Steady drainage in emulsions: corrections for surface Plateau borders and a model for high aqueous volume fraction

Peron, N., Cox, S.J., Hutzler, S. and Weaire, D. (2007) Steady drainage in emulsions: corrections for surface Plateau borders and a model for high aqueous volume fraction. The European Physical Journal E - Soft Matter. 22: 341-351. Sponsorship: This research was supported by the European Space Agency (14914/02/NL/SH, 14308/00/NL/SG) (AO-99-031) CCN 002 MAP Project AO-99-075) and Science Foundation Ireland (RFP 05/RFP/PHY0016). SJC acknowledges support from EPSRC (EP/D071127/1).

Heterogeneities in fullerene nanoparticle aggregates affecting reactivity, bioactivity, and transport.

Properties of nanomaterial suspensions are typically summarized by average values for the purposes of characterizing these materials and interpreting experimental results. We show in this work that the heterogeneity in aqueous suspensions of fullerene C(60) aggregates (nC(60)) must be taken into account for the purposes of predicting nanomaterial transport, exposure, and biological activity. The production of reactive oxygen species (ROS), microbial inactivation, and the mobility of the aggregates of the nC(60) in a silicate porous medium all increased as suspensions were fractionated to enrich with smaller aggregates by progressive membrane filtration. These size-dependent differences are attributed to an increasing degree of hydroxylation of nC(60) aggregates with decreasing size. As the quantity and influence of these more reactive fractions may increase with time, experiments evaluating fullerene transport and toxicity end points must take into account the evolution and heterogeneity of fullerene suspensions.

Fluid flow control with transformation media.

We introduce a new concept for the manipulation of fluid flow around three-dimensional bodies. Inspired by transformation optics, the concept is based on a mathematical idea of coordinate transformations and physically implemented with anisotropic porous media permeable to the flow of fluids. In two situations-for an impermeable object placed either in a free-flowing fluid or in a fluid-filled porous medium-we show that the object can be coated with an inhomogeneous, anisotropic permeable medium, such as to preserve the flow that would have existed in the absence of the object. The proposed fluid flow cloak eliminates downstream wake and compensates viscous drag, hinting at the possibility of novel propulsion techniques.

Three-Dimensional Analysis of Seepage below and around Hydraulic Structures

This paper investigates the problem of seepage under the floor of hydraulic structures considering the compartment of flow that seeps through the surrounding banks of the canal. A computer program, utilizing a finite-element method and capable of handling three-dimensional (3D) saturated–unsaturated flow problems, was used. Different ratios of canal width/differential head applied on the structure were studied. The results produced from the two-dimensional (2D) analysis were observed to deviate largely from that obtained from 3D analysis of the same problem, despite the fact that the porous medium was isotropic and homogeneous. For example, the exit gradient obtained from 3D analysis was as high as 2.5 times its value obtained from 2D analysis. Uplift force acting upwards on the structure has also increased by about 46% compared with its value obtained from the 2D solution. When the canal width/ differential head ratio was 10 or higher, the 3D results were comparable to the 2D results. It is recommended to construct a core of low permeability soil in the banks of canal to reduce the seepage losses, uplift force, and exit gradient.

Quantifying the influence of humic acid adsorption on colloidal microsphere deposition onto iron-oxide-coated sand.

This article describes an approach for quantifying microsphere deposition onto iron-oxide-coated sand under the influence of adsorbed Suwannee River Humic Acid (SRHA). The experimental technique involved a triple pulse injection of model latex microspheres (microspheres) in pulses of (1) microspheres, followed by (2) SRHA, and then (3) microspheres, into a column filled with iron-coated quartz sand as a water-saturated porous medium. A random sequential adsorption model (RSA) simulated the gradual rise in the first (microsphere) breakthrough curve (BTC). Using the same model calibration parameters a dramatic increase in concentration at the start of the second particle BTC, generated after SRHA injection, could be simulated by matching microsphere concentrations to extrapolated RSA output. RSA results and microsphere/SRHA recoveries showed that 1 mg of SRHA could block 5.90 plus or minus 0.14 x 10^9 microsphere deposition sites. This figure was consistent between experiments injecting different SRHA masses, despite contrasting microsphere deposition/release regimes generating the second microsphere BTC.

