Dissipation internal friction

Drawing Hot drawing and cold drawing are differentiated, whereby dissipation (internal friction) results in temperatures in the flow zone of up to 120 °C in cold drawing. 

A fluid is said to be viscous when there is spatial inhomogeneity in the fluid s velocity field (adapted with permission from Reference 26). Such inhomogeneity can arise both from differential momentum transport of fluid and the presence of particles within the fluid that alter the velocity field, which contribute additional dissipative internal friction to the fluid. The amount of viscosity that a macromolecule contributes to a fluid is easy to measure and can be related to conformational and other properties of the macromolecule, making viscosity measurements a valuable characterization tool. 

The deforming forces which induce flow in fluids are not recovered when these forces are removed. These forces impart kinetic energy to the fluid, an energy which is dissipated within the fluid. This is the origin of the idea that viscosity represents an internal friction which resists flow. This friction originates from the way molecules of the sample interact during flow. 

The dissipation factor (the ratio of the energy dissipated to the energy stored per cycle) is affected by the frequency, temperature, crystallinity, and void content of the fabricated stmcture. At certain temperatures and frequencies, the crystalline and amorphous regions become resonant. Because of the molecular vibrations, appHed electrical energy is lost by internal friction within the polymer which results in an increase in the dissipation factor. The dissipation factor peaks for these resins correspond to well-defined transitions, but the magnitude of the variation is minor as compared to other polymers. The low temperature transition at —97° C causes the only meaningful dissipation factor peak. The dissipation factor has a maximum of 10 —10 Hz at RT at high crystallinity (93%) the peak at 10 —10 Hz is absent. 

Dissipative systems whether described as continuous flows or Poincare maps are characterized by the presence of some sort of internal friction that tends to contract phase space volume elements. They are roughly analogous to irreversible CA systems. Contraction in phase space allows such systems to approach a subset of the phase space, C P, called an attractor, as t — oo. Although there is no universally accepted definition of an attractor, it is intuitively reasonable to demand that it satisfy the following three properties ([ruelle71], [eckmanSl]) ... 

Because of internal friction, some of the translational kinetic energy of flow dissipates over a period of time. For the physical situation pictured in Figure 2.3, Stokes was able to show that the rate of energy dissipation dE/dt is given by... 

Measurements of <5 yield direct information about the magnitude of the energy dissipation and the phase angle. 0 measures the fractional energy loss per cycle due to the anelasticity and is often termed the internal friction. According to the discussion above, 8 will be a function of the frequency, to should approach zero at both low and high frequencies and will have a maximum at some intermediate frequency. The maximum occurs at a frequency that is the reciprocal of the relaxation time for the re-population of the point defects. 

When a typical elastic solid is stressed, it immediately deforms by an amount proportional to the applied stress and maintains a constant deformation as long as the stress remains constant - i.e. it obeys Hooke s law. On removal of the stress, the elastic energy stored in the solid is released and the solid immediately recovers its original shape. Newtonian liquids, on the other hand, deform at a rate proportional to the applied stress and show no recovery when the stress is removed, the energy involved having been dissipated as heat in overcoming the internal frictional resistance. 

This equation simply states that the increase in internal energy of a fluid element riding with the stream is due to the heat flux, the reversible increase of internal energy per unit volume by compression, and viscous dissipation or the irreversible conversion of internal friction to heat. Should there be another type of heat source (e.g., chemical reaction), it can be added to the equation. 

When a multi-particle model of the macromolecule (Slonimskii-Kargin-Rouse model) is considered, one must assume that the force acting on each particle is determined by the difference between the velocities of all the particles u7 — vP. These quantities must be introduced in such a way that dissipative forces do not appear on the rotation of the macromolecular coil as a whole, whereupon uj = Qjirf. Thus, in terms of a linear approximation with respect to velocities, the internal friction force must be formulated as follows... 

The phenomenon of friction may be described as the degradation of mechanical work (work performed by moving forces) into heat. From a molecular point of view such degradation occurs through the change in the uniform motion of an initially exerted force into an increased random motion of motecules. This latter is manifested as an increase in temperature. When such dissipation is observed in fluids, the process is referred to as internal friction, or viscosity. 

The classical solution suggested by Frenkel (l945), is based on a spherical pore enclosed in a homogeneous viscous material. By equalizing the work done by surface tension with the energy dissipated by internal friction, Frenkel derived the relation... 

This work is equal to the energy dissipated by internal friction during viscous deformation ... 

Eddies with wave numbers in the region of (fcg) (see Fig. 1.6) contain the largest part of the energy and contribute little to energy dissipation by internal friction. However, small eddies with wave numbers in the region of... 

The coefficient of restitution depends on the mechanical properties of the particle and surface. For perfectly elastic collisions, e — 1 and the particle energy is conserved after collision. Deviations from unity result from dissipative processes, including internal friction, that lead to the generation of heat and the radiation of compressive waves into the. surface material. 

We shall see that the sum p(V u) + T E on the right-hand side of (2 52) represents the conversion of kinetic energy to heat, due to the internal friction within the fluid and is known as the viscous dissipation term. The last term on the left-hand side of (2 52) is related to the work required for compressing the fluid. Although this term is identically zero only for constant-pressure conditions (that is, the material is a solid or it is stationary so that Dp jDt = 0), it is frequently small compared with other terms in (2-52) because the density at constant pressure is only weakly dependent on the temperature, and we shall generally adopt this approximation in the analyses of nonisothermal systems in later chapters. 

If the fluid temperature at the entry cross-section is equal to the wall temperature Ts, then, along some initial part of the tube, the fluid is gradually heated by internal friction until a balance is achieved between the heat withdrawal through the walls and the dissipative heat release. In the region where such an equilibrium is established, the fluid temperature does not vary along the channel, that is, the temperature field is stabilized (provided that the velocity profile is also stabilized). In what follows we just study this thermally and hydrodynamically stabilized flow. 

The Brinkmann number Br = ( yuli)l[k TKm - Te)] is introduced to account for the influence of viscous dissipation, such as heating or cooling of the fluid due to internal friction in high-velocity flow, highly viscous fluid, or in cases in which viscous dissipation cannot be ignored. When viscous dissipation is considered, the asymptotic Nusselt number in a very long pipe, found by Ou and Cheng [5], is 9.6 and independent of the Brinkmann number. 

These equations are often used in terms of complex variables such as the complex dynamic modulus, E = E + E", where E is called the storage modulus and is related to the amount of energy stored by the viscoelastic sample. E" is termed the loss modulus, which is a measure of the energy dissipated because of the internal friction of the polymer chains, commonly as heat due to the sinusoidal stress or strain applied to the material. The ratio between E lE" is called tan 5 and is a measure of the damping of the material. The Maxwell mechanical model provides a useful representation of the expected behavior of a polymer however, because of the large distribution of molecular weights in the polymer chains, it is necessary to combine several Maxwell elements in parallel to obtain a representation that better approximates the true polymer viscoelastic behavior. Thus, the combination of Maxwell elements in parallel at a fixed strain will produce a time-dependent stress that is the sum of all the elements ... 

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