Second‐order chemical reactions in a nonhomogeneous turbulent fluid

Abstract

Very rapid, ropid, and slow second-order reactions were studied in an isothermal turbulent flow reactor. The two aqueous reactant solutions were separately introduced through many alternote jets and the reaction took place in the resulting nonhomogeneous mixture. Very rapid reactions were diffusion controlled and were in agreement with earlier theory. All reactions followed second-order rote laws based on time average quantities. The apparent reaction velocity constant was controlled by the mixing for very rapid reactions, by the chemical kinetics for slow reactions, ond by both mechanisms for ropid reactions.When a homogeneous chemical reaction takes place in a turbulent fluid the local instantaneous rate of reaction can be assumed to be described by the normal laws of homogeneous chemical kinetics. However, the local time average rate of reaction, r,, the mean rate, may be greater than, equal to, or less than the homogeneous rate at the local time average concentration, the homogeneous mean rate. Although the above statements are true whether or not the system is isothermal, in this paper only isothermal situations are considered.For the purposes of this discussion a homogeneous solution or mixture is one in which the RMS concentration fluctuations of all species are zero. The mean rate obviously equals the homogeneous mean rate in homogeneous solutions and this is true even in nonhomogeneous solutions if the reaction is first order.In nonhomogeneous solutions the mean rate of a type I second-order reaction, A -+ A + product, is greater than the homogeneous mean rate, while the mean rate of a type I1 second-order reaction, A + B + product, may be greater or less than the homogeneous mean rate, depending upon how the reactants are introduced; greater if the reactants are premixed, less if they are not. (The above assertions are easily justified by examining the appropriate time average expressions and noting that premixing gives a positive correlation between the fluctuating reactant concentrations. while lack of premixing gives a negative correlation. ) The deviation from the homogeneous mean rate depends upon the rate of the reaction relative to the rate of mixing. Three arbitrary divisions are convenient: very rapid reactions, rapid reactions, and slow reactions. They correspond, respectively, to reaction rates much faster than the rate of mixing, reaction rates of the same order as the rate of mixing, and reaction rates much slower than the rate of mixing. The latter case is the simplest, and most reactor design studies have been concerned with this problem. It is under reasonably good control. [It is noted that in the flow methods of studying rapid chemical reactions in solution ( 1 4 ) , the reactions are slow in the above sense, since the experiments are designed to make the mixing much faster than the reaction.]Very rapid and rapid reactions present an entirely different problem, for here the detailed turbulent motion can have a profound effect on the rate of reaction, es- pecially with type I1 second-or...

Turbulent reactive mixing of reversible reactions

“…By arguments similar to those used for nonpremixed irreversible reaction (Vassilatos and Toor, 1965;Bourne and Toor, 1977) we expect uin to be negative, and because XL = X b , u:D must be positive.…”

Turbulent mixing with multiple second‐order chemical reactions

“…Modeling using this closure was tested by direct experimentation on acid-base reactions in one idealized reactor design. The experimental conversion measurements were made by a heat balance using the heat of reaction (Ma0 and Toor, 197.0, 1971;Vassilatos and Toor, 1965). The velocity field was measured by conventional anemometer methods and the conversion accurately predicted from these results by McKelvey et.…”

An experimental study of reactive turbulent mixing

“…Keeler,et al ((et 5), and Vassilatos and Toor (ref. 6) have utilized very fast, acid-base neutra i ization reactions for the study of turbulent-chemica' interactions in one dimensional flow experi•-mP r tts.…”