A semianalytical approach for solving first-order perturbation equations of dissolution-timescale reactive infiltration instability problems in fluid-saturated rocks

This paper presents a semianalytical approach for solving first-order perturbation (FOP) equations, which are used to describe dissolution-timescale reactive infiltration instability (RII) problems in fluid-saturated rocks. The proposed approach contains two parts because the chemical dissolution reaction divides the whole problem domain into two subdomains. In the first part, the interface-condition substitution strategy is used to derive the analytical expressions of purely mathematical solutions for the FOP equations in the upstream subdomain, where the dissolution chemical reaction is ceased and the FOP equations are weakly coupled. In the second part, the finite element method (FEM) is used to derive the analytical expressions of numerical solutions for the FOP equations in the downstream subdomain, where the dissolution chemical reaction needs to be considered and the FOP equations are strongly coupled so that it is impossible to derive purely mathematical solutions for them. Particular attention is paid to the development of the element-by-element forward marching strategy, which is associated with the use of the FEM for solving this new kind of scientific problem. The related analytical results demonstrated that (1) both the dynamic characteristic of a reactive infiltration system and the dimensionless wavenumber can have pronounced influences on the distribution of the FOP dimensionless acid concentration within the entire domain of the dissolution-timescale RII problems in fluid-saturated rocks and (2) the FOP dimensionless acid concentration distribution exhibits two significantly different patterns in the upstream and downstream subdomains of the dissolution-timescale RII system.     

Theoretical analyses of nonaqueous phase liquid dissolution‐induced instability in two‐dimensional fluid‐saturated porous media

This paper deals with the theoretical aspects of nonaqueous phase liquid (NAPL)‐dissolution‐induced instability in two‐dimensional fluid‐saturated porous media including solute dispersion effects.After some weaknesses associated with the previous work are analyzed and overcome, a comprehensive dimensionless number, known as the Zhao number, is proposed to represent the main driving force and three controlling mechanisms of an NAPL‐dissolution system that has a finite domain. The linear stability analysis is carried out to derive the critical value of the comprehensive dimensionless number of the NAPL‐dissolution system in a limit case as the ratio of the equilibrium concentration to the density of the NAPL approaches zero. As a result, a theoretical criterion that can be used to assess the instability of planar NAPL‐dissolution fronts in two‐dimensional fluid‐saturated porous media of finite domains has been established. Not only can the present theoretical results be used for the theoretical understanding of the effect of solute dispersion on the instability of an NAPL‐dissolution front in the fluid‐saturated porous medium of either a finite domain or an infinite domain, but also they can be used as benchmark solutions for verifying numerical methods employed to simulate detailed morphological evolution processes of NAPL‐dissolution fronts in two‐dimensional fluid‐saturated porous media. Copyright © 2009 John Wiley & Sons, Ltd.     

Theoretical analyses of acidization dissolution front instability in fluid‐saturated carbonate rocks

This paper presents an instability theory that can be used to understand the fundamental behavior of an acidization dissolution front when it propagates in fluid‐saturated carbonate rocks. The proposed theory includes two fundamental concepts, namely the intrinsic time and length of an acidization dissolution system, and a theoretical criterion that involves the comparison of the Zhao number and its critical value of the acidization dissolution system. The intrinsic time is used to determine the time scale at which the acidization dissolution front is formed, while the intrinsic length is used to determine the length scale at which the instability of the acidization dissolution front can be initiated. Under the assumption that the acidization dissolution reaction is a fast process, the critical Zhao number, which is used to assess the instability likelihood of an acidization dissolution front propagating in fluid‐saturated carbonate rocks, has been derived in a strictly mathematical manner. Based on the proposed instability theory of a propagating acidization dissolution front, it has been theoretically recognized that: (i) the increase of the mineral dissolution ratio can stabilize the acidization dissolution front in fluid‐saturated carbonate rocks; (ii) the increase of the final porosity of the carbonate rock can destabilize the acidization dissolution front, while the increase of the initial porosity can stabilize the acidization dissolution front in fluid‐saturated carbonate rocks; (iii) the increase of the mineral dissolution ratio can cause an increase in the dimensionless propagation speed of the acidization dissolution front; (iv) the increase of the initial porosity can enable the acidization dissolution front to propagate faster, while the increase of the final porosity can enable the acidization dissolution front to propagate slower in the acidization dissolution system. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical modeling of toxic nonaqueous phase liquid removal from contaminated groundwater systems: mesh effect and discretization error estimation

