{'fraction_non_alphanumeric': 0.05386875612144956, 'fraction_numerical': 0.03330068560235064, 'mean_word_length': 4.4190981432360745, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Invariantly propagating dissolution fingers in finite-width systems

Dissolution fingers are formed in porous medium due to positive feedback between transport of reactant and chemical reactions [1-4]. We investigate two-dimensional semiinfinite systems, with constant width W in one direction. In numerical simulations we solve the Darcy flow problem combined with advection-dispersion-reaction equation for the solute transport to track the evolving shapes of the fingers. We find the stationary, invariantly propagating finger shapes for different widths of the system W, flow rates and reaction rates. Shape of the reaction front, turns out to be controlled by two dimensionless numbers – the (width-based) Péclet number PeW = v W D φ0 and Damköhler number DaW = ksW v , where k is the reaction rate, s – specific reactive surface area, v characteristic flow rate, D – diffusion coefficient of the solute, and φ0 – initial porosity of the rock matrix. Length of the stationary finger L turns out to be proportional to PeWW. Velocity of propagating front in initial stages of finger formation as a function of system parameters is also calculated. Fig. 1 Dissolution finger in the limestone quarry in Smerdyna (left) and porosity φ/φ0 obtained in simulation for Péclet number PeW = 128 and Damköhler number DaW = 25.6 (right). Inset shows close-up of the dissolution front. References 1. P. Ortoleva, Chadam, J. E., Merino, and A. Sen, Geochemical self-organization II: the reactive-infiltration instability, Am. J. Sci, 287, 1008-1040 (1987). 2. M. L. Hoefner, and H. S. Fogler. Pore evolution and channel formation during flow and reaction in porous media, AIChE Journal 34, 45-54 (1988). 3. C. E. Cohen, D. Ding, M. Quintard, and B. Bazin, From pore scale to wellbore scale: impact of geometry on wormhole growth in carbonate acidization, Chemical Engineering Science 63, 3088-3099 (2008). 4. P. Szymczak and A. J. C. Ladd, Reactive infiltration instabilities in rocks. Dissolution of a porous matrix, J. Fluid Mech. 738, 591-630 (2014)