Mass Transfer: Molecular Diffusion flux (JA) and Total Diffusion Flux (NA)

Diffusion is the process of transfer of molecules when there is a concentration difference. Diffusion can occur in two ways; one is molecular diffusion and other is convective diffusion. In molecular diffusion the driving force is concentration difference while in convective diffusion there is bulk velocity of particles and medium.

For example (assume unidirectional diffusion) if a person has put perfume on his body, when he and observer both are either stationary or moving with same velocity, then the flux of perfume molecules with reference to observer is due to concentration difference i.e. molecular diffusion flux (J_A) and if the person is moving and the observer is stationary then diffusion of molecules is observed having both the effects: molecular as well as convective (due to motion of person) i.e. total flux (N_A).

Total Flux = molecular flux + convective flux

N_A          =          J_A + c_A.v

c_A.v_{A     =}              c_A(v_{A –} v) + c_A.v

Where v_A is the avg. velocity of all A like species and v is the avg. velocity of the carrier relative to observer means average of carrier velocity and velocity of A molecules.  In the above example, v_A is the velocity of all perfume particles and v is the avg. velocity of the person and perfume particles. So, the difference c_A(v_{A –} v) corresponds to molecular diffusion and c_A.v corresponds to convective diffusion. If a person is moving with perfume put on body and other person is stationary with perfume put on his body, then the difference between the two fluxes corresponds to convective diffusion. The other example can be taken of the fragrance particles of air freshener, the particles are diffusing through molecular diffusion and if air blows, then there will be combined effect of molecular diffusion and convective diffusion.

In distillation column, the flow of liquid and vapor streams leads to molecular as well as convective diffusion.