75 research outputs found
Front propagation in laminar flows
The problem of front propagation in flowing media is addressed for laminar
velocity fields in two dimensions. Three representative cases are discussed:
stationary cellular flow, stationary shear flow, and percolating flow.
Production terms of Fisher-Kolmogorov-Petrovskii-Piskunov type and of Arrhenius
type are considered under the assumption of no feedback of the concentration on
the velocity. Numerical simulations of advection-reaction-diffusion equations
have been performed by an algorithm based on discrete-time maps. The results
show a generic enhancement of the speed of front propagation by the underlying
flow. For small molecular diffusivity, the front speed depends on the
typical flow velocity as a power law with an exponent depending on the
topological properties of the flow, and on the ratio of reactive and advective
time-scales. For open-streamline flows we find always , whereas for
cellular flows we observe for fast advection, and for slow advection.Comment: Enlarged, revised version, 37 pages, 14 figure
Front speed enhancement in cellular flows
The problem of front propagation in a stirred medium is addressed in the case
of cellular flows in three different regimes: slow reaction, fast reaction and
geometrical optics limit. It is well known that a consequence of stirring is
the enhancement of front speed with respect to the non-stirred case. By means
of numerical simulations and theoretical arguments we describe the behavior of
front speed as a function of the stirring intensity, . For slow reaction,
the front propagates with a speed proportional to , conversely for
fast reaction the front speed is proportional to . In the geometrical
optics limit, the front speed asymptotically behaves as .Comment: 10 RevTeX pages, 10 included eps figure
Reaction Spreading on Graphs
We study reaction-diffusion processes on graphs through an extension of the
standard reaction-diffusion equation starting from first principles. We focus
on reaction spreading, i.e. on the time evolution of the reaction product,
M(t). At variance with pure diffusive processes, characterized by the spectral
dimension, d_s, for reaction spreading the important quantity is found to be
the connectivity dimension, d_l. Numerical data, in agreement with analytical
estimates based on the features of n independent random walkers on the graph,
show that M(t) ~ t^{d_l}. In the case of Erdos-Renyi random graphs, the
reaction-product is characterized by an exponential growth M(t) ~ e^{a t} with
a proportional to ln, where is the average degree of the graph.Comment: 4 pages, 3 figure
Thin front propagation in steady and unsteady cellular flows
Front propagation in two dimensional steady and unsteady cellular flows is
investigated in the limit of very fast reaction and sharp front, i.e., in the
geometrical optics limit. In the steady case, by means of a simplified model,
we provide an analytical approximation for the front speed,
, as a function of the stirring intensity, , in good
agreement with the numerical results and, for large , the behavior
is predicted. The large scale of the
velocity field mainly rules the front speed behavior even in the presence of
smaller scales. In the unsteady (time-periodic) case, the front speed displays
a phase-locking on the flow frequency and, albeit the Lagrangian dynamics is
chaotic, chaos in front dynamics only survives for a transient. Asymptotically
the front evolves periodically and chaos manifests only in the spatially
wrinkled structure of the front.Comment: 12 pages, 13 figure
Discreteness effects in a reacting system of particles with finite interaction radius
An autocatalytic reacting system with particles interacting at a finite
distance is studied. We investigate the effects of the discrete-particle
character of the model on properties like reaction rate, quenching phenomenon
and front propagation, focusing on differences with respect to the continuous
case. We introduce a renormalized reaction rate depending both on the
interaction radius and the particle density, and we relate it to macroscopic
observables (e.g., front speed and front thickness) of the system.Comment: 23 pages, 13 figure
Combustion dynamics in steady compressible flows
We study the evolution of a reactive field advected by a one-dimensional
compressible velocity field and subject to an ignition-type nonlinearity. In
the limit of small molecular diffusivity the problem can be described by a
spatially discretized system, and this allows for an efficient numerical
simulation. If the initial field profile is supported in a region of size l <
lc one has quenching, i.e., flame extinction, where lc is a characteristic
length-scale depending on the system parameters (reacting time, molecular
diffusivity and velocity field). We derive an expression for lc in terms of
these parameters and relate our results to those obtained by other authors for
different flow settings.Comment: 6 pages, 5 figure
Mixing and reaction efficiency in closed domains
We present a numerical study of mixing and reaction efficiency in closed
domains. In particular we focus our attention on laminar flows. In the case of
inert transport the mixing properties of the flows strongly depend on the
details of the Lagrangian transport. We also study the reaction efficiency.
Starting with a little spot of product we compute the time needed to complete
the reaction in the container. We found that the reaction efficiency is not
strictly related to the mixing properties of the flow. In particular, reaction
acts as a "dynamical regulator".Comment: 11 pages, 10 figure
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