Homogeneous isothermal

A mathematical model for this polymerization reaction based on homogeneous, isothermal reaction is inadequate to predict all of these effects, particularly the breadth of the MWD. For this reason a model taking explicit account of the phase separation has been formulated and is currently under investigation. 

The results in this chapter are restricted in large part to steady-state, homogeneous, isothermal systems. More general theories can be developed. The next few sections briefly outline some extensions of residence time theory. 

Consider the homogeneous isothermal gas phase decomposition of CH3CHO. 

Provided that the polyelectrolyte chains are much larger than the solvent molecules, the solvent can be treated as a homogeneous isothermal viscous... 

In a homogeneous isothermal liquid polymerization, 20% of the monomer disappears in 34 minutes for initial monomer concentration of 0.04 and also for 0.8 mol/liter. What rate equation represents the disappearance of the monomer ... 

Kattawar, G. W., and M. Eisner, 1970. Radiation from a homogeneous isothermal sphere, Appl. Opt., 9, 2685-2690. 

However, electroneutrality implies that vyz + v2z2 = 0, so I = zxF3x + z2FJ2, where J, and J2 are the absolute flows, J] = c, v, and J2 = c2v2, respectively. Ohm s law holds for homogeneous, isothermal salt solutions, therefore, the relation between the current and the electric field intensity may be reduced to... 

Tronconi et al. [52] have validated against experiment a more complex model, accounting also for the reaction and diffusion of NO and NH3 inside the porous walls of homogeneous isothermal honeycomb SCR catalysts. The model equations are as follows ... 

In a homogeneous isothermal flow reactor, the rate of change of the species concentrations at a constant volume can simply be represented as... 

Another example of an oscillating reaction is provided by the Bray reaction, the first identified homogeneous isothermal chemical oscillator, which is a complex reaction of iodate, iodine, and hydrogen peroxide. As hydrogen peroxide decomposes to oxygen and water, the resulting rate of the evolution of oxygen and I2 vary periodically. 

As a consequence, a pseudo-homogeneous isothermal model has been assumed, consisting of mass balance equations on the gas phase and on the active centres The model equations are the following ... 

In each case of Section 4.3 the reactor models obtained on the basis of the mixing models were left in general form, with specific results for concentration or conversion versus reactor size depending on the type of rate law to be used. In the following we shall derive a number of expressions for particular rate laws which relate conversion, reactor size, and residence time for the particular case of homogeneous, isothermal ideal reactors. 

Although oscillatory behavior can be seen in many chemical systems, we shall concentrate primarily on homogeneous, isothermal reactions in aqueous solution. In later chapters, we shall broaden our horizons a bit. While the study of oscillating reactions did not become well established until the mid-1970s, theoretical discussions go back to at least 1910. We consider here some of the early theoretical and experimental work that led up to the ideas of Prigogine on nonequilibrium thermodynamics and to the experimental and theoretical work of Belousov,... 

Although the above simple illustration of the concept for a homogeneous isothermal lumped system is applicable to other more complicated systems, the situation for catalytic reactors is much more involved because of the complexity of the intrinsic kinetics as well as the complex interaction among reactions, heat release (or absorption), and mass and heat diffusion inside the reactor. For example, many catalytic and biocatalytic reactions show nonmonotonic dependence of the rate of reaction on reactant concentrations. For example, the hydrogenation of benzene to cyclohexane over different types of nickel catalyst has an intrinsic rate of reaction of the form... 

FIG. 26 Comparison of steady-state or plateau elongational viscosities of polyethylene melts from homogeneous isothermal elongation tests (unfilled s mibols) and transient tensile viscosities evaluated from converging flow (filled symbols). Unfilled symbols with tick denote tensile creep measurements. T = 150°C. 

In this section we ouUine the use of RTDs to predict the yield of homogeneous isothermal reactions, based on the pioneering treatments of Danckwerts (1953) and Zwietering (1959) and a proof of optimality due to Chauhan et al. (1972). If there are multiple reactants, the feed stream is assumed to be premixed. 

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