Problems of the Nonuniform Relaxation and Description of Complex Nonequilibrium Structures
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
Some new possibilities of the spatially nonuniform relaxation problem (see 1, 2) for the Boltzmann equation and for kinetic relaxation models are considered. This problem intends to describe the nonequilibrium structure in the open system as a result of the operation of relaxation processes and advection processes in gases (or fluids). Methods of direct solving the Boltzmann equation or kinetic models are used to study these new types of the problems. The developed hybrid method 3 which combines solution of the kinetic and continuum equations (in different zones of a flow) can be also applied. This approach now is being developed for multicomponent gases. For simple 1D cases for Maxwell molecules an analytical method of expansion on a small parameter (the inverse Mach number) can be used. This problem deal with the nonequilibrium phenomena on a scale of the characteristic length, which is the mean free path (this scale can be large for a low speed flow). There is no assumption of the local equilibrium as in the thermodynamics of irreversible processes. Study of 1D problem (for which the nonequilibrium boundary condition is accepted for the semi-infinite region) revealed interesting characteristics of the structures. The heat flux has the same sign as the temperature gradient. This denotes that, e.g. positive heat flux from the boundary with the nonequilibrium condition leads to increase of temperature in the flow. The behaviour of the nonequilibrium entropy, i.e. - H-function, is also investigated. Under some conditions the entropy can decrease downflow. Possible application of these nontraditional heat properties for constructing the thermal micro-scale devices is suggested, namely, the scheme of the micro-refrigerator (with a small efficiency) without mechanical parts is proposed. More complex structures can be obtained for gas mixtures: the 1D and 2D problems with nonequilibrium boundary conditions are studied. The influence of the nonequilibrium conditions on the spatial structures is determined. One can change the character of the spatial structures by changing the nonequilibrium distribution functions for gas components at the boundaries. The perspectives of development of this problem for multi-component mixtures with chemical reactions are discussed. It is supposed that the model of nonuniform relaxation could simulate properties of complex natural objects, because biological structures can be treated as open flux systems.
Acknowledgements\\
This work was supported by the Program No 15 of the Presidium of the Russian Academy of Sciences.
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