C18_Time_Dependent___2D_Component_Transfer_2

# C18_Time_Dependent_ - Time Dependent 2D Component Transfer Applications of isothermal equation of continuity of components Steady state gas

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Time Dependent & 2D Component Transfer Applications of isothermal equation of continuity of components Steady state gas absorption by diffusion into a falling liquid film - Assumption: constant diffusivity, diffusion is negligible in z - Non-zero components: u z , dc A /dz, dc A /dx, dc B /dz, dc B /dx - Balance for component A Recall that 2 max 1 z x uu δ ⎛⎞ =− ⎜⎟ ⎝⎠ 2 * 2 A A z cc uD z x ∂∂ = 2 2 max 2 1 A A x z x ⎡⎤ ⇒− = ⎢⎥ ⎣⎦ with boundary conditions 0 00 0 0 A AA A A A zx x c c N D x == = = =

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Time Dependent & 2D Component Transfer Applications of isothermal equation of continuity of components Steady state gas absorption by diffusion into a falling liquid film This equation could be solved using the method of variable combination 0 max 1 4/ A A c xx erf erfc c Dz u =− = The local flux of gas at a given z position on the gas-liquid interface 0 0 0 A AA x x uD c ND c x z π = = ⎛⎞ = ⎜⎟ ⎝⎠ called penetration model Total flux over the interface can also be calculated * . x x Dx t α ⎡⎤ + ∇= ⎣⎦ u
Time Dependent & 2D Component Transfer Applications of isothermal equation of continuity of components Dissolution and diffusion from solid surface into a falling liquid film - Assumption: constant diffusivity, diffusion is negligible in z - Non-zero components: u z , dc A /dz, dc A /dx, dc B /dz, dc B /dx - Balance for component A for a short exposure time Due to the coordinate change 2 2 2 2 z gy y xy u ρδ δ μδ ⎛⎞ =− = ⎜⎟ ⎝⎠ 2 2 AA cc ay D zy g a μ ∂∂ = = For the region very close to the surface () 2 2 2 z yy u a y δδ >> = =

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## This note was uploaded on 09/01/2011 for the course PGE 312 taught by Professor Peters during the Fall '08 term at University of Texas at Austin.

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C18_Time_Dependent_ - Time Dependent 2D Component Transfer Applications of isothermal equation of continuity of components Steady state gas

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