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.

Three-dimensional hydrogen-bonded structures in the hydrated proton-transfer salts of isonipecotamide with the dicarboxylic oxalic and adipic acid analogues

The structures of the 1:1 hydrated proton-transfer compounds of isonipecotamide (piperidine-4-carboxamide) with oxalic acid, 4-carbamoylpiperidinium hydrogen oxalate dihydrate, C6H13N2O+·C2HO4-·2H2O, (I), and with adipic acid, bis­(4-car­bam­oylpiperidinium) adipate dihydrate, 2C6H13N2O+·C6H8O42-·2H2O, (II), are three-dimensional hydrogen-bonded constructs involving several different types of enlarged water-bridged cyclic associations. In the structure of (I), the oxalate monoanions give head-to-tail carb­oxy­lic acid O-HOcarboxyl hydrogen-bonding inter­actions, forming C(5) chain substructures which extend along a. The isonipecotamide cations also give parallel chain substructures through amide N-HO hydrogen bonds, the chains being linked across b and down c by alternating water bridges involving both carboxyl and amide O-atom acceptors and amide and piperidinium N-HOcarboxyl hydrogen bonds, generating cyclic R43(10) and R32(11) motifs. In the structure of (II), the asymmetric unit comprises a piperidinium cation, half an adipate dianion, which lies across a crystallographic inversion centre, and a solvent water mol­ecule. In the crystal structure, the two inversion-related cations are inter­linked through the two water mol­ecules, which act as acceptors in dual amide N-HOwater hydrogen bonds, to give a cyclic R42(8) association which is conjoined with an R44(12) motif. Further N-HOwater, water O-HOamide and piperidinium N-HOcarbox­yl hydrogen bonds give the overall three-dimensional structure. The structures reported here further demonstrate the utility of the isonipecotamide cation as a synthon for the generation of stable hydrogen-bonded structures. The presence of solvent water mol­ecules in these structures is largely responsible for the non-occurrence of the common hydrogen-bonded amide-amide dimer, promoting instead various expanded cyclic hydrogen-bonding motifs.

Coordination polymeric structures in the sodium salt of 4-chloro-3-nitrobenzoic acid and the sodium and potassium salts of 4-nitroanthranilic acid

The structures of the hydrated sodium salts of 4-chloro-3-nitrobenzoic acid {poly[aqua(μ4-4-chloro-3-nitrobenzoato)sodium(I)], [Na(C7H3ClNO4)(H2O)]n, (I)} and 2-amino-4-nitrobenzoic acid {poly[μ-aqua-aqua(μ3-2-amino-4-nitrobenzoato)sodium(I)], [Na(C7H5N2O4)(H2O)2]n, (II)}, and the hydrated potassium salt of 2-amino-4-nitrobenzoic acid {poly[μ-aqua-aqua(μ5-2-amino-4-nitrobenzoato)potassium(I)], [K(C7H5N2O4)(H2O)]n, (III)} have been determined and their complex polymeric structures described. All three structures are stabilized by intra- and intermolecular hydrogen bonding and strong π–π ring interactions. In the structure of (I), the distorted trigonal bipyrimidal NaO5 coordination polyhedron comprises a monodentate water molecule and four bridging carboxylate O-atom donors, generating a two-dimensional polymeric structure lying parallel to (001). Intra-layer hydrogen-bonding associations and strong inter-ring π–π interactions are present. Structure (II) has a distorted octahedral NaO6 stereochemistry, with four bridging O-atom donors, two from a single carboxylate group and two from a single nitro group and three from the two water molecules, one of which is bridging. Na centres are linked through centrosymmetric four-membered duplex water bridges and through 18-membered duplex head-to-tail ligand bridges. Similar centrosymmetric bridges are found in the structure of (III), and in both (II) and (III) strong inter-ring π–π interactions are found. A two-dimensional layered structure lying parallel to (010) is generated in (II), whereas in (III) the structure is three-dimensional. With (III), the irregular KO7 coordination polyhedron comprises a doubly bridging water molecule, a single bidentate bridging carboxylate O-atom donor and three bridging O-atom donors from the two nitro groups. A three-dimensional structure is generated. These coordination polymer structures are among the few examples of metal complexes of any type with either 4-chloro-3-nitrobenzoic acid or 4-nitroanthranilic acid.

