Ideal mixer

Between 1 s and 1 min specific contact time, conduction heat-transfer performance decreases theoretically as the 0.29 power of contact time. This is consistent with empirical data from several forms of indirect-heat dryers which show performance variation as the 0.4 power of rotational speed (21). In agitator-stirred and rotating indirect-heat dryers, specific contact time can be related to rotational speed provided that speed does not affect the physical properties of the material. To describe the mixing efficiency of various devices, the concept of a mixing parameter is employed. An ideal mixer has a parameter of 1. 

A comparison of the various types of reactor concepts, in a general sense, is actually only possible between the batch, the CSTR and the PFR. The cascade of CSTRs, depending on the number of vessels n in the series, more or less behaves as an ideal mixer for n->l or an ideal plug flow for n- - . The fed-batch reactor is more difficult to situate. Although the concentration of compounds important for the rate of reaction can be controlled optimally during the whole fed period, the reactor volume is only partially utilized, especially in the beginning. Nevertheless, this reactor concept certainly has decisive advantages in many cases, as shown by the fact that it is one of the most widely used. 

It will be assumed that the well-known age distribution for an ideal mixer also holds for the age distribution in the dispersed phase, which assumption is allowed if the total number of drops is large enough and there are no dead corners or short circuiting in the reactor (only microscale segregation). 

Effect of Orientation on Distributive Mixing — Erwin s Ideal Mixer... 

Using this concept, Erwin [9] demonstrated that the upper bound for the ideal mixer is found in a mixer that applies a plane strain extensional flow or pure shear flow to the fluid and where the surfaces are maintained ideally oriented during the whole process this occurs when N = 00 and each time an infinitesimal amount of shear is applied. In such a system the growth of the interfacial areas follows the relation given by... 

In Erwin s ideal mixer, the amount of mixing increases in an exponential fashion, compared to a linear increase, if the orientation of the fluids interfaces remain undisturbed. 

The function SDF depends on mixer geometry operating conditions and the rheological properties of the fluid. Next, we derive the SDF for some simple idealized mixers. 

Hydrodynamic Analysis of an Idealized Internal Mixer Consider the idealized mixer shown in the accompanying figure, consisting of two concentric cylinders in relative motion with a step change in clearance. Calculate the mean shear stress in the narrow gap. 

Continuous stirred tank reactor Sometimes called a continuous-flow stirred-tank reactor, ideal mixer, or mixed-flow reactor, all describing reactors with continuous input and output of material. The outlet concentration is assumed to be the same as the concentration at any point in the reactor. 

Kinetic equations have been derived for the calculation of rate constants from measured absorbancies, the flow rate, and known spectral data for reactants and products [4]. For an ideal mixer, the expression for the first-order rate constant is given by Eq. 1,... 

The ideal mixer should rapidly produce a complete blend with as gentle as possible a mixing action to avoid damage. It should be easily cleaned and discharged, be dust-tight, and require low maintenance and low power consumption. 

Residence time distribution experiments have shown that the reactor behaves almost like a plug flow tubular reactor with a small dispersion [6]. The RTD can be described using a tanks in series model with 35 ideal mixers. As the simulated reactor behaviour based on the kinetic model is only slightly influenced by the number of ideal mixers for more than 8 tanks, this value was used for all simulations in order to reduce the calculation time needed for parameter optimisation. 

The Peclet number NPe represents the effect of longitudinal backmixing. Backmixing can be neglected when the Peclet number is very large (Npe 1). In the extreme case of pure plug flow, the Peclet number Npe = when Npe = 0, the entire flow channel acts as an ideal mixer. 

According to Eq. (4.10.123), the empty spaces of a packed bed with a gas flow can be regarded as ideal mixers, and each particle layer acts as one stirrer. Consequently, for a ratio of tube length to particle diameter of more than 40 (cascade with N = 40), a fixed bed can be regarded as an ideal plug flow reactor (Section 4.10.2.3). For liquids, similar consideration leads to a tube length of 160 particle diameters to reach almost plug flow behavior. 

Another, more recently developed design is shown in the Figure 3[16]. The detector body consists of Perspex. The detection occurs at DME in a cylindrical space with a volume of about 1 pi. The detector exhibits good geometry of the electrodes, while into the vertical side channel a third electrode can be inserted. Standard deviation (which is for ideal mixer conditions equal to the response volume) was found to be 10-30 pi. 

Table 2 also shows that the number of ideal mixers is so large that solids mixing in axial direction can be neglected. It appears that the number of mixers is of the same order of magnitude as the average number of times a particle rolls down the surface of the solids bed. 

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