Dilute Fluid Research Articles

An Incompressible Polymer Fluid Interacting with a Koiter Shell

We study a mutually coupled mesoscopic-macroscopic-shell system of equations modeling a dilute incompressible polymer fluid which is evolving and interacting with a flexible shell of Koiter type. The polymer constitutes a solvent-solute mixture where the solvent is modelled on the macroscopic scale by the incompressible Navier–Stokes equation and the solute is modelled on the mesoscopic scale by a Fokker–Planck equation (Kolmogorov forward equation) for the probability density function of the bead-spring polymer chain configuration. This mixture interacts with a nonlinear elastic shell which serves as a moving boundary of the physical spatial domain of the polymer fluid. We use the classical model by Koiter to describe the shell movement which yields a fully nonlinear fourth order hyperbolic equation. Our main result is the existence of a weak solution to the underlying system which exists until the Koiter energy degenerates or the flexible shell approaches a self-intersection.

Stochastic motion of finite-size immiscible impurities in a dilute quantum fluid at finite temperature

The dynamics of an active, finite-size and immiscible impurity in a dilute quantum fluid at finite temperature is characterized by means of numerical simulations of the projected Gross--Pitaevskii equation. The impurity is modeled as a localized repulsive potential and described with classical degrees of freedom. It is shown that impurities of different sizes thermalize with the fluid and undergo a stochastic dynamics compatible with an Ornstein--Uhlenbeck process at sufficiently large time-lags. The velocity correlation function and the displacement of the impurity are measured and an increment of the friction with temperature is observed. Such behavior is phenomenologically explained in a scenario where the impurity exchanges momentum with a dilute gas of thermal excitations, experiencing an Epstein drag.

Fluid geochemistry and isotope compositions to delineate physical processes in Wayang Windu geothermal reservoir, Indonesia

Wayang Windu geothermal field, which is situated in quaternary volcanic rock, has been delivering 227 MW of electricity and is planned to be developed in near future. Isotope and geochemistry study has been done to support understanding of the system. Samples were taken from thermal manifestations and production wells (two-phase and dry steam wells) to analyse its isotope and chemical compositions. Most of the hot springs are bicarbonate type and have neutral pH values, except for steam heated waters found near fumarolic fields, which are acid sulfate type waters. Deep brine fluids are of mature chloride type, while other deep dilute fluids are bicarbonate type indicates the existance of condensate layer. Solute and gas geothermometer calculation showed good agreement with measured temperature, i.e., 280–300 °C. However, gas-gas equilibria calculation showed increasing T and decreasing y (steam fraction) compare to previous study which indicates contribution form hotter source with high liquid saturation. Aside from different recharge area of thermal manifestation and production wells, the isotopes composition also shows physical processes in reservoir, i.e., adiabatic boiling, steam separation at different temperature (140–260 °C) and steam fraction (0.30–0.65), and also mixing process with meteoric water.

A Simple Construction of a Thermodynamically Consistent Mathematical Model for Non-Isothermal Flows of Dilute Compressible Polymeric Fluids

We revisit some classical models for dilute polymeric fluids, and we show that thermodynamically consistent models for non-isothermal flows of these fluids can be derived in a very elementary manner. Our approach is based on the identification of energy storage mechanisms and entropy production mechanisms in the fluid of interest, which, in turn, leads to explicit formulae for the Cauchy stress tensor and for all of the fluxes involved. Having identified these mechanisms and derived the governing equations, we document the potential use of the thermodynamic basis of the model in a rudimentary stability analysis. In particular, we focus on finite amplitude (nonlinear) stability of a stationary spatially homogeneous state in a thermodynamically isolated system.

