Viscous dissipation, mechanical energy

The storage modulus is the elastic component and is related to a sample s stiffness. The loss modulus is the viscous component and is related to the material s ability to dissipate mechanical energy through molecular motion, tan 8 provides information on the relationship between the elastic and inelastic components. 

Polymeric materials, such as rubber, exhibit a mechanical response which cannot be properly described neither by means of elastic nor viscous effects only. In particular, elastic effects account for materials which are able to store mechanical energy with no dissipation. On the other hand, a viscous fluid in a hydrostatic stress state dissipates energy, but is unable to store it. As the experimental results reported in Part 1 have shown, filled rubber present both the characteristics of a viscous fluid and of an elastic solid. Viscoelastic constitutive relations have been introduced with the intent of describing the behavior of such materials able to both store and dissipate mechanical energy. 

Note that the total pressure drop consists of 0.5 velocity heads of frictional loss contrihiition, and 1 velocity head of velocity change contrihiition. The frictional contrihiition is a permanent loss of mechanical energy hy viscous dissipation. The acceleration contrihiition is reversible if the fluid were subsequently decelerated in a frictionless diffuser, a 4,000 Pa pressure rise would occur. 

In shear layers, large-scale eddies extract mechanical energy from the mean flow. This energy is continuously transferred to smaller and smaller eddies. Such energy transfer continues until energy is dissipated into heat by viscous effects in the smallest eddies of the spectrum. 

As reviewed thermoplastics (TPs) being viscoelastic materials respond to induced stress by two mechanisms viscous flow and elastic deformation. Viscous flow ultimately dissipates the applied mechanical energy as frictional heat and results in permanent material deformation. Elastic deformation stores the applied mechanical energy as completely recoverable material deformation. The extent to which one or the other of these mechanisms dominates the overall response of the material is determined by the temperature and by the duration and magnitude of the stress or strain. The higher the temperature, the most freedom of movement of the individual plastic molecules that comprise the... 

It has been found from MD simulations that friction of SAMs on diamond decreases with the increasing chain length of hydrocarbon molecules, but it remains relatively constant when the number of carbon atoms in the molecule chain exceeds a certain threshold [44], which confirmed the experimental observations. In simulations of sliding friction of L-B films, Glosli and McClelland [45] identified two different mechanisms of energy dissipation, namely, the viscous mechanism, similar to that in viscous liquid under shear, and the plucking mechanism related to the system instability that transfers the mechanical energy into heat, similar to that proposed in the Tomlinson model (see Chapter 9). On the basis of a series work of simulations performed in the similar... 

In case that the decay of impact kinetic energy due to viscous dissipation is the predominant mechanism in droplet flattening, Madejski s full model reduces to ... 

As shown in Chapter 10, molecular dynamics in polymers is characterized by localised and cooperative motions that are responsible for the existence of different relaxations (a, (3, y). These, in turn, are responsible for energy dissipation, mechanical damping, mechanical transitions and, more generally, of what is called a viscoelastic behavior - intermediary between an elastic solid and a viscous liquid (Ferry, 1961 McCrum et al., 1967). 

Frictional dissipation of mechanical energy can result in significant heating of fluids, particularly for very viscous liquids in small channels. Under adiabatic conditions, the bulk liquid temperature rise is given by AT=AP/CV p for incompressible flow through a channel of constant cross-sectional area. For flow of polymers, this amounts to about 4°C per 10 MPa pressure drop, while for hydrocarbon liquids it is about... 

Removal of the melt, also discussed in Section 5.1, is made possible, in principle, by two mechanisms drag-induced flow and pressure-induced flow (Fig. 5.4). In both cases, the molten layer must be sheared, leading to viscous dissipation. The latter provides an additional, important source of thermal energy for melting, the rate of which can be controlled externally either by the velocity of the moving boundary in drag-induced melt removal or the external force applied to squeeze the solid onto the hot surface, in pressure-induced melt removal. 

This equation is based on the assumption that the change of state resulting from the process is accomplished reversibly. However, the viscous nature of real fluids induces fluid friction that makes changes of state in flow processes inherently irreversible because of the dissipation of mechanical energy into internal energy. In order to correct for this, we add to the equation a friction term F. The mechanical-energy balance is then written ... 

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