Tracer Methods Research Articles

Three-dimensional imaging of pore water diffusion and motion in porous media by nuclear magnetic resonance imaging

We report on the use of a pulsed gradient spin-echo imaging sequence for the three-dimensional (3D) imaging of water transport properties in two porous media: 2mm glass-beads and 0.15mm quartz-sand mixed with 2mm glass-beads. In contrast to tracer methods, which monitor the tracer motion by its effect on the signal relaxation of 1H, this sequence measures the echo signal intensity I0 without and I with applied diffusion gradient, respectively. For the wide-pore glass-bead system, the intensity loss is controlled by nearly free self-diffusion in the pores. A mean apparent diffusion coefficient is calculated from the ratio ln(I0/I) as 〈Dloc〉=1.9×10−9m2s−1, which is slightly lower than that of free water (D=2.3×10−9m2s−1). Increasing the mean pore flow velocity from 0 to 0.14mms−1 results in a linear increase of 〈Dloc〉 to 2.3×10−9m2s−1, caused by mechanical dispersion. The spatial distribution is of the log-normal type, where the width increases with increasing pore velocity. Correlation lengths are also calculated.For the fine porous medium, frequent contacts of the water molecules with the pore boundaries lead to a significant decrease of I0 by increased T2 relaxation. The resulting ratio of the signal intensities ln(I0/I) is then smaller than expected for pure diffusion, which is caused by the restricted diffusion in the fine pore system. The spatial distribution (normal) is broader than for the glass-bead system and the mean local apparent diffusion coefficient is calculated as 1×10−9m2s−1, a dependence on the pore flow velocity could not be detected.For the glass-bead system, the 3D image clearly shows regions of increased dispersivity (50% greater than the 〈Dloc〉), caused by packing errors, leading to preferential flow. This macroscopic effect on the column scale is quantified by a numerical simulation of tracer transport, based on the 3D diffusion coefficient field, assuming a linear relation to local velocities. From this simulation, the effective dispersion coefficient is obtained for the column scale (Deff=130×10−9m2s−1), which is comparable to that obtained from classical break-through curves with tracer substances.

Recycling by electrodialysis: from lab to industrial applications

The purpose of this paper is to describe an experimental method developed to study the use of electrodialysis (ED) as a recycling process introduced within some operations in the surface treatment industry. The case study is acid picking before electroplating. The first step is the study and selection of ion-exchange membrane couples. The second step is the development of tools to promote the use of ED applied to industry. Tracer methods and surface treatment models are described.

Spatial and temporal variability of ground water recharge in central Australia: a tracer approach.

Two environmental tracer methods are applied to the Ti-Tree Basin in central Australia to shed light on the importance of recharge from floodouts of ephemeral rivers in this arid environment. Ground water carbon-14 concentrations from boreholes are used to estimate the average recharge rate over the interval between where the ground water sample first entered the saturated zone and the bore. Environmental chloride concentrations in ground water samples provide estimates of the recharge rate at the exact point in the landscape where the sample entered the saturated zone. The results of the two tracer approaches indicate that recharge rates around one of the rivers and an extensive floodplain are generally higher than rates of diffuse recharge that occurs in areas of lower topographic relief. Ground water 2H/1H and 18O/16O compositions are all depleted in the heavier isotopes (delta2H = -67 per thousand to -50 per thousand; delta18O = -9.2 per thousand to -5.7%o) compared with the long-term, amount-weighted mean isotopic composition of rainfall in the area (delta2H = -33.8 per thousand; delta18O = -6.3 per thousand). This indicates that recharge throughout the basin occurs only after intense rainfall events of at least 150 to 200 mm/month. Finally, a recharge map is developed to highlight the spatial extent of the two recharge mechanisms. Floodout recharge to the freshest ground water (TDS <1,000 mg/L) is approximately 1.9 mm/year compared with a mean recharge rate of approximately 0.2 mm/year to the remainder of the basin. These findings have important implications for management of the ground water resource.

Elucidation of Behavior of Sulfur on Mo Catalysts Supported on TiO2 with Various Surface Areas Using 35S Tracer Methods

A series of Mo catalysts supported on TiO2 with various surface areas were prepared. In hydrodesulfurization (HDS) of dibenzothiophene (DBT) the activities of the series of catalysts were estimated. The results show that the activities of the series of catalysts increased linearly with the surface areas of TiO2 supports. The sulfur mobility on the sulfided Mo/TiO2 catalysts under the reaction conditions was elucidated by a 35S radioisotope tracer method using 35S-labeled DBT. The results suggest that the sulfur exchange rate constants (kRE) were approximately the same for all catalysts at a given temperature and that the amount of labile sulfur (S0) increases linearly with the surface area of TiO2 supports. The sulfidation states of the series of catalysts were also investigated by a 35S radioisotope pulse tracer method using 35S-labeled H2S. The results indicate that in spite of the coverage of Mo species on TiO2 support, the sulfidation of TiO2 support would still occur at 300°C. The sulfided catalysts could be reduced under H2 atmosphere.

Stormflow‐hydrograph separation based on isotopes: the thrill is gone — what's next?

Hprovedanirresistibletemptation, and was a vast improvement over graphical separationand solute tracer methods that were prevalent at the time. Eventu-ally, hydrologists realized that this new method entailed a plethoraof assumptions about temporal and spatial homogeneity of isotopiccomposition (many of which were commonly violated). Nevertheless,hydrologists forged ahead with dozens of isotope-based hydrograph-separation studies that were published in the 1970s and 1980s.Hortonian overland flow was presumed dead. By the late 1980s,the new isotope-based hydrograph separation technique had movedinto adolescence, accompanied by typical adolescent problems suchas confusion and a search for identity. As experienced hydrologistscontinued to use the isotope technique to study stormflow hydrol-ogy in forested catchments in humid climates, their younger peersfollowed obligingly—again and again. Was Hortonian overland flowreally dead and forgotten, though? What about catchments in whichpeople live and work? And what about catchments in dry climatesand the tropics? How useful were study results when several of theassumptions about the homogeneityof source waters were commonlyviolated? What if two components could not explain the variation ofisotopic composition measured in the stream during stormflow? Andwhat about uncertainty? As with many new tools, once the initialshine wore off, the limitations of the method became a concern—oneof which was that isotope-based hydrograph separations alone couldnot reveal much about the flow paths by which water arrives at astream channel during storms.During the late 1980s and early 1990s, isotope-based hydro-graph separation techniques matured into young adulthood. Unlikethe early studies that separated hydrographs into two componentsbased only on time, increasingly complex approaches emerged thatallowed stormflow-hydrograph separation into three-componentsthat reflected the geographic source areas of runoff. Hydrologistsalso began to incorporate error into their studies, and, most impor-tantly, began to combine isotope-based hydrograph separations withphysical measurements such as groundwater levels and soil watercontent to learn more about hydrologic flow paths. As the sciencematured further in the 1990s, a point was reached at which isotope-based hydrograph separations alone were insufficient to guarantee

Gestion de l'azote en syst�me d'�levage d�velopp�. Enjeux scientifiques et environnementauxNitrogen management from intensive livestock production : scientific and environmental issues

Growing environmental concern led to increased public and scientific attention to nitrogen transfers from animal manure and slurry. Major environmental problems arise from the excessive use of nitrogen compounds. Amongst these are (i) acidification of forests and natural ecosystems through atmospheric deposition of ammonia (NH3), (ii) eutrophication of inland waters and coastal seas mainly by organic N and nitrates, (iii) contamination of groundwater by nitrates and (iv) a contribution to the global warming problem by nitrous oxide, N2O. Tracer methods using 15N stable isotope provide and excellent tool for studying such complex transfers during the different stages of animal slurry management including storage, treatment and land spreading. In this article, we present a brief review of isotopic tracer principles and history through a general description of terms, definitions and assumptions follow by the methodologies developed in our laboratory to label the ammoniacal nitrogen fraction of pig slurry using artificial 15N enrichment. The aim of our studies is to gather information concerning nitrogen pig slurry turnover and to focus on those processes, where major progress is made using the stable isotope 15N. Recent research findings are Presented. La connaissance du cycle de l'azote des déjections animales (lisiers) est un enjeu primordial au regard de préoccupations environnementales : accroissement de l'efficacité agronomique et/ou réduction des pollutions atmosphