Simulation of geochemical banding: Theoretical modeling and fractal structure in acidization-diffusion-precipitation dynamics

Modeling the Chemical Pollution of the Area by the Random-Addition Method

Currently, a significant group of industrial facilities can be classified as chemically hazardous facilities (CHFs). To predict the spread of harmful impurities in the programs being developed, Gaussian and Lagrangian models are actively used, on the basis of which the complexes used both in the EMERCOM of Russia and in research organizations are being implemented. These complexes require the introduction of a large amount of information, including the characteristics of the wind field in the distribution of an emergency chemically hazardous substance, which limits their use. In systems, the formation of which is influenced by a large number of different random factors, spatial scaling (similarity) is often found, and one or another parameter can be described using the methods of fractal geometry, which in the past few decades has been actively and successfully applied to the description of various physical objects. The purpose of this study is to analyze the possibility of using the random-addition method for early prediction of the distribution of harmful impurities in the surface air layer during the short-term release of a substance on the surface as a result of an emergency.

Chemical Tracking of Temperature by Concurrent Periodic Precipitation Pattern Formation in Polyacrylamide Gels

In nature, nonequilibrium systems reflect environmental changes, and these changes are often "recorded" in their solid body as they develop. Periodic precipitation patterns, aka Liesegang patterns (LPs), are visual sums of complex events in nonequilibrium reaction-diffusion processes. Here we aim to achieve an artificial system that "records" the temperature changes in the environment with the concurrent LP formation. We first illustrate the differences in 1-D LPs developing at different temperatures in terms of band spacings, which can demonstrate the time, ramp steepness, and extent of a temperature change. These results are discussed and augmented by a mathematical model. Using scanning electron microscopy, we show that the average size of the CuCrO₄ precipitate also reflects the temperature changes. Finally, we show that these changes can also be "recorded" in the 2-D and 3-D LPs, which can have applications in long-term temperature tracking and complex soft material design.

Dynamics of A+B→C reaction fronts under radial advection in a Poiseuille flow

A+B→C reaction fronts describe a wide variety of natural and engineered dynamics, according to the specific nature of reactants and product. Recent works have shown that the properties of such reaction fronts depend on the system geometry, by focusing on one-dimensional plug flow radial injection. Here, we extend the theoretical formulation to radial deformation in two-dimensional systems. Specifically, we study the effect of a Poiseuille advective velocity profile on A+B→C fronts when A is injected radially into B at a constant flow rate in a confined axisymmetric system consisting of two parallel impermeable plates separated by a thin gap. We analyze the front dynamics by computing the temporal evolution of the average over the gap of the front position, the maximum production rate, and the front width. We further quantify the effects of the nonuniform flow on the total amount of product, as well as on its radial concentration profile. Through analytical and numerical analyses, we identify three distinct temporal regimes, namely (i) the early-time regime where the front dynamics is independent of the reaction, (ii) the transient regime where the front properties result from the interplay of reaction, diffusion that smooths the concentration gradients and advection, which stretches the spatial distribution of the chemicals, and (iii) the long-time regime where Taylor dispersion occurs and the system becomes equivalent to the one-dimensional plug flow case.