A mathematical model for estimating the extent of solute- and water-flux heterogeneity in multiple sample percolation experiments

Multiple sampling is widely used in vadose zone percolation experiments to investigate the extent in which soil structure heterogeneities influence the spatial and temporal distributions of water and solutes. In this note, a simple, robust, mathematical model, based on the beta-statistical distribution, is proposed as a method of quantifying the magnitude of heterogeneity in such experiments. The model relies on fitting two parameters, alpha and zeta to the cumulative elution curves generated in multiple-sample percolation experiments. The model does not require knowledge of the soil structure. A homogeneous or uniform distribution of a solute and/or soil-water is indicated by alpha = zeta = 1, Using these parameters, a heterogeneity index (HI) is defined as root 3 times the ratio of the standard deviation and mean. Uniform or homogeneous flow of water or solutes is indicated by HI = 1 and heterogeneity is indicated by HI > 1. A large value for this index may indicate preferential flow. The heterogeneity index relies only on knowledge of the elution curves generated from multiple sample percolation experiments and is, therefore, easily calculated. The index may also be used to describe and compare the differences in solute and soil-water percolation from different experiments. The use of this index is discussed for several different leaching experiments. (C) 1999 Elsevier Science B.V. All rights reserved.

Wave-induced seepage flux into anisotropic seabeds

Considerable effort has been devoted to quantifying the wave-induced soil response in a porous seabed in the last few decades. Most previous investigations have focused on the analysis of pore pressure and effective stresses within isotropic sediments, despite strong evidence of anisotropic soil behaviour reported in the literature. Furthermore, the seepage flux, which is important in the context of contaminant transport, has not been examined. In this paper, we focus on water wave-driven seepage in anisotropic marine sediments of finite thickness. The numerical results predict that the effects of hydraulic anisotropy and anisotropic soil behaviour on the wave-driven seepage in marine sediment are significant. Copyright (C) 2001 John Wiley & Sons, Ltd.

Scope for further analytical solutions for constant flux infiltration into a semi-infinite soil profile or redistribution in a finite soil profile

[1] We attempt to generate new solutions for the moisture content form of the one-dimensional Richards' [1931] equation using the Lisle [1992] equivalence mapping. This mapping is used as no more general set of transformations exists for mapping the one-dimensional Richards' equation into itself. Starting from a given solution, the mapping has the potential to generate an infinite number of new solutions for a series of nonlinear diffusivity and hydraulic conductivity functions. We first seek new analytical solutions satisfying Richards' equation subject to a constant flux surface boundary condition for a semi-infinite dry soil, starting with the Burgers model. The first iteration produces an existing solution, while subsequent iterations are shown to endlessly reproduce this same solution. Next, we briefly consider the problem of redistribution in a finite-length soil. In this case, Lisle's equivalence mapping is generalized to account for arbitrary initial conditions. As was the case for infiltration, however, it is found that new analytical solutions are not generated using the equivalence mapping, although existing solutions are recovered.

Transport in bidisperse adsorbents: Significance of the macroscopic adsorbate flux

Transport in bidisperse adsorbents is investigated here, while incorporating a two-dimensional model for adsorbate diffusion in the microparticles. The latter treatment permits consideration of the macropore concentration variation around the microparticle surface, and thereby predicts an adsorbate through-flux on the macroscopic coordinate. Such a through-flux has earlier been postulated in the literature, but with unrealistic mechanistic justification. The new model therefore resolves the existing ambiguity in this regard, and covers the entire spectrum of behaviour between microparticle and macropore diffusion control. Computational results show that if the macroscopic adsorbate flux, ignored in the conventional analysis, has a significant contribution to the total flux under macropore control conditions then it is always important even when the microparticle diffusion resistance is not negligible. The effect of various parameters such as relative microparticle size and isotherm heterogeneity on the uptake is also studied and discussed. (C) 1997 Elsevier Science Ltd.

Percutaneous absorption of sunscreen agents from liquid paraffin: Self-association of octyl salicylate and effects on skin flux

This study provides an investigation of the availability of octyl salicylate (OS), a common sunscreen agent, from liquid paraffin and the effect of OS on skin permeability. A model membrane system to isolate the vehicle effect from membrane permeability has been developed. Partitioning of OS between liquid paraffin and aqueous receptor phases was conducted. Partition coefficients increased with increase in OS concentration. A range of OS concentrations in liquid paraffin was diffused across human epidermis and synthetic membranes into 4% bovine serum albumin in phosphate-buffered saline and 50% ethanol. Absorption profiles of OS obtained from silicone and low-density polyethylene (LDPE) membranes were similar to each other but higher than for the high-density polyethylene [HDPE (3 times)] membrane and human epidermis (15 times). The steady state fluxes and apparent permeability coefficients (K-p') obtained from the diffusion studies showed the same trends with all membranes, except for the HDPE membrane which showed greater increase in flux and K-p' at concentrations above 30%. IR spectra showed that several bands of OS were shifted with concentrations, and the molecular models further suggested that the main contribution to the self-association is from non-1,4 van der Waals interactions.

