Mass diffusivity

The diffusion coefficient, also known as the diffusion constant or diffusivity, is used in the Fick's laws to calculate the thermally induced transport of a substance due to the random motion of the particles. These may be individual atoms in a solid or particles in a gas or a liquid. The diffusion coefficient is thus a measure of the mobility of the particles and can be determined from the distance traveled in a certain time distance.

Always belongs to specify the diffusion coefficient that specifies which material in which material diffuses, as well as the most important factor influencing the temperature. The SI unit of the diffusion coefficient is.

Diffusion coefficients in gases

Diffusion coefficients in gases are strongly dependent on temperature and pressure. Applies a first approximation, that doubling the pressure to halve the diffusion coefficient leads.

The diffusion coefficient follows according to the Chapman - Enskog theory, the following numerical value equation for two gaseous substances (indices 1 and 2):

With

  • D - diffusion coefficient (cm2 / s)
  • T - temperature ( K)
  • M - molar mass (g / mol)
  • - (Mean ) collision diameter ( values ​​tabulated ) ( Å)
  • Ω - Collision integral, depending on the temperature (Values ​​tabulated ) (-).

For the self-diffusion (ie, for the case that only one particle is present) simplifies the above Related to:

With

  • - Mean thermal velocity of the particles (m · s-1)
  • L - mean free path (m)
  • N - number density ( 1/m3 )
  • D - particle diameter ( m)
  • KB - Boltzmann's constant ( J · K-1)
  • π - Pi
  • M - molecular weight ( kg).

Empirical approximation formulas for the calculation of diffusion coefficients in gases can be found in the corresponding standard works.

Diffusion coefficients in liquid

Diffusion coefficients in liquids generally takes about one ten -thousandth of diffusion coefficients in gases. They are described by the Stokes-Einstein equation:

With

  • KB - Boltzmann's constant ( J · K-1)
  • T - temperature ( K)
  • π - Pi
  • η - dynamic viscosity of the solvent (in N · s · m-2)
  • R0 - hydrodynamic radius of the diffusing particles (m)

In this equation based many empirical correlations.

Since the viscosity of the solvent is a function of the temperature dependence of the diffusion coefficient of the temperature is not linear.

Diffusion coefficient in solids

Diffusion coefficients in solids are usually several thousand times smaller than diffusion coefficients in liquids.

For the diffusion in solids jumps between different lattice sites are required. The particles must overcome an energy barrier E, which at higher temperature is easier than at low. This is described by the relationship:

  • E - energy barrier (in J · mol -1)
  • R - universal gas constant (in J · K- 1 mol -1)
  • T - temperature ( in K).

D0 can be calculated approximately as:

  • α0 - atomic distance (in m)
  • N - Proportion of vacant lattice sites ( no units)
  • ω - jump frequency (in Hz)

However, it is advisable to determine, in particular diffusion coefficients in solids experimentally.

Effective diffusion coefficient

The effective diffusion coefficient describes diffusion through the pore space of porous media. Since he does not consider individual pores, but the total pore space, it is a macroscopic size:

With

  • εt - porosity that is available for the transport; it corresponds to the total porosity of less pores, which are not accessible due to their size for the diffusing particles, and less dead end and blind pores ( pores without connection to the remaining pore system )
  • δ - Konstriktivität; describes slowing the diffusion through an increase in viscosity in narrow pores, as a result of the greater average closeness to the pore wall and is a function of pore diameter and the size of the diffusing particles.
  • τ - tortuosity ( " tortuosity " )

Apparent diffusion coefficient

The apparent ( apparent ) coefficient of diffusion enlarges the effective diffusion coefficient of the influence of the sorption.

For linear sorption, it is calculated as:

With

  • Kd - linear sorption coefficient (m3 · kg -1)
  • ρ - density ( in kg · m -3)
  • ε - porosity ( unitless )

In nonlinear sorption isotherm, the apparent diffusion coefficient is always a function of the concentration, which greatly complicates the calculation of the diffusion.

Chemical substance Electron mobility Boltzmann constant Empirical research Stokes radius Network covalent bonding Anomalous diffusion
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