A two-Dimensional finite volume method for variable density flow and solute transport through saturated-unsaturated media

Extensive groundwater withdrawal has resulted in a severe seawater intrusion problem in the Gooburrum aquifers at Bundaberg, Queensland, Australia. Better management strategies can be implemented by understanding the seawater intrusion processes in those aquifers. To study the seawater intrusion process in the region, a two-dimensional density-dependent, saturated and unsaturated flow and transport computational model is used. The model consists of a coupled system of two non-linear partial differential equations. The first equation describes the flow of a variable-density fluid, and the second equation describes the transport of dissolved salt. A two-dimensional control volume finite element model is developed for simulating the seawater intrusion into the heterogeneous aquifer system at Gooburrum. The simulation results provide a realistic mechanism by which to study the convoluted transport phenomena evolving in this complex heterogeneous coastal aquifer.

Efficient simulation of unsaturated flow using exponential time integration

We assess the performance of an exponential integrator for advancing stiff, semidiscrete formulations of the unsaturated Richards equation in time. The scheme is of second order and explicit in nature but requires the action of the matrix function φ(A) where φ(z) = [exp(z) - 1]/z on a suitability defined vector v at each time step. When the matrix A is large and sparse, φ(A)v can be approximated by Krylov subspace methods that require only matrix-vector products with A. We prove that despite the use of this approximation the scheme remains second order. Furthermore, we provide a practical variable-stepsize implementation of the integrator by deriving an estimate of the local error that requires only a single additional function evaluation. Numerical experiments performed on two-dimensional test problems demonstrate that this implementation outperforms second-order, variable-stepsize implementations of the backward differentiation formulae.

Preliminary characterisation of the surface of cartilage following exposure to saturated and unsaturated synthetic lipids

Articular cartilage is covered by a microscopic structure known as surface amorphous layer. This surface structure is often the first victim of attack during cartilage degeneration, thereby resulting in a gross impairment in cartilage function such as lubrication and load bearing. We hypothesize that incubation of degraded cartilage in solutions of different species of synthetic surface active phospholipids (saturated and unsaturated species) can remodel this lost surface structure. To test this hypothesis, the structural configuration of the surface of articular cartilage was studied and characterised with the lipid filled surface amorphous layer intact using the AFM. The results were then compared with those obtained following a systematic removal (delipidization) and replacement (relipidization) of this layer. Our results show that the unsaturated surfactant partially restored the lost surface amorphous layer while the saturated surfactant specie settled on the surface due to its poor solubility in aqueous solution.

Application of electrical resistivity method to detect deep cracks in unsaturated residual soil slope

Crack is a significant influential factor in soil slope that could leads to rainfall-induced slope instability. Existence of cracks at soil surface will decrease the shear strength and increase the hydraulic conductivity of soil slope. Although previous research has shown the effect of surface-cracks in soil stability, the influence of deep-cracks on soil stability is still unknown. The limited availability of deep crack data due to the difficulty of effective investigate methods could be one of the obstacles. Current technology in electrical resistivity can be used to detect deep-cracks in soil. This paper discusses deep cracks in unsaturated residual soil slopes in Indonesia using electrical resistivity method. The field investigation such as bore hole and SPT tests was carried out at multiple locations in the area where the electrical resistivity testing have been conducted. Subsequently, the results from bore-hole and SPT test were used to verify the results of the electrical resistivity test. This study demonstrates the benefits and limitations of the electrical resistivity in detecting deep-cracks in a residual soil slopes.

Laboratory measurement of hydraulic conductivity functions of two unsaturated sandy soils during drying and wetting processes

The importance of applying unsaturated soil mechanics to geotechnical engineering design has been well understood. However, the consumption of time and the necessity for a specific laboratory testing apparatus when measuring unsaturated soil properties have limited the application of unsaturated soil mechanics theories in practice. Although methods for predicting unsaturated soil properties have been developed, the verification of these methods for a wide range of soil types is required in order to increase the confidence of practicing engineers in using these methods. In this study, a new permeameter was developed to measure the hydraulic conductivity of unsaturated soils using the steady-state method and directly measured suction (negative pore-water pressure) values. The apparatus is instrumented with two tensiometers for the direct measurement of suction during the tests. The apparatus can be used to obtain the hydraulic conductivity function of sandy soil over a low suction range (0-10 kPa). Firstly, the repeatability of the unsaturated hydraulic conductivity measurement, using the new permeameter, was verified by conducting tests on two identical sandy soil specimens and obtaining similar results. The hydraulic conductivity functions of the two sandy soils were then measured during the drying and wetting processes of the soils. A significant hysteresis was observed when the hydraulic conductivity was plotted against the suction. However, the hysteresis effects were not apparent when the conductivity was plotted against the volumetric water content. Furthermore, the measured unsaturated hydraulic conductivity functions were compared with predictions using three different predictive methods that are widely incorporated into numerical software. The results suggest that these predictive methods are capable of capturing the measured behavior with reasonable agreement.

