the diffusion of the free particle in any medium is mainaly due to
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DIFFUSION
Mostinsky, I.L.
DOI: 10.1615/AtoZ.d.diffusion
Diffusion is a process leading to equalization of substance concentrations in a system or establishing in a system an equilibrium concentration distribution that results from random migration of the system's elements.
Three types of diffusion are distinguished, viz., molecular, Brownian, and turbulent. Molecular diffusion occurs in gases, liquids, and solids; both diffusion of molecules of extraneous substances (impurities) and self-diffusion are observed. Molecular diffusion occurs as a result of thermal motion of the molecules. It proceeds at a maximum rate in gases, at a lower rate in liquids, and at a still lower rate in solids—these differences being accounted for by the nature of thermal motion in these media.
In a gaseous phase, molecules possess a certain mean velocity depending on the temperature, but their motion is chaotic and in colliding, they change the direction of this motion. However, on the whole, the molecules of the substance migrate at a velocity much lower than the mean velocity of the molecular free motion. The higher the pressure, the denser is the molecule packing, the less is the free-path length, and the slower is the diffusion. The same occurs as molecule mass and size increase. Conversely, elevation of temperature causes an increase in the free-path length, a decrease in the number of collisions, and growth of free-motion velocity. These factors all lead to a speed-up of diffusion.
In liquids, molecular diffusion occurs by jumps of the molecules from one position to another; this arises when the energy of the molecule is high enough to rupture the bonds with the neighboring molecules allowing the molecule to move. On average, the jump does not exceed an intermolecular spacing, and since in a liquid this is much less than in a gas, the diffusion is substantially lower. Since a liquid is virtually incompressible, the diffusion rate is independent of pressure. Elevation of temperature increases intermolecular spacings and the velocity of vibrations and jumps of molecules, which enhances diffusion.
Gases contained in solids diffuse as ions or atoms migrating through interstitials of the crystal lattice, and the same is observed for atoms and ions with a radius much smaller than that of the ion or atom of the base substance constituting the solid. Diffusion of solid impurities occurs by interchange of sites of atoms and vacancies (unoccupied sites of crystal lattice), by migration of atoms through interstitials, by a simultaneous cyclic migration of several atoms, by a direct interchange of sites of two neighboring atoms, etc. Each displacement requires imparting to a particle a definite amount of energy (activation energy). Therefore, diffusion is extremely sensitive to temperature elevation, which manifests itself in its exponential dependence on temperature. Nevertheless, even at high temperature, diffusion in solids is much slower than in liquids.
So far, the above discussion has focused on the so-called pure concentration diffusion proceeding under the effect of concentration gradient (or chemical potential) in a medium unaffected by external factors. However, it is known that temperature gradient gives rise to a thermal diffusion, pressure gradient to pressure diffusion, an electrical field to electrical diffusion of charged particles, and so on. These diffusion types are beyond the scope of this discussion.
Molecular diffusion
In the general case, at a constant temperature and pressure, the molar diffusion flux  of substance A is proportional to the molar concentration gradient dCA/dy and a one-dimensional formulation is described by an equation called Fick's law

where DA is the diffusion coefficient. In a binary system, the flow of one component must be balanced by the counterflow of the other component

but since CA + CB = const, then

DAB is said to be the interdiffusion coefficient.
In order to describe a unidirectional diffusion of A molecules in a multicomponent mixture of ideal gases, the Stefan-Maxwell equation