Hydrogen-bonded two- and three-dimensional polymeric structures in the ammonium salts of 3,5-dinitrobenzoic acid, 4-nitrobenzoic acid and 2,4-dichlorobenzoic acid

The structures of the ammonium salts of 3,5-dinitrobenzoic acid, NH4+ C7H3N2O6- (I), 4-nitrobenzoic acid, NH4+ C7H4N2O4- . 2H2O (II) and 2,4-dichlorobenzoic acid, NH4+ C7H3Cl2O2- . 0.5H2O (III), have been determined and their hydrogen-bonded structures are described. All salts form hydrogen-bonded polymeric structures, three-dimensional in (I) and two-dimensional in (II) and (III). With (I), a primary cation-anion cyclic association is formed [graph set R3/4(10)] through N-H...O hydrogen bonds, involving a carboxyl O,O' group on one side and a single carboxyl O-atom on the other. Structure extension involves both N-H...O hydrogen bonds to both carboxyl and nitro O-atom acceptors. With structure (II), the primary inter-species interactions and structure extension into layers lying parallel to (0 0 1) are through conjoined cyclic hydrogen-bonding motifs: R3/4(10) [one cation, a carboxyl (O,O') group and two water molecules] and centrosymmetric R2/4(8) [two cations and two water molecules]. The structure of (III) also has conjoined R3/4(10) and centrosymmetric R2/4(8) motifs in the layered structure but these differ in that he first involves one cation, a carboxyl (O,O') as well as a carboxyl (O) group and one water molecule, the second, two cations and two carboxyl O-groups. The layers lie parallel to (1 0 0). The structures of the salt hydrates (II) and (III) reported in this work, giving two-dimensional layered arrays through conjoined hydrogen-bonded nets provide further illustrations of a previously indicated trend among ammonium salts of carboxylic acids, but the anhydrous three-dimensional structure of (I) is inconsistent.

Resistance of microbial populations in DDT-contaminated and uncontaminated soils

One DDT-contaminated soil and two uncontaminated soils were used to enumerate DDT-resistant microbes (bacteria, actinomycetes and fungi) by using soil dilution agar plates in media either with 150 μg DDT ml -1 or without DDT at different temperatures (25, 37 and 55°C). Microbial populations in this study were significantly (p<0.001) affected by DDT in the growth medium. However, the numbers of microbes in long-term contaminated and uncontaminated soils were similar, presumably indicating that DDT-resistant microbes had developed over a long time exposure. The tolerance of isolated soil microbes to DDT varied in the order fungi>actinomycetes>bacteria. Bacteria from contaminated soil were more resistant to DDT than bacteria from uncontaminated soils. Microbes isolated at different temperatures also demonstrated varying degrees of DDT resistance. For example, bacteria and actinomycetes isolated at all incubation temperatures were sensitive to DDT. Conversely fungi isolated at all temperatures were unaffected by DDT.

Crystal structures and hydrogen bonding in the proton transfer salts of nicotine with 3,5-dinitrosalicylic acid and 5-sulfosalicylic acid