Numerical modeling has now become an indispensable tool for investigating the fundamental mechanisms of toxic nonaqueous phase liquid (NAPL) removal from contaminated groundwater systems. Because the domain of a contaminated groundwater system may involve irregular shapes in geometry, it is necessary to use general quadrilateral elements, in which two neighbor sides are no longer perpendicular to each other. This can cause numerical errors on the computational simulation results due to mesh discretization effect. After the dimensionless governing equations of NAPL dissolution problems are briefly described, the propagation theory of the mesh discretization error associated with a NAPL dissolution system is first presented for a rectangular domain and then extended to a trapezoidal domain. This leads to the establishment of the finger‐amplitude growing theory that is associated with both the corner effect that takes place just at the entrance of the flow in a trapezoidal domain and the mesh discretization effect that occurs in the whole NAPL dissolution system of the trapezoidal domain. This theory can be used to make the approximate error estimation of the corresponding computational simulation results. The related theoretical analysis and numerical results have demonstrated the following: (1) both the corner effect and the mesh discretization effect can be quantitatively viewed as a kind of small perturbation, which can grow in unstable NAPL dissolution systems, so that they can have some considerable effects on the computational results of such systems; (2) the proposed finger‐amplitude growing theory associated with the corner effect at the entrance of a trapezoidal domain is useful for correctly explaining why the finger at either the top or bottom boundary grows much faster than that within the interior of the trapezoidal domain; (3) the proposed finger‐amplitude growing theory associated with the mesh discretization error in the NAPL dissolution system of a trapezoidal domain can be used for quantitatively assessing the correctness of computational simulations of NAPL dissolution front instability problems in trapezoidal domains, so that we can ensure that the computational simulation results are controlled by the physics of the NAPL dissolution system, rather than by the numerical artifacts. Copyright © 2014 John Wiley & Sons, Ltd.     

Theoretical and numerical analyses of chemical‐dissolution front instability in fluid‐saturated porous rocks

The chemical‐dissolution front propagation problem exists ubiquitously in many scientific and engineering fields. To solve this problem, it is necessary to deal with a coupled system between porosity, pore‐fluid pressure and reactive chemical‐species transport in fluid‐saturated porous media. Because there was confusion between the average linear velocity and the Darcy velocity in the previous study, the governing equations and related solutions of the problem are re‐derived to correct this confusion in this paper. Owing to the morphological instability of a chemical‐dissolution front, a numerical procedure, which is a combination of the finite element and finite difference methods, is also proposed to solve this problem. In order to verify the proposed numerical procedure, a set of analytical solutions has been derived for a benchmark problem under a special condition where the ratio of the equilibrium concentration to the solid molar density of the concerned chemical species is very small. Not only can the derived analytical solutions be used to verify any numerical method before it is used to solve this kind of chemical‐dissolution front propagation problem but they can also be used to understand the fundamental mechanisms behind the morphological instability of a chemical‐dissolution front during its propagation within fluid‐saturated porous media. The related numerical examples have demonstrated the usefulness and applicability of the proposed numerical procedure for dealing with the chemical‐dissolution front instability problem within a fluid‐saturated porous medium. Copyright © 2007 John Wiley & Sons, Ltd.     

Why asymptotic limit of the acid dissolution capacity can lead to a sharp dissolution front in chemical dissolution of porous rocks?

The use of the asymptotic limit can greatly simplify the theoretical analysis of chemical dissolution front instabilities in fluid‐saturated rocks and therefore make it possible to obtain mathematical solutions, which often play a crucial role in understanding the propagation behavior of chemical dissolution fronts in chemical dissolution systems. However, there has been a debate in recent years that the asymptotic limit of the acid dissolution capacity (i.e., the acid dissolution capacity number approaching zero) alone cannot lead to a sharp dissolution front of the Stefan type in the acidization dissolution system, in which the dissolvable minerals of carbonate rocks are chemically dissolved by the injected acid flow. The acid dissolution capacity number is commonly defined as the ratio of the volume of the carbonate rock dissolved by an acid to that of the acid. In this paper, we use four different proof methods, including (i) direct use of the fundamental concepts; (ii) use of the mathematical governing equations of an acidization dissolution system; (iii) use of the different time scaling approach; and (iv) use of a moving coordinate system approach, to demonstrate that the asymptotic limit of the acid dissolution capacity can indeed lead to sharp dissolution fronts of the Stefan type in acidization dissolution systems on a much larger time scale (than the dissolution time scale). Our new finding is that on the reaction time scale, the condition of the conventional time derivative of porosity approaching zero alone can ensure that the acidization dissolution front has a sharp shape of the Stefan type. Copyright © 2017 John Wiley & Sons, Ltd.     