Ge and Si Isotope Behavior During Intense Tropical Weathering and Ecosystem Cycling

AbstractChemical weathering of volcanic rocks in warm and humid climates contributes disproportionately to global solute fluxes. Geochemical signatures of solutes and solids formed during this process can help quantify and reconstruct weathering intensity in the past. Here, we measured silicon (Si) and germanium (Ge) isotope ratios of the soils, clays, and fluids from a tropical lowland rainforest in Costa Rica. The bulk topsoil is intensely weathered and isotopically light (mean ± 1σ: δ30Si = −2.1 ± 0.3‰, δ74Ge = −0.13 ± 0.12‰) compared to the parent rock (δ30Si = −0.11 ± 0.05‰, δ74Ge = 0.59 ± 0.07‰). Neoforming clays have even lower values (δ30Si = −2.5 ± 0.2‰, δ74Ge = −0.16 ± 0.09‰), demonstrating a whole‐system isotopic shift in extremely weathered systems. The lowland streams represent mixing of dilute local fluids (δ30Si = 0.2 − 0.6‰, δ74Ge = 2.2 − 2.6‰) with solute‐rich interbasin groundwater (δ30Si = 1.0 ± 0.2‰, δ74Ge = 4.0‰). Using a Ge‐Si isotope mass balance model, we calculate that 91 ± 9% of Ge released via weathering of lowland soils is sequestered by neoforming clays, 9 ± 9% by vegetation, and only 0.2 ± 0.2% remains dissolved. Vegetation plays an important role in the Si cycle, directly sequestering 39 ± 14% of released Si and enhancing clay neoformation in surface soils via the addition of amorphous phytolith silica. Globally, volcanic soil δ74Ge closely tracks the depletion of Ge by chemical weathering (τGe), whereas δ30Si and Ge/Si both reflect the loss of Si (τSi). Because of the different chemical mobilities of Ge and Si, a δ74Ge‐δ30Si multiproxy system is sensitive to a wider range of weathering intensities than each isotopic system in isolation.

Multiple sulfur isotope fractionation in hydrothermal systems in the presence of radical ions and molecular sulfur

This study is aimed to evaluate the role played by the sulfur radical ions (S3− and S2−) and molecular sulfur (S0) on sulfur isotope fractionation and to investigate if these species may leave an isotope fingerprint in hydrothermal systems. For this purpose, we combined (i) experiments using a hydrothermal reactor with aqueous S3−(S2−)-S0-sulfate-sulfide fluids and pyrite across a wide range of temperatures (300–450 °C), pressures (300–800 bars), fluid acidity (4 < pH < 8) and with elevated total sulfur concentrations (0.1–1.0 mol/kg fluid) favorable for formation of those polymeric sulfur species, (ii) precise quadruple S isotope analyses of the different S-bearing aqueous species in sampled fluids and in-situ precipitated pyrite, and (iii) thermodynamic modeling of sulfur aqueous speciation and solubility. Our results quantitatively confirm both equilibrium and kinetic SO4-H2S and pyrite-H2S mass dependent fractionation (MDF) factors previously established using extensive experimental and natural data from more dilute fluids in which polymeric sulfur species are negligible. MDF signatures of S0 measured in the sampled fluids of this study reveal different S0-forming pathways such as (i) breakdown on cooling of S3− (and S2−) and other chain-like S0 polymers only stable at high temperature and being isotopically identical to H2S; (ii) cyclooctasulfur (S80, liquid or solid) precipitating by recombination of sulfate and sulfide and/or by exchange with polysulfide dianions (Sn2−) on cooling and being slightly 34S-enriched compared to H2S (by ∼2‰ of δ34S); and iii) a different type of S0 resulting from thiosulfate irreversible breakdown and being highly 34S-depleted (by ∼12‰) relative to H2S. Our data do not show any significant mass independent fractionation (MIF) of 33S and 36S, with Δ33S and Δ36S values of any S aqueous species and pyrite being within ±0.1‰ and ±1.0‰, respectively. Therefore, under the investigated experimental conditions, the radical S3− ion is unlikely to generate significant MIF in the hydrothermal fluid phase and in pyrite and native sulfur precipitated therefrom. Our study supports the existing interpretations of small Δ33S and Δ36S variations between sulfide/sulfate-bearing fluid and pyrite as MDF in terms of reaction kinetics, different reaction pathways, and mass conservation effects such as mixing of S reservoirs or Rayleigh distillation. Our data extend, across a wider range of sulfur concentration and chemical speciation, the existing multiple S isotopes models that exploit such variations as a complement to the traditional δ34S tracer to monitor the approach to equilibrium and evolution of hydrothermal fluids.

