Dissolution in a field

Network models of dissolution of porous media

We investigate the chemical dissolution of porous media using a 2D network model in which the system is represented as a series of interconnected pipes with the diameter of each segment increasing in proportion to the local reactant consumption. Moreover, the topology of the network is allowed to change dynamically during the simulation: As the diameters of the eroding pores become comparable with the interpore distances, the pores are joined together, thus changing the interconnections within the network. With this model, we investigate different growth regimes in an evolving porous medium, identifying the mechanisms responsible for the emergence of specific patterns. We consider both the random and regular network and study the effect of the network geometry on the patterns. Finally, we consider practically important problem of finding an optimum flow rate that gives a maximum increase in permeability for a given amount of reactant.

Ring-shaped luminescence pattern in biased quantum wells studied as a steady-state reaction front

Under certain conditions, focused laser excitation in semiconductor quantum well structures can lead to a charge separation and a circular reaction front, which is visible as a ring-shaped photoluminescence pattern. The diffusion-reaction equations governing the system are studied here with the aim of a detailed understanding of the steady state. The qualitative asymmetry in the sources for the two carriers is found to lead to unusual effects which dramatically affect the steady-state configuration. Analytic expressions are derived for carrier distributions and interface positions for a number of cases. These are compared with steady-state information obtained from simulations of the diffusion-reaction equations.

Diffusion-controlled annihilation A+B-->0: the growth of an A-particle island from a localized A source in the B-particle sea

We present the growth dynamics of an island of particles A injected from a localized A source into a sea of particles B and dying in the course of diffusion-controlled annihilation A+B-->0. We show that in the one-dimensional (1D) case the island grows unlimitedly at any source strength Lambda, and the dynamics of its growth does not depend asymptotically on the diffusivity of B particles. In the 3D case the island grows only at Lambda> Lambda(c), achieving asymptotically a stationary state (static island). In the marginal 2D case the island unlimitedly grows at any Lambda but at Lambda< Lambda(*) the time of its formation becomes exponentially large. For all cases the numbers of surviving and dying A particles are calculated, and the scaling of the reaction zone is derived.

Dynamic transition in etching with poisoning

We study a lattice model for etching of a crystalline solid including the deposition of a poisoning species. The model considers normal and lateral erosion of the columns of the solid by a flux of etching particles and the blocking effects of impurities formed at the surface. As the probability p of formation of this poisoning species increases, the etching rate decreases and a continuous transition to a pinned phase is observed. The transition is in the directed percolation (DP) class, with the fraction of the exposed columns as the order parameter. This interpretation is consistent with a mapping of the interface problem in d+1 dimensions onto a d-dimensional contact process, and is confirmed by numerical results in d=1 and d=2. In the etching phase, the interface width scales with Kardar-Parisi-Zhang (KPZ) exponents, and shows a crossover from the critical DP behavior (W approximately t) to KPZ near the critical point, at etching times of the order of (pc-p)(-nu(||)). Anomalous roughening is observed at criticality, with the roughness exponent related to DP exponents as alphac=nu(||)/nu(perpendicular)>1. The main differences from previously studied DP transitions in growth models and isotropic percolation transitions in etching models are discussed. Investigations in real systems are suggested.