Diffusion in general physics and the theory of the convective diffusion

In this article, basic ideas of the diffusion in the gases and liquids are presented. In the last part of it, the problem of diffusion in the concentrated mixtureswhen the concentration of components is not considered minor admixturesis examined. In this case, Onsager’s equations are utilized in molecular physics.


INTRODUCTION
The thermal motion of atoms and molecules in the substance leads to their continuous mixing, which depends on density, temperature T , pressure P , and other values.
In the gases, the molecules disorderly collide. These collisions are not similar to the collisions of elastic spheres. Molecules are complex systems, their collisions are caused by repulsive forces with the approchement up to the small distances i.e. taking into account one particle , moreover the vibration frequency in the position of equilibrium is

Diffusion in the liquid and gas mixture
Two different contiguous gases by means of the molecular motion mutually penetrate and get mixed. This process is called the diffusion. It continues to the formation of the uniform mixture of molecules, in all parts of volume of which leveled the partial gas pressures, their density, temperature and other values. They all are uniformly distributed in the volume of mixture. If initially there existed a layer of gas with different speeds, in which by the way of the exchange of momentum, fast layers slow down, slow are accelerated, and as a result, the motion of gases either ceases or their all mass moves as single entirely. This motion is called convection. The levelling off of speeds of layers is accompanied by the transformation of kinetic energy of the regulated motion of fast layers into the energy of disorder motion, i.e., thermal motion. This process is of dissipating the energy. The mechanism of the levelling off of all values is caused by the appearance of the preferred direction of molecular collisions. Growing the collision rate of molecules with the speeds, directed to those parts of the volume of mixtures, in which are less density, temperature, pressure, etc. The gradients of these macroscopic characteristics of the state of the gas mixture as a result, decrease. With the description of diffusion, molecular ideas presented above are conserved, and at the same time, substance is considered as continuous medium with the macroscopic characteristics. Respectively, the possibility to describe the directivity of molecular motion at the macroscopic level appears. For this, the quantity of substance where D-the diffusion coefficient, ∇cconcentration gradient. In the one-dimensional case the flow along the axis is determined by replacement, This formula is called Fick law.
Concentration gradient (or derivative dc dx ) is the motive power of the diffusion, in which the molecular theory corresponds to the preferred directivity of the molecular motion. In general physics, it proves that for gases But for the liquids

Diffusion in the hydrodynamics
The motion of liquid with unifor m composition is described, as is known, by the equations of the hydrodynamics. In the case of the mixture of several different liquids, these equations change. Mixture is described by the concentrations, defined as the ratio of a quantity of particles of the component (or their mass) in the given volume of mixture to its total quantity of the particles. In the course of time, particle distribution in the volume can change with two methods. During the macroscopic motion each section of liquid (drop of liquid) mechanically is moved as single entirely with the constant composition. In spite of its conser vation, concentrations in the section can change. In the absence of thermal conductivities and viscosities, this change is thermodynamically reversed and does not lead to the dissipation of the energy.
However, a change in the concentrations is possible and by the molecular transfer of components of one section to another. This levelling off of concentrations due to a direct change of the composition of drop in the hydrodynamics is also called the diffusion. It is not reversed, and together with the thermal conductivity and the viscosity serves as one of the sources of the dissipation of energy in the liquid mixture. Energies of the particles of different sections are unequal and their transition lead to its scattering. Accordingly, the form of Fick law given above is generalized. The flow of diffusion taking into account the energy interaction factors of particles into the mixture and the external field influences is determined by the formula where L-Onsager's coefficient, µ-Chemical potential.

Theory of Onsager of mass transfer in the concentrated multicomponent mixtures
The processes of isothermal mass transfer in the liquid   (7) is the simpler form of Onsager's equations (4). From (7) we obtain the limiting case of admixtures diffusion with the small concentrations 5 . Actually, assume that in (7), concentration of one of the components (solvent) predominates, i.e. the concentrations of remaining components are considerably less. Then with it will be ...(9) Therefore, to the right of (7) is substantial, only one term with , and we have for any other Left side of (12) represents the density of the thermodynamic force, which acts on the particles of component. Taking into account its one mole Right side of (12) treats as the resisting force with the coefficient of braking , analogous to the force of stoke with In the general case of several components it is necessary to consider their pairwise interactions. for this, let us change in (12) the indexing of values Then, let us introduce the statistical weight of i component and will sum up interactions of all pairs of components. As a result, we will obtain (7). According to (7), Onsager's model diffusion in the concentrated liquid mixtures presents the motion of the components, which are mutually rubbed with the force . it is possible to name it the hydrodynamic idea of diffusion.