Fluid pressure anomalies

Hasegawa, T., Suganuma, M., Watanabe, H., Anomaly of excess pressure drops of the flow through very small orifices. Phys. Fluids. 1987 9, 1-3. 

Particle-fluid flow has been in existence in industrial processes since the nineteenth century. Applications include pneumatic conveying, which deals with pipe flow of solid material transported by a gas, slurry transport and processing of solids in a fluid. The necessity of predicting blower or pumping power for a given amount of material to be conveyed led to measurements of pressure drops and attempts in the correlation of physical parameters. That anomaly exists in the correlation in terms of simple parameter is one of the motivations for the exploration into the details of distributions in density and velocity and the present state of development of instrumentation. 

Liquid polymorphism in one-component fluids is an example of so-called anomalous phase behavior. This term is used to emphasized the difference with respect to the normal behavior characterizing prototypical (i.e., argon like) simple liquids. Anomalous behavior includes, in addition to polymorphism in the liquid and solid phases, reentrant melting, that is, melting by compression at constant temperature, and a number of other thermodynamic, dynamic, and structural anomalies, as, for example, the density anomaly (a decrease in density upon cooling), the diffusion anomaly (an increase of diffusivity upon pressurizing), and the structural anomaly (a decrease of structural order for increasing pressure). 

For both a = 2.1 and a = 3.3, in the reentrant-fluid region coexisting with the bcc solid, a density anomaly occurs, that is, the number density decreases upon cooling at constant pressure. This region is bounded from above by the temperature of the maximum density line (see Figs. 4 and 5). Similarly to water, the region of density anomaly is encompassed by the region of anomalous diffusion that in turn is enclosed by that of structural anomaly. A compendium of anomalous behaviors of the YK system with a = 3.3 is shown in Fig. 6. 

These results imply that the extension of equilibrium theories to nonequiUbrium states is not always valid in a straightforward way. Particularly, the diffusion tensor is proportional to the components of the pressure tensor or equivalently to the velocity gradient Vvq, which implies that the amplitude of the noise in the dynamics of the tagged particle is not simply thermal as in equilibrium since the diffusion tensor cannot be characterized entirely by the thermodynamic temperature. In similar manner, Eq. (5) does not depend on the irreversible heat flux. This is an anomaly of the Maxwell potential, for other potentials there will be an additional contribution to the drift vector that would depend on the any temperature gradient in the fluid. 

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