The structures of the 1:1 anhydrous salts of nicotine (NIC) with 3,5-dinitrosalicylic acid (DNSA) and 5-sulfosalicylic acid (5-SSA), namely (1R,2S)-1-methyl-2-(3-pyridyl)-1H-pyrrolidin-1-ium 2-carboxy-4,6-dinitrophenolate, C10H15N2+ C7H3N2O7-, (I) and (1R,2S)-1-methyl-2-(3-pyridyl)-1H-pyrrolidin-1-ium 3-carboxy-4-hydroxybenzenesulfonate, C10H15N2+ C7H5O6S-, (II) are reported. The asymmetric units of both (I) and (II) comprise two independent nicotinium cations (C and D) and either two DNSA or two 5-SSA anions (A and B), respectively. One of the DNSA anions shows a 25% rotational disorder in the benzene ring system. In the crystal of (I), inter-unit pyrrolidinium N-H...N(pyridine) hydrogen bonds generate zigzag NIC cation chains which extend along a while the DNSA anions are not involved in any formal inter-species hydrogen bonding but instead form pi--pi associated stacks which parallel the NIC chains along a [ring centroid separation, 3.857(2)A]. Weak C-H...O interactions between chain substructures give an overall three-dimensional structure. With (II), A and B anions form independent zigzag chains with C and D cations, respectively, through carboxylic acid O-H...N(pyridine) hydrogen bonds. These chains, which extend along b are pseudo-centrosymmetrically related and give pi--pi interactions between the benzene rings of anions A and B and the pyridine rings of the NIC cations C and D, respectively [ring centroid separations, 3.6422(19) and 3.7117(19)A]. Present also are weak intermolecular C-H...O hydrogen-bonding interactions between the chains, giving an overall three-dimensional structure.

Two-dimensional hydrogen-bonded polymers in the crystal structures of the ammonium salts of phenoxyacetic acid, (4-fluorophenoxy)acetic acid and (4-chloro-2-methylphenoxy)acetic acid

The structures of the ammonium salts of phenoxyacetic acid, NH4+ C8H6O3- (I), (4-fluorophenoxy)acetic acid NH4+ C8H5FO3- (II) and the herbicidally active (4-chloro-2-methylphenoxy)acetic acid (MCPA), NH4+ C9H8ClO3-. 0.5(H2O) (III) have been determined. All have two-dimensional layered structures based on inter-species ammonium N-H...O hydrogen-bonding associations which give core substructures consisting primarily of conjoined cyclic motifs. Crystals of (I) and (II) are isomorphous with the core comprising R2/1(5), R2/1(4) and centrosymmetric R2/4(8) ring motifs, giving two-dimensional layers lying parallel to (100). In (III), the water molecule of solvation lies on a crystallographic twofold rotation axis and bridges two carboxyl O-atoms in an R4/4(12) hydrogen-bonded motif, creating two R3/4(10) rings which together with a conjoined centrosymmetric R2/4(8) ring incorporating both ammonium cations, generate two-dimensional layers lying parallel to (100). No pi-pi ring associations are present in any of the structures.

Crystal structures and hydrogen bonding in the anhydrous tryptaminium salts of the isomeric (2,4-dichlorophenoxy)acetic and (3,5-dichlorophenoxy)acetic acids

The anhydrous salts of 1H-indole-3-ethanamine (tryptamine) with isomeric (2,4-dichlorophenoxy)acetic acid (2,4-D) and (3,5-dichlorophenoxy)acetic (3,5-D), C10H13N2+ (C8H5Cl2O3)-, [(I) and (II), respectively] have been determined and their one-dimensional hydrogen-bonded polymeric structures are described. In the crystal of (I),the aminium H-atoms are involved in three separate inter-species N-H...O hydrogen-bonding interactions, two with carboxyl O-atom acceptors and the third in an asymmetric three-centre bidentate carboxyl O,O' chelate [graph set R2/1(4)]. The indole H-atom forms an N-H...O~carboxyl~ hydrogen bond, extending the chain structure along the b axial direction. In (II), two of the three aminium H-atoms are also involved in N-H...O(carboxyl) hydrogen bonds similar to (I) but with the third, a three-centre asymmetric interaction with carboxyl and phenoxy O-atoms is found [graph set R2/1(5)]. The chain polymeric extension is also along b. There are no pi--pi ring interactions in either of the structures. The aminium side chain conformations differ significantly between the two structures, reflecting the conformational ambivalence of the tryptaminium cation, as found also in the benzoate salts.

