Volume dilation

Here p is the molecular viscosity the second term on the right-hand side of the equation is the effect of volume dilation. 

The influence the ion exerts on the bulk of the solvent, including volume dilation. 

For uniaxial (hexagonal) symmetry the 6 strain components are subdivided in two (invariant) one-dimensional subsets (indicated by the superscript a, and subscripts 1 and 2 for the volume dilatation and the axial deformation, respectively), and two different two-dimensional subsets, indicated by y for deformations in the (hexagonal) plane, and by e for skew deformations. These modes are also depicted in fig. 3. In this case, the magnetostriction can be expressed as... 

A new ultrasonic technique for studying dewetting and cumulative internal damage in solid propints has been reported (Refs 17 20). This technique yields volume-dilatation data on proplnt in tension, and on damage in uniaxial compression and shear strain fields. Estimates of vacuole size and number density arising from dewetting can be made, as well as can the time dependent void growth at constant strain be observed... 

The absolute values of the intermolecular change of the internal energy and entropy associated with the volume dilation may be written as... 

Equation (55) differs from Eq. (39) by the term (—yaT) and hence (AU/W)V T should be independent of extension ratio X, since (—yaT) is not a function of deformation. Equation (54) leads also to the following expression for the strain-induced volume dilation... 

Interchain changes arising from the deformation of polymer networks are a result of strain-induced volume dilation. Typical results obtained by various methods (Fig. 6) demonstrate that the statistical theory predicts the volume dilation and... 

Fig. 6. The relative strain-induced volume dilation of polymer networks as a function of strain. A - NR, B — EPR. O and -calorimetric data 241 + — di-...

On the other hand, Kilian 50) having analysed the strain-induced volume dilation 24 91 using the van der Waals equation of state (Fig. 6) emphasized that only pressure dependence of the interchain parameter, a, is required for a full explanation of the relative volume changes. He arrived at a conclusion that non-crystalline rubbers are anisotropic equilibrium liquids and a higher compressibility of NR was only necessary for fitting the extension data. Hence, on using the van der Waals approach, there is no need of postulating volume dependence of the front factor as proposed by Tobolsky and Shen. 

Fluxes of chemical components may arise from several different types of driving forces. For example, a charged species tends to flow in response to an applied electrostatic field a solute atom induces a local volume dilation and tends to flow toward regions of lower hydrostatic compression. Chemical components tend to flow toward regions with lower chemical potential. The last case—flux in response to a chemical potential gradient—leads to Fick s first law, which is an empirical relation between the flux of a chemical species, J, and its concentration gradient, Vcj in the form J, = —DVcj, where the quantity D is termed the mass diffusivity. 

Crack tip blunting is attributed to localized yielding at the crack tip. Localized yielding may result from shear deformation, or normal stress deformation. Unlike shear deformation, which occurs at constant colume, normal stress deformation involves a volume dilatation and is considered to be responsible for the formation of crazes in thermoplastics. Since crazes are not observed in highly crosslinked epoxies, it is generally assumed that plastic deformation at the crack tip takes place via a shear yielding process. 

The magnitude of the fluctuations in volume (dilatation) and density (condensation) associated with US wave is controlled by the properties of the medium and the applied forces. The velocity of sound in mixtures and suspensions will therefore be controlled by the mean density and mean compressibility as expressed by the Urick equation (see Eq.9.7-9.10). The equation can be formulated in terms of partial molar volumes by forming an identity between the volume fraction of the solute, its partial volume Vm2), the mean molar volume of the solution Vm) and the mole fraction Cm) as follows ... 

The asymmetry is easily explained by consideration of the effect of free volume on T. Equilibration at a low temperature produces a low free volume after an increase in temperature, the process of volume dilation is therefore sluggish until the free volume has expanded, and the rate of dilation then accelerates autocatalytically. The reverse occurs after a downward jump in temperature the rate of volume shrinkage slows as the free volume collapses. Similar phenomena occur when the pressure, rather than the temperature, is increased or decreased (Ferry 1980). 

The origin of solution is connected neither with volume contraction nor with volume dilatation. 

In Section 3.1.3.1., it was shown that the ideal mixing of components is connected neither with volume contraction nor with volume dilatation. However, in real binary mixtures, positive as well as negative deviations from the ideal behavior can be observed. The dependence of molar volume on composition is usually expressed in the polynomial form... 

Normally, in sediment volume measurements, the initial volume (or height Hjj) is compared with the ultimately reached value V (or H). A coUoidally stable suspension gives a close-packed structure with relatively small sediment volume (dilatant sediment, referred to as clay). A weakly flocculated or structured suspension gives a more open sediment, and hence a higher sediment volume. Thus, by comparing the relative sediment volume V/V or height H/H, it is possible to distinguish between a clayed and flocculated suspension. 

Figure 4 illustrates the typical volume dilatation-strain behavior along with its first and second derivatives. Clearly these measures are realistic in that the derivatives do take on the character of cumulative and instantaneous frequency distributions. Similar models can be constructed to relate the loss in stiffness to the number of vacuoles that have formed resulting in very simple but accurate stress-strain relations (1). 

In a uniaxial tensile test the volume dilatation simply be-... 

Increases in system temperature give rise to volume dilation, resulting in increased amounts of free volume. This explains the strong tendency for the diffusion coefficient to increase with temperature. The free-volume fraction in Eq (20.4-4) may be represented as a linear addition of the several variables that affect its value ... 

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