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Lecture 5 Diffusion through a Falling Film

Lecture 5 Diffusion through a Falling Film - Lecture 5...

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2/27/2012 1 Lecture 5: Diffusion through a Falling Film • Diffusion in a falling film of liquid. - A physical description of the problem - Simplification of the governing equations - Calculation of C A (x,z) and the flux. 1 Mass Transfer Operations Involving Diffusion in Fluids in Laminar Flow Fluid Flowing Down a Vertical Surface Fluid Flowing through a Tube or a Pipe. Oxygenation of a Fluid Gas A Liquid Wall Liquid Pipe Fouling Or a column, where curvature can be neglected (Wetted Wall Column)

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2/27/2012 2 Velocity Profile when Fluid is Flowing Down a Wall by Gravity z x 0 Back in fluids….you learned that the velocity of a fluid flowing down a wall by gravity: • Varies with x… • In fact, the profile is parabolic… v z = v MAX 1 - x δ ( 2 δ • Is laminar… Liquid Wall Pure Gas A z x 0 δ Liquid B The Wall z = 0 x 0 c A = 0 z 0 x = 0 c A = c A 0 • As soon as the gas and liquid contact one another at the top of the column, “A” dissolves in liquid B until equilibrium is achieved. • This relationship is maintained as the water flows down the column. • We will assume here that diffusion does not disrupt velocity profile (it is still parabolic). • So, A is moving in x by diffusion, and it is moving downstream in z by the fluid due to gravity. • Initially there is no A in liquid B.
2/27/2012 3 Pure Gas A z 0 δ Liquid B The Wall x Knowing that the concentration is constant at the interface between the gas and liquid, how, if at all, will the concentration of A in liquid B will vary with position “x” as the fluid moves down the wall from z = point 1 to z = point 2. 0.0 0.2 0.4 0.6 0.8 1.0 0 1 2 3 4 5 Distance into Film (cm) 0.0 0.2 0.4 0.6 0.8 1.0 0 1 2 3 4 5 Distance into Film (cm) 1 2 1 & 2 2 1 (a) (b) c A c A 0 c A0 Assume steady-state.

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