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Stability analysis for Butlerov chemical reaction in batch reactor

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Abstract

In the present paper, we study the productivity of sugars, the formation of which is involved from formaldehyde through an original Butlerov chemical reaction (BCR). In order to theoretically obtain the productivity of sugars through the original BCR in the batch reactor, we analyze the ordinary differential equation (ODE) describing the dynamics of concentrations of species in the BCR with a general type of kinetics. By decomposing the whole network into some subnetworks and analyzing the stability of each subnetwork, we show that any positive solution to the ODE converges to a non-negative equilibrium point, at which the concentration of formaldehyde is zero while the concentrations of some sugars are non-zero. Our result shows the possibility that the BCR in the batch reactor produces a sugar obtained from sugar canes, and suggests the applicability to the food industry. In fact, by using a numerical simulation under the mass action kinetics, we can verify the above result.

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Authors and Affiliations

  1. National Institute of Technology Toyota College, Aichi, 471-8525, Japan

    Hirokazu Komatsu

  2. RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), Saitama, 606-8507, Japan

    Hiroshi Yokota

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  1. Hirokazu Komatsu
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  2. Hiroshi Yokota
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Correspondence to Hirokazu Komatsu.

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Komatsu, H., Yokota, H. Stability analysis for Butlerov chemical reaction in batch reactor. J Math Chem 61, 689–711 (2023). https://doi.org/10.1007/s10910-022-01424-w

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