Theoretical analyses of chemical dissolution‐front instability in fluid‐saturated porous media under non‐isothermal conditions

This paper mainly deals with the theoretical aspects of chemical dissolution‐front instability problems in two‐dimensional fluid‐saturated porous media under non‐isothermal conditions. In the case of the mineral dissolution ratio (that is defined as the ratio of the dissolved‐mineral equilibrium concentration in the pore fluid to the molar concentration of the dissolvable mineral in the solid matrix of the fluid‐saturated porous medium) approaching zero, the corresponding critical condition has been mathematically derived when temperature variation effects are considered. As a complementary tool, the computational simulation method is used to simulate the morphological evolution of chemical dissolution fronts in two‐dimensional fluid‐saturated porous media under non‐isothermal conditions. The related theoretical and numerical results have demonstrated that: (i) a temperature increase in a non‐isothermal chemical dissolution system can have some influence on the propagation speed of the planar chemical dissolution front in the system. Generally, the chemical dissolution front in the non‐isothermal chemical dissolution system propagates slower than that in the counterpart isothermal chemical dissolution system when the temperature of the non‐isothermal chemical dissolution system is higher than that of the counterpart isothermal chemical dissolution system; (ii) a temperature increase in the non‐isothermal chemical dissolution system can stabilize the chemical dissolution front propagating in the system, because it can cause a decrease in the Zhao number of the system but does not affect the critical Zhao number of the system; and (iii) the temperature gradient in the upstream direction of a chemical dissolution front is smaller than that in the downstream direction of the chemical dissolution front when the non‐isothermal chemical dissolution system is supercritical. Copyright © 2014 John Wiley & Sons, Ltd.     

Effects of medium and pore‐fluid compressibility on chemical‐dissolution front instability in fluid‐saturated porous media

Theoretical analysis and computational simulations have been carried out to investigate how medium and pore‐fluid compressibility affects the chemical‐dissolution front propagation, which is associated with a fully‐coupled nonlinear problem between porosity, pore‐fluid pressure, pore‐fluid density and reactive chemical‐species transport within a deformable and fluid‐saturated porous medium. When the fully‐coupled nonlinear system is in a subcritical state, some analytical solutions have been derived for a special case, in which the ratio of the equilibrium concentration to the solid molar density of the chemical species is approaching zero. To investigate the effect of either medium compressibility or pore‐fluid compressibility on the evolutions of chemical dissolution fronts in supercritical chemical dissolution systems, numerical algorithms and procedures have been also proposed. The related theoretical and numerical results have demonstrated that: (i) not only can pore‐fluid compressibility affect the propagating speeds of chemical dissolution fronts in both subcritical and supercritical systems, but also it can affect the growth and amplitudes of irregular chemical dissolution fronts in supercritical systems; (ii) medium compressibility may have a little influence on the propagating speeds of chemical dissolution fronts, but it can have significant effects on the growth and amplitudes of irregular chemical dissolution fronts in supercritical systems; and (iii) both medium and pore‐fluid compressibility may stabilize irregular chemical‐dissolution‐fronts in supercritical chemical dissolution systems. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical modeling of three‐phase dissolution of underground cavities using a diffuse interface model

Natural evaporite dissolution in the subsurface can lead to cavities having critical dimensions in the sense of mechanical stability. Geomechanical effects may be significant for people and infrastructures because the underground dissolution may lead to subsidence or collapse (sinkholes). The knowledge of the cavity evolution in space and time is thus crucial in many cases. In this paper, we describe the use of a local nonequilibrium diffuse interface model for solving dissolution problems involving multimoving interfaces within three phases, that is, solid–liquid–gas as found in superficial aquifers and karsts. This paper generalizes developments achieved in the fluid–solid case, that is, the saturated case [1]. On one hand, a local nonequilibrium dissolution porous medium theory allows to describe the solid–liquid interface as a diffuse layer characterized by the evolution of a phase indicator (e.g., porosity). On the other hand, the liquid–gas interface evolution is computed using a classical porous medium two‐phase flow model involving a phase saturation, that is, generalized Darcy's laws. Such a diffuse interface model formulation is suitable for the implementation of a finite element or finite volume numerical model on a fixed grid without an explicit treatment of the interface movement. A numerical model has been implemented using a finite volume formulation with adaptive meshing (e.g., adaptive mesh refinement), which improves significantly the computational efficiency and accuracy because fine gridding may be attached to the dissolution front. Finally, some examples of three‐phase dissolution problems including density effects are also provided to illustrate the interest of the proposed theoretical and numerical framework. Copyright © 2014 John Wiley & Sons, Ltd.     

风浪相互作用的Stokes模型

结合非线性Stokes波和平行流线性稳定理论推导出了高阶无粘Orr-Sommerfeld方程及相应的波面压力和能量传递计算公式。针对二阶模型,引入拟非线性能量传递系数以考虑非线性能量,并建立了总能量的统一表达式。采用数值方法求解含有奇点的一阶无粘Orr-Sommerfeld方程,获得了考虑水深影响时的能量传递系数。结果表明,Stokes波各阶分量对应着相同的临界层高度,高阶无粘Orr-Sommerfeld方程可通过坐标变换统一求解。水深变浅将降低小量纲一波速c/U₁时的风浪能量传递系数。     

Computational simulation for the morphological evolution of nonaqueous phase liquid dissolution fronts in two-dimensional fluid-saturated porous media

This paper deals with the computational aspects of nonaqueous phase liquid (NAPL) dissolution front instability in two-dimensional fluid-saturated porous media of finite domains. After the governing equations of an NAPL dissolution system are briefly described, a combination of the finite element and finite difference methods is proposed to solve these equations. In the proposed numerical procedure, the finite difference method is used to discretize time, while the finite element method is used to discretize space. Two benchmark problems, for which either analytical results or previous solutions are available, are used to verify the proposed numerical procedure. The related simulation results from these two benchmark problems have demonstrated that the proposed numerical procedure is useful and applicable for simulating the morphological evolution of NAPL dissolution fronts in two-dimensional fluid-saturated porous media of finite domains. As an application, the proposed numerical procedure has been used to simulate morphological evolution processes for three kinds of NAPL dissolution fronts in supercritical NAPL dissolution systems. It has been recognized that: (1) if the Zhao number of an NAPL dissolution system is in the lower range of the supercritical Zhao numbers, the fundamental mode is predominant; (2) if the Zhao number is in the middle range of the supercritical Zhao numbers, the (normal) fingering mode is the predominant pattern of the NAPL dissolution front; and (3) if the Zhao number is in the higher range of the supercritical Zhao numbers, the fractal mode is predominant for the NAPL dissolution front.     

A porosity-gradient replacement approach for computational simulation of chemical-dissolution front propagation in fluid-saturated porous media including pore-fluid compressibility

In dealing with chemical-dissolution-front propagation problems in fluid-saturated porous media, the chemical dissolution front represented by the porosity of the medium may have a very steep slope (i.e., a very large porosity gradient) at the dissolution front, depending on the mineral dissolution ratio that is defined as the equilibrium concentration of the dissolved minerals in the pore-fluid to the solid molar density of the dissolvable minerals in the solid matrix. When the mineral dissolution ratio approaches zero, the theoretical value of the porosity gradient tends to infinity at the chemical dissolution front. Even for a very small value of the mineral dissolution ratio, which is very common in geochemical systems, the porosity gradient can be large enough to cause the solution hard to converge when the conventional finite element method is used to solve a chemical dissolution problem in a fluid-saturated porous medium where the pore-fluid is compressible. To improve the convergent speed of solution, a porosity-gradient replacement approach, in which the term involving porosity-gradient computation is replaced by a new term consisting of pore-fluid density-gradient and pressure-gradient computation, is first proposed and then incorporated into the finite element method in this study. Through comparing the numerical results obtained from the proposed approach with the theoretical solutions for a benchmark problem, it has been demonstrated that not only can the solution divergence be avoid, but also the accurate simulation results can be obtained when the proposed porosity-gradient replacement approach is used to solve chemical-dissolution-front propagation problems in fluid-saturated porous media including pore-fluid compressibility.     

