DIFFUSION

 DIFFUSION:

► Diffusion is the tendency of molecules to move toward areas of lower concentration until the concentration is uniform throughout.

► FICK’S LAW OF DIFFUSION :First law of diffusion (Steady state Law)

► Adolf Fick (1955) first described the molecular diffusion in an isothermal, isobaric, binary system of components A and B.

► According to his idea of molecular diffusion, the molar flux of a species relative to an observer moving with molar average velocity is proportional to the concentration gradient in a certain direction.

► Where, JA is the molar flux of component A in the Z direction.

► CA is the concentration of A and Z is the distance of diffusion.

► The proportionality constant, DAB is the diffusion coefficient of

► the molecule A in B. This is valid only at steady state condition of diffusion.

► The Equation is called Fick’s first law of diffusion 

 

CONCEPT OF DIFFUSION 

                                                                                                            

 

A cylinder of air and a cylinder                    Bromine vapour diffuse upward    After several hours bromine     of bromine vapor are sealed together   Through air                reaches top of Colum                                      

APPLICATION OF CONCEPT/ EXAMPLES IN REAL LIFE:

·         Diffusion may occur in one phase or in both phases I all the mass transfer operations.

·         In Distillation, gas absorption, crystallisation, leaching, adsorption, extraction, drying etc.

 

 

DERIVATION OF THE EQUATION FOR STEADY STATE DIFFUSION THROUGH A STAGNANT GAS FILM.

    Assume steady state diffusion in the Z direction without any chemical reaction in a binary gaseous mixture of species A and B. For one dimensional diffusion of species A, the Equation of molar flux can be written as 

 

    For the gaseous mixture, at constant pressure and temperature C and DAB are constant, independent of position and composition. Also all the molar fluxes are constant in Equation. Therefore the Equation can be integrated between two boundary conditions as follows

 

    Where 1 indicates the start of the diffusion path and 2 indicates the end of the diffusion path. After integration with the above boundary conditions the Equation for diffusion for the said condition can be expressed as 

 

    For steady state one dimensional diffusion of A through non-diffusing B, NB = 0 and NA = constant. Therefore NA /(NA + NB ) =1 . Hence Equation becomes

 

    Since for an ideal gas C=p/RT and for mixture of ideal gasesyA=pA /P, the Equation can be expressed in terms of partial pressures as

   

    Where P is the total pressure and pA1 and pA2 are the partial pressures of A at point 1 and 2 respectively. For diffusion under turbulent conditions, the flux is usually calculated based on linear driving force. For this purpose the Equation can be manipulated to rewrite it in terms of a linear driving force. Since for the binary gas mixture of total pressure P, P-pA2=pB2.; P-pA1=pB1 ; pA1-pA2=pB2 -pB1 Then the Equation can be written as

 

 

DERIVE THE EQUATION FOR STEADY STATE EQUIMOLAR COUNTER DIFFUSION. 

    This is the case for the diffusion of two ideal gases, where an equal number of moles of the gases diffusing counter-current to each other.

     In this case NB = -NA = constant and NA+ NB = 0. The molar flux Equation at steady state can then be written as

   

    Integrating the Equation with the boundary conditions: at Z = Z1, yA = yA1; at Z = Z2 yA = yA2, the Equation of molar diffusion for steady-state equimolar counter diffusion can be represented as

   

 

It may be noted here also that molar latent heats of vaporization of A and B are equal.