American University of Sharjah College of Engineering Chemical Engineering Department
Transport Phenomena Lab II (CHE 451) Writing Assignment Effects of Temperature and Concentration on Diffusivity Coefficient
AbdulahIbraheem Al Hamadi @29371
October 21st 2010
EFFECTS OF TEMPERATURE AND CONCENTRATION ON DIFFUSIVITY
Diffusivity or diffusion coefficient is the proportionality constant between the molar flux (J) due to molecular diffusion and the concentration gradient (which is the driving force of mass transfer) of certain species in a mixture. The diffusion coefficient depends upon temperature, pressure, and concentration (composition) of the system [1]. In this paper, the effects of temperature and concentration on the diffusion coefficient will be discussed. First of all, as one might expect from the consideration of the mobility of the molecules, the diffusion coefficients are generally higher for gases than for liquids which ar e higher than the values reported for solids. For example, Carbon dioxide in air has a diffusion coefficient of (16×10 -6 m²/s), and in water its coefficient is (16×10 -10 m²/s)[2].Based on this the effect of temperature on the diffusion coefficient is not the same for the three phases. In general, as the temperature increases the diffusion coefficient increases. The dependence of the diffusion coefficient on temperature for gases can be expressed using the following equation [3]:
Where: T : Temperature (K), M : molar mass (g/mol), P : pressure (atm), : a temperaturedependent collision integral (dimensionless), D AB: diffusion coefficient (cm 2/s),
and which is the average collision diameter (Å). So it can be seen that for gases the relation between diffusion coefficient and temperature is given by:
An approximate dependence of the diffusion coefficient on temperature in liquids can often be found using Stokes-Einstein equation, which predicts that:
Where: T1 and T2 denote temperatures 1 and 2, respectively, D is the diffusion coefficient (cm²/s), T is the absolute temperature (K), and is the dynamic viscosity of the solvent (Pa·s) So it can be seen that for liquid the relation between diffusion coefficient and temperature is given by:
Finally The diffusion coefficient in solids at different temperatures is related to temperature by the following equation:
Where: D is the diffusion coefficient, D ois the maximum diffusion coefficient (at infinite temperature), E Ais the activation energy for diffusion in dimensions of (energy per amount of substance), T is the temperature (K or oR), and R is the gas constant in dimensions of (energy per temperature per amount of substance). The effect of concentration on the diffusion coefficient can be seen from the equation:
From this equation it can be seen that as the concentration gradient increases the diffusion coefficient increases. Also, the values of liquid diffusion coefficients r eveals that they depend on concentration due to the changes in viscosity with concentration and the changes in the degree of ideality of the solution.
References
[1]Welty, J. R., Wicks, C.E. (1969). Fundamentals of Momentum, Heat, and Mass Transfer.USA: Wiley. [2] http://www.cco.caltech.edu/~brokawc/Bi145/Diffusion.html [3] E.L. Cussler, "Diffusion. Mass Transfer in Fluid Systems", 2nd edition, Cambridge University Press, 1997
