Energy dissipation, separation

Figure 2.1 served as the basis for our initial analysis of viscosity, and we return to this representation now with the stipulation that the volume of fluid sandwiched between the two plates is a unit of volume. This unit is defined by a unit of contact area with the walls and a unit of separation between the two walls. Next we consider a shearing force acting on this cube of fluid to induce a unit velocity gradient. According to Eq. (2.6), the rate of energy dissipation per unit volume from viscous forces dW/dt is proportional to the square of the velocity gradient, with t]q (pure liquid, subscript 0) the factor of proportionality ... 

The studies on adhesion are mostly concerned on predictions and measurements of adhesion forces, but this section is written from a different standpoint. The author intends to present a dynamic analysis of adhesion which has been recently published [7], with the emphasis on the mechanism of energy dissipation. When two solids are brought into contact, or inversely separated apart by applied forces, the process will never go smoothly enough—the surfaces will always jump into and out of contact, no matter how slowly the forces are applied. We will show later that this is originated from the inherent mechanical instability of the system in which two solid bodies of certain stiffness interact through a distance dependent on potential energy. 

In principle, the energy dissipation (friction loss) associated with the gas-liquid, gas-wall, and liquid-wall interactions can be evaluated and summed separately. However, even for distributed (nonhomogeneous) flows it is common practice to evaluate the friction loss as a single term, which, however, depends in a complex manner on the nature of the flow and fluid properties in both phases. This is referred to as the homogeneous model ... 

This model was introduced by Neville and Hunter (13,14) for the case of sterically stabilized dispersions which have undergone reversible flocculation. It is assumed that the major contribution to the excess energy dissipation in such pseudoplastic systems comes from the need to provide energy from the shear field to separate contacting particles. Under these conditions, the extrapolated yield value is given by the expression (13,32,33),... 

The secondary electroviscous effect is often interpreted in terms of an increase in the effective collision diameter of the particles due to electrostatic repulsive forces (i.e., the particles begin to feel the presence of other particles even at larger interparticle separations because of electrical double layer). A consequence of this is that the excluded volume is greater than that for uncharged particles, and the electrostatic particle-particle interactions in a flowing dispersion give an additional source of energy dissipation. 

The main scheme is shown in Fig. 17. The photogenerated electron hole pairs transfer to the soliton-antisoliton pairs in 10 13s. Two kinks appeared in the polymer structure, which separates the degenerated regions. Due to the degeneration, two charged solitons may move without energy dissipation in the electric field and cause the photoconductivity. The size of the soliton was defined as 15 monomer links with the mass equal to the mass of the free electron. In the scheme in Fig. 17, the localized electron levels in the forbidden gap correspond to the free ( + ) and twice occupied ( — ) solitons. The theory shows the suppression of the interband transitions in the presence of the soliton. For cis-(CH)n the degeneration is absent, the soliton cannot be formed and photoconductivity practically does not exist. 

To find the influence function rj(s), we shall consider shear deformation of the system at velocity gradient 7y, while two macromolecular coils, separated by a distance dj, move beside each other at velocity 7ijdj. We add to the sum the contributions of every coil, apart from the chosen one, and find the density distribution of the energy dissipation for the chosen coil. The proportionality coefficient depends only on the concentration of the Brownian particles, if an assumption is made that local dissipation is determined by relative velocities of macromolecular coils,... 

Thus retention parameter A can be considered as a ratio of two energies dissipative energy 5 7 and the energy F w expended in driving components across channel thickness w. We have shown before (see Section 8.2) that energy ratios of this kind are crucial to separation. 

Other processes that lead to nonlinear compartmental models are processes dealing with transport of materials across cell membranes that represent the transfers between compartments. The amounts of various metabolites in the extracellular and intracellular spaces separated by membranes may be sufficiently distinct kinetically to act like compartments. It should be mentioned here that Michaelis-Menten kinetics also apply to the transfer of many solutes across cell membranes. This transfer is called facilitated diffusion or in some cases active transport (cf. Chapter 2). In facilitated diffusion, the substrate combines with a membrane component called a carrier to form a carrier-substrate complex. The carrier-substrate complex undergoes a change in conformation that allows dissociation and release of the unchanged substrate on the opposite side of the membrane. In active transport processes not only is there a carrier to facilitate crossing of the membrane, but the carrier mechanism is somehow coupled to energy dissipation so as to move the transported material up its concentration gradient. 

The functions g(9) and h 6) represent two separate effects of disentanglement g(6) is the fractional reduction of entanglement density due to steady shear flow and h(ff) is the fractional reduction in energy dissipation rate per molecule due to dis-entanglement in steady shear flow (for details, see Graessley, 1974, Chap. 8). Eqs. (16.52)-(16.55) define an implicit expression for the master curve rj/rj0 vs. qzn, the reduced viscosity also being present in the arguments of the functions g(6) and h(6). 

In principle, an equality between the thermodynamic work of adhesion of liquid-solid systems and the work needed to separate an interface might be expected for simple systems and this has been observed for failure of adhesive-polymer interfaces bonded by van der Waals forces, (Kinloch 1987). Similarly, empirical correlations of interfacial strengths and work of adhesion values of solidified interfaces have been reported for some nominally non-reactive pure metal/ceramic systems. However, mechanical separation of such interfaces is a complex process that usually involves plastic deformation of the lattices, and hence their works of fracture are often at least ten and sometimes one hundred times larger than the works of adhesion, (Howe 1993). Nevertheless, for non-reactive metal/ceramic couples, it is now widely recognised that the energy dissipated by plasticity (and as a result the fracture energy of the interface) scales with the thermodynamic work of adhesion (Reimanis et al. 1991, Howe 1993, Tomsiaet al. 1995). 

Second-law analysis can determine the level of energy dissipation from the rate of entropy production in the system. The entropy production approach is especially important in terms of process optimality since it allows the entropy production of each process to be determined separately. The map of the volumetric entropy production rate identifies the regions within the system where excessive entropy production occurs due to irreversible processes. Minimizing of excessive irreversibilities allows a thermodynamic optimum to be achieved for a required task. Estimation of the trade-offs between the various contributions to the rate of entropy production may be helpful for attaining thermodynamically optimum design and operation. 

---