化学実験法 II - kuchem.kyoto-u.ac.jp

1 14 II ( ) II 2014. 5. 15 ..1 ..1 ..1 ..2 ..2 ..3 ..4 Taylor ..4 ..4 ..5 ..6 mass transport convection dispersion X X X J x X X - 1/6 - 14 II ( )

2 D J = D c x [ ]/[ ] 2 c t = D 2c x2 1 c/ t = 0 c0 c1 L J = D(c1 c0)/L c t = D ( 2c x2 + 2c y2 + 2c z2) D 2c a X X c(a) X cs r X c(r) = D ar cs X J J = D cs/a X X X c0 0 z z = x/4Dt c(x, 0) = 0 c(0, t) = c0 c( , t) = 0 z = 0 c = c0 z = c = 0 z dcdz z t = D d2cdz2 z x2 - 2/6 - 14 II ( ) d2cdz2 + 2z dcdz = 0 dcdz = A exp( z2) A * erf(z) c0 c(z) = c0 erf(z) A = 2c0/ J = D ( c/ x) x = 0 = D t c0 z = x/4Dt 2/ 1 cm 10 1 mm mm 0.

3 00 1 v 2/ v 100 m/s 10 pm 10-9 m2/s 1 atm m 10-5 m2/s 25 C 1 atm (20 C) 109 D/ m2 s-1 105 D / m2 s-1 10 cm (10 cm)2/D 2 107 s 8 1 mm 100 mL m * erf(z) 2 2d 0 - 3/6 - 14 II ( ) 1 ms ( ) - 1/10 1/100 Taylor X 0 X X X a u t = 0 X M X Taylor c(x, t) = M/ a24 Et exp[ 4Et(x ut)2] E D au >> D E = (au)

4 248D X E D X e u eu dispersion coefficient * * Taylor E - 4/6 - 14 II ( ) mm cm/s E 10 5 m2/s m m/s E 10 m2/s 1 L /u 0. 1 m/s 1 mm2/s 10 m (10 m)2/D s cm mm m nm K 1/(1 + K) D/(1 + K) 1 + K 1 + K J = (1 + K)D t(1 + K) c0 = t(1 + K)D c0 D+ D 1.

5 1 1 c/ x V/ x - Nernst-Planck F R T = xVRTcFxcDJ xcDxcDDJ = += +)/1()/1(2 - 5/6 - 14 II ( ) 30 g/L 1 cm2 10 cm g 10 9 m2 s 1 - 6/6.