The incompressible limit of compressible finitely extensible nonlinear bead-spring chain models for dilute polymeric fluids

We explore the behaviour of global-in-time weak solutions to a class of bead-spring chain models, with finitely extensible nonlinear elastic (FENE) spring potentials, for dilute polymeric fluids. In the models under consideration the solvent is assumed to be a compressible, isentropic, viscous, isothermal Newtonian fluid, confined to a bounded open domain in R3, and the velocity field is assumed to satisfy a complete slip boundary condition. We show that as the Mach number tends to zero the system is driven to its incompressible counterpart.

ON SUSPENSION STABILITY OF NANOPARTICLES TO ENHANCE THERMAL PERFORMANCE OF MHD NANOFLUID FLOW OVER A STRETCHABLE ROTATING DISK WITH BIOCONVECTION EFFECTS

Heat and flow characteristics for bioconvection of nanofluid due to a radially stretching and rotating disk are examined. The nanofluid bioconvection is caused by the combined effects of magnetic field and buoyancy force on the interaction of motile gyrotactic microorganisms and nanoparticles in a dilute base fluid. The doping of suspended gyrotactic microorganisms and nanoparticles produces innovative heat transfer enhancement with provision of higher thermal conductivity through stability of nano particles. The motile microorganisms are self-propelled and they can actively swim in the fluid in response to such stimuli as gravity, light or chemical attraction. The computational results for physical quantities of interest due to influential thermophysical parameters and bioconvection parameters have been evaluated by employing bvp4c solver in Matlab. It is observed that the cooling rate becomes faster when radial stretching, Brownian diffusion and thermophoretic diffusion are increased.

The geochemistry of produced waters from the Tuscaloosa Marine Shale, USA

Produced water is a byproduct of oil and gas production. The chemistry of produced water may provide information about the source of the fluid and its evolution, leading to an improved understanding of the hydrology of petroleum systems. In this study, samples from 19 wells from the Tuscaloosa Marine Shale (TMS) in Mississippi and Louisiana, USA were analyzed for their major and trace element compositions. Data obtained from produced waters from the TMS were compared to existing chemical data from produced waters collected from nearby hydrocarbon reservoir rocks within the Gulf Coast Basin. The results show that produced waters from the TMS are highly saline, with a mean concentration of 15.9 g/L of total dissolved solids. Comparison of the chemistry of produced water from the TMS to early flowback waters demonstrated a rapid shift from the more dilute fracturing fluid to the formation water endmember composition. Most of the trace metals showed a moderate to strong correlation with the overall salinity of the waters. Concentrations of Cu and V showed a moderate correlation with the amount of oil produced from the TMS wells, suggesting that these elements are strongly affiliated with the kerogen and subsequent dissolved (<0.45 μm) organic phases. Analysis of the volume of produced water compared to the volume of water used during hydraulic fracturing indicates that 15%–110% of the water volume used for fracking had been returned to the surface over the 2–5 year production period of the sampled wells. Chloride to bromide ratios suggest that the formation water in the TMS was derived from evaporated seawater. Comparison to historical data for produced waters in other formations in and around the Mississippi Salt Basin showed that waters in all the formations had a consistent origin (bitterns likely derived from the formation of the Louann salt). This implies that over geologic time periods fluids migrated through the TMS despite its low permeability present-day. The TMS also exhibited lower concentrations of dissolved transition metals such as Zn and Pb relative to those described in adjacent formations. This observation may suggest the presence of larger amounts of H2S, limiting the solubility of sulfide phases, in the shale unit relative to adjacent reservoir units.

Jianite: Massive Dunite Solely Made of Virtually Pure Forsterite from Ji’an County, Jilin Province, Northeast China

A rare massive yellowish-green serpentinized dunite, covering a minimum area up to ~50 m2, has been found in Ji’an County, Jilin Province, Northeast China. It contains primary olivine and secondary serpentine (antigorite) and brucite. Other primary minerals like orthopyroxene, clinopyroxene, and aluminum-rich phase (such as garnet, spinel, and plagioclase), frequently appearing in ultramafic rocks, have not been identified. The olivine is essentially pure forsterite, with an Mg# (100 × Mg/(Mg + Fe)) of ~99.6–99.7. Due to these distinct features, we especially name the protolith of this dunite as jianite (集安岩). The forsterite grains range up to ~2 mm, show clear equilibrium textures such as nearly straight grain boundaries and ~120° dihedral angles at their triple junctions, and display no intragranular or intergranular composition variations. They are extensively ruptured and hydrated (i.e., serpentinized), with the fractures (and the grain boundaries as well) filled by fine-grained antigorite (ideally Mg6(Si4O10)(OH)8) and brucite (ideally Mg(OH)2). These secondary phases are also extremely poor in Fe, indicating a good chemical equilibrium with the forsterite. The serpentinization reaction may have proceeded as forsterite + fluid = antigorite + brucite at temperatures of ~425(25) °C and at relatively low but undetermined pressures. The fluid was likely a B-rich, but Si-poor dilute aqueous fluid, as implied by the trace element characteristics and water-related infrared features of the forsterites in equilibrium. The petrogenesis of the jianite is presently unclear.

Hard convex lens-shaped particles: Characterization of dense disordered packings.

Among the family of hard convex lens-shaped particles (lenses), the one with aspect ratio equal to 2/3 is "optimal" in the sense that the maximally random jammed (MRJ) packings of such lenses achieve the highest packing fraction ϕ_{MRJ}≃0.73 [G. Cinacchi and S. Torquato, Soft Matter 14, 8205 (2018)1744-683X10.1039/C8SM01519H]. This value is only a few percent lower than ϕ_{DKP}=0.76210⋯, the packing fraction of the corresponding densest-known crystalline (degenerate) packings [G. Cinacchi and S. Torquato, J. Chem. Phys. 143, 224506 (2015)JCPSA60021-960610.1063/1.4936938]. By exploiting the appreciably reduced propensity that a system of such optimal lenses has to positionally and orientationally order, disordered packings of them are progressively generated by a Monte Carlo method-based procedure from the dilute equilibrium isotropic fluid phase to the dense nonequilibrium MRJ state. This allows us to closely monitor how the (micro)structure of these packings changes in the process of formation of the MRJ state. The gradual changes undergone by the many structural descriptors calculated here can coherently and consistently be traced back to the gradual increase in contacts between the hard particles until the isostatic mean value of ten contact neighbors per lens is reached at the effectively hyperuniform MRJ state. Compared to the MRJ state of hard spheres, the MRJ state of such optimal lenses is denser (less porous), more disordered, and rattler-free. This set of characteristics makes them good glass formers. It is possible that this conclusion may also hold for other hard convex uniaxial particles with a correspondingly similar aspect ratio, be they oblate or prolate, and that, by using suitable biaxial variants of them, that set of characteristics might further improve.

The Genesis of the Salt Diapir-Related Mississippi Valley-Type Ba-Pb-(± Zn) Ore of the Slata District, Tunisia: The Role of Halokinesis, Hydrocarbon Migration, and Alpine Orogenesis

AbstractThe juxtaposition of a Triassic evaporite diapir with the organic matter-rich Fahdene Formation (Albian-Vra-conian) along major faults in the Slata ore district raises the question of the roles played by halokinesis, hydrocarbons, and tectonics in mineralization. The Slata mining district, located in the Tunisian salt diapiric zone, contains Ba-Pb-(± Zn) ore hosted in the Aptian carbonates. The mineralogical paragenetic sequence consists of barite (Ba-1)–galena ± sphalerite ± calcite (Ca-1)–barite (Ba-2) and finally, late calcites (Ca-2 and Ca-3). Fluid inclusions from early barite reveal that it was precipitated from a warm (134°–157°C), H2O-NaCl-KCl-CaCl2, moderately saline (13.3–24.6 wt % NaCl equiv) basinal brine. This fluid is thought to have resulted from the mixing of a deep-seated, hot, metal-bearing fluid with a cooler, dilute SO42−-rich fluid. Early calcite and cogenetic sulfides (galena and sphalerite) precipitated from fluids of similar salinities and temperatures as the barite-forming fluids, but with the additional involvement of hydrocarbons. Sulfur isotope data suggest that thermochemical sulfate reduction of Triassic gypsum was the main source of reduced sulfur for sulfides. Late barite precipitated as a result of the mixing between a Ba-rich, hot, ascending fluid with a cooler, dilute Triassic sulfate-rich fluid in the absence of hydrocarbons. The homogeneous Pb isotope compositions of galena along with the Sr isotope compositions of barite point to a Paleozoic reservoir as the main source of metals with a contribution from the Triassic-Cretaceous rocks. The emplacement of the ore occurred during the Eocene-Miocene Alpine compressional tectonic activity that triggered the circulation of Paleozoic-derived metal-bearing fluids.

Combined rotational diffusion of a superparamagnetic particle and its magnetic moment: Solution of the kinetic equation

This paper develops a theory of rotational diffusion of a uniaxial superparamagnetic particle, suspended in a fluid. A kinetic equation for the joint distribution function of orientations of anisotropy axis and magnetic moment of the particle is examined and a consistent method of its solution is proposed. The approach involves the introduction of a kinetic operator that generates the time evolution of the distribution function, and the usage of quantum-mechanical formalism, particularly, elements of the representation theory and the theory of additions of angular momenta. A convenient representation, in which matrix of the kinetic operator is close to diagonal, is specified. In this representation the evolution equation takes a form of linear recurrence–differential relations for statistical moments of the distribution function. Their numerical integration can be performed by one of the standard methods, giving the average (observed) magnetization of the system for any instant of time. The presented scheme assumes that frequency of an applied magnetic field is well below ferromagnetic resonance range (that is typical for majority of experiments) but it does not impose any restrictions on the field amplitude, material parameters of the particle, viscosity of fluid or temperature. It can serve as a theoretical basis for a consistent description of relaxation spectrum, dynamic magnetic susceptibility and nonlinear magnetic response of a dilute magnetic fluid with considering the interplay between mechanical and magnetic degrees of freedom of suspended nanoparticles. Also, it can be used for cross-checking of approximate models.

Effects of diet detail nursing on swallowing function and quality of life in patients with mild-to-moderate dysphasia after oral cancer surgery

