# Transport Phenomena

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## Transport Phenomena

irreversible processes resulting in the movement of such physical entities as electric charge, mass, momentum, energy, or entropy within a physical system. They are described by kinetic equations.

Transport phenomena can be caused by the action of an external electric field or by the presence of spatial inhomogeneities of composition, temperature, or average velocity of the particles of the system. The transport of the physical entity occurs in the direction opposite to the gradient of the entity. Transport phenomena bring a system closer to the equilibrium state.

Transport phenomena include electric conduction, or the transport of electric charge under the action of an external electric field; diffusion, or the transport of matter (a component of a mixture) when a concentration gradient is present in the system; thermal conduction, or the transport of heat as a result of a temperature gradient; and viscous flow, or the transport of momentum as a result of a gradient of average mass velocity. Also of interest are thermal diffusion, or the transport of matter owing to a temperature gradient, and the Dufour effect, which is the inverse of thermal diffusion. Thermal diffusion, the Dufour effect, galvanomagnetic phenomena, and thermomagnetic phenomena are referred to as cross processes, since a gradient of one entity here causes the transport of another physical entity. Under certain conditions, the Onsager theorem is satisfied for cross processes. The phenomena mentioned are examples of transport phenomena in homogeneous systems within which there are no interfaces.

Transport phenomena also occur in heterogeneous systems consisting of homogeneous parts, or subsystems, separated either by natural interfaces—such as a liquid and its vapor—or by semipermeable membranes.

When a difference, or drop, in electric potential, pressure, or temperature appears in a heterogeneous system, irreversible flows of charge, mass, and heat arise between subsystems. Examples of such transport phenomena are electrokinetic phenomena —the transport of charge and mass owing to a drop in electric potential and pressure—and thermomechanical effects—the transport of heat and mass as a result of a temperature and pressure drop. A particularly interesting case of the latter is the mechanocaloric effect—heat transfer as a result of a pressure difference.

Transport phenomena in gases are studied by the kinetic theory of gases on the basis of the Boltzmann kinetic, or transport, equation for the distribution function of particles. The investigation of transport phenomena in metals is carried out on the basis of the transport equation for electrons in metals. Energy transport in nonconducting crystals is studied with the aid of the transport equation for the phonons of the crystal lattice.

The thermodynamics of nonequilibrium processes gives a general phenomenological theory of transport phenomena; this theory can be applied to any system—gaseous, liquid, or solid. The theory of transport phenomena has undergone intensive development since the 1950’s and 1960’s on the basis of nonequilibrium statistical mechanics.

D. N. ZUBAREV

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