Stirrer, energy input

The conventional scale-up criteria scale-up with constant stirrer speed , scale-up with constant tip speed and scale-up with constant specific energy input are all based on the assumption that only one mixing process is limiting. If, for example, the specific energy input is kept constant with scale-up, the same micromixing behaviour could be expected on different scales. The mesomixing time, however, will change with scale-up as a result, the kinetic rates and particle properties will be different and scale-up will fail. 

If specific heat capacities can be assumed constant and the mechanical energy input by the stirrer, Wagit, is significant, the energy balance equation simplifies... 

Include any other source of heat gain or heat loss (e.g., energy input from a stirrer, heat loss from a condenser, etc.) and... 

A fermentation broth contained in a batch-operated stirred-tank fermentor, 2.4m in inside diameter D, is equipped with a paddle-type stirrer of diameter (L) of 0.8 m that rotates at a speed Af = 4s -. The broth temperature is maintained at 30 °C with cooling water at 15°C, which flows through a stainless steel helical coil that has a 50 mm outside diameter and is 5 mm thick. The maximum rate of heat evolution by biochemical reactions, plus dissipation of mechanical energy input by the stirrer, is 51000 kcal h , although the rate varies with time. The physical properties of the broth at 30 °C were density p = 1000 kg m " , viscosity p = 0.013 Pa s, specific heat Cp = 0.90 kcal kg °C , and thermal conductivity K = 0.49 kcal h m °C = 0.000136 kcals m °C . ... 

The above assumption [78] was convincingly confirmed in a stirred media mill with a perforated stirrer disc of given size (V = 5.54 1) at a constant energy input per unit mass, E/pV = 103 kj/kg. In batch-wise performed measurements, the kinetic energy of the beads has been varied by the tip speed of the perforated disk stirrers as well as by the density of the grinding media (glass, steel) and, in particular, by the bead diameter (dM = 97-4 000 pm). 

We first note that the conditions of validity of the simplified closed system energy balance equation, Equation 11.3-13, are all satisfied verify)-, moreover, since the system has constant volume and the energy input due to the stirrer is presumed negligible, W = 0. The equation therefore becomes... 

This equation relates temperature and conversion through the mole balance, 6. The energy balance for this adiabatic reaction in which there is negligible energy input provided by the stirrer is... 

The temperature inside the calorimeter depends on (a) the thermal energy input, that is ultrasonic power input W(t) plus secondary heat sources (e.g. mechanical stirrer) q(t), and (b) heat losses -k(Tt - T). The following equations can be written ... 

Two corrections to the measured energy are required. The power dissipated in the vessel by the continuously running stirrer is of the order of 100 fjiW. This causes the steady temperature of the vessel to be higher than that of the thermostat by an amount AT 0.01 K. The calorimeter therefore shows a small blank correction which is evaluated from the results of a run where the same liquid is used in both the burette and the mixing vessel. At first sight it would appear that the energy input required to maintain constant temperature in a blank run would be... 

Much of the accuracy in bomb calorimetry depends upon the care taken in the construction of the auxiliary equipment of the calorimeter, also called the addenda. It must be designed such that the heat flux into or out of the measuring water is at a minimum, and the remaining flux must be amenable to a calibration. In particular, the loss due to evaporation of water must be kept to a minimum, and the energy input from the stirrer must be constant throughout the experiment. With an apparatus such as shown in Fig. 4.30 anyone can reach, with some care, a precision of 1%, but it is possible by most careful bomb calorimetry to reach an accuracy of 0.01%. 

The decisive parameters for the final size distribution are the average number of stress events A stress of each feed particle, the stress intensity and specific energy input E . The number of stress events refers either to the rapid flow between the surface of two approaching particles or to the particle capture between two beads in contact. It increases linearly with dispersion time t and rotational speed ca of the stirrer ... 

Fig. 7 Observations on the different rate of coagulation in stirred systems under identical conditions of energy input for differently designed stirrers (after [7])...

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