Objective To explore effects of diet detail nursing on swallowing function and quality of life in patients with mild-to-moderate dysphasia after oral cancer surgery. Methods Totally 66 patients with dysphasia after oral cancer surgery in Department of Head and Neck Surgery of Liaoning Cancer Hospital were selected by convenience sampling and divided into control group and observation group by random number table method, with 33 cases in each group. The two groups were given dysphasia training, and the control group was given regular diet nursing, on which basis the observation group was given diet detail nursing. The dysphasia degree was assessed by water swallow test. The pharyngeal contraction rate was evaluated by swallowing radiography, and the correctness of swallowing methods was evaluated. The quality of life of patients was assessed by University of Washington Quality of Life Scale (UWQOL) , and the nutritional status and postoperative complications were observed. Results After intervention, the dysphasia degree in observation group was lighter than that in control group (P<0.05) . The pharyngeal contraction rates of swallowing dilute fluid and thick fluid in observation group[ (34.47±7.56) % and (36.48±9.46) %] were smaller than those in control group [ (38.94±9.27) % and (41.46±10.42) %] (P<0.05) . The correct rate of swallowing methods in observation group (84.85%) was significantly higher than that in control group (63.64%) (P<0.05) . The scores of five items of swallowing, chewing, mood, anxiety and self-assessment quality of life in observation group were higher than those in the control group (P<0.05) . The serum albumin level in observation group (38.66±4.85g/L) was higher than that in control group (35.84±5.16 g/L) (P<0.05) . The incidence rate of aspiration in observation group (12.12%) was smaller than that in control group (33.33%) (P<0.05) . Conclusions Diet detail nursing management for patients with dysphasia after oral cancer surgery can guide patients to master the correct swallowing methods, effectively reduce the pharyngeal contraction rate, improve the swallowing ability, reduce the occurrence of aspiration, and improve their quality of life and nutritional status to a certain extent. Key words: Oral cancer; Deglutition disorders; Quality of life; Nutrition; Swallowing function; Aspiration; Diet detail nursing

Density-dependent finite system-size effects in equilibrium molecular dynamics estimation of shear viscosity: Hydrodynamic and configurational study.

We study the intrinsic nature of the finite system-size effect in estimating shear viscosity of dilute and dense fluids within the framework of the Green-Kubo approach. From extensive molecular dynamics simulations, we observe that the size effect on shear viscosity is characterized by an oscillatory behavior with respect to system size L at high density and by a scaling behavior with an L-1 correction term at low density. Analysis of the potential contribution in the shear-stress autocorrelation function reveals that the former is configurational and is attributed to the inaccurate description of the long-range spatial correlations in finite systems. Observation of the long-time inverse-power decay in the kinetic contribution confirms its hydrodynamic nature. The L-1 correction term of shear viscosity is explained by the sensitive change in the long-time tail obtained from a finite system.

Experiments and Simulations on the Magnetorheology of Magnetic Fluid Based on Fe3O4 Hollow Chains.

This work reports an experiment/simulation combination study on the magnetorheological (MR) mechanism of magnetic fluid based on Fe3O4 hollow chains. The decrease of shear stress versus the increasing magnetic field was observed in a dilute magnetic fluid. Hollow chains exhibited a higher MR effect than pure Fe3O4 hollow nanospheres under a small magnetic field. A modified particle level simulation method including the translational and rotational motion of chains was developed to comprehend the correlation between rheological properties and microstructures. Sloping cluster-like microstructures were formed under a weak external field (24 mT), while vertical column-like microstructures were observed under a strong field (240 mT). The decrease of shear stress was due to the strong reconstruction process of microstructures and the agglomeration of chains near the boundaries. The chain morphology increased the dip angle of microstructures and thus improved the MR effect under a weak field. This advantage made Fe3O4 hollow chains to be widely applied for small and low-power devices in the biomedical field. Dimensionless viscosity as a function of the Mason number was collapsed onto linear master curves. Magnetic fluid in Poiseuille flow in a microfluidic channel was also observed and simulated. A qualitative and quantitative correspondence between simulations and experiments was obtained.

Extremely slow settling behavior of particles in dilute wormlike micellar fluid with broad spectrum of relaxation times

We selected a 1.4 wt% Octadecyl trimethyl ammonium chloride (OTAC) concentration wormlike micellar fluid with broad relaxation time spectrum and another single relaxation Maxwell fluid of 4.0 wt% OTAC concentration with a constant weight ratio of OTAC to NaSal of 5:1. The shear viscosity, dynamic modulus as well as the extensional viscosity were tested. The steady and unsteady motion of spheres were investigated by high-speed video images in these two wormlike micellar fluids. Extremely slow settling velocity is found when smaller spheres with diameters of 3.2 and 4.0 mm settles in the 1.4 wt% OTAC solution. Stronger rebound of these spheres occurs in this fluid. Comparing with particle settling velocity in inelastic power law fluid, we concluded that this extremely slow sedimentation in the 1.4 wt% OTAC solution seems to be dominated by the slowest stress relaxation of this solution. The rheology test demonstrated that this wormlike micellar fluid has more tensile hardening, low viscosity and strong elasticity. The oscillation of sphere results from the elasticity of the entangled microstructures of wormlike micelles. For a Maxwell viscoelastic 4.0 wt% OTAC solution, settling behaviors of spheres agree with previous literatures that the flow becomes instability as the Wi number exceeds a critical value.

