Viscous component

Usually it is not easy to predict the viscosity of a mixture of viscous components. Certain binary systems, such as methanol and water, have viscosities much greater than either compound. 

In the Maxwell model, the two units are connected in series, so that each bears the full stress individually and the deformations of the elastic and viscous components are additive ... 

In a shear experiment the first of these is given by Eq. (3.50). For the viscous component we do not have an expression for 7, only for the way 7 varies with time. Hence it is not possible to develop this relationship any further as an explicit equation, but only as a differential equation. Differentiating Eq. (3.53) with respect to time, we obtain... 

It is interesting to note that the Voigt model is useless to describe a relaxation experiment. In the latter a constant strain was introduced instantaneously. Only an infinite force could deform the viscous component of the Voigt model instantaneously. By constrast, the Maxwell model can be used to describe a creep experiment. Equation (3.56) is the fundamental differential equation of the Maxwell model. Applied to a creep experiment, da/dt = 0 and the equation becomes... 

Materials such as metals are nearly elastic and show almost no flow or viscous component. Polymers and many of their solutions are both viscous and elastic, and both types of deformation must be taken into account to explain their behavior. 

Figure 16 (145). For an elastic material (Fig. 16a), the resulting strain is instantaneous and constant until the stress is removed, at which time the material recovers and the strain immediately drops back to 2ero. In the case of the viscous fluid (Fig. 16b), the strain increases linearly with time. When the load is removed, the strain does not recover but remains constant. Deformation is permanent. The response of the viscoelastic material (Fig. 16c) draws from both kinds of behavior. An initial instantaneous (elastic) strain is followed by a time-dependent strain. When the stress is removed, the initial strain recovery is elastic, but full recovery is delayed to longer times by the viscous component.

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. 

Figure 9.8. Deformation-time curves, (a) Material showing substantial ordinary elastic, high elastic and viscous components of deformation, (b) Material in which high elastic deformation...

The dashpot is the viscous component of the response and in this case the stress (72 is proportional to the rate of strain f2> ie... 

Example 2.14 A plastic is subjected to the stress history shown in Fig. 2.45. The behaviour of the material may be assumed to be described by the Maxwell model in which the elastic component = 20 GN/m and the viscous component r) = 1000 GNs/m. Determine the strain in the material (a) after u seconds (b) after 1/2 seconds and (c) after 3 seconds. 

A plastic with a time dependent creep modulus as in the previous example is stressed at a linear rate to 40 MN/m in 100 seconds. At this time the stress in reduced to 30 MN/m and kept constant at this level. If the elastic and viscous components of the modulus are 3.5 GN/m and 50 x 10 Ns/m, use Boltzmann s Superposition Principle to calculate the strain after (a) 60 seconds and (b) 130 seconds. 

To add to this picture it should be realised that so far only the viscous component of behaviour has been referred to. Since plastics are viscoelastic there will also be an elastic component which will influence the behaviour of the fluid. This means that there will be a shear modulus, G, and, if the channel section is not uniform, a tensile modulus, , to consider. If yr and er are the recoverable shear and tensile strains respectively then... 

These two moduli are not material constants and typical variations are shown in Fig. 5.3. As with the viscous components, the tensile modulus tends to be about three times the shear modulus at low stresses. Fig. 5.3 has been included here as an introduction to the type of behaviour which can be expected from a polymer melt as it flows. The methods used to obtain this data will be described later, when the effects of temperature and pressure will also be discussed. 

The rate dependence of fatigue strength demands careful consideration of the potential for heat buildup in both the fatigue test and in service. Generally, since the buildup is a function of the viscous component of the material, the materials that tend toward... 

The all-important difference between the friction properties of elastomers and hard solids is its strong dependence on temperature and speed, demonstrating that these materials are not only elastic, but also have a strong viscous component. Both these aspects are important to achieve a high friction capability. The most obvious effect is that temperature and speed are related through the so-called WLF transformation. For simple systems with a well-defined glass transition temperature the transform is obeyed very accurately. Even for complex polymer blends the transform dominates the behavior deviations are quite small. 

