Mesoscopic Thermodynamics in the Presence of Flow

Abstract

Thermodynamics is a powerful theory that has been succesfully applied to describe the properties and behavior of macroscopic systems under a very wide range of physical conditions (Callen, 1985). Thermal and caloric information is obtained by performing experiments that agree with the constraints imposed (Callen, 1985; Kondepudi & Prigogine, 1999; Ragone, 1995). However, a considerable number of experimental, practical problems and systems of interest are often found in nonequilibrium or metastable states in which static thermodynamic relations are only valid locally, and frequently are insufficient to describe complicated time dependent situations (Demirel, 2007). Macroscopic systems in flow conditions are good examples of this peculiar behavior through non-Newtonian rheological effects, phase transitions and generalized statistics of turbulent motion. In fact, although there is a large amount of theoretical work proposing generalizations of the thermodynamic theory to nonequilibrium or quasiequilibrium situations (Beck & Cohen, 2003; Beris & Edwards, 1994; C. Beck & Swinney, 2005; de Groot & Mazur, 1984; Demirel, 2007; Kondepudi & Prigogine, 1999; Onuki, 2004; Rodriguez & Santamaria Holek, 2007), some of them very succesful (de Groot & Mazur, 1984; Demirel, 2007; Kondepudi & Prigogine, 1999), they are restricted due to the assumption and validity of local thermodynamic equilibrium. Recently, some interesting generalizations of thermodynamics to describe macroscopic systems in the presence of flow have been systematically developed in Refs. (Beris & Edwards, 1994; Onuki, 2004). Nevertheless, there are still a good deal of open questions, for instance those concerning the validity of the usual relations for the thermal and caloric equations of state, arising further research on this subject. Related to these general questions, there are several particular manifestations of the effects of flow on the thermodynamic behavior of systems. For example, diffusion of suspended particles in a heat bath in equilibrium, may strongly differ from that when the particles diffuse in a heat bath under the presence of shear flow. These effects have been analyzed along the years in studies ranging from experiments (Breedveld, 1998; Guasto & Gollub, 2007; Pine, 2005; Taylor & Friedman, 1996) and computer simulations (Sarman, 1992) to kinetic 5