TY - JOUR
T1 - Asymptotics of reaction-diffusion fronts with one static and one diffusing reactant
AU - Bazant, Martin Z.
AU - Stone, H. A.
N1 - Funding Information:
The authors thank C. Léger and R.R. Rosales for useful discussions. This work was supported by an NSF infrastructure grant (MZB) and grants from the Harvard MRSEC DMR-980-9363 and the Army Research Office DAAG-55-97-1-0114 (HAS).
PY - 2000/12/1
Y1 - 2000/12/1
N2 - The long-time behavior of a reaction-diffusion front between one static (e.g. porous solid) reactant A and one initially separated diffusing reactant B is analyzed for the mean-field reaction-rate density R(ρA,ρB)=kρAmρ Bn. A uniformly valid asymptotic approximation is constructed from matched self-similar solutions in a "reaction front" (of width w~tα, where R~tβ enters the dominant balance) and a "diffusion layer" (of width W~t1/2, where R is negligible). The limiting solution exists if and only if m,n≥1, in which case the scaling exponents are uniquely given by α=(m-1)/2(m+1) and β=m/(m+1). In the diffusion layer, the common ad hoc approximation of neglecting reactions is given mathematical justification, and the exact transient decay of the reaction rate is derived. The physical effects of higher-order kinetics (m,n>1), such as the broadening of the reaction front and the slowing of transients, are also discussed.
AB - The long-time behavior of a reaction-diffusion front between one static (e.g. porous solid) reactant A and one initially separated diffusing reactant B is analyzed for the mean-field reaction-rate density R(ρA,ρB)=kρAmρ Bn. A uniformly valid asymptotic approximation is constructed from matched self-similar solutions in a "reaction front" (of width w~tα, where R~tβ enters the dominant balance) and a "diffusion layer" (of width W~t1/2, where R is negligible). The limiting solution exists if and only if m,n≥1, in which case the scaling exponents are uniquely given by α=(m-1)/2(m+1) and β=m/(m+1). In the diffusion layer, the common ad hoc approximation of neglecting reactions is given mathematical justification, and the exact transient decay of the reaction rate is derived. The physical effects of higher-order kinetics (m,n>1), such as the broadening of the reaction front and the slowing of transients, are also discussed.
KW - 02.30.Jr
KW - 05.40+j
KW - 82.20. - w
KW - Asymptotic analysis
KW - Diffusion
KW - Partial differential equations
KW - Reaction kinetics
KW - Similarity solutions
UR - http://www.scopus.com/inward/record.url?scp=0039149514&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0039149514&partnerID=8YFLogxK
U2 - 10.1016/S0167-2789(00)00140-8
DO - 10.1016/S0167-2789(00)00140-8
M3 - Article
AN - SCOPUS:0039149514
VL - 147
SP - 95
EP - 121
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
SN - 0167-2789
IS - 1-2
ER -