Modeling colloid deposition on a protein layer adsorbed to iron-oxide-coated sand

Our recent study reported that conformation change of granule-associated Bovine Serum Albumin (BSA) may influence the role of the protein controlling colloid deposition in porous media (Flynn et al., 2012). The present study conceptualized the observed phenomena with an ellipsoid morphology model, describing BSA as an ellipsoid taking a side-on or end-on conformation on granular surface, and identified the following processes: (1) at low adsorbed concentrations, BSA exhibited a side-on conformation blocking colloid deposition; (2) at high adsorbed concentrations, BSA adapted to an end-on conformation promoted colloid deposition; and (3) colloid deposition on the BSA layer may progressively generate end-on molecules (sites) by conformation change of side-on BSA, resulting in sustained increasing deposition rates. Generally, the protein layer lowered colloid attenuation by the porous medium, suggesting the overall effect of BSA was inhibitory at the experimental time scale. A mathematical model was developed to interpret the ripening curves. Modeling analysis identified the site generation efficiency of colloid as a control on the ripening rate (declining rate in colloid concentrations), and this efficiency was higher for BSA adsorbed from a more dilute BSA solution. © 2012 Elsevier B.V.

Estudo de sistemas de protecção térmica húmidos sujeitos a condições de incêndio

O presente trabalho tem como principal objectivo o estudo e a interpretação dos mecanismos de transferência de calor e massa no interior de um meio poroso húmido actuando como barreira térmica de protecção em condições de incêndio, visando, sobretudo, melhorar o desempenho destes sistemas. A barreira térmica estudada é constituída por camadas de fibra de vidro, cuja face exposta à chama é protegida por uma folha de alumínio perfurada. A realização deste estudo envolveu a concepção, realização e operação de uma montagem experimental, com a qual se obteve a evolução temporal da temperatura e da taxa de evaporação de água no interior de uma amostra da barreira térmica, submetida à acção directa de uma chama. A análise do processo de protecção foi complementada com resultados obtidos por simulação numérica do processo, designadamente a evolução das propriedades térmicas, que determinam os mecanismos de transferência de calor e massa no interior da barreira. Para esse efeito foi desenvolvido um modelo matemático de simulação do processo de protecção para as barreiras em estudo, que permitiu obter resultados que acompanham bem as evoluções verificadas nos ensaios experimentais. A barreira térmica estudada mostrou claramente possuir um bom desempenho no processo de protecção, face às barreiras térmicas secas. Com a realização deste estudo identificaram-se e quantificaram-se os mecanismos de transferência de calor e massa dominantes nas diversas fases do processo de protecção, o que permitiu extrair conclusões valiosas quanto às características dos meios porosos que contribuem para o seu bom desempenho como barreiras térmicas húmidas.

Consistent Dirichlet Boundary Conditions for Numerical Solution of Moving Boundary Problems

We consider the imposition of Dirichlet boundary conditions in the finite element modelling of moving boundary problems in one and two dimensions for which the total mass is prescribed. A modification of the standard linear finite element test space allows the boundary conditions to be imposed strongly whilst simultaneously conserving a discrete mass. The validity of the technique is assessed for a specific moving mesh finite element method, although the approach is more general. Numerical comparisons are carried out for mass-conserving solutions of the porous medium equation with Dirichlet boundary conditions and for a moving boundary problem with a source term and time-varying mass.

Industrial radioactive barite scale: suppression of radium uptake by introduction of competing ions

Incorporation of radioactive isotopes during the formation of barite mineral scale is a widespread phenomenon occurring within the oil, mining and process industries. In a series of experiments radioactive barite/celestite solid solutions (SSBarite-Celcstite) have been synthesized under controlled conditions by the counter diffusion of Ra-226, Ba2+, Sr24+ and SO42- ions through a porous medium (silica gel), to investigate inhibiting effects in Ra uptake associated with the introduction of a competing ion (Sr2+). From characterization studies, the particle size and the morphology of the crystals appear to be related to the initial [Sr]/[Ba] molar ratio of the starting solution. Typically, systems richer in Sr produce smaller sized crystals and clusters characterized by a lower degree of order. The activity introduced to the system is mainly incorporated in the crystals generated from the barite/celestite solid solution as suggested by the activity profiles of the hydrogel columns analysed by gamma-spectrometry. There is a relationship between the initial [Sr]/[Ba] molar ratio of the starting solution and the activity exhibited by the synthesized crystals. An effective inhibition of the Ra-226 uptake during formation of the crystals (SSBarite-Celestite) was obtained through the introduction of a competing ion (Sr2+): the higher the initial [Sr]/[Ba] molar ratio of the starting solution, the lower the intensity of the activity peak in the crystals. (C) 2003 Published by Elsevier Ltd.

