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Mixing 255

(a) (b)

(c)
FIGURE 10.14 Example of mixing animation by CFD for a Rushton system. (a) Perspective. (b) Top view. (c) Side view. (From Bakker, A.
et al., The Use of Large Eddy Simulation to Study Stirred Vessel Hydrodynamics, The On-line CFM Book, www.bakker.org=cfm, updated
2010 (downloaded as an Adobe Acrobat pdf file). With permission.)

element. If all but one force can be neglected then the ratio,
BOX 10.4 RUSHTON’S ROLE IN MIXING ma=F, is a particular dimensionless number with the designa-
tion of F, depending upon which force is dominant. The
The idea of similitude in mixing started in 1950 when
forces that pertain to mixing include viscous, pressure, and
J. H. Rushton and his associates published the initial
gravity; the respective dimensionless numbers are Reynolds,
results of an experimental program conducted over the
R; Euler, E; and Froude, F. These numbers are defined in
previous several years at the Mixing Equipment Com-
Table 10.2 in terms of a rotating impeller; as a note, the power
pany (Rushton et al., 1950a,b). The experiments num-
number is a form of the Euler number.
bered several thousand and involved various diameters
of tanks and impellers, different impeller types, varying
baffles sizes and numbers, various power levels, and
TABLE 10.2
different fluid properties such as viscosity and density.
Dimensionless Numbers in Mixing
The plots generated were in terms of dimensionless
(see Appendix G)
variables, e.g., the power number vs. Reynolds number
for constant geometry. This initial work was followed by Name Group Equation
a series of articles on mixing similitude and how to scale rnD 2
Reynolds number R ¼ (10.22)
up from models and limitations of scale-up (Rushton m
P
1951, 1952a,b, 1954; Rushton and Oldshue, 1953a,b). Power number (10.23)
3
rn D 5
P ¼
These works represented the first systematic studies of
2
n D
the effects of different variables on mixing regime and Froude number F ¼ (10.24)
g
power required. They remain primary references on the
topic. Later state-of-the-art books on the topic by Old-
shue (1983) and Amirtharajah and Tambo (1991) lead to where
the conclusion that mixing design remains an ‘‘art.’’ R is the Reynolds number: ratio inertia force=viscous force
3
r is the density of fluid (kg=m )
n is the rotational velocity of impeller (rev=s)
D is the diameter of impeller (m)
2
m is the dynamic viscosity (N s=m )
10.3.3.1 Dimensionless Numbers P is the power number: ratio drag force=inertia force
The dimensionless numbers involving inertia are really ratios P is the power applied to impeller (N m=s)
of the two sides of Newton’s second law, i.e., F ¼ ma,in F is the Froude number: inertia force=gravity force
2
which F is the sum of the different forces acting on a fluid g is the gravitation constant (9.806650 m=s )