Mixing perfect

In the second model (Fig. 2.16) the continuous well-stirred model, feed and product takeoff are continuous, and the reactor contents are assumed to he perfectly mixed. This leads to uniform composition and temperature throughout. Because of the perfect mixing, a fluid element can leave at the instant it enters the reactor or stay for an extended period. The residence time of individual fluid elements in the reactor varies. 

Although molecular diffusion itself is very slow, its effect is nearly always enhanced by turbulent eddies and convection currents. These provide almost perfect mixing in the bulk of each Hquid phase, but the effect is damped out in the vicinity of the interface. Thus the concentration profiles at each... 

If perfect mixing occurs in each stage and the solute is not adsorbed preferentially at the surface of the sohd, then the concentration of the solution in the underflow is the same as that in the overflow and... 

Determination of Crystallization Kinetics. Under steady-state conditions, the total number production rate of crystals in a perfectly mixed crystallizer is identical to the nucleation rate, B. Accordingly,... 

Preferential Removal of Crystals. Crystal size distributions produced ia a perfectiy mixed continuous crystallizer are highly constraiaed the form of the CSD ia such systems is determined entirely by the residence time distribution of a perfectly mixed crystallizer. Greater flexibiUty can be obtained through iatroduction of selective removal devices that alter the residence time distribution of materials flowing from the crystallizer. The... 

Clearly, the form of the population density function resulting from a clear-Hquor advance system is identical to that expected from perfectly mixed systems in which T., is identical to T,. Unless the increase in magma density associated with clear-Hquor advance results in significant increases in... 

At the bottom of the column, a liquid sump of constant and perfectly mixed molar liquid holdup Mg is provided. A portion of the hq-uid flowing from this sump passes to a thermosiphon reboiler, with the... 

The liquid holdup on each of the Nt eqmlibrium trays is assumed to be perfectly mixed but will vary as liquid rates leaving the trays vary. Vapor holdup is assumed to be negligible everywhere. Tray molar vapor rates V vary with time but at any instant in time are eveiy-where equal. 

Equations for the decanter are as follows if it is assumed that (1) there are constant holdups in the decanter of both phases in the same ratio as the ratio of the flow rates leaving the decanter, (2) there is a constant decanter temperature, and (3) the two hquid phases in the decanter are in physical equilibrium and each is perfectly mixed. 

This is an old, familiar analysis that applies to any continuous culture with a single growth-limiting nutrient that meets the assumptions of perfect mixing and constant volume. The fundamental mass balance equations are used with the Monod equation, which has no time dependency and should be apphed with caution to transient states where there may be a time lag as [L responds to changing S. At steady state, the rates of change become zero, and [L = D. Substituting ... 

Figure 24-23 is a sketch of continuous culture with recycle. The symbols for flow rates and organism concentrations are F and X, respec tively Assuming perfect mixing and steady state so that the derivatives can be set to zero, mass balances lead to ... 

The growth of long chains ( > 10 ) in the perfectly mixed 1 1 crystals of ethylene with chlorine and bromine at 20-70 K was studied in detail by Wight et al. [1993]. Active radicals were generated by pulse photolysis of CI2 or Br2. The rate constant was found to be /Cc = 8-12s below Tc = 45 K. The chain grows according to the well known radical mechanism including the reactions... 

The material balance for steady-state operation of a perfectly mixed reactor is ... 

This program helps calculate the rate of methanol formation in mol/m s at any specified temperature, and at different hydrogen, carbon monoxide and methanol concentrations. This simulates the working of a perfectly mixed CSTR specified at discharge condition, which is the same as these conditions are inside the reactor at steady-state operation. Corresponding feed compositions and volumetric rates can be calculated from simple material balances. 

Perfect mixing is assumed. The temperature profile of the tank with respect to time is then given by the following expression reported in the literature. 

Assume perfect mixing in the reactor, and because it is operated adiabatically (i.e., no exchange of heat between the reactor and its environment), Q = 0 and equation 6-53 becomes... 

Consider a first order, exothermic reaction (aA —> products) in a CFSTR having a constant supply of new reagents, and maintained at a steady state temperature T that is uniform throughout the system volume. Assuming perfect mixing and no density change, the material balance equation based on reactants is expressed as uC g = +... 

In using the normalized distribution function, it is possible to directly compare the flow performance inside different reactors. If the normalized function E(6) is used, all perfectly mixed CSTRs have numerically the same RTD. If E(t) is used, its numerical values can change for different CSTRs. 

If die equivalent number of perfectly mixed stages N is not an integer, let i be an integer slightly smaller dian N. A fraction 0 < h < 1 is defined as... 

Equation 9-15 gives the conversion expression for the second order reaction of a macrofluid in a mixed flow. An exponential integral, ei(a), which is a function of a, and its value can be found from tables of integrals. However, the conversion from Equation 9-15 is different from that of a perfectly mixed reactor without reference to RTD. An earlier analysis in Chapter 5 gives... 

The name continuous flow-stirred tank reactor is nicely descriptive of a type of reactor that frequently for both production and fundamental kinetic studies. Unfortunately, this name, abbreviated as CSTR, misses the essence of the idealization completely. The ideality arises from the assumption in the analysis that the reactor is perfectly mixed, and that it is homogeneous. A better name for this model might be continuous perfectly mixed reactor (CPMR). 

In rooms where energy is introduced primarily by supply air jets, air distribution methods are referred to as mixing type. With a perfect mixing-type air distribution, airflow pattern and air velocity at any point in the room are... 

FIGURE 7.IS Exhaust from a room with perfect mixing. The tocacion of exhaust openings is not important. 

The complex of coefficients having constant value (1 + cr)6/ 2 cthermal characteristic of the diffuser jet, K2, and characterizes the temperature decay along the air jet. Assuming perfect mixing in the room (i.e., 0 ), 0 can... 

In a room with perfect mixing of the air, it theoretically does not matter where the exhaust opening is located (Fig. 8.40). In practice, air seldom mixes as completely as in theory. One reason for this is temperature differences or density differences. The contaminants are often warmer than the room air, and in some cases the density of the contaminant itself differs from the air density. These topics are treated in the later paragraphs. This paragraph will focus on isothermal, non-buoyant cases. 

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