Solute movement through intact columns of cryoturbated Upper Chalk

Cryoturbated Upper Chalk is a dichotomous porous medium wherein the intra-fragment porosity provides water storage and the inter-fragment porosity provides potential pathways for relatively rapid flow near saturation. Chloride tracer movement through 43 cm long and 45 cm diameter undisturbed chalk columns was studied at water application rates of 0.3, 1.0, and 1.5 cm h(-1). Microscale heterogeneity in effluent was recorded using a grid collection system consisting of 98 funnel-shaped cells each 3.5 cm in diameter. The total porosity of the columns was 0.47 +/- 0.02 m(3) m(-3), approximately 13% of pores were >15 mu m diameter, and the saturated hydraulic conductivity was 12.66 +/- 1.31 m day(-1). Although the column remained unsaturated during the leaching even at all application rates, proportionate flow through macropores increased as the application rate decreased. The number of dry cells (with 0 ml of effluent) increased as application rate decreased. Half of the leachate was collected from 15, 19 and 22 cells at 0.3, 1.0, 1.5 cm h(-1) application rates respectively. Similar breakthrough curves (BTCs) were obtained at all three application rates when plotted as a function of cumulative drainage, but they were distinctly different when plotted as a function of time. The BTCs indicate that the columns have similar drainage requirement irrespective of application rates, as the rise to the maxima (C/C-o) is almost similar. However, the time required to achieve that leaching requirement varies with application rates, and residence time was less in the case of a higher application rate. A two-region convection-dispersion model was used to describe the BTCs and fitted well (r(2) = 0.97-0-99). There was a linear relationship between dispersion coefficient and pore water velocity (correlation coefficient r = 0.95). The results demonstrate the microscale heterogeneity of hydrodynamic properties in the Upper Chalk. Copyright (C) 2007 John Wiley & Sons, Ltd.

Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Velocity-based moving mesh methods for nonlinear partial differential equations

This article describes a number of velocity-based moving mesh numerical methods formultidimensional nonlinear time-dependent partial differential equations (PDEs). It consists of a short historical review followed by a detailed description of a recently developed multidimensional moving mesh finite element method based on conservation. Finite element algorithms are derived for both mass-conserving and non mass-conserving problems, and results shown for a number of multidimensional nonlinear test problems, including the second order porous medium equation and the fourth order thin film equation as well as a two-phase problem. Further applications and extensions are referenced.

Direct Computation of Stochastic Flow in Reservoirs with Uncertain Parameters

A direct method is presented for determining the uncertainty in reservoir pressure, flow, and net present value (NPV) using the time-dependent, one phase, two- or three-dimensional equations of flow through a porous medium. The uncertainty in the solution is modelled as a probability distribution function and is computed from given statistical data for input parameters such as permeability. The method generates an expansion for the mean of the pressure about a deterministic solution to the system equations using a perturbation to the mean of the input parameters. Hierarchical equations that define approximations to the mean solution at each point and to the field covariance of the pressure are developed and solved numerically. The procedure is then used to find the statistics of the flow and the risked value of the field, defined by the NPV, for a given development scenario. This method involves only one (albeit complicated) solution of the equations and contrasts with the more usual Monte-Carlo approach where many such solutions are required. The procedure is applied easily to other physical systems modelled by linear or nonlinear partial differential equations with uncertain data.

Sea ice is a mushy layer

[1] Sea ice is a two-phase, two-component, reactive porous medium: an example of what is known in other contexts as a mushy layer. The fundamental conservation laws underlying the mathematical description of mushy layers provide a robust foundation for the prediction of sea-ice evolution. Here we show that the general equations describing mushy layers reduce to the model of Maykut and Untersteiner (1971) under the same approximations employed therein.

Modelagem e previsão da perda de injetividade em poços canhoneados

Waterflooding is a technique largely applied in the oil industry. The injected water displaces oil to the producer wells and avoid reservoir pressure decline. However, suspended particles in the injected water may cause plugging of pore throats causing formation damage (permeability reduction) and injectivity decline during waterflooding. When injectivity decline occurs it is necessary to increase the injection pressure in order to maintain water flow injection. Therefore, a reliable prediction of injectivity decline is essential in waterflooding projects. In this dissertation, a simulator based on the traditional porous medium filtration model (including deep bed filtration and external filter cake formation) was developed and applied to predict injectivity decline in perforated wells (this prediction was made from history data). Experimental modeling and injectivity decline in open-hole wells is also discussed. The injectivity of modeling showed good agreement with field data, which can be used to support plan stimulation injection wells