16 research outputs found
Liesegang patterns : Studies on the width law
The so-called "width law" for Liesegang patterns, which states that the
positions x_n and widths w_n of bands verify the relation x_n \sim w_n^{\alpha}
for some \alpha>0, is investigated both experimentally and theoretically. We
provide experimental data exhibiting good evidence for values of \alpha close
to 1. The value \alpha=1 is supported by theoretical arguments based on a
generic model of reaction-diffusion.Comment: 7 pages, RevTeX, two columns, 5 figure
Derivation of the Matalon-Packter law for Liesegang patterns
Theoretical models of the Liesegang phenomena are studied and simple
expressions for the spacing coefficients characterizing the patterns are
derived. The emphasis is on displaying the explicit dependences on the
concentrations of the inner- and the outer-electrolytes. Competing theories
(ion-product supersaturation, nucleation and droplet growth, induced sol-
coagulation) are treated with the aim of finding the distinguishing features of
the theories. The predictions are compared with experiments and the results
suggest that the induced sol-coagulation theory is the best candidate for
describing the experimental observations embodied in the Matalon-Packter law.Comment: 9 pages, 7 figures, RevTe
Pattern of Reaction Diffusion Front in Laminar Flows
Autocatalytic reaction between reacted and unreacted species may propagate as
solitary waves, namely at a constant front velocity and with a stationary
concentration profile, resulting from a balance between molecular diffusion and
chemical reaction. The effect of advective flow on the autocatalytic reaction
between iodate and arsenous acid in cylindrical tubes and Hele-Shaw cells is
analyzed experimentally and numerically using lattice BGK simulations. We do
observe the existence of solitary waves with concentration profiles exhibiting
a cusp and we delineate the eikonal and mixing regimes recently predicted.Comment: 4 pages, 3 figures. This paper report on experiments and simulations
in different geometries which test the theory of Boyd Edwards on flow
advection of chemical reaction front which just appears in PRL (PRL Vol
89,104501, sept2002
Reaction front propagation in a turbulent flow
The propagation of reaction fronts was studied by direct numerical simulations. The velocity field was obtained by integrating the Navier-Stokes equation. The structure of the reaction front and the enhancement of the front propagation speed were investigated. The ratio of eddy turnover times and of the characteristic chemical time scale was determined
Simulation of fluid-solid coexistence in finite volumes: A method to study the properties of wall-attached crystalline nuclei
The Asakura-Oosawa model for colloid-polymer mixtures is studied by Monte
Carlo simulations at densities inside the two-phase coexistence region of fluid
and solid. Choosing a geometry where the system is confined between two flat
walls, and a wall-colloid potential that leads to incomplete wetting of the
crystal at the wall, conditions can be created where a single nanoscopic
wall-attached crystalline cluster coexists with fluid in the remainder of the
simulation box. Following related ideas that have been useful to study
heterogeneous nucleation of liquid droplets at the vapor-liquid coexistence, we
estimate the contact angles from observations of the crystalline clusters in
thermal equilibrium. We find fair agreement with a prediction based on Young's
equation, using estimates of interface and wall tension from the study of flat
surfaces. It is shown that the pressure versus density curve of the finite
system exhibits a loop, but the pressure maximum signifies the "droplet
evaporation-condensation" transition and thus has nothing in common with a van
der Waals-like loop. Preparing systems where the packing fraction is deep
inside the two-phase coexistence region, the system spontaneously forms a "slab
state", with two wall-attached crystalline domains separated by (flat)
interfaces from liquid in full equilibrium with the crystal in between;
analysis of such states allows a precise estimation of the bulk equilibrium
properties at phase coexistence
Liesegang patterns: Effect of dissociation of the invading electrolyte
The effect of dissociation of the invading electrolyte on the formation of
Liesegang bands is investigated. We find, using organic compounds with known
dissociation constants, that the spacing coefficient, 1+p, that characterizes
the position of the n-th band as x_n ~ (1+p)^n, decreases with increasing
dissociation constant, K_d. Theoretical arguments are developed to explain
these experimental findings and to calculate explicitly the K_d dependence of
1+p.Comment: RevTex, 8 pages, 3 eps figure
Strong-coupling limit in cold-molecule formation via photoassociation or Feshbach resonance through Nikitin exponential resonance crossing
The strong-coupling limit of molecule formation in an atomic Bose-Einstein
condensate via two-mode one-color photoassociation or sweep across a Feshbach
resonance is examined using a basic nonlinear time-dependent two-state model.
For the general class of term-crossing models with constant coupling, a common
strategy for attacking the problem is developed based on the reduction of the
initial system of semiclassical equations for atom-molecule amplitudes to a
third order nonlinear differential equation for the molecular state
probability. This equation provides deriving exact solution for a class of
periodic level-crossing models. These models reveal much in common with the
Rabi problem. Discussing the strong-coupling limit for the general case of
variable detuning, the equation is further truncated to a limit first-order
nonlinear equation. Using this equation, the strong nonlinearity regime for the
first Nikitin exponential-crossing model is analyzed and accurate asymptotic
expressions for the nonlinear transition probability to the molecular state are
derived. It is shown that, because of a finite final detuning involved, this
model displays essential deviations from the Landau-Zener behavior. In
particular, it is shown that in the limit of strong coupling the final
conversion probability tends to 1/6. Thus, in this case the strong interaction
limit is not optimal for molecule formation. We have found that if optimal
field intensity is applied the molecular probability is increased up to 1/4
(i.e., the half of the initial atomic population)
Density and Graviton Perturbations in the Cosmic Microwave Background
This paper evaluates and compares the gravitational wave and density
perturbation contributions to the cosmic microwave background radiation, on the
basis of the same power law inflationary model. The inflation to radiation
transition is treated as instantaneous, but a model is constructed to allow for
a smooth transition from the radiation to the matter dominated eras. The
equations are numerically investigated and integrated, without any basic
approximations being made. Use is made of the synchronous gauge, with
appropriate gauge invariant variables, thus eliminating any confusion arising
from unphysical gauge modes. We find a non- negligible gravitational wave
contribution, which becomes dominant for a power law expansion with exponent . We also explore the dependence of our results with the main
characteristic of the transition region, its length.Comment: 19 page