Asymptotic properties of radial A+B→C reaction fronts

Philip Trevelyan, Alan Walker

Research output: Contribution to journalArticle

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Abstract

If two initially separated solutions of reactants are put in contact and a simple A + B → C reaction takes place, reaction-diffusion profiles develop due to the coupling of reaction and diffusion. The properties of such fronts are well known in the case of an initially planar contact line between the two solutions. In this study one of the reactants is injected at a constant flux from a point source into a miscible solution of the other reactant so that the reaction front expands out radially. Both the leading order large time and small time asymptotic limits of the reactant concentrations and reaction front position are obtained analytically. Just as in the planar reaction front case, the position of the reaction front scales like t1/2 and the width of the reaction front scales with t1/6. In the large Peclet number limit the large time asymptotic properties of the radial reaction front are
found to be similar to those of the planar front except that the profiles are advected with the fluid flow. The distance between the contact line and the position of the radial reaction front is 1/√2 of the distance that a planar reaction fronts travels. Further, the length scales inside and outside of the reaction zone are reduced by factors of 2 1/6 and √2, respectively, compared to the planar
reaction front.
Original languageEnglish
Article number032118
Number of pages15
JournalPhysical Review E
Volume98
DOIs
Publication statusPublished - 13 Sep 2018

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asymptotic properties
Asymptotic Properties
Contact Line
Large Time Asymptotics
Asymptotic Limit
Peclet number
Reaction-diffusion
Point Source
Length Scale
profiles
Expand
Fluid Flow
point sources
travel
fluid flow

Cite this

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title = "Asymptotic properties of radial A+B→C reaction fronts",
abstract = "If two initially separated solutions of reactants are put in contact and a simple A + B → C reaction takes place, reaction-diffusion profiles develop due to the coupling of reaction and diffusion. The properties of such fronts are well known in the case of an initially planar contact line between the two solutions. In this study one of the reactants is injected at a constant flux from a point source into a miscible solution of the other reactant so that the reaction front expands out radially. Both the leading order large time and small time asymptotic limits of the reactant concentrations and reaction front position are obtained analytically. Just as in the planar reaction front case, the position of the reaction front scales like t1/2 and the width of the reaction front scales with t1/6. In the large Peclet number limit the large time asymptotic properties of the radial reaction front arefound to be similar to those of the planar front except that the profiles are advected with the fluid flow. The distance between the contact line and the position of the radial reaction front is 1/√2 of the distance that a planar reaction fronts travels. Further, the length scales inside and outside of the reaction zone are reduced by factors of 2 1/6 and √2, respectively, compared to the planarreaction front.",
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language = "English",
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Asymptotic properties of radial A+B→C reaction fronts. / Trevelyan, Philip; Walker, Alan.

In: Physical Review E, Vol. 98, 032118 , 13.09.2018.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Asymptotic properties of radial A+B→C reaction fronts

AU - Trevelyan, Philip

AU - Walker, Alan

PY - 2018/9/13

Y1 - 2018/9/13

N2 - If two initially separated solutions of reactants are put in contact and a simple A + B → C reaction takes place, reaction-diffusion profiles develop due to the coupling of reaction and diffusion. The properties of such fronts are well known in the case of an initially planar contact line between the two solutions. In this study one of the reactants is injected at a constant flux from a point source into a miscible solution of the other reactant so that the reaction front expands out radially. Both the leading order large time and small time asymptotic limits of the reactant concentrations and reaction front position are obtained analytically. Just as in the planar reaction front case, the position of the reaction front scales like t1/2 and the width of the reaction front scales with t1/6. In the large Peclet number limit the large time asymptotic properties of the radial reaction front arefound to be similar to those of the planar front except that the profiles are advected with the fluid flow. The distance between the contact line and the position of the radial reaction front is 1/√2 of the distance that a planar reaction fronts travels. Further, the length scales inside and outside of the reaction zone are reduced by factors of 2 1/6 and √2, respectively, compared to the planarreaction front.

AB - If two initially separated solutions of reactants are put in contact and a simple A + B → C reaction takes place, reaction-diffusion profiles develop due to the coupling of reaction and diffusion. The properties of such fronts are well known in the case of an initially planar contact line between the two solutions. In this study one of the reactants is injected at a constant flux from a point source into a miscible solution of the other reactant so that the reaction front expands out radially. Both the leading order large time and small time asymptotic limits of the reactant concentrations and reaction front position are obtained analytically. Just as in the planar reaction front case, the position of the reaction front scales like t1/2 and the width of the reaction front scales with t1/6. In the large Peclet number limit the large time asymptotic properties of the radial reaction front arefound to be similar to those of the planar front except that the profiles are advected with the fluid flow. The distance between the contact line and the position of the radial reaction front is 1/√2 of the distance that a planar reaction fronts travels. Further, the length scales inside and outside of the reaction zone are reduced by factors of 2 1/6 and √2, respectively, compared to the planarreaction front.

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