Applying HYDRUS to flow in a sodic clay soil with solution composition–dependent hydraulic conductivity

Management of sodic soils under irrigation often requires application of chemical ameliorants to improve permeability combined with leaching of excess salts. Modeling irrigation, soil treatments, and leaching in these sodic soils requires a model that can adequately represent the physical and chemical changes in the soil associated with the amelioration process. While there are a number of models that simulate reactive solute transport, UNSATCHEM and HYDRUS-1D are currently the only models that also include an ability to simulate the impacts of soil chemistry on hydraulic conductivity. Previous researchers have successfully applied these models to simulate amelioration experiments on a sodic loam soil. To further gauge their applicability, we extended the previous work by comparing HYDRUS simulations of sodic soil amelioration with the results from recently published laboratory experiments on a more reactive, repacked sodic clay soil. The general trends observed in the laboratory experiments were able to be simulated using HYDRUS. Differences between measured and simulated results were attributed to the limited flexibility of the function that represents chemistry-dependent hydraulic conductivity in HYDRUS. While improvements in the function could be made, the present work indicates that HYDRUS-UNSATCHEM captures the key changes in soil hydraulic properties that occur during sodic clay soil amelioration and thus extends the findings of previous researchers studying sodic loams.

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.

Crystal structures and hydrogen bonding in the morpholinium salts of four phenoxyacetic acid analogues

The anhydrous salts morpholinium (tetrahydro-2-H-1,4-oxazine) phenxyacetate, C4H10NO+ C8H7O3- (I), (4-fluorophenoxy)acetate, C4H10NO+ C8H6FO3- (II) and isomeric morpholinium (3,5-dichlorophenoxy)acetate (3,5-D) (III) and morpholinium (2,4-dichlorophenoxy)acetate (2,4-D), C4H10NO+ C8H5Cl2O3- (IV), have been determined and their hydrogen-bonded structures are described. In the crystals of (I), (III) and (IV), one of the the aminium H atoms is involved in a three-centre asymmetric cation-anion N-H...O,O' R2/1(4) hydrogen-bonding interaction with the two carboxyl O-atom acceptors of the anion. With the structure of (II), the primary N---H...O interaction is linear. In the structures of (I), (II) and (III), the second N-H...O(carboxyl) hydrogen bond generates one-dimensional chain structures extending in all cases along [100]. With (IV), the ion pairs are linked though inversion-related N-H...O hydrogen bonds [graph set R2/4(8)], giving a cyclic heterotetrameric structure.

Rice husk biochar and crop residue amendment in subtropical cropping soils: Effect on biomass production, nitrogen use efficiency and greenhouse gas emissions

We investigated the effect of maize residues and rice husk biochar on biomass production, fertiliser nitrogen recovery (FNR) and nitrous oxide (N2O) emissions for three different subtropical cropping soils. Maize residues at two rates (0 and 10 t ha−1) combined with three rates (0, 15 and 30 t ha-1) of rice husk biochar were added to three soil types in a pot trial with maize plants. Soil N2O emissions were monitored with static chambers for 91 days. Isotopic 15N-labelled urea was applied to the treatments without added crop residues to measure the FNR. Crop residue incorporation significantly reduced N uptake in all treatments but did not affect overall FNR. Rice husk biochar amendment had no effect on plant growth and N uptake but significantly reduced N2O and carbon dioxide (CO2) emissions in two of the three soils. The incorporation of crop residues had a contrasting effect on soil N2O emissions depending on the mineral N status of the soil. The study shows that effects of crop residues depend on soil properties at the time of application. Adding crop residues with a high C/N ratio to soil can immobilise N in the soil profile and hence reduce N uptake and/or total biomass production. Crop residue incorporation can either stimulate or reduce N2O emissions depending on the mineral N content of the soil. Crop residues pyrolysed to biochar can potentially stabilise native soil C (negative priming) and reduce N2O emissions from cropping soils thus providing climate change mitigation potential beyond the biochar C storage in soils. Incorporation of crop residues as an approach to recycle organic materials and reduce synthetic N fertiliser use in agricultural production requires a thorough evaluation, both in terms of biomass production and greenhouse gas emissions.

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.