Diffusivity

Diffusivity or diffusion coefficient is proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species (or the driving force for diffusion). Diffusivity is encountered in Fick's law and numerous other equations of physical chemistry.

Fick's first law said that substances flow from regions with higher concentrations to lower concentrations. Fick's law can be expressed as

J = -D dφ/dx (1)

J = diffusion flux - the amount of substance that flows through an unit area per unit time (mass or mol /m2s)

D = diffusion coefficient (m2/s)

φ = concentration of substance (mass or mol / m3)

x = length (m)

Diffusion of gases is intermixing of two or more gases to form a homogeneous mixture without any chemical change. Diffusion is purely a physical phenomenon. Gases diffuse very quickly due to large empty spaces among molecules and low molecular weight. Different gases diffuse with different rates (velocities). The rate of diffusion of a gas is inversely proportional to the square root of its density. (1)

Gas and liquid diffusion coefficients are have particular importance in considering mass transfer in gas-liquid chromatography as mass transfer may affect the column efficiency considerably. The Stefan-Winkelmann method for measuring diffusivities of vapors is based on determining the rate of evaporation of a volatile liquid that can be followed by the rate of descent of the liquid surface in a glass tube or diffusion cell. The diffusion cell contains a liquid mixture of a volatile solvent A and a high boiling point compound, I, that does not diffuse into the gas phase. At the top of the cell there is a flow of gas B insoluble with the liquid at the bottom of the cell which is A.

Diffusion of A takes place through a stagnant film of A + B and for each time t is the interface depth time. By measuring these variables the mass flux NA*12=o can be determined and also the diffusion coefficient DAB. If the vapor source is a homogeneous mixture of A with a high boiling compound I as a polymer, most of the assumptions implicit still hold, but the concentration potential in the gas phase that responsible for the diffusion process, will be a function of time as the solvent concentration in the liquid phase decreases with time. (2)

By Winklemann method the diffusivity of the vapor of a volatile liquid in air can be conveniently determined in which liquid is contained in a narrow diameter vertical tube, maintained at a constant temperature, and an air stream is passed over the top of the tube to ensure that the partial pressure of the vapor is transferred from the surface of the liquid to the air stream by molecular diffusion. The apparatus that we are concerned with for this experiment is the Gas Dispersion Apparatus that consists of an acrylic assembly which is sub-divided into two compartments. One compartment is constructed from clear acrylic and is used as a constant temperature water bath. The other compartment incorporates an air pump and the necessary electrical controls for the equipment. The instillation is mounted on adjustable feet. Quantifying mass transfer allows for design and manufacture of separation process equipment that can meet specified requirements, estimate what will happen in real life situations (chemical spill), etc. Mass transfer coefficients can be estimated from many different theoretical equations, correlations, and analogies that are functions of material properties, intensive properties and flow regime (laminar or turbulent flow). Selection of the most applicable model is dependent on the materials and the system, or environment, being studied. (3)

REFERENCES

1-) Diffusion (2012). GRAHAM'S LAW OF DIFFUSION. Retrieved at May 14, 2013, from http://www.citycollegiate.com/grahams_lawXI.htm

2-) Coca, J., Bueno, J. and Alvarez R. (1980). Gaseous Diffusion Coefficients by the Stefan-Winkelmann Method Using a Polymer-Solvent Mixture as Evaporation Source. American Chemical Society. (19), 219-221.


3-) Yusri, E. (n.d.). Diffusion Coefficients. Retrieved at May 14, 2013, from http://www.scribd.com/doc/38085961/Diffusion-Coeff-Mass-Transfer-Eda