P. Ortoleva

Fluctuations and transitions at chemical instabilities: The analogy to phase transitions

The properties of a reacting system near an instability are investigated and the analogy between transitions in unstable systems and equilibrium phase transitions is developed in detail. The set of macroscopic steady state rate equations plays the role of an equation of state. The bifurcation points of this set are analogous to transition and critical points of equilibrium phase transitions. Hard transitions of unstable systems correspond to first order and soft transitions to second and higher order phase transitions. Critical exponents are defined for those properties of the unstable systems which are singular at the transition points, and relations between these critical exponents are investigated. Critical fluctuations are studied with stochastic analogs of the macroscopic rate equations. Both master and Langevin equations are considered and lead to the following conclusions: When a transition or a critical point is approached (a) the amplitude of fluctuations grows; (b) the lifetime of these fluctuat...

Pressure solution in sandstones: influence of clays and dependence on temperature and stress

Abstract The enhancement of dissolution of quartz under the influence of clays has been recognized in sandstones for many years. It is well known that a grain of quartz in contact with a clay flake dissolves faster than when in contact with another grain of quartz. This phenomenon promotes silica transfer during the diagenesis of sandstones and is responsible of deformation and porosity variations. Here we make an attempt to explain the process of this rock deformation using a pressure solution mechanism. The model of water film diffusion assumes that matter is dissolved inside the contact between two grains. The resulting solutes are transported to the pore fluid through diffusion along an adsorbed water film. Between two micas, this trapped film is thicker than between two grains of quartz. As a consequence diffusion is easier and the rate of pressure solution faster. Experiments on pressure solution show that diffusion controls the mechanism at great depth whereas a model based on natural mica indentation indicates that kinetics is the limiting process through the precipitation rate of quartz at low depth, thus temperature is a crucial parameter. There should be a transition between thermally controlled rate and diffusion limited evolution.

Oscillatory zoning in plagioclase feldspar.

A kinetic mathematical model of crystal growth from the melt is used to describe quantitatively the phenomenon of oscillatory zoning in plagioclase feldspar. In this model, the functional dependence of crystal growth rate on both melt and crystal surface composition and the transport of material within the melt are explicitly considered. Oscillatory zoning is found to develop for a wide variety of such functional dependence and to be sensitive to the initial composition of the melt.

On a variety of wave phenomena in chemical reactions

A variety of wave phenomena are analyzed and discussed for systems in which chemical reactions and transport take place. Certain families of wave solutions of reaction‐transport equations arise owing to the weak stability of a reference state to a class of perturbations. We consider both wave induction by heterogeneities and autonomous waves and seek perturbation solutions which provide the dispersion relation and the wave vector dependence of the amplitude for one‐parameter families of waves characterized by the wave vector. For the case of an arbitrary reaction mechanism possessing a homogeneous steady state we derive, by use of bifurcation theory and frequency renormalization, small amplitude autonomous plane waves and standing and rotating waves. We find solutions corresponding to long wavelength waves, static structures, and phenomena existing only at intermediate frequencies and wavelengths. The theory is found to have a nonuniformity in convergence in the core region of pacemaker and spiral‐like so...

A coupled reaction/transport/mechanical model for intergranular pressure solution, stylolites, and differential compaction and cementation in clean sandstones

Abstract “Pressure solution” at grain-grain contacts and free-face dissolution and growth kinetics coupled to solute transport and texture-dependent effective stress are shown to lead to pervasive intergranular compaction and the development of stylolites in sandstones. Reaction/transport modeling studies presented here demonstrate that stylolite formation may arise from an instability of a chemically compacting rock, leading to the enhancement of spatial heterogeneities in rock texture. Textural and geochemical criteria distinguishing between conditions favoring stylolites vs. pervasive intergranular pressure solution for both the water film diffusion (WFD) and free-face pressure solution (FFPS) mechanisms (so denoted in Tada et al., 1987) are outlined. WFD and FFPS each show a characteristic grain size dependence which aids in the recognition of the kinetic mechanism responsible for pressure solution. Results from our simulations concerning the effect of grain size on the stable compaction of sandstones compare favorably to observations and data in Houseknecht (1988). They suggest that FFPS is operative in clean sandstones, while WFD is operative in clay-rich sandstones. Spatially discrete domains of heightened cementation and intergranular pressure solution-induced compaction are shown to develop from certain types of initial spatial variations in grain textural parameters. These features, predicted by our computer simulation, show differential cementation/compaction trends similar to examples observed in Paleozoic sandstones. The greatest contrasts in cementation, compaction, and porosity attend the FFPS mechanism.

Periodic precipitation and coarsening waves: Applications of the competitive particle growth modela)

It has been shown earlier that the competitive growth dynamics of particles in a sol can account for spontaneous precipitation patterns that arise as a uniform sol ages. Here it is found that this dynamics can, unlike the classic Ostwald–Prager theory, account for a complete range of precipitation pattern types including Runge–Liesegang bands, invert bands, secondary banding, spontaneous pattern formation from a uniform sol and propagation, and destabilization of fronts of coarsening. Effects of electrical fields on banding are also investigated. A characteristic length is obtained and is found to be a strictly nonlinear effect.

Theory of propagation of discontinuities in kinetic systems with multiple time scales: Fronts, front multiplicity, and pulses

We consider a reaction–diffusion system far from chemical equilibrium, with kinetics on multiple time scales and the capacity of attaining one or multiple homogeneous stable steady states. For such systems we present a theory of the structure (concentration profile) and velocity of fronts based on a matched asymptotic solution of the singular perturbation problem. We analyze single front (wave) propagation as a transition occurs from one stable stationary state to another; show the possibility of multiple mode front propagation; and discuss single pulse propagation in systems with one stable stationary state. For each process we confirm the theory by comparison with numerical solutions of the coupled differential equations for a model system. Finally, by application of the theory we discuss a reduction of the complexity of the stability analysis of these fronts.

Generation of evenly-spaced pressure-solution seams during (late) diagenesis: A kinetic theory

AbstractStylolites and pressure-solution seams can form during diagenesis of rocks subjected to stress through a feedback involving texture and pore-fluid solute concentration. This feedback destabilizes the state of uniform texture (represented here only by porosity, for simplicity). A mathematical kinetic model that includes pressure solution, diffusion, and reprecipitation predicts the spontaneous generation, even in initially uniform rocks, of regions alternatingly (in space) more and less soluble. A region that becomes more soluble also becomes simultaneously more porous. The kinetic theory predicts that Stylolites can form at roughly constant spacings; this agrees with many field and petrographic observations. Bedding planes between beds that have initially different texture are shown by the theory to be the focus of a porosity instability that can lead to the formation of a stylolite and to the generation of more Stylolites within each bed. This prediction agrees with the observation that many Stylolites have developed at bedding planes.Finally, the theory, on the basis of transport, kinetic and thermodynamic properties for calcite and quartz and their aqueous ions, predicts the order of magnitude of both the spacing between Stylolites and their time of formation. For limestones the predicted spacing has a very large range, perhaps from 10−4 to 102 cm, and for quartz arenites, chert, and quartzites it is between 0.025 and 3 cm. These values agree crudely with spacings observed in rocks. The predicted times of formation of Stylolites in quartzose rocks are not unreasonable: 6,300 to 1.7×106 years. The range of formation times for Sstylolites in limestones is very large due, as for the predicted spacings, to the sensitivity of both the solubility and growth/dissolution kinetics of calcite to pH,

Phase Waves in Oscillatory Chemical Reactions.

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