NON-EXTENSIVE VISCOELASTIC THEORY .3. SIM PLE THEORY WITH TRANSLATIONAL MODES

The non-extensive visco-elastic theory with rotational modes developed in (I) is extended to the case of translational modes. A full paralle lism between the two formalisms exists. This theory predicts a thermal phase transition as in the rotational case. The expressions of the tr anslational elastic constant, viscosity and self-diffusion coefficient as a function of temperature and size sample are derived. A detailed study of thermodynamical properties is made. Explicit expressions of t he thermal energy and specific heat associated with the modes are esta blished, as well as formal expressions for the entropy, pressure and e quation of state. The importance of translational macroscopic motions associated with linear velocity gradients is outlined. These motions l imit the amplitude of long wavelength modes, thus avoiding ''catastrop hic'' situations predicted by the theory for very large samples, in th e absence of such motions. The fundamental notions of ''dissipative di stance'' and ''finite velocity for heat propagation'', which appear na turally in the description, lead inevitably to the notion of dynamical instability (translational turbulence). In Appendix B, it is shown ho w the rotational theory of (I) should be modified to take into account the existence of angular velocity gradients. The generalization of th e theory to the case where translational and rotational motions are si multaneouly taken into account, and the problem of coupling between th e two kinds of motions, is discussed. It is argued that this theory sh ould be adequate to describe the main macroscopic properties of common liquids.