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03 Diffusion and Fluid Flow

03 Diffusion and Fluid Flow - III Diffusion and Fluid Flow...

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III. Diffusion and Fluid Flow HM 614/714 CHM 614/714 Fall 2011
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1. Diffusion and diffusion coefficient Mass transport occurs by diffusion (microscopic, random motion, on molecular scale), by convection (bulk flow, stirring, movement of segments of solution, on scale of apparatus), or by migration (movement of ions along an electric field). Forced diffusion is diffusion as a result of external force field (e.g., centrifugation). Field flow fractionation is a one-phase separation. Solutes interact strongly with field (e.g., gravity field) and move closer to the bottom wall. There is no partitioning. Separation is based on forced diffusion. * J. C. Giddings, Anal. Chem., 1981, 53, 1170A; K. D. Caldwell, Anal. Chem., 1988, 60, 959A.
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Linear diffusion Fick (1855) studied the linear diffusion phenomena. Linear (one-dimensional) diffusion: the flux of a substance O at a given location x at a time t, written as J o (x, t), is the net mass transfer rate of O in unit of amount per unit time per unit area ( e.g., mol/sec.cm 2 ). Thus flux represents the number of moles of O that pass given location per second per square cm of area a given location per second per square cm of area normal (perpendicular) to the axis of diffusion.
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Fick's first law Fick’s first law tates that the flux, is proportional to the c s st a states t at t e u , s p opo t o a to t e concentration gradient. , gradient ion Concentrat t x coefficien Diffusion rate Diffusion (1) x t) (x, C D t) (x, J o o o Fick's first law can be derived from the microscopic odel as follows model as follows. igure 1 Fluxes at point x in solution Figure 1. Fluxes at point x in solution.
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Δ x) (x N (x) N o o (2) Δ t 2 2 A 1 J o : get we x, /A N C by given is O of ion concentrat that the noting and / x by g multiplyin By o o 2 2 x (3) Δ x (x) C Δ x) (x C 2 t) (x, J - o o 2 o t x t and x allowing and t, /2 Δ x D molecule), the of nt displaceme the is x t, 2D x ( t coefficien diffusion the of definition the From 2 o o 2 Where: A = cross sectional area (cm 2 ), N o = # of moles of substance O (1). Equation obtain we zero, approach to (mol), D o = diffusion coefficient of substance O (cm 2 /sec), J o = flux (mol/sec.cm 2 ), and C o = concentration (mol/cm 3 ).
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Fick’s second law Fick's second law pertains to the change in concentration of O with time, or change of diffusion rate with distance.
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03 Diffusion and Fluid Flow - III Diffusion and Fluid Flow...

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