Analytic approach to the space-time kinetics of annihilation reactions

Reaction efficiency effects on binary chemical reactions

We study the effect of the variation of reaction efficiency in binary reactions. We use the well-known A + B → 0 model, which has been extensively studied in the past. We perform simulations on this model where we vary the efficiency of reaction, i.e., when two particles meet they do not instantly react, as has been assumed in previous studies, but they react with a probability γ, where γ is in the range 0 < γ < 1. Our results show that at small γ values the system is reaction limited, but as γ increases it crosses over to a diffusion limited behavior. At early times, for small γ values, the particle density falls slower than for larger γ values. This fall-off goes over a crossover point, around the value of γ = 0.50 for high initial densities. Under a variety of conditions simulated, we find that the crossover point was dependent on the initial concentration but not on the lattice size. For intermediate and long times simulations, all γ values (in the depleted reciprocal density versus time plot) converge to the same behavior. These theoretical results are useful in models of epidemic reactions and epidemic spreading, where a contagion from one neighbor to the next is not always successful but proceeds with a certain probability, an analogous effect with the reaction probability examined in the current work.

Initial Distribution Effects on Diffusion-Limited Reactions in Constrained Geometries

We present a study of the effects of the initial distribution on the kinetic evolution of irreversible binary reactions in low dimensions. We focus on the role of initial density fluctuations and, in particular, on the role of the long wavelength components of the initial fluctuations, in the creation of the macroscopic patterns that lead to the well-known kinetic anomalies in this system. The frequently studied random initial distribution is but one of a variety of possible distributions leading to interesting anomalous behavior. Our discussion includes initial distributions that suppress and ones that enhance the initial long wavelength components.

Reaction kinetics of diffusing particles injected into a reactive substrate

We analyze the kinetics of trapping (A+B-->B) and annihilation (A+B-->0) processes on a one-dimensional substrate with homogeneous distribution of immobile B particles while the A particles are supplied by a localized source. For the imperfect reaction case, we analyze both problems by means of a stochastic model and compare the results with numerical simulations. In addition, we present the exact analytical results of the stochastic model for the case of perfect trapping.

Trapping reactions for mobile particles and a trap in the laboratory frame

We have used a stochastic model to obtain the exact spatial particle density profile for the trapping process A+B-->B in a one-dimensional lattice with a single trap, as seen from the laboratory frame. We obtain the profile for either perfect or imperfect reactions when A particles are immobile, but only for perfect absorption in the general case where both particles are mobile with different diffusivities. This profile is found to be similar to that seen from the reference system attached to the trap, the most noticeable difference being near the origin.