Finally, it is worth mentioning that though there have been attempts to define certain terms, it has not really worked in many cases. Thus, the literature, the users and the manufacturers of equipment may equally well refer to mixing, stirring or agitation, impellers, stirrers or agitators, vessel or tank, etc. It is not the intention of the author here to try to change that rather casual usage, but to follow it.

Figure 1. A wood cut from De Re Metallica, by Agricola, 1556, showing a series of three stirred reactors (O), each with a paddle stirrer (S) driv- en by a water wheel (A) via three gear boxes (X, T) (modified from [6]).

tors by White et al. [8], who defined the power number as in Eq. (3) and essentially showed

Po = f(Re, Fr, dimensionless geometric  parameters) (4)

where Re is the Reynolds number, which physically can be considered the ratio of inertial to viscous forces, and Fr is the Froude number, the ratio of inertial to gravitational forces. The dimensionless geometric parameters refer to all dimensions, whether the impeller, the vessel or the impel- ler/vessel configuration being normalized with respect to one dimension, typically the diameter of the vessel T. They also include the number of blades on the stirrer. The approach was further developed by Hixson et al. [9]. This approach reached its peak with the work of Rushton et al. [10], which in a recent survey was considered to be one of the  21  most  influential  contributions  to  mixing research

[11]. They defined the Reynolds number as rLND2/m and the Froude number as N2D/g. The latter was particularly important with swirling flow as obtained with a centrally

placed impeller in a cylindrical vessel. However, if baffles were introduced into the vessel (Fig. 2) to prevent the swirl, the Froude number could be ignored. Once baffled, they ob- tained the standard Po versus Re plot on logarithmic coor- dinates (power characteristic) that is still used today (Fig. 3).

2 Turning the Art of Stirring into an Engineering Science

The first indication that engineering science was bringing quantitative understanding to stirring technology was in 1855. James Thompson (the brother of Lord Kelvin, after whom the SI temperature units are named) undertook a study [7] related to the efficiency of water wheels. In it, he measured the power P required to rotate a disc in water and found that

P / N3D5 (1)

or, on rearranging,

P=N3D5  ¼ const: (2)

where N was the rate of rotation of the disc (stirrer speed) and D the (stirrer) diameter. This relationship is exactly that which today gives rise to the dimensionless group, power or Newton number Po where

Po ¼ P=rL N3D5 (3)

Figure 2. Baffled stirred tank reactor. (a) Heating or cooling coil; (b) motor drive; (c) baffle (4 off); (d) gear box; (e) seal;

(f) manhole; (g) ring sparger;

(h) Rushton turbines; (i) heat- ing or cooling jacket (from [12] with permission).

Though each impeller/vessel configuration has its own power characteristic, they all have the same general shape (Fig. 3) and most importantly, for geometrically similar sys- tems, the plots are essentially independent of scale. In the laminar region (Re < ~10 to ~50),

Po = Kp/Re (5)

so   P a m,  independent   of   rL.  In   the  turbulent  region

and Po is a constant in the turbulent flow region for any particular impeller/vessel configuration (as is generally the case under realistic operating conditions in low viscosity liquids such as water). It was not until the 1930s that the power number was actually measured for stirred-tank reac-