about the viscoelastic response of the system. In a dynamic experiment it may... 

A parameter indicating whether viscoelastic effects are important is the Deborah number, which is the ratio of the characteristic relaxation time of the fluid to the characteristic time scale of the flow. For small Deborah numbers, the relaxation is fast compared to the characteristic time of the flow, and the fluid behavior is purely viscous. For veiy large Deborah numbers, the behavior closely resembles that of an elastic solid. 

Steady state, fuUy developed laminar flows of viscoelastic fluids in straight, constant-diameter pipes show no effects of viscoelasticity. The viscous component of the constitutive equation may be used to develop the flow rate-pressure drop relations, which apply downstream of the entrance region after viscoelastic effects have disappeared. A similar situation exists for time-dependent fluids. 

Johnson [109] for linear viscoelastic effects inside the cohesive zone. For growing cracks... 

Via an ad hoc extension of the viscoelastic Hertzian contact problem, Falsafi et al. [38] incorporated linear viscoelastic effects into the JKR formalism by replacing the elastic modulus with a viscoelastic memory function accounting for time and deformation, K t) ... 

Wahl, K.J., Stepnowski, S.V. and Unertl, W.N., Viscoelastic effects in nanometer-scale contacts under shear. Tribal. Lett., 5, 103-107 (1998). 

Because of the assumption that linear relations exist between shear stress and shear rate (equation 3.4) and between distortion and stress (equation 3.128), both of these models, namely the Maxwell and Voigt models, and all other such models involving combinations of springs and dashpots, are restricted to small strains and small strain rates. Accordingly, the equations describing these models are known as line viscoelastic equations. Several theoretical and semi-theoretical approaches are available to account for non-linear viscoelastic effects, and reference should be made to specialist works 14-16 for further details. 

Ide and White W studied the viscoelastic effects in agitating polystyrene solutions with a turbine. At concentrations below 50% PS, flow was normal. Abovfe 35%, the viscoelastic forces caused the flow to reverse, moving away from the impeller along the axis. At 30 to 35% PS, both occurred, causing a segregated secondary flow around the turbine. 

At sufficiently low strain, most polymer materials exhibit a linear viscoelastic response and, once the appropriate strain amplitude has been determined through a preliminary strain sweep test, valid frequency sweep tests can be performed. Filled mbber compounds however hardly exhibit a linear viscoelastic response when submitted to harmonic strains and the current practice consists in testing such materials at the lowest permitted strain for satisfactory reproducibility an approach that obviously provides apparent material properties, at best. From a fundamental point of view, for instance in terms of material sciences, such measurements have a limited meaning because theoretical relationships that relate material structure to properties have so far been established only in the linear viscoelastic domain. Nevertheless, experience proves that apparent test results can be well reproducible and related to a number of other viscoelastic effects, including certain processing phenomena. 

To separate purely viscoelastic effects from swelling effects in the set of experiments reported in Figure 6, a simple model of diffusion of TCP in the rubber substrate has been developed. 

Viscoelastic effects and impact on functionality Solubility changes of polymer Dimensional effects Moisture content in polymer... 

The viscoelastic effects on the morphology and dynamics of microphase separation of diblock copolymers was simulated by Huo et al. [ 126] based on Tanaka s viscoelastic model [127] in the presence and absence of additional thermal noise. Their results indicate that for

bulk modulus of both blocks, the area fraction of the A-rich phase remains constant during the microphase separation process. For each block randomly oriented lamellae are preferred. 

We examine next how the viscoelastic effect, recently discussed in the literature [190,267-270], may also account for the resistance of globules and mesoglobules against precipitation. 

As noted in Chapter 1, viscoelastic fluids exhibit a combination of solid-like and liquid-like behaviour. Even a simple analysis of viscoelastic effects in process plant is beyond the scope of this book. This section is restricted to an outline of practical implications of elastic effects and a demonstration of the fact that viscoelastic liquids exhibit stronger elastic behaviour as the deformation rate is increased. 

This is the rule of mixtures for stress, as given in Eq. (5.82). Fibers and matrix are assumed to carry pure axial tension, with no stress in the 2-3 plane that is, Of2 = Of2 = a 2 = Tms = 0. We treat the fibers and matrix as acting in a purely elastic manner and neglect the viscoelastic effects of the polymer matrix. Hooke s Law then applies to both the fiber and the matrix... 

The second assumption is based on contact mechanics models in which viscoelastic effects that might influence the instability point (pull-off) and adhesion are negligible or can be allowed for. The third assumption is based on representing the cantilever with a point mass model. Simulations using a distributed mass model indicate that ultrasonic vibration of the cantilever is relatively small and in many cases less than 0.05 of the UFM normal deflection (Hirsekorn et al. 1997). 

---