based on the kinetic theory of gases is used, where YA is the mole fraction of component A, CT = p/RT, the total concentration (density) of mixture; CA = pYA/RT, cj = pYj/RT, DAj, the interdiffusion coefficient for a pair A, j; and uj and uA are the diffusion rates for the respective components of the pair.
Library Subscription: Guest
A-to-Z Guide to Thermodynamics,
Heat & Mass Transfer, and Fluids Engineering
HOMESEMANTIC MAPA-Z INDEXVISUAL GALLERYAUTHORSMY THERMOPEDIA
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
VISUAL MAP NAVIGATION
View in A-Z Index
RELATED CONTENT IN OTHER PRODUCTS
International Heat Transfer ConferenceDigital LibraryInternational Centre for Heat and Mass Transfer Digital LibraryBegell HouseJournalsAnnual Review of Heat Transfer
DIFFUSION
Mostinsky, I.L.
DOI: 10.1615/AtoZ.d.diffusion
Diffusion is a process leading to equalization of substance concentrations in a system or establishing in a system an equilibrium concentration distribution that results from random migration of the system's elements.
Three types of diffusion are distinguished, viz., molecular, Brownian, and turbulent. Molecular diffusion occurs in gases, liquids, and solids; both diffusion of molecules of extraneous substances (impurities) and self-diffusion are observed. Molecular diffusion occurs as a result of thermal motion of the molecules. It proceeds at a maximum rate in gases, at a lower rate in liquids, and at a still lower rate in solids—these differences being accounted for by the nature of thermal motion in these media.
In a gaseous phase, molecules possess a certain mean velocity depending on the temperature, but their motion is chaotic and in colliding, they change the direction of this motion. However, on the whole, the molecules of the substance migrate at a velocity much lower than the mean velocity of the molecular free motion. The higher the pressure, the denser is the molecule packing, the less is the free-path length, and the slower is the diffusion. The same occurs as molecule mass and size increase. Conversely, elevation of temperature causes an increase in the free-path length, a decrease in the number of collisions, and growth of free-motion velocity. These factors all lead to a speed-up of diffusion.
In liquids, molecular diffusion occurs by jumps of the molecules from one position to another; this arises when the energy of the molecule is high enough to rupture the bonds with the neighboring molecules allowing the molecule to move. On average, the jump does not exceed an intermolecular spacing, and since in a liquid this is much less than in a gas, the diffusion is substantially lower. Since a liquid is virtually incompressible, the diffusion rate is independent of pressure. Elevation of temperature increases intermolecular spacings and the velocity of vibrations and jumps of molecules, which enhances diffusion.
Gases contained in solids diffuse as ions or atoms migrating through interstitials of the crystal lattice, and the same is observed for atoms and ions with a radius much smaller than that of the ion or atom of the base substance constituting the solid. Diffusion of solid impurities occurs by interchange of sites of atoms and vacancies (unoccupied sites of crystal lattice), by migration of atoms through interstitials, by a simultaneous cyclic migration of several atoms, by a direct interchange of sites of two neighboring atoms, etc. Each displacement requires imparting to a particle a definite amount of energy (activation energy). Therefore, diffusion is extremely sensitive to temperature elevation, which manifests itself in its exponential dependence on temperature. Nevertheless, even at high temperature, diffusion in solids is much slower than in liquids.
So far, the above discussion has focused on the so-called pure concentration diffusion proceeding under the effect of concentration gradient (or chemical potential) in a medium unaffected by external factors. However, it is known that temperature gradient gives rise to a thermal diffusion, pressure gradient to pressure diffusion, an electrical field to electrical diffusion of charged particles, and so on. These diffusion types are beyond the scope of this discussion.
Molecular diffusion
In the general case, at a constant temperature and pressure, the molar diffusion flux  of substance A is proportional to the molar concentration gradient dCA/dy and a one-dimensional formulation is described by an equation called Fick's law

where DA is the diffusion coefficient. In a binary system, the flow of one component must be balanced by the counterflow of the other component

but since CA + CB = const, then

DAB is said to be the interdiffusion coefficient.
In order to describe a unidirectional diffusion of A molecules in a multicomponent mixture of ideal gases, the Stefan-Maxwell equation

based on the kinetic theory of gases is used, where YA is the mole fraction of component A, CT = p/RT, the total concentration (density) of mixture; CA = pYA/RT, cj = pYj/RT, DAj, the interdiffusion coefficient for a pair A, j; and uj and uA are the diffusion rates for the respective components of the pair.
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diffusion of free particle in any medium is mainly duo concentration gradient
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