Chemical reactions in chaotic flows

Muzzio, Fernando J.; Liu, M.

doi:10.1016/s0923-0467(96)03108-9

Cited by 43 publications

(46 citation statements)

References 53 publications

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“…[9], where finite reaction rates are considered, but for a parallel-competitive reaction scheme). These simulations [6] have demonstrated the influence of the mixing on the yield: in general a chaotic fluid flow contains regions of both regular and chaotic motion, and each affect the progress of the reactions in different ways. The regular regions act as poorly mixed reservoirs for the reactants, allowing only a slow leakage out into the chaotic region, through diffusion.…”

Section: Introductionmentioning

confidence: 92%

“…When the reactions take place in a liquid phase that is stirred continuously, their progress correspondingly depends strongly upon the details of the fluid mechanical mixing [1][2][3][4][5][6][7][8][9]. In this paper, we examine the influence of fluid mixing upon a competitiveconsecutive (or series-parallel) reaction, A + B → R, B + R → S [1], that takes place in a two-dimensional, laminar, chaotic fluid flow.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we compare full twodimensional simulations with corresponding one-dimensional simulations of lamellar models (of varying degrees of sophistication), to evaluate the lat-ter. It is not a priori obvious how quantitatively accurate one should expect the lamellar models to be, given that they generally ignore many details of the striations generated by the flow, for instance: the curvature of the striations [22,23], the nonuniformity of the stretching [24], the nonuniformity of the striation widths [16], the presence of islands in the flow [6,9], and the continual regeneration of striations (by fluid mechanical stretching and folding, which lead to more, thinner striations, which then recombine diffusively). One would not be surprised to find that they perform well at low Péclet numbers, where diffusion rapidly homogenises the reactant distribution, and poorly at high Péclet numbers, where the flow details cited above become more significant.…”

Section: Introductionmentioning

confidence: 99%

“…Numerical simulations of the two-dimensional problem tackled here have previously been carried out by Muzzio and Liu [6] but in the special case of an infinitely fast primary reaction, rather than for the finite reaction rates contemplated here (cf. [9], where finite reaction rates are considered, but for a parallel-competitive reaction scheme).…”

Section: Introductionmentioning

confidence: 99%

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Chaotic mixing of a competitive–consecutive reaction

Cox

2004

Physica D: Nonlinear Phenomena

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The evolution of a competitive-consecutive chemical reaction is computed numerically in a two-dimensional chaotic fluid flow with initially segregated reactants. Results from numerical simulations are used to evaluate a variety of reduced models commonly adopted to model the full advection-reaction-diffusion problem. Particular emphasis is placed upon fast reactions, where the yield varies most significantly with Péclet number (the ratio of diffusive to advective time scales). When effects of the fluid mechanical mixing are strongest, we find that the yield of the reaction is underestimated by a one-dimensional lamellar model that ignores the effects of fluid mixing, but overestimated by two other lamellar models that include fluid mixing.

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Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Chaotic mixing of a competitive–consecutive reaction

Cox

2004

Physica D: Nonlinear Phenomena

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“…This spatially dependent mixing index σ(z) should be distinguished from the global mixing index σ(t) defined in equation (6). The reactants become better mixed as they go downstream.…”

Section: Steady State Mixermentioning

confidence: 99%

Design criteria of a chemical reactor based on a chaotic flow

Tang

Boozer

1999

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We consider the design criteria of a chemical mixing device based on a chaotic flow, with an emphasis on the steady-state devices. The merit of a reactor, defined as the Q-factor, is related to the physical dimension of the device and the molecular diffusivity of the reactants through the local Lyapunov exponents of the flow. The local Lyapunov exponent can be calculated for any given flow field and it can also be measured in experimental situations. Easy-to-compute formulae are provided to estimate the Q-factor given either the exact spatial dependence of the local Lyapunov exponent or its probability distribution function. The requirements for optimization are made precise in the context of local Lyapunov exponents.

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Evolution of Nonlinear Rheology and Network Formation during Thermoplastic Polyurethane Polymerization and Its Relationship to Reaction Kinetics, Phase Separation, and Mixing

Jana

2010

Nonlinear Dynamics With Polymers

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Understanding the evolution of nonlinear rheological properties during polymerization has been of significant industrial and academic interest [1]. The industrial interest originated from the design, operation, and control requirements of polymerization processes [2,3]. The industrial polymerization processes cover a broad spectrum from bulk production of thermoplastics, such as polyolefins, to production of thermosets, such as tires, comprising many simultaneous steps, such as chemical reactions and mixing, followed by compounding, molding, and cross-linking reactions [4,5]. The most relevant and widely documented rheological property for success of industrial processes is the viscosity of the polymerizing medium, which directly influences mass, heat, and momentum transfer processes. The academic interest, on the other hand, has its roots in utilizing rheology as a valuable tool to understand the properties of polymer chains whether in bulk, in solution, or in a polymerizing medium [6]. Monitoring the changes in rheological properties, such as normal stresses, relaxation times, storage, and loss moduli, which are usually nonlinear functions of time, temperature, and morphology, has undeniable significance in providing insights into structure and properties of polymers as they develop during polymerization or during shape-forming operations such as of extrusion, injection molding, casting, and film blowing, to name a few.The nonlinear rheological properties of growing polymer chains, irrespective of the growth mechanisms -such as free-radical or step-growth -are governed by similar parameters. Chemical structure, flexibility, and mobility of chains, the available free volume during polymerization, the degree of conversion, the extent of chain entanglements, the degree of phase separation, and the presence of chemical or physical cross-links are a few of the morphological features and physical phenomena [7] with strong influence on polymerization.

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Chemical reactions in chaotic flows

Cited by 43 publications

References 53 publications

Chaotic mixing of a competitive–consecutive reaction

Chaotic mixing of a competitive–consecutive reaction

Design criteria of a chemical reactor based on a chaotic flow

Evolution of Nonlinear Rheology and Network Formation during Thermoplastic Polyurethane Polymerization and Its Relationship to Reaction Kinetics, Phase Separation, and Mixing

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