A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case. (C) 2000 Elsevier Science Ltd. All rights reserved.

Liquid distribution in wet granulation: dimensionless spray flux

This study investigates binder distribution in wet granulation and focuses on the nucleation zone, which is the area where the liquid binder and powder surface come into contact and form the initial nuclei. An equipment independent parameter, dimensionless spray flux Psi (a), is defined to characterise the most important process parameters in the nucleation process: solution flowrate, powder flux, and binder drop size. Ex-granulator experiments are used to study the relationship between dimensionless spray flux, process variables and the coverage of binder fluid on the powder surface. Lactose monohydrate powder on a variable speed riffler passed under a flat spray once only. Water and 7% HPC solution at two spray pressures were used as binders. Experiments with red dye and image analysis demonstrate that changes in dimensionless spray flux correlate with a measurable difference in powder surface coverage. Nucleation experiments show that spray flux controls the size and shape of the nuclei size distribution. At low Psi (a), the system operates in the drop controlled regime, where one drop forms one nucleus and the nuclei size distribution is narrow. At higher Psi (a), the powder surface cakes creating a broader size distribution. For controlled nucleation with the narrowest possible size distribution, it is recommended that the dimensionless spray flux be less than 0.1 to be in the drop-controlled regime. (C) 2001 Elsevier Science S.A. All rights reserved.

Violation of multiparticle Bell inequalities for low- and high-flux parametric amplification using both vacuum and entangled input states

We show how polarization measurements on the output fields generated by parametric down conversion will reveal a violation of multiparticle Bell inequalities, in the regime of both low- and high-output intensity. In this case, each spatially separated system, upon which a measurement is performed, is comprised of more than one particle. In view of the formal analogy with spin systems, the proposal provides an opportunity to test the predictions of quantum mechanics for spatially separated higher spin states. Here the quantum behavior possible even where measurements are performed on systems of large quantum (particle) number may be demonstrated. Our proposal applies to both vacuum-state signal and idler inputs, and also to the quantum-injected parametric amplifier as studied by De Martini The effect of detector inefficiencies is included, and weaker Bell-Clauser-Horne inequalities are derived to enable realistic tests of local hidden variables with auxiliary assumptions for the multiparticle situation.

Effect of vehicle pretreatment on the flux, retention, and diffusion of topically applied penetrants in vitro

Purpose. The flux of a topically applied drug depends on the activity in the skin and the interaction between the vehicle and skin. Permeation of vehicle into the skin can alter the activity of drug and the properties of the skin barrier. The aim of this in vitro study was to separate and quantify these effects. Methods. The flux of four radiolabeled permeants (water, phenol, diflunisal, and diazepam) with log K-oct/water values from 1.4 to 4.3 was measured over 4 h through heat-separated human epidermis pretreated for 30 min with vehicles having Hildebrand solubility parameters from 7.9 to 23.4 (cal/cm(3))(1/2). Results. Enhancement was greatest after pretreatment with the more lipophilic vehicles. A synergistic enhancement was observed using binary mixtures. The flux of diazepam was not enhanced to the same extent as the other permeants, possibly because its partitioning into the epidermis is close to optimal (log K-oct 2.96). Conclusion. An analysis of the permeant remaining in the epidermis revealed that the enhancement can be the result of either increased partitioning of permeant into the epidermis or an increasing diffusivity of permeants through the epidermis.

Transdermal penetration of vasoconstrictors - Present understanding and assessment of the human epidermal flux and retention of free bases and ion-pairs

Purpose. As reductions in dermal clearance increase the residence time of solutes in the skin and underlying tissues we compared the topical penetration of potentially useful vasoconstrictors (VCs) through human epidermis as both free bases and ion-pairs with salicylic acid (SA). Methods. We determined the in vitro epidermal flux of ephedrine, naphazoline, oxymetazoline, phenylephrine, and xylometazoline applied as saturated solutions in propylene glycol: water (1: 1) and of ephedrine, naphazoline and tetrahydrozoline as 10% solutions of 1: 1 molar ratio ion-pairs with SA in liquid paraffin. Results. As free bases, ephedrine had the highest maximal flux, Jmax = 77.4 +/- 11.7 mug/cm(2)/h, being 4-fold higher than tetrahydrozoline and xylometazoline, 6-fold higher than phenylephrine, 10-fold higher than naphazoline and 100-fold higher than oxymetazoline. Stepwise regression of solute physicochemical properties identified melting point as the most significant predictor of flux. As ion-pairs with SA, ephedrine and naphazoline had similar fluxes (11.5 +/- 2.3 and 12.0 +/- 1.6 mug/cm(2)/h respectively), whereas tetrahydrozoline was approximately 3-fold slower. Corresponding fluxes of SA from the ion-pairs were 18.6 +/- 0.6, 7.8 +/- 0.8 and 1.1 +/- 0.1 respectively. Transdermal transport of VC's is discussed. Conclusions. Epidermal retention of VCs and SA did not correspond to their molar ratio on application and confirmed that following partitioning into the stratum corneum, ion-pairs separate and further penetration is governed by individual solute characteristics.

Comparing a current-carrying circular wire with polygons of equal perimeter: Magnetic field versus magnetic flux

We compare the magnetic field at the centre and the self-magnetic flux through a current-carrying circular loop, with those obtained for current-carrying polygons with the same perimeter. As the magnetic field diverges at the position of the wires, we compare the self-fluxes utilizing several regularization procedures. The calculation is best performed utilizing the vector potential, thus highlighting its usefulness in practical applications. Our analysis answers some of the intuition challenges students face when they encounter a related simple textbook example. These results can be applied directly to the determination of mutual inductances in a variety of situations.

Influence of growth temperature and carrier flux on the structure and transport properties of highly oriented CrO2 on Al2O3 (0001)

In this work we report on the structure and magnetic and electrical transport properties of CrO2 films deposited onto (0001) sapphire by atmospheric pressure (AP)CVD from a CrO3 precursor. Films are grown within a broad range of deposition temperatures, from 320 to 410 degrees C, and oxygen carrier gas flow rates of 50-500 seem, showing that it is viable to grow highly oriented a-axis CrO2 films at temperatures as low as 330 degrees C i.e., 60-70 degrees C lower than is reported in published data for the same chemical system. Depending on the experimental conditions, growth kinetic regimes dominated either by surface reaction or by mass-transport mechanisms are identified. The growth of a Cr2O3 interfacial layer as an intrinsic feature of the deposition process is studied and discussed. Films synthesized at 330 degrees C keep the same high quality magnetic and transport properties as those deposited at higher temperatures.

Cu2ZnSnS4 absorber layers obtained through sulphurization of metallic precursors: Graphite box versus sulphur flux

In this work we employed a hybrid method, combining RF-magnetron sputtering with evaporation, for the deposition of tailor made metallic precursors, with varying number of Zn/Sn/Cu (ZTC) periods and compared two approaches to sulphurization. Two series of samples with 1×, 2× and 4× ZTC periods have been prepared. One series of precursors was sulphurized in a tubular furnace directly exposed to a sulphur vapour and N2+5% H2 flux at a pressure of 5.0×10+4 Pa. A second series of identical precursors was sulphurized in the same furnace but inside a graphite box where sulphur pellets have been evaporated again in the presence of N2+5% H2 and at the same pressure as for the sulphur flux experiments. The morphological and chemical analyses revealed a small grain structure but good average composition for all three films sulphurized in the graphite box. As for the three films sulphurized in sulphur flux grain growth was seen with the increase of the number of ZTC periods whilst, in terms of composition, they were slightly Zn poor. The films' crystal structure showed that Cu2ZnSnS4 is the dominant phase. However, in the case of the sulphur flux films SnS2 was also detected. Photoluminescence spectroscopy studies showed an asymmetric broad band emission whichoccurs in the range of 1–1.5 eV. Clearly the radiative recombination efficiency is higher in the series of samples sulphurized in sulphur flux. We have found that sulphurization in sulphur flux leads to better film morphology than when the process is carried out in a graphite box in similar thermodynamic conditions. Solar cells have been prepared and characterized showing a correlation between improved film morphology and cell performance. The best cells achieved an efficiency of 2.4%.

Particulate matter flux deposition in the vicinity of a coal-fired power plant

This paper describes the methodology adopted to assess local air quality impact in the vicinity of a coal power plant located in the south of Portugal. Two sampling areas were selected to assess the deposition flux of dust fallout and its potential spatial heterogeneity. The sampling area was divided into two subareas: the inner, with higher sampling density and urban and suburban characteristics, inside a 6-km circle centered on the stacks, and an outer subarea, mainly rural, with lower sampling density within a radius of 20 km. Particulate matter deposition was studied in the vicinity of the coal fired power plant during three seasonal sampling campaigns. For the first one, the average annual flux of dust fallout was 22.51 g/(m2 yr), ranging from 4.20 to 65.94 g/(m2 yr); for the second one was 9.47 g/(m2 yr), ranging from 0.78 to 32.72 g/(m2 yr) and for the last one was 38.42 g/(m2 yr), ranging from 1.41 to 117.48 g/(m2 yr). The fallout during the second campaign turned out to be much lower than for others. This was in part due to meteorological local patterns but mostly due to the fact that the power plant was not working at full power during the second sampling campaign.155