454 research outputs found
Front motion in an type reaction-diffusion process: Effects of an electric field
We study the effects of an external electric field on both the motion of the
reaction zone and the spatial distribution of the reaction product, , in an
irreversible reaction-diffusion process. The electrolytes
and are initially separated in space
and the ion-dynamics is described by reaction-diffusion equations obeying local
electroneutrality. Without an electric field, the reaction zone moves
diffusively leaving behind a constant concentration of -s. In the presence
of an electric field which drives the reagents towards the reaction zone, we
find that the reaction zone still moves diffusively but with a diffusion
coefficient which slightly decreases with increasing field. The important
electric field effect is that the concentration of -s is no longer constant
but increases linearly in the direction of the motion of the front. The case of
an electric field of reversed polarity is also discussed and it is found that
the motion of the front has a diffusive, as well as a drift component. The
concentration of -s decreases in the direction of the motion of the front,
up to the complete extinction of the reaction. Possible applications of the
above results to the understanding of the formation of Liesegang patterns in an
electric field is briefly outlined.Comment: 13 pages, 13 figures, submitted to J. Chem. Phy
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
Formation of Liesegang patterns: Simulations using a kinetic Ising model
A kinetic Ising model description of Liesegang phenomena is studied using
Monte Carlo simulations. The model takes into account thermal fluctuations,
contains noise in the chemical reactions, and its control parameters are
experimentally accessible. We find that noisy, irregular precipitation takes
place in dimension d=2 while, depending on the values of the control
parameters, either irregular patterns or precipitation bands satisfying the
regular spacing law emerge in d=3.Comment: 7 pages, 8 ps figures, RevTe
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
Phase separation of binary fluids with dynamic temperature
Phase separation of binary fluids quenched by contact with cold external
walls is considered. Navier-Stokes, convection-diffusion, and energy equations
are solved by lattice Boltzmann method coupled with finite-difference schemes.
At high viscosity, different morphologies are observed by varying the thermal
diffusivity. In the range of thermal diffusivities with domains growing
parallel to the walls, temperature and phase separation fronts propagate
towards the inner of the system with power-law behavior. At low viscosity
hydrodynamics favors rounded shapes, and complex patterns with different
lengthscales appear. Off-symmetrical systems behave similarly but with more
ordered configurations.Comment: Accepted for publication in Phys. Rev. E, 11 figures, best quality
figures available on reques
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
Band Formation during Gaseous Diffusion in Aerogels
We study experimentally how gaseous HCl and NH_3 diffuse from opposite sides
of and react in silica aerogel rods with porosity of 92 % and average pore size
of about 50 nm. The reaction leads to solid NH_4Cl, which is deposited in thin
sheet-like structures. We present a numerical study of the phenomenon. Due to
the difference in boundary conditions between this system and those usually
studied, we find the sheet-like structures in the aerogel to differ
significantly from older studies. The influence of random nucleation centers
and inhomogeneities in the aerogel is studied numerically.Comment: 7 pages RevTex and 8 figures. Figs. 4-8 in Postscript, Figs. 1-3 on
request from author
Calcium and phosphorus metabolism in peripartal dogs
Recommended allowances for calcium and phosphorus are mostly based on factorial calculations partly set at the level determined adequate for giant breeds (Nutrient requirements of dogs and cats. Washington, DC, USA: The National Academies Press. 2006). Information about appropriateness of supply with both minerals during the peripartal phase is limited. From other species is known that bone mineral stores are used in addition to oral intake of calcium and phosphorus in periods of higher needs such as gestation and lactation. The aim of this study was to determine parameters of calcium and phosphorus homeostasis in female dogs receiving the recommended amount of these minerals according to NRC (Nutrient requirements of dogs and cats. Washington, DC, USA: The National Academies Press. 2006) during the peripartal phase. In five Beagles and four Foxhound crossbreds, all primiparous with a litter size of 1–8 puppies, apparent digestibility of calcium and phosphorus as well as serum parameters of mineral metabolism (total and ionised calcium, phosphorus, parathyroid hormone, bone specific alkaline phosphatase, crosslaps) was determined in the period of 12–9 days before and 4–9 days after parturition. The apparent digestibility of calcium was relatively low and did not differ significantly between both peripartal phases, whereas the apparent digestibility of phosphorus increased during lactation. Serum concentrations of calcium (total as well as ionised), phosphorus and parathyroid hormone did not differ between gestation and lactation. The bone resorption marker serum crosslaps increased in lactating dogs but most individual values were within the reference range for adult female dogs at maintenance. On the other hand, the bone formation marker bone specific alkaline phosphatase decreased from prepartal to postpartal phase with values clearly above reference range in both phases. Based on the results especially of the bone markers, which stayed within the reference range during the peripartal phase without indicating predominant bone resorption, we hypothesise that the applied recommended daily allowances defined for peripartal dogs are appropriate
Formation of Liesegang patterns: A spinodal decomposition scenario
Spinodal decomposition in the presence of a moving particle source is
proposed as a mechanism for the formation of Liesegang bands. This mechanism
yields a sequence of band positions x_n that obeys the spacing law
x_n~Q(1+p)^n. The dependence of the parameters p and Q on the initial
concentration of the reagents is determined and we find that the functional
form of p is in agreement with the experimentally observed Matalon-Packter law.Comment: RevTex, 4 pages, 4 eps figure
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