OnLine Ozonolysis Methods for the Determination of Double Bond Position in Unsaturated Lipids

Modern lipidomics relies heavily on mass spectrometry for the structural characterization and quantification of lipids of biological origins. Structural information is gained by tandem mass spectrometry (MS/MS) whereby lipid ions are fragmented to elucidate lipid class, fatty acid chain length, and degree of unsaturation. Unfortunately, however, in most cases double bond position cannot be assigned based on MS/MS data alone and thus significant structural diversity is hidden from such analyses. For this reason, we have developed two online methods for determining double bond position within unsaturated lipids; ozone electrospray ionization mass spectrometry (OzESI-MS) and ozone-induced dissociation (OzID). Both techniques utilize ozone to cleave C-C double bonds that result in chemically induced fragment ions that locate the position(s) of unsaturation

Formation and Fragmentation of Unsaturated Fatty Acid M-2H+Na (-) Ions: Stabilized Carbanions for Charge-Directed Fragmentation

Fatty acids are long-chain carboxylic acids that readily produce \[M - H](-) ions upon negative ion electrospray ionization (ESI) and cationic complexes with alkali, alkaline earth, and transition metals in positive ion ESI. In contrast, only one anionic monomeric fatty acid-metal ion complex has been reported in the literature, namely \[M - 2H + (FeCl)-Cl-II](-). In this manuscript, we present two methods to form anionic unsaturated fatty acid-sodium ion complexes (i.e., \[M - 2H + Na](-)). We find that these ions may be generated efficiently by two distinct methods: (1) negative ion ESI of a methanolic solution containing the fatty acid and sodium fluoride forming an \[M - H + NaF](-) ion. Subsequent collision-induced dissociation (CID) results in the desired \[M - 2H + Na](-) ion via the neutral loss of HF. (2) Direct formation of the \[M - 2H + Na](-) ion by negative ion ESI of a methanolic solution containing the fatty acid and sodium hydroxide or bicarbonate. In addition to deprotonation of the carboxylic acid moiety, formation of \[M - 2H + Na](-) ions requires the removal of a proton from the fatty acid acyl chain. We propose that this deprotonation occurs at the bis-allylic position(s) of polyunsaturated fatty acids resulting in the formation of a resonance-stabilized carbanion. This proposal is supported by ab initio calculations, which reveal that removal of a proton from the bis-allylic position, followed by neutral loss of HX (where X = F- and -OH), is the lowest energy dissociation pathway.

Elucidation of double bond position in unsaturated lipids by ozone electrospray ionization mass spectrometry

