Evaluation of Mass Transfer Coefficient of Gas Absorption into Falling Liquid Film

The analytic, open-form solution for the steady-state, 2-dimensinal partial differential equation describing the concentration profile for the gas solute in a falling liquid film flowing under a steady-state laminar condition was shown. The overall mass transfer coefficient, c k , for a binary diffusion system, was evaluated in light of the analytic solution and was tested for oxygen absorption into falling water film. c k was expressed as a function of Reynolds number, Peclet number for mass transfer, and geometrical properties of the film. A case study of O2/water system was examined to validate the mass transfer based on the derived model for c k versus that given by the bulk terms. It was found that the estimated value of c k predicted a mass transfer rate that has about 10 % percent relative error (PRE) compared with that given by the convective mass transfer. SYMBOLS USED CA: [mol L-1] concentration of solute (dissolved gas) A in falling liquid film; CAi: [mol L-1] interfacial concentration of A; CAo: [mol L-1] inlet concentration of A; AL C : [mol L-1] the average outlet concentration of A: DAB: [m2 s-1] diffusivity of solute A in medium B; Deq: [m] the equivalent diameter for a non-circular area, defined as four times the hydraulic radius; c k : [m s-1] the overall mass transfer coefficient; L: [m] length of the falling liquid film; NA: [mol m-2 s-1] the molar flux of solute A; A n& : [mol s-1] the molar flow rate of A absorbing into the falling liquid film; M Pe N : [dimensionless] Peclet number for mass transfer defined as: 4 M y Pe Re Sch AB u N N N D δ = × = ; NRe: [dimensionless] Reynolds number; a dimensionless group; Sch N : [dimensionless] Schmidt number defined as: / Sch AB AB AB N D D D μ μ ρ ν ρ = = = ; uy: [m s-1] the y-component velocity of the falling liquid; y u : [m s-1] the average y-component velocity of the falling liquid; W: [m] the width of the falling liquid film GREEK SYMBOLS Γ: [kg m-1 s-1] the mass velocity (i.e., mass flow rate of falling liquid per unit width of solid boundary); δ: [m] the liquid film thickness; η : [dimensionless] defined as: 8 1 3 M Pe N L η δ = ×       ; θ: [dimensionless] dimensionless concentration of A, defined as: