Visco-elastic solid

A final remark should be made as to the validity of eq. (2.13). This equation suggests the existence of a set of independent relaxation mechanisms. A general proof for the existence of such mechanisms could be given for visco-elastic solids in terms of the thermodynamics of irreversible processes (52) at small deviation from equilibrium. For liquid systems, however, difficulties arise from the fact that in these systems displacements occur which are not related to the thermodynamic functions. 

For viscoelastic fluids, the formalism of a viscous fluid and an elastic solid are mixed [31]. The equations for the effective viscosity, dynamic viscosity, and the creep compliance are given in Table 12.4 for a viscous fluid, an elastic solid, and a visco-elastic solid and fluid. For the viscoelastic fluid model the dynamic viscosity, >j (tu), and the elastic contribution, G (ti)), are plotted as a function of (w) in Figure 12.31. With one relaxation time, X, the breaks in the two curves occur at co. 

TABLE 12.4 Mechanical Behavior of Viscous Fluid, Elastic Solid, Visco-elastic Fluid, and Visco-elastic Solid... 

Viscous fluid Elastic solid Visco-elastic fluid Visco-elastic solid ... 

FIGURE 12J31 Shear modulus and d3mamic viscosity as a fiuiction of frequency. Mechanic behavior of a visco.elastic fluid and visco-elastic solid from models in Table 12.4. 

JSA Deformation of Visco-Elastic Solids and FluiiU... 

FIGURE 13J37 Pressing cycle for visco-elastic solids. 

When the material behaves as a linear visco-elastic solid at small applied stressed, the equation (3.172) is reduced to ... 

Pressure-sensitive adhesives (PSAs) (Creton and Fabre 2002), soft visco-elastic solids that are able to develop adhesive interactions instantly with the pressure of a finger (exerted on the rear of the material being affixed), are generally applied at room temperature. 

Visco-elastic fluids like pectin gels, behave like elastic solids and viscous liquids, and can only be clearly characterized by means of an oscillation test. In these tests the substance of interest is subjected to a harmonically oscillating shear deformation. This deformation y is given by a sine function, [ y = Yo sin ( t) ] by yo the deformation amplitude, and the angular velocity. The response of the system is an oscillating shear stress x with the same angular velocity . 

Although QCM has originally been devised as a mass sensor for operation in vacuum or gas, it also appeared to be suitable for measurements of the mass and visco-elastic changes at a solid-liquid interface. That was possible due to elaboration of the dedicated oscillator circuitry [115]. The Sauerbrey Equation (2) was derived for resonator oscillations in vacuum. However, it also holds for solution measurements provided that (1) the deposited film is rigid and (2) it is evenly... 

At this voliime fraction, the viscosity diverges because the shear stress is now given by the particle-particle contact in the tightly packed structure. As a result, we obtain a fluid with visco-elastic properties similar to polymeric solids. In ceramic processing, we extrude and press these pastes into green shapes. As a result, the rheology of ceramic pastes is of importance. The rheology of very concentrated suspensions is not particularly well developed, with the exception of model systems of monodisperse spheres. This section first discusses visco-elastic fluids and second the visco-elastic properties of ceramic pastes of monodisperse spheres. The material on visco-elastic fluids draws heavily from the book Colloidal Dispersions by Russel, Saville, and Schowalter [31]. 

Visco-elastic models have been developed for the nonlinear mechanical properties of fluids and solids. For a viscous fluid in simple shear flow, the shear stress, r y y), is a function of the effective viscosity, rj(-y) and the shear rate, y, as follows ... 

FIGURE 12.32 Shear moduli and dynamic viscosities measured for silica spheres at = 0.46, a = 28 2nm, O + a = 76 2nm(Mellemaetal. [68]). The broken lines correspond to the infinite shear viscosities (de Kruif et al. [43]) and the solid curves to the frequency dependence predicted by the visco-elastic fluid model of Table 12.4 with the measured values of 170,171 , and Gi. Redrawn from Russel et al. [31]. Reprinted with the permission of Cambridge University Press. 

As with solid-gas systems, food analysis is one of the widest fields of application of US-based detection since typical foods such as ice cream or whipped cream consist of air bubbles distributed in a visco-elastic liquid [137]. 

Polymers are viscoelastic materials, meaning they exhibit both liquid-hke properties (visco) and solid-like properties (elastic). Whether a material behaves more as a viscous or more as an elastic material depends upon the temperature, the particular polymer and its prior treatment, polymer structure, and the time scale of deformation. The particular property demonstrated by a polymer under given conditions allows polymers to act as solid or viscous liquids, as plastics, elastomers, or fibers, and so on. 

Therefore, when Jenike developed his methods to mathematically model the flow of bulk solids, he concluded that a bulk solid must be modeled as a plastic, and not a visco-elastic, continuum of solid particles (1). This approach included the postulation of a flow-no-flow criterion that states the bulk solid would flow from a bin when the stresses applied to the bulk solid exceed the strength of the bulk solid. The terms stress and strength are further discussed in this section on cohesive strength tests below. The flow properties test methods discussed are used to obtain the equipment parameters required to provide consistent, reliable flow. 

Ludema KC, Tabor D (1966) The friction and visco-elastic properties of polymeric solids. Wear 9 329-348... 

Perfectly elastic solid Perfectly viscos liquid Viscoelastic system... 

Rigid Solid (Euclidian) Linear Elastic Solid (Hookean) Nonlinear Elastic Solid (Non-Hookean) Visco-Elastic Fluids and Solids (Non-Linear) Nonlinear Viscous Fluid (Non-Newtonian) Linear Viscous Fluid (Newtonian) Inviscid Fluid (Pascalian)... 

For the transport of heavy ions to a solid surface coated with an adherent water film, like aluminium oxide, the visco-elastic properties of electric field forces and the concentration of heavy ions may be important for the rate of adsorption. For this reason we need information not only on relaxations restricted to a surface of an extended liquid, but also on the adherent water layer at the adsorbents. The last issue may be a bridge to the thermodynamics and flow properties of thin liquid films have been studied by some excellent research groups. 

Rheology is concerned with the flow and/or deformation of matter under the influence of externally imposed mechanical forces. Two limiting types of behaviour arc possible. The deformation may reverse spontaneously (relax) when the external force is removed this is called elastic behaviour and is exhibited by rigid solids. The energy used in causing the deformation is stored, and then recovered when the solid relaxes. At the other extreme, matter flows and the flow ceases (but is not reversed) when the force is removed this is called viscous behaviour and is characteristic of simple liquids. The energy needed to maintain the flow is dissipated as heat. Between the two extremes arc systems whose response to an applied force depends on the lime-scale involved. Thus pitch behaves as an elastic solid if struck but flows if left for years on a slope. Similarly, a ball of Funny Putty , a form of silicone rubber, bounces when dropped on a hard surface, when the contact time is a few milliseconds, but flows if deformed slowly on a time-scale of seconds or minutes. Systems of this kind are said to be visco-elastic. The precise nature of the observable phenomena depends on the ratio of the time it takes for the system to relax to the time taken to make an observation. This ratio is called the Deborah number (De) ... 

When De is very large, the system behaves like a solid and has elastic properties when De is very small, it flows like a liquid. The importance of rheology in studying colloidal dispersions arises from the fact that De is often around unity so that a wide range of visco-elastic phenomena are observed. 

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