Response of coastal plain rivers to falling relative sea-level: allogenic controls on the aggradational phase

This study combines mathematical modelling and supporting flume experiments to address the problem of how coastal plain rivers respond to a steady fall in relative sea-level. The theoretical component of the study focuses on the development of a moving boundary model of fluviodeltaic progradation that treats rigorously the dynamics of the shoreline and alluvial–basement transition (the upstream limit of the alluvial river system). Dimensional analysis and numerical solutions to the model governing equations together suggest that, at first order, coastal plain rivers will remain aggradational on a timescale that varies with allogenic sediment and water supply and the fall rate of relative sea-level. In natural fluviodeltaic systems, this intrinsic timescale is likely to vary by several orders of magnitude, suggesting that the aggradational phase of river response can be geologically long-lived. At second order, the duration of alluvial aggradation is controlled by two dimensionless numbers that embody system geometry and the kinematics of alluvial sediment transport. Model predictions were tested in a series of carefully scaled flume experiments. The level of agreement between predicted and measured trajectories for the shoreline and alluvial–basement transition strongly suggests that the moving boundary theory developed here successfully captures the response of small-scale fluviodeltaic systems to falling sea-level. The results of this study have several sequence-stratigraphic implications: a fall in relative sea-level at the shoreline is not a sufficient condition for river incision; the onset of alluvial degradation and sequence-boundary formation need not coincide with a maximum in the rate of sea-level fall; and the onset of sequence-boundary formation is sensitive to allogenic sediment supply.     

Reactive infiltration instability of a granitization front during the generation and development of granite-gneiss domes

The origin of granite-gneiss domes is traditionally attributed to gravity tectonics, the ascent of granite-gneiss diapirs in a gravitational field owing to a relative decrease in the density of granitized rocks compared with their protolith. This is usually considered by the example of a two-layer medium with a lower layer of granitized rocks overlain by a denser protolith layer; the development of gravitational instability in the system results in the ascent of a granite-gneiss diapir. However, the diapiric process can be initiated only if Archimedes?? buoyancy forces at the roof of the granite-gneiss layer will overcome the resistance of the protolith rocks related to their long-term strength. Under the conditions of plastic deformations, this requires the existence of a large-scale irregularity in the relief of the layer boundary, namely, an antiform cusp in the roof of the granite-gneiss layer. The model is based on the assumption that such antiforms appear owing to the reactive infiltration instability of the morphology of the granitization front caused by an increase in the fluid permeability of granitized rocks compared with that of the protolith. The results of computer modeling support the geological feasibility of the reactive infiltration mechanism of the generation and development of the protodiapiric forms of the granitization front triggering the development of the diapiric process of the gravitational upwelling of granite-gneiss domes. The model of a protodiapir stage allows us to consider dome formation as a result of the development of two sequential instabilities: the reactive infiltration instability of the granitization front related to an increase in the permeability of the transformed rock followed by the gravitational instability related to a relative decrease in rock density.     

直-增-稳剖面设计问题的解析解

使用无量纲化方法对设计方程组进行了改写,新的无量纲化设计方程组有利于充分利用三角函数公式求解析解,所得到的解析解计算公式具有简洁的数学形式。将设计方程组求解问题分成两类,对于已知最大井斜角的第Ⅰ类问题,使用线性代数解方程组的克莱默法则直接就可以得出解析解。最大井斜角为未知数的第Ⅱ类问题,使用三角函数公式进行化简,得到形式简单、统一的解析解公式,避免了使用半角公式所带来的解析解计算公式的复杂性。所使用无量纲化方法具有一定的普适性,可以用于解决其他类型的二维剖面设计问题。     

Structural characterization and chemical reactivity of synthetic Mn-goethites and hematites

Several goethites were obtained through the hydrolysis at 60 °C of Fe(III) solutions containing variable amounts of Mn(II) ions. The obtained samples were thermally treated at temperatures ranging from 180 to 310 °C until the complete phase transformation to hematite was achieved. The effect of Mn in the dehydroxylation process was investigated using X-ray diffraction (XRD) and the Rietveld refinement of XRD data together with scanning electron microscopy (SEM), differential thermogravimetric analysis (DTA) and Fourier transform infrared spectroscopy (FTIR). In all cases, the formed hematites retained the acicular shape of the precursor goethite. The dehydroxylation temperature increased with the increase of the Mn content in the parent goethite. The cell parameters of both phases decreased with the thermal treatment, however the decrease in the goethite b-parameter was more pronounced. This fact could be attributed to the distortion in the goethite structure by the presence of manganese. The band shifts in the FT-IR spectra of the goethites with different Mn substitution were analysed. The intensities of the hydroxyl vibrations were indicative of the degree of dehydroxylation.The chemical reactivity of all the samples, before and after the thermal treatment, was also studied. The kinetic experiments were carried out at 40 °C in 4 mol dm^− 3 HCl. The acid dissolution of all Mn-goethites showed a congruent behavior indicative of a homogeneous distribution of Mn in the goethite crystals, this trend was not observed in the formed hematites presenting a high Mn content. The dissolution rate in goethites increased with the increase of Mn content, the opposite effect was observed in the corresponding hematites. The activation energy in both phases was also obtained and indicated that the Mn substitution produces an opposite effect on goethite- and hematite-phases. Different kinetic laws were applied in order to explain the dissolution behavior, but the modified first-order Kabai equation described the dissolution data best.     

考虑非饱和浸润区的改进Green-Ampt模型

经典Green-Ampt入渗模型计算简单,广泛应用于土壤入渗问题的研究,但在湿润锋处理上采用明显的干湿分离界面,存在一定的理论假设。鉴于此,基于饱和区−非饱和浸润区分层模型,结合达西定律,推导出入渗过程中饱和区厚度与非饱和浸润区厚度关系的理论公式,提出了水分剖面理论模型,消除了饱和区厚度和浸润区厚度的关系假设。在此基础上,建立了考虑土壤水分剖面形状和非饱和浸润区等效参数的改进Green-Ampt模型,并采用试验和有限元数值仿真对该模型进行了验证,结果表明：该模型有很高的精度,对不同类型的土有很好的适应性。同时该模型求解简单,参数物理意义明确,便于工程应用。     

The effect of Fe-oxidizing bacteria on Fe-silicate mineral dissolution

Acidithiobacillus ferrooxidans are commonly present in acid mine drainage (AMD). A. ferrooxidans derive metabolic energy from oxidation of Fe²⁺ present in natural acid solutions and also may be able to utilize Fe²⁺ released by dissolution of silicate minerals during acid neutralization reactions. Natural and synthetic fayalites were reacted in solutions with initial pH values of 2.0, 3.0 and 4.0 in the presence of A. ferrooxidans and in abiotic solutions in order to determine whether these chemolithotrophic bacteria can be sustained by acid-promoted fayalite dissolution and to measure the impact of their metabolism on acid neutralization rates. The production of almost the maximum Fe³⁺ from the available Fe in solution in microbial experiments (compared to no production of Fe³⁺ in abiotic controls) confirms A. ferrooxidans metabolism. Furthermore, cell division was detected and the total cell numbers increased over the duration of experiments. Thus, over the pH range 2–4, fayalite dissolution can sustain growth of A. ferrooxidans. However, ferric iron released by A. ferrooxidans metabolism dramatically inhibited dissolution rates by 50–98% compared to the abiotic controls.

Two sets of abiotic experiments were conducted to determine why microbial iron oxidation suppressed fayalite dissolution. Firstly, fayalite was dissolved at pH 2 in fully oxygenated and anoxic solutions. No significant difference was observed between rates in these experiments, as expected, due to extremely slow inorganic ferrous iron oxidation rates at pH 2. Experiments were also carried out to determine the effects of the concentrations of Fe²⁺, Mg²⁺ and Fe³⁺ on fayalite dissolution. Neither Fe²⁺ nor Mg²⁺ had an effect on the dissolution reaction. However, Fe³⁺, in the solution, inhibited both silica and iron release in the control, very similar to the biologically mediated fayalite dissolution reaction. Because ferric iron produced in microbial experiments was partitioned into nanocrystalline goethite (with very low Si) that was loosely associated with fayalite surfaces or coated the A. ferrooxidans cells, the decreased rates of accumulation of Fe and Si in solution cannot be attributed to diffusion inhibition by goethite or to precipitation of Fe–Si-rich minerals. The magnitude of the effect of Fe³⁺ addition (or enzymatic iron oxidation) on fayalite dissolution rates, especially at low extents of fayalite reaction, is most consistent with suppression of dissolution by interaction between Fe³⁺ and surface sites. These results suggest that microorganisms can significantly reduce the rate at which silicate hydrolysis reactions can neutralize acidic solutions in the environment.