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et al., 1985; Higbie, 1935) may suggest that a surface renewal
Sh = a Sc˛ × Reˇ (4)
The present experimental data will be used to obtain the values of a and ˇ in the above dimensionless mass trans- fer equation. Following previous theoretical and experimental
mechanism contributes in enhaning the rate of mass transfer at the rotating cylindrical blade. During rotation, each blade contacts a fresh solution for a time tc given by
db
mass transfer studies, Sc exponent ˛ was fixed at the value
0.33 (Walsh, 1993; Incropera and De Witt, 1980). Fig. 5 shows
tc = V
(7)
the effect of impeller rotation speed on the mass transfer coef- ficient, the data fit the following equation:
K = a N0.42 (5)
(where v = ωr, ω = 2wN/60).
During this contact time unsteady state diffusion takes place between the fresh solution and the impeller blade according to the following equation:
The increase in K with impeller speed is attributed to the decrease in the average developing diffusion layer thickness on each rotating blade as a result of the decrease in the over-
lying developing hydrodynamic boundary layer thickness. It is also possible that recycled flow induced by impeller rota- tion in the cylindrical container contribute to enhancing the rate of mass transfer at the rotating impeller. Moo-Young et al. (1972) who studied the effect of impeller geometry on the mix- ing efficiency of agitated vessels found that an impeller with a single cylindrical blade induces radial flow pattern, this was confirmed in the present work by using polystyrene particles as a tracer (Fig. 6).
Fig. 7 shows the effect of blade length (impeller diameter) on the mass transfer coefficient, the data show that the mass transfer coefficient increases with increasing blade length probably because of the increase in the average linear velocity
(V) with increasing the distance from the center of the impeller (r) [V = ωr, ω = 2wN/60].
An overall mass transfer correlation was envisaged in terms of the dimensionless groups Sh, Sc and Re, Fig. 8 shows that the present data for the conditions 1735 < Sc < 4032, 6300 < Re < 3200 fit Eq. (6) with an average deviation of ±13.8%.
Sh = 0.429 Sc0.33 Re0.42 (6)
The N exponent 0.42 in Eq. (5) which is a fair agreement with the value 0.5 predicted by the surface renewal theory (McCabe
With the boundary conditions
C = Ci for y = 0 at t > 0
C = Cb for y → ∞ at t > 0
C = Cb for y = 0 at t = 0
-1.7
-1.9
-2.1
-2.3
-2.5
-2.7
-2.9
1.7 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7
Log N (rpm)
Fig. 7 – Effect of cylinder blade length on the mass transfer coefficient.
Fig. 8 – Overall mass transfer correlation for single impeller.
Integration of the above equation leads eventually to the following equation (McCabe et al., 1985; Higbie, 1935):
. D .0.5
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