50 research outputs found
Scaling of Reaction Zones in the A+B->0 Diffusion-Limited Reaction
We study reaction zones in three different versions of the A+B->0 system. For
a steady state formed by opposing currents of A and B particles we derive
scaling behavior via renormalization group analysis. By use of a previously
developed analogy, these results are extended to the time-dependent case of an
initially segregated system. We also consider an initially mixed system, which
forms reaction zones for dimension d<4. In this case an extension of the
steady-state analogy gives scaling results characterized by new exponents.Comment: 4 pages, REVTeX 3.0 with epsf, 2 uuencoded postscript figures
appended, OUTP-94-33
Reaction-diffusion dynamics: confrontation between theory and experiment in a microfluidic reactor
We confront, quantitatively, the theoretical description of the
reaction-diffusion of a second order reaction to experiment. The reaction at
work is \ca/CaGreen, and the reactor is a T-shaped microchannel, 10 m
deep, 200 m wide, and 2 cm long. The experimental measurements are
compared with the two-dimensional numerical simulation of the
reaction-diffusion equations. We find good agreement between theory and
experiment. From this study, one may propose a method of measurement of various
quantities, such as the kinetic rate of the reaction, in conditions yet
inaccessible to conventional methods
The Reaction-Diffusion Front for in One Dimension
We study theoretically and numerically the steady state diffusion controlled
reaction , where currents of and particles
are applied at opposite boundaries. For a reaction rate , and equal
diffusion constants , we find that when the
reaction front is well described by mean field theory. However, for , the front acquires a Gaussian profile - a result of
noise induced wandering of the reaction front center. We make a theoretical
prediction for this profile which is in good agreement with simulation.
Finally, we investigate the intrinsic (non-wandering) front width and find
results consistent with scaling and field theoretic predictions.Comment: 11 pages, revtex, 4 separate PostScript figure
Diffusion-Limited Annihilation with Initially Separated Reactants
A diffusion-limited annihilation process, A+B->0, with species initially
separated in space is investigated. A heuristic argument suggests the form of
the reaction rate in dimensions less or equal to the upper critical dimension
. Using this reaction rate we find that the width of the reaction front
grows as in one dimension and as in two
dimensions.Comment: 9 pages, Plain Te
Refined Simulations of the Reaction Front for Diffusion-Limited Two-Species Annihilation in One Dimension
Extensive simulations are performed of the diffusion-limited reaction
AB in one dimension, with initially separated reagents. The reaction
rate profile, and the probability distributions of the separation and midpoint
of the nearest-neighbour pair of A and B particles, are all shown to exhibit
dynamic scaling, independently of the presence of fluctuations in the initial
state and of an exclusion principle in the model. The data is consistent with
all lengthscales behaving as as . Evidence of
multiscaling, found by other authors, is discussed in the light of these
findings.Comment: Resubmitted as TeX rather than Postscript file. RevTeX version 3.0,
10 pages with 16 Encapsulated Postscript figures (need epsf). University of
Geneva preprint UGVA/DPT 1994/10-85
Exact Solution of Two-Species Ballistic Annihilation with General Pair-Reaction Probability
The reaction process is modelled for ballistic reactants on an
infinite line with particle velocities and and initially
segregated conditions, i.e. all A particles to the left and all B particles to
the right of the origin. Previous, models of ballistic annihilation have
particles that always react on contact, i.e. pair-reaction probability .
The evolution of such systems are wholly determined by the initial distribution
of particles and therefore do not have a stochastic dynamics. However, in this
paper the generalisation is made to , allowing particles to pass through
each other without necessarily reacting. In this way, the A and B particle
domains overlap to form a fluctuating, finite-sized reaction zone where the
product C is created. Fluctuations are also included in the currents of A and B
particles entering the overlap region, thereby inducing a stochastic motion of
the reaction zone as a whole. These two types of fluctuations, in the reactions
and particle currents, are characterised by the `intrinsic reaction rate', seen
in a single system, and the `extrinsic reaction rate', seen in an average over
many systems. The intrinsic and extrinsic behaviours are examined and compared
to the case of isotropically diffusing reactants.Comment: 22 pages, 2 figures, typos correcte
Renormalization Group Study of the A+B->0 Diffusion-Limited Reaction
The diffusion-limited reaction, with equal initial densities
, is studied by means of a field-theoretic renormalization
group formulation of the problem. For dimension an effective theory is
derived, from which the density and correlation functions can be calculated. We
find the density decays in time as a,b \sim C\sqrt{\D}(Dt)^{-d/4} for , with \D = n_0-C^\prime n_0^{d/2} + \dots, where is a universal
constant, and is non-universal. The calculation is extended to the
case of unequal diffusion constants , resulting in a new
amplitude but the same exponent. For a controlled calculation is not
possible, but a heuristic argument is presented that the results above give at
least the leading term in an expansion. Finally, we address
reaction zones formed in the steady-state by opposing currents of and
particles, and derive scaling properties.Comment: 17 pages, REVTeX, 13 compressed figures, included with epsf. Eq.
(6.12) corrected, and a moderate rewriting of the introduction. Accepted for
publication in J. Stat. Phy
Kinetics of A+B--->0 with Driven Diffusive Motion
We study the kinetics of two-species annihilation, A+B--->0, when all
particles undergo strictly biased motion in the same direction and with an
excluded volume repulsion between same species particles. It was recently shown
that the density in this system decays as t^{-1/3}, compared to t^{-1/4}
density decay in A+B--->0 with isotropic diffusion and either with or without
the hard-core repulsion. We suggest a relatively simple explanation for this
t^{-1/3} decay based on the Burgers equation. Related properties associated
with the asymptotic distribution of reactants can also be accounted for within
this Burgers equation description.Comment: 11 pages, plain Tex, 8 figures. Hardcopy of figures available on
request from S
Delocalization Transition of a Rough Adsorption-Reaction Interface
We introduce a new kinetic interface model suitable for simulating
adsorption-reaction processes which take place preferentially at surface
defects such as steps and vacancies. As the average interface velocity is taken
to zero, the self- affine interface with Kardar-Parisi-Zhang like scaling
behaviour undergoes a delocalization transition with critical exponents that
fall into a novel universality class. As the critical point is approached, the
interface becomes a multi-valued, multiply connected self-similar fractal set.
The scaling behaviour and critical exponents of the relevant correlation
functions are determined from Monte Carlo simulations and scaling arguments.Comment: 4 pages with 6 figures, new comment