Viscoelasticity illustrates materials that exhibit both viscous and elastic characteristics. Viscous materials tike honey resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain instantaneously when stretched and just as quickly return to their original state once the stress is removed. Viscoelastic materials have elements of both of these properties and, as such, exhibit time-dependent strain. Viscoelasticity is the result of the diffusion of atoms or molecules inside an amorphous material. Rubber is highly elastic, but yet a viscous material. This property can be defined by the term viscoelasticity. Viscoelasticity is a combination of two separate mechanisms occurring at the same time in mbber. A spring represents the elastic portion, and a dashpot represents the viscous component (Figure 28.7). 

The transcellular fluid includes the viscous components of the peritoneum, pleural space, and pericardium, as well as the cerebrospinal fluid, joint space fluid, and the gastrointestinal (GI) digestive juices. Although the transcellular fluid normally accounts for about 1% of TBW, this amount can increase significantly during various illnesses favoring fluid collection in one of these spaces (e.g., pleural effusions or ascites in the peritoneum). The accumulation of fluid in the transcellular space is often referred to as third spacing. To review the calculations of the body fluid compartments in a representative patient, see Patient Encounter 1. 

The topological transformations in an incompatible blend can be described by the dynamic phase diagram that is usually determined experimentally at a constant shear rate. For equal viscosities, a bicontinuous morphology is observed within a broad interval of the volume fractions. When the viscosity ratio increases, the bicontinuous region of the phase diagram shrinks. At large viscosity ratios, the droplets of a more viscous component in a continuous matrix of a less viscous component are observed practically for all allowed geometrically volume fractions. 

Figure 18. (A) Fourier transformation spectra of the time trace of surface pressure for the steady loop (see Figure 17). Top real part (elastic component), bottom imaginary part (viscous component). (B) Inverted Fourier Spectra for the real and imaginary parts.

Figure 18A shows the Fourier spectra thus obtained. The real and imaginary parts correspond to the elastic and viscous components of the DOPC thin film, respectively. We can see that the spectrum is composed not only from the fundamental (coo) but also from the higher (2harmonic components. Such a trend indicates that the DOPC thin film exhibits rather large nonlinearity in the viscoelastic characteristics. 

From equation 1.41, the total shear stress varies linearly from a maximum fw at the wall to zero at the centre of the pipe. As the wall is approached, the turbulent component of the shear stress tends to zero, that is the whole of the shear stress is due to the viscous component at the wall. The turbulent contribution increases rapidly with distance from the wall and is the dominant component at all locations except in the wall region. Both components of the mean shear stress necessarily decline to zero at the centre-line. (The mean velocity gradient is zero at the centre so the mean viscous shear stress must be zero, but in addition the velocity fluctuations are uncorrelated so the turbulent component must be zero.)... 

The viscous component is dominant in liquids hence their flow properties may be described by Newton s law (Equation 14.3) where 17 is the viscosity, which states that the applied stress 5 is proportional to the rate of strain Ay/At, but is independent of the strain y or applied velocity gradient. 

The viscosity isotherm of the system with nitrobenzene is according to Usa ov jch [S], the result of the formation of an unstable compound, whose viscosity is low er than that of the more viscous component. According to the views expressed by one of us [3], however, this isotherm is the result of the formation of a compound of low stability, but whose viscosity is not necessarily lower than the viscosity of the more viscous component. The contribution of the compound to the viscosity of the mixtures is in this case also insufficient to produce a viscosity maximum, but is nevertheless apparent in the part- of the viscosity isotherm concave towards the composition axis. 

A similar exercise was undertaken much more recently using a microprocessor controlled Shore meter59 with emphasis on investigating the viscous component of behaviour, which was found to be very sensitive to... 

The measurements presented here on emulsions of polyurethane and polyacrylonitrile dissolved in N-methylpyrrolidone can be explained well by theory. However, in the literature certain examples of comparable systems are given (e.g., polyacrylonitrile and cellulose-acetate dissolved in dimethylformamide (2)), which show a much more complicated behavior. These emulsions have even lower viscosities than that of the least viscous component. Thus, the viscosity-composition curves have minima. Such behavior cannot be explained by any of the models discussed above. It seems that the basic assumptions used in our analysis are not valid for such systems. 

Elastic modulus E The viscous component of a material, e.g., tissue fluids... 

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