scholarly journals The Effects of Mixing, Reaction Rates, and Stoichiometry on Yield for Mixing Sensitive Reactions—Part II: Design Protocols

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Syed Imran A. Shah ◽  
Larry W. Kostiuk ◽  
Suzanne M. Kresta
Keyword(s):  
Rate Ratio ◽  
Reaction Rate ◽  
Relative Rate ◽  
Reaction Diffusion ◽  
Reaction Rates ◽  
Reaction Scheme ◽  
Considerable Effect ◽  
Mixing Condition ◽  
Reaction Diffusion Model ◽  
Rate Ratios

Competitive-consecutive and competitive-parallel reactions are both mixing sensitive reactions where the yield of desired product depends on how fast the reactants are brought together. Recent experimental results have suggested that the magnitude of the mixing effect may depend strongly on the stoichiometry of the reactions. To investigate this, a 1D, dimensionless, reaction-diffusion model was developed at the micromixing scale, yielding a single general Damköhler number. Dimensionless reaction rate ratios were derived for both reaction schemes. A detailed investigation of the effects of initial mixing condition (striation thickness), dimensionless reaction rate ratio, and reaction stoichiometry on the yield of desired product showed that the stoichiometry has a considerable effect on yield. All three variables were found to interact strongly. Model results for 12 stoichiometries are used to determine the mixing scale and relative rate ratio needed to achieve a specified yield for each reaction scheme. The results show that all three variables need to be considered when specifying reactors for mixing sensitive reactions.

scholarly journals The Effects of Mixing, Reaction Rates, and Stoichiometry on Yield for Mixing Sensitive Reactions—Part I: Model Development

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Syed Imran A. Shah ◽  
Larry W. Kostiuk ◽  
Suzanne M. Kresta
Keyword(s):  
Rate Ratio ◽  
Reaction Rate ◽  
Model Development ◽  
Reaction Diffusion ◽  
Reaction Rates ◽  
Considerable Effect ◽  
Reaction Diffusion Model ◽  
Effect On Yield ◽  
Reaction Stoichiometry ◽  
Rate Ratios

There are two classes of mixing sensitive reactions: competitive-consecutive and competitive-parallel. The yield of desired product from these coupled reactions depends on how fast the reactants are brought together. Recent experimental results have suggested that the mixing effect may depend strongly on the stoichiometry of the reactions. To investigate this, a 1D, dimensionless, reaction-diffusion model at the micromixing scale was developed. Assuming constant mass concentration and mass diffusivities, systems of PDE's were derived on a mass fraction basis for both types of reactions. Two dimensionless reaction rate ratios and a single general Damköhler number emerged from the analysis. The resulting dimensionless equations were used to investigate the effects of mixing, reaction rate ratio, and reaction stoichiometry. As expected, decreasing either the striation thickness or the dimensionless rate ratio maximizes yield, the reaction stoichiometry has a considerable effect on yield, and all three variables interact strongly.

scholarly journals Domain-Dependent Stability Analysis of a Reaction–Diffusion Model on Compact Circular Geometries

2018 ◽  
Vol 28 (08) ◽  
pp. 1830024
Author(s):  
Wakil Sarfaraz ◽  
Anotida Madzvamuse
Keyword(s):  
Numerical Solutions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Domain Size ◽  
Reaction Rates ◽  
Polar Coordinates ◽  
Angular Variable ◽  
Diffusion Operator ◽  
Nodal Lines ◽  
Reaction Diffusion Model

In this work an activator-depleted reaction–diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven instabilities. Quantitative relationships are found in the form of necessary conditions on the area of a disk-shape domain with respect to the diffusion and reaction rates for certain types of diffusion-driven instabilities to occur. Robust analytical methods are applied to find explicit expressions for the eigenvalues and eigenfunctions of the diffusion operator on a disk-shape domain with homogenous Neumann boundary conditions in polar coordinates. Spectral methods are applied using Chebyshev nonperiodic grid for the radial variable and Fourier periodic grid for the angular variable to verify the nodal lines and eigen-surfaces subject to the proposed analytical findings. The full classification of the parameter space in light of the bifurcation analysis is obtained and numerically verified by finding the solutions of the partitioning curves inducing such a classification. Spatiotemporal periodic behavior is demonstrated in the numerical solutions of the system for a proposed choice of parameters and a rigorous proof of the existence of infinitely many such points in the parameter plane is presented under a restriction on the area of the domain, with a lower bound in terms of reaction–diffusion rates.

Influence of molecular rebindings on the reaction rate of complex formation

2021 ◽  
Author(s):  
Tomasz Kalwarczyk ◽  
Krzysztof Bielec ◽  
Krzysztof Burdzy ◽  
Robert Holyst
Keyword(s):  
Complex Formation ◽  
Reaction Rate ◽  
Diffusion Processes ◽  
Reaction Diffusion ◽  
Reaction Rates ◽  
Brownian Diffusion ◽  
Bimolecular Reactions

We simulated the Brownian diffusion and reaction-diffusion processes to study molecular rebinding’s influence on the reaction rates of bimolecular reactions. We found that the number of rebindings, Nreb , is...

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