Emergence and percolation of rigid domains during the colloidal glass transition.

Using video microscopy, we measure local spatial constraints in disordered binary colloidal samples, ranging from dilute fluids to jammed glasses, and probe their spatial and temporal correlations to local dynamics during the glass transition. We observe the emergence of significant correlations between constraints and local dynamics within the Lindemann criterion, which coincides with the onset of glassy dynamics in supercooled liquids. Rigid domains in fluids are identified based on local constraints and demonstrate a percolation transition near the glass transition, accompanied by the emergence of dynamical heterogeneities. Our results show that spatial constraint instead of the geometry of amorphous structures is the key that connects the complex spatial-temporal correlations in disordered materials.

Thermocapillary motion of a Newtonian drop in a dilute viscoelastic fluid

In this work we investigate the role played by viscoelasticity on the thermocapillary motion of a deformable Newtonian droplet embedded in an immiscible, otherwise quiescent non-Newtonian fluid. We consider a regime in which inertia and convective transport of energy are both negligible (represented by the limit condition of vanishingly small Reynolds and Marangoni numbers) and free from gravitational effects. A constant temperature gradient is maintained by keeping two opposite sides of the computational domain at different temperatures. Consequently the droplet experiences a motion driven by the mismatch of interfacial stresses induced by the non-uniform temperature distribution on its boundary. The departures from the Newtonian behaviour are quantified via the “thermal” Deborah number, DeT and are accounted for by adopting either the Oldroyd-B model, for relatively small DeT, or the FENE-CR constitutive law for a larger range of DeT. In addition, the effects of model parameters, such as the concentration parameter c=1−β (where β is the viscoelastic viscosity ratio), or the extensibility parameter, L2, have been studied numerically using a hybrid volume of fluid-level set method. The numerical results show that the steady-state droplet velocity behaves as a monotonically decreasing function of DeT, whilst its shape deforms prolately. For increasing values of DeT, the viscoelastic stresses show the tendency to be concentrated near the rear stagnation point, contributing to an increase in its local interface curvature.

Granite Hydrolysis to Form Deep Brines

Reaction path calculations suggest that water fixation by zeolite and chlorite formation can account for much of the high salinity of deep brines in contact with deep granites, as well as their Ca/Na ratios, which reflect the rock-dominated chemistry of such brines. Resultant brines, undiluted by the influx of shallower fresher waters, are likely to be at equilibrium with laumontite, chlorite, calcite, dolomite, anhydrite/gypsum, K-feldspar, quartz, plagioclase, and possibly halite. The growth of laumontite and chlorite consumes water, causing the concentration of residual salts to increase during the formation of such brines. In these analyses, the major trends suggest that these fundamental processes drive this outcome naturally. Predicted phase assemblages and end-point water compositions are relatively unaffected by the chemistry of the starting/reacting fluid. Additionally, mineralogical and mineral compositional variations both appear to have no major impact on brine formational trends. More precise analysis involves the use of Pitzer coefficients and considers Br/Cl exchange in the alteration phases. Explicit consideration of silicate dissolution points to water availability as a key control over granite alteration. Diffusion-limited water availability appears to lead to stagnant systems dominated by the increasing brine density and Ca/Na ratios with depth. Alteration phases tend to decrease permeability and porosity, further isolating such systems from the flow of shallower dilute fluids.