PTEL Chemical Mass Transfer Oeration MODULE : DIFFUSIO LECTURE O.. STEDY STTE MOLECULR DIFFUSIO I FLUIDS UDER STGT D LMIR FLOW CODITIOS.. Steady state diffusion through a constant area Steady state diffusion through a stagnant gas film ssume steady state diffusion in the Z direction without any chemical reaction in a binary gaseous mixture of secies and. For one dimensional diffusion of secies, the Equation of molar flux can be written as dy CD y ( (. Searating the variables in Equation (., it can be exressed as dy y ( CD (. For the gaseous mixture, at constant ressure and temerature C and D are constant, indeendent of osition and comosition. lso all the molar fluxes are constant in Equation (.. Therefore the Equation (. can be integrated between two boundary conditions as follows: at Z = Z, y = y at Z = Z, y = y where indicates the start of the diffusion ath and indicates the end of the diffusion ath. fter integration with the above boundary conditions the Equation for diffusion for the said condition can be exressed as y CD ( ln (.3 ( Z Z y ( PTEL Chemical Mass Transfer Page of 5
PTEL Chemical Mass Transfer Oeration For steady state one dimensional diffusion of through non-diffusing, = 0 and = constant. Therefore /(. Hence Equation (.3 becomes CD y ln (.4 Z Z y Since for an ideal gas C and for mixture of ideal gases RT y P, the Equation (.4 can be exressed in terms of artial ressures as PD P ln (.5 ( Z Z RT P Where P is the total ressure and and are the artial ressures of at oint and resectively. For diffusion under turbulent conditions, the flux is usually calculated based on linear driving force. For this urose the Equation (.3 can be maniulated to rewrite it in terms of a linear driving force. Since for the binary gas mixture of total ressure P, P ; P ;. Then the Equation (.5 can be written as PD ln (.6 ( Z Z RT Or PD ( (.7 ( Z Z RT, M Where, is called logarithmic mean artial ressure of secies which is M defined as, M (.8 ln schematic concentration rofile for diffusion through stagnant is shown in Figure.. The comonent diffuses by concentration gradient, dy. Here flux is inversely roortional to the distance through which diffusion occurs and the PTEL Chemical Mass Transfer Page of 5
PTEL Chemical Mass Transfer Oeration concentration of the stagnant gas (, M because with increase in Z and, M, resistance increases and flux decreases..0 0 0.8, (atm 0.6 0.4 = + 0. 0 0.0 0.0 0. 0.4 0.6 0.8.0 Distance, Z (cm Figure.: Partial ressure distribution of in non-diffusing.. 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 = - = constant and + = 0. The molar flux Equation (Equation (. at steady state can then be written as D P dy (.9 RT Integrating the Equation (.9 with the boundary conditions: at Z = Z, y = y ; at Z = Z y = y, the Equation of molar diffusion for steady-state equimolar counter diffusion can be reresented as PTEL Chemical Mass Transfer Page 3 of 5
PTEL Chemical Mass Transfer Oeration D RT ( Z D RT ( Z P ( y Z ( P P Z y (.0 It may be noted here also that molar latent heats of vaorization of and are equal. So, H H, where, H and H are molar latent heats of vaorization of and, resectively. The concentration rofile in terms of artial ressure is shown in Figure...0 0.8, (atm 0.6 0.4 0. 0.0 0.0 0. 0.4 0.6 0.8.0 Z Figure.: Equimolar counter diffusion of and : Partial ressure distribution with osition PTEL Chemical Mass Transfer Page 4 of 5
PTEL Chemical Mass Transfer Oeration..3 on-equimolar counter diffusion In some ractical cases, and molecules diffuse in oosite directions at different molar velocities []. Let carbon monoxide is generated from the reaction between hot char and oxygen. The stoichiometry is as follows: C O ( CO( (. When one mole oxygen molecule diffuses towards char, two moles carbon monoxide molecules diffuse in oosite direction. Here, / and molar latent heats of vaorization are not equal. Hence, H H (. PTEL Chemical Mass Transfer Page 5 of 5