The position(s) of carbon-carbon double bonds within lipids can dramatically affect their structure and reactivity and thus has a direct bearing on biological function. Commonly employed mass spectrometric approaches to the characterization of complex lipids, however, fail to localize sites of unsaturation within the molecular structure and thus cannot distinguish naturally occurring regioisomers. In a recent communication \[Thomas, M. C.; Mitchell, T. W.; Blanksby, S. J. J. Am. Chem. Soc. 2006, 128, 58-59], we have presented a new technique for the elucidation of double bond position in glycerophospholipids using ozone-induced fragmentation within the source of a conventional electrospray ionization mass spectrometer. Here we report the on-line analysis, using ozone electrospray mass spectrometry (OzESI-MS), of a broad range of common unsaturated lipids including acidic and neutral glycerophospholipids, sphingomyelins, and triacylglycerols. All lipids analyzed are found to form a pair of chemically induced fragment ions diagnostic of the position of each double bond(s) regardless of the polarity, the number of charges, or the adduction (e.g., \[M - H](-), \[M - 2H](2-), \[M + H](+), \[M + Na](+), \[M + NH4](+)). The ability of OzESI-MS to distinguish lipids that differ only in the position of the double bonds is demonstrated using the glycerophosphocholine standards, GPCho(9Z-18:1/9Z-18:1) and GPCho(6Z-18:1/6Z-18:1). While these regioisomers cannot be differentiated by their conventional tandem mass spectra, the OzESI-MS spectra reveal abundant fragment ions of distinctive mass-to-charge ratio (m/z). The approach is found to be sufficiently robust to be used in conjunction with the m/z 184 precursor ion scans commonly employed for the identification of phosphocholine-containing lipids in shotgun lipidomic analyses. This tandem OzESI-MS approach was used, in conjunction with conventional tandem mass spectral analysis, for the structural characterization of an unknown sphingolipid in a crude lipid extract obtained from a human lens. The OzESI-MS data confirm the presence of two regioisomers, namely, SM(d18:0/15Z-24:1) and SM(d18:0/17Z-24:1), and suggest the possible presence of a third isomer, SM(d18:0/19Z-24:1), in lower abundance. The data presented herein demonstrate that OzESI-MS is a broadly applicable, on-line approach for structure determination and, when used in conjunction with established tandem mass spectrometric methods, can provide near complete structural characterization of a range of important lipid classes. As such, OzESI-MS may provide important new insight into the molecular diversity of naturally occurring lipids.

Two-scale computational modelling of unsaturated flow in soils exhibiting small scale heterogeneities

Unsaturated water flow in soil is commonly modelled using Richards’ equation, which requires the hydraulic properties of the soil (e.g., porosity, hydraulic conductivity, etc.) to be characterised. Naturally occurring soils, however, are heterogeneous in nature, that is, they are composed of a number of interwoven homogeneous soils each with their own set of hydraulic properties. When the length scale of these soil heterogeneities is small, numerical solution of Richards’ equation is computationally impractical due to the immense effort and refinement required to mesh the actual heterogeneous geometry. A classic way forward is to use a macroscopic model, where the heterogeneous medium is replaced with a fictitious homogeneous medium, which attempts to give the average flow behaviour at the macroscopic scale (i.e., at a scale much larger than the scale of the heterogeneities). Using the homogenisation theory, a macroscopic equation can be derived that takes the form of Richards’ equation with effective parameters. A disadvantage of the macroscopic approach, however, is that it fails in cases when the assumption of local equilibrium does not hold. This limitation has seen the introduction of two-scale models that include at each point in the macroscopic domain an additional flow equation at the scale of the heterogeneities (microscopic scale). This report outlines a well-known two-scale model and contributes to the literature a number of important advances in its numerical implementation. These include the use of an unstructured control volume finite element method and image-based meshing techniques, that allow for irregular micro-scale geometries to be treated, and the use of an exponential time integration scheme that permits both scales to be resolved simultaneously in a completely coupled manner. Numerical comparisons against a classical macroscopic model confirm that only the two-scale model correctly captures the important features of the flow for a range of parameter values.

Using ambient ozone for assignment of double bond position in unsaturated lipids

Unsaturated lipids deposited onto a range of materials are observed to react with the low concentrations of ozone present in normal laboratory air. Parent lipids and ozonolysis cleavage products are both detected directly from surfaces by desorption electrospray ionisation mass spectrometry (DESI-MS) with the resulting mass spectra providing clear evidence of the double bond position within these molecules. This serendipitous process has been coupled with thin-layer chromatography (TLC) to provide a simple but powerful approach for the detailed structural elucidation of lipids present in complex biological extracts. Lipid extracts from human lens were deposited onto normal phase TLC plates and then developed to separate components according to lipid class. Exposure of the developed plates to laboratory air for ca. 1 h prior to DESI-MS analysis gave rise to ozonolysis products allowing for the unambiguous identification of double bond positions in even low abundant, unsaturated lipids. In particular, the co-localization of intact unsaturated lactosylceramides (LacCer) with products from their oxidative cleavage provide the first evidence for the presence of three isomeric LacCer (d18:0/24:1) species in the ocular lens lipidome, i.e., variants with double bonds at the n-9, n-7 and n-5 positions.

Analysis of unsaturated lipids by ozone-induced dissociation

Recent developments in analytical technologies have driven significant advances in lipid science. The sensitivity and selectivity of modern mass spectrometers can now provide for the detection and even quantification of many hundreds of lipids in a single analysis. In parallel, increasing evidence from structural biology suggests that a detailed knowledge of lipid molecular structure including carbon-carbon double bond position, stereochemistry and acyl chain regiochemistry is required to fully appreciate the biochemical role(s) of individual lipids. Here we review the capabilities and limitations of tandem mass spectrometry to provide this level of structural specificity in the analysis of lipids present in complex biological extracts. In particular, we focus on the capabilities of a novel technology termed ozone-induced dissociation to identify the position (s) of double bonds in unsaturated lipids and discuss its possible role in efforts to develop workflows that provide for complete structure elucidation of lipids by mass spectrometry alone: so-called top-down lipidomics. This article is part of a Special Issue entitled: Lipodomics and Imaging Mass Spectrom. (C) 2011 Elsevier B.V. All rights reserved.

Characterization of acyl chain position in unsaturated phosphatidylcholines using differential mobility-mass spectrometry

Glycerophospholipids (GPs) that differ in the relative position of the two fatty acyl chains on the glycerol backbone (i.e., sn-positional isomers) can have distinct physicochemical properties. The unambiguous assignment of acyl chain position to an individual GP represents a significant analytical challenge. Here we describe a workflow where phosphatidylcholines (PCs) are subjected to ESI for characterization by a combination of differential mobility spectrometry and MS (DMS-MS). When infused as a mixture, ions formed from silver adduction of each phospholipid isomer {e.g., [PC (16:0/18:1) + Ag]+ and [PC (18:1/16:0) + Ag]+} are transmitted through the DMS device at discrete compensation voltages. Varying their relative amounts allows facile and unambiguous assignment of the sn-positions of the fatty acyl chains for each isomer. Integration of the well-resolved ion populations provides a rapid method (< 3 min) for relative quantification of these lipid isomers. The DMS-MS results show excellent agreement with established, but time-consuming, enzymatic approaches and also provide superior accuracy to methods that rely on MS alone. The advantages of this DMS-MS method in identification and quantification of GP isomer populations is demonstrated by direct analysis of complex biological extracts without any prior fractionation.

Two-scale computational modelling of water flow in unsaturated soils containing irregular-shaped inclusions

The focus of this paper is two-dimensional computational modelling of water flow in unsaturated soils consisting of weakly conductive disconnected inclusions embedded in a highly conductive connected matrix. When the inclusions are small, a two-scale Richards’ equation-based model has been proposed in the literature taking the form of an equation with effective parameters governing the macroscopic flow coupled with a microscopic equation, defined at each point in the macroscopic domain, governing the flow in the inclusions. This paper is devoted to a number of advances in the numerical implementation of this model. Namely, by treating the micro-scale as a two-dimensional problem, our solution approach based on a control volume finite element method can be applied to irregular inclusion geometries, and, if necessary, modified to account for additional phenomena (e.g. imposing the macroscopic gradient on the micro-scale via a linear approximation of the macroscopic variable along the microscopic boundary). This is achieved with the help of an exponential integrator for advancing the solution in time. This time integration method completely avoids generation of the Jacobian matrix of the system and hence eases the computation when solving the two-scale model in a completely coupled manner. Numerical simulations are presented for a two-dimensional infiltration problem.

Direct shear testing on unsaturated silty soils to investigate the effects of drying and wetting on shear strength parameters at low suction

A modified conventional direct shear device was used to measure unsaturated shear strength of two silty soils at low suction values (0 ~ 50 kPa) that were achieved by following drying and wetting paths of soil water characteristic curves (SWCCs). The results revealed that the internal friction angle of the soils was not significantly affected by either the suction or the drying wetting SWCCs. The apparent cohesion of soil increased with a decreasing rate as suction increased. Shear stress-shear displacement curves obtained from soil specimens subjected to the same net normal stress and different suction values showed a higher initial stiffness and a greater peak stress as suction increased. A soil in wetting exhibited slightly higher peak shear stress and more contractive volume change behavior than that of soil in drying at the same net normal stress and suction.

Efficient simulation of unsaturated flow in heterogeneous soils using an exponential integrator

- Provided a practical variable-stepsize implementation of the exponential Euler method (EEM). - Introduced a new second-order variant of the scheme that enables the local error to be estimated at the cost of a single additional function evaluation. - New EEM implementation outperformed sophisticated implementations of the backward differentiation formulae (BDF) of order 2 and was competitive with BDF of order 5 for moderate to high tolerances.