Mixers dimensionless groups

Heat Transfer In general, the fluid mechanics of the film on the mixer side of the heat transfer surface is a function of what happens at that surface rather than the fluid mechanics going on around the impeller zone. The impeller largely provides flow across and adjacent to the heat-transfer surface and that is the major consideration of the heat-transfer result obtained. Many of the correlations are in terms of traditional dimensionless groups in heat transfer, while the impeller performance is often expressed as the impeller Reynolds number. 

Mixers. See also Agitation blend time, 290 dimensionless groups, 290 gas dispersion, 296-301 in line type, 300,301 liquids, power and speed need, 293,295 powders and pastes, 301,303,304 power number, 290-292 quality characterization, 290-292 suspension of solids, 295-299 tank desien. 287.288 Moisture c tent, critical, 237 Molecular distillation, 425-427 equipment sketches, 427 Hickman still, 427 operating conditions, rate of evaporation. 

Dimensionless groups are Reynolds - Kt nD pIt], Froude - Fr = r Dg/ g, while 5, to S are geometrical similarity ratios. The notations are - mixer diameter,... 

In most mixing investigations it has been found that the prediction of power requirement can usually be dealt with satisfactorily by empirical relationships, usually based on dimensionless groups, derived from experimental results. The description of mixing rate is usually much more difTicult, as are the experiments, while scale-up has presented problems in most areas of mixing. For the static mixer the major variables requiring attention in any study are flow rate and viscosity, bearing in mind that in many processes there will be two or more fluids involved and that each inlet stream may have a different flow rate and viscosity. 

The two dimensionless groups are based on the empty pipe diameter (D,), including the value of u, which is a superficial velocity. In principle it only requires one value of AP to be measured at one value of v, to define the product Re for any static mixer but a range of measurements can give useful information regarding the slight variability of tf> Re and also the upper limit of the laminar flow regime in terms of Re ... 

Sulzer mixers in terms of the Newton number and other dimensionless groups defined in terms of hydraulic diameter (for the SMV element D,/D, %4.2)... 

For a simple vertical mixer design, the key dimensions are the impeller diameter D, which is usually equal to the bowl diameter, the chopper diameter Dc, and the fill height H. The dimensionless groups that need to be held constant for geometric similarity are... 

The second important requirement is to maintain constant key dimensionless groups that control the important granulation rate process of most interest during scale. This is somewhat easier to do in fluidized beds than in high-shear mixers. 

Scale-up in fixed bowl mixer-granulators has been studied by Rowe and Cliffs group using the classical dimensionless numbers of Newton (power), Reynolds, and Froude to predict the end-point in geometrically similar high-shear Fielder PMA 25, 100, and 600 L machines. 

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