Second-order unmixed

The binary polymer blend exliibits a second-order unmixing transition. Close to the critical temperature the... 

SECOND-ORDER (UNMIXED) AND UNMIXED BIMOLECULAR REACTIONS... 

It is possible to combine the two equations in one hyperbolic second-order PDE. This has the property of finite wave speed, both boundary conditions at the entrance are easily calculable, and it accounts for some of the phenomena of unmixing. This is not the place to treat this model in detail and, indeed, it is still finding fruitful applications.5 Another method for a hyperbolic model is to be found in [173]. 

Figure 10, Equivalence between the C-D model and the IEM model. Reactor with two inlets having different RTDs equivalent to that of 2 and 6 tanks in series, respectively. Unmixed feedstreams of A and B (equal flowrates), second-order reaction, =8, ...

Fig. 13. Comparison of conversion for a bimolecular second-order reaction in a homogeneous tubular reactor for premixed and unmixed reactant feeding.

To quantify the effect of the incomplete mixing on reaction rates in the front of the reactor channel, this same simulation was repeated assuming second order kinetics (first order in each of the two components) and Cjj = C2j = 100 mol m. A rate constant of 1.0 X 10 m moh s was used to give an intermediate level of conversion (near 25%). This case can be compared with a simulation in which the inlet boimdary conditions were changed to assume complete mixing (50 mol m of each component across the entire inlet cross section). The axial fractional conversion profiles for these two cases (unmixed and premixed feeds) are shown in Fig. 13.4, where the unmixed feed curve is the average of the calculated values for the two components. The computed conversions for the two components were... 

Second-Order Reactions with Unmixed Feed... 

This equivalence also holds for predicting chemical conversion as can be seen in Fig. 12 where reaction extent was calculated for a second order reaction with unmixed feedstreams. The agreement is excellent. More generally, equivalence relationships can be established between all one-parameter micromixing models. For instance, the various models cited above yield approximately the same results under the equivalence conditions ... 

Figure 13 shows an example of results obtained with the lEM-model in a CSTR for zero-order and second-order reactions (unmixed and premixed feed). The following conclusions can be drawn from such simulations ... 

Patterson, G. K. (1973). Model with no arbitrary parameters for mixing effects on second-order reaction with unmixed feed reactants, in Fluid Mechanics of Mixing, E. M. Uram, and V. W. Goldschmidt, eds., ASME, New York, pp. 31-38. 

The first situation involves two algebraic equations, the second involves an algebraic equation (the mixed phase) and a first-order ordinary differential equation (the unmixed phase), and the third situation involves two coupled differential equations. Countercurrent flow is in fact more compHcated than cocurrent flow because it involves a two-point boundary-value problem, which we will not consider here. 

With this object, we have chosen experimental conditions in which micromixing effects were expected to be a maximum i.e. a continuous stirred reactor and a rapid liquid phase reaction close to zero order with unmixed feed of reactants. Experimental parameters were adjusted to such values that the space time, the reaction time and the micromixing time was of the same order of magnitude, ranging from 1 to 10 seconds. Micromixing effects were thus clearly and reliably observed. 

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