Selection in the Saffman-Taylor finger problem and the Taylor-Saffman bubble problem without surface tension

AbstractWe consider the Saffman-Taylor problem describing the displacement of one fluid by another having a smaller viscosity, in a porous medium or in a Hele-Shaw configuration, and the Taylor-Saffman problem of a bubble moving in a channel containing moving fluid. Each problem is known to possess a family of solutions, the former corresponding to propagating fingers and the latter to propagating bubbles, with each member characterized by its own velocity and each occupying a different fraction of the porous channel through which it propagates. To select the correct member of the family of solutions, the conventional approach has been to add surface tension σ and then take the limit σ → 0. We propose a selection criterion that does not rely on surface tension arguments

Effect of milnacipran on suicidality in patients with mild to moderate depressive disorder

The presence of suicidal manifestations (thoughts and behavior) was studied in a cohort of 30 patients with mild to moderate depression during a 6-week treatment with the serotonin-norepinephrine reuptake inhibitor, milnacipran. At baseline mild suicidal thoughts were present in 46.7% of patients, the mean Hamilton Depression Rating Score (HDRS17) was 23.9 ± 1.8 and the mean suicidality score on the Beck Scale for Suicidal Ideation (BSS) was 4.9 ± 4.9. Suicidal thoughts decreased progressively throughout the study in parallel with other depressive symptoms. At no time during treatment was there any indication of an increased suicidal risk. Notably, the items retardation and psychic anxiety on the HDRS17 decreased in parallel. This may possibly explain the lack of any “activation syndrome”, which is occasionally observed at the early stages of therapy with some antidepressants and may be linked to a temporary increase in suicidal ideation. To our knowledge this is the first detailed report of suicidality during treatment with milnacipran

Fingering Instability in Combustion

A thin solid (e.g., paper), burning against an oxidizing wind, develops a fingering instability with two decoupled length scales. The spacing between fingers is determined by the P\'eclet number (ratio between advection and diffusion). The finger width is determined by the degree two dimensionality. Dense fingers develop by recurrent tip splitting. The effect is observed when vertical mass transport (due to gravity) is suppressed. The experimental results quantitatively verify a model based on diffusion limited transport

Self-similarity in Laplacian Growth

We consider Laplacian Growth of self-similar domains in different geometries. Self-similarity determines the analytic structure of the Schwarz function of the moving boundary. The knowledge of this analytic structure allows us to derive the integral equation for the conformal map. It is shown that solutions to the integral equation obey also a second order differential equation which is the one dimensional Schroedinger equation with the sinh inverse square potential. The solutions, which are expressed through the Gauss hypergeometric function, characterize the geometry of self-similar patterns in a wedge. We also find the potential for the Coulomb gas representation of the self-similar Laplacian growth in a wedge and calculate the corresponding free energy.Comment: 16 pages, 9 figure

Microscopic Selection of Fluid Fingering Pattern

We study the issue of the selection of viscous fingering patterns in the limit of small surface tension. Through detailed simulations of anisotropic fingering, we demonstrate conclusively that no selection independent of the small-scale cutoff (macroscopic selection) occurs in this system. Rather, the small-scale cutoff completely controls the pattern, even on short time scales, in accord with the theory of microscopic solvability. We demonstrate that ordered patterns are dynamically selected only for not too small surface tensions. For extremely small surface tensions, the system exhibits chaotic behavior and no regular pattern is realized.Comment: 6 pages, 5 figure

Scaling, Propagation, and Kinetic Roughening of Flame Fronts in Random Media

We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the background reactant density. We first show analytically and numerically that there is a finite critical value of the background density, below which the front associated with the temperature field stops propagating. The critical exponents associated with this transition are shown to be consistent with mean field theory of percolation. Second, we study the kinetic roughening associated with a moving planar flame front above the critical density. By numerically calculating the time dependent width and equal time height correlation function of the front, we demonstrate that the roughening process belongs to the universality class of the Kardar-Parisi-Zhang interface equation. Finally, we show how this interface equation can be analytically derived from our model in the limit of almost uniform background density.Comment: Standard LaTeX, no figures, 29 pages; (to appear in J. Stat. Phys. vol.81, 1995). Complete file available at http://www.physics.helsinki.fi/tft/tft.html or anonymous ftp at ftp://rock.helsinki.fi/pub/preprints/tft

Toward the Control of the Smoldering Front in the Reaction-Trailing Mode in Oil Shale Semicoke Porous Media

Results of an experimental investigation on the feasibility of propagating a smoldering front in reaction-trailing mode throughout an oil shale semicoke porous medium are reported. For oil recovery applications, this mode is particularly interesting to avoid low-temperature oxidation reactions, which appear simultaneously with organic matter devolatilization in the reaction-leading mode and are responsible for oxidation of part of the heavy oil. The particularity of this mode is that, contrary to the reaction-leading mode largely studied in the literature, the heat-transfer layer precedes the combustion layer. This leads to two separated high-temperature zones: (i) a devolatilization zone (free of oxygen), where the organic matter is thermally decomposed to incondensable gases, heavy oil, andfixed carbon, also called coke in the literature, without any oxidation, followed by (ii) an oxidation zone, where thefixed carbon left by devolatilization is oxidized. The transition from reaction-leading to reaction-trailing mode was obtained using low oxygen contents in the fed air. It is shown that two distinct layers, the heat-transfer layer and the combustion layer, propagate in a stable and repeatable way. The decrease of the oxygen fraction leads to a decrease of the smoldering temperature and to strongly limit the decarbonation of the mineral matrix. The CO2 emissions are limited. Regardless of the front temperature, all of the fed oxygen is consumed and all of thefixed carbon is oxidized at the passage of the smoldering front

The effect of pH, grain size, and organic ligands on biotite weathering rates

Biotite dissolution rates were determined at 25 °C, at pH 2–6, and as a function of mineral composition, grain size, and aqueous organic ligand concentration. Rates were measured using both open- and closed-system reactors in fluids of constant ionic strength. Element release was non-stoichiometric and followed the general trend of Fe, Mg > Al > Si. Biotite surface area normalised dissolution rates (ri) in the acidic range, generated from Si release, are consistent with the empirical rate law: ri=kH,iaxiH+ where kH,i refers to an apparent rate constant, aH+ designates the activity of protons, and xi stands for a reaction order with respect to protons. Rate constants range from 2.15 × 10−10 to 30.6 × 10−10 (molesbiotite m−2 s−1) with reaction orders ranging from 0.31 to 0.58. At near-neutral pH in the closed-system experiments, the release of Al was stoichiometric compared to Si, but Fe was preferentially retained in the solid phase, possibly as a secondary phase. Biotite dissolution was highly spatially anisotropic with its edges being ∼120 times more reactive than its basal planes. Low organic ligand concentrations slightly enhanced biotite dissolution rates. These measured rates illuminate mineral–fluid–organism chemical interactions, which occur in the natural environment, and how organic exudates enhance nutrient mobilisation for microorganism acquisition

Apophyllite alteration in aqueous solutions

Die Reaktionen von Apophyllit (einem K-Ca-Schichtsilikathydrat) mit wäßrigen Lösungen wurden bei verschiedenen pH-Werten (1,5 - 10) und verschiedenen Temperaturen (20 - 135°C) untersucht. Dabei ergab die Anwendung einer Kombination aus hydrothermaler Rasterkraftmikroskopie (HAFM) und mehreren spektroskopischen Methoden detaillierte Erkenntnisse über den Mechanismus und die Kinetik der Alteration von Apophyllit in wäßrigen Lösungen. Auf der (001) Oberfläche von Apophyllit treten in Abhängigkeit des pH-Wertes und der Temperatur verschiedene Reaktionstypen auf. Mit dem HAFM gelang es erstmalig, die Schichtaufweitung von Schichtsilikaten in-situ mit nano-skaliger Ortsauflösung zu beobachten. Aufgrund der Datenbasis wurden Parallelen zu anderen Schichtsilikaten unter entsprechenden Bedingungen gezogen. Die vorliegenden Ergebnisse betonen die Reaktivität der Basisflächen von Schichtsilikaten und liefern neue Details über ihr Quellverhalten in wäßrigen Lösungen.The reactions of apophyllite (a hydrous K-Ca-phyllosilicate) with aqueous solutions were studied at different pH (1.5 - 10) and different temperature (20 - 135°C). A combination of hydrothermal atomic force microscopy (HAFM) with several spectroscopic methods provided detailed knowledge on the mechanisms and kinetics of apophyllite alteration in aqueous solutions. Depending on pH and temperature, different types of reactions occur on apophyllite (001) surface. By using HAFM, it was for the first time possible to observe crystalline swelling of phyllosilicates in-situ at a nanoscale resolution. On the basis of the data, analogues to the behaviour of other phyllosilicates at appropriate conditions have been drawn. Present results stress the reactivity of the basal surfaces of phyllosilicates and provide new details about their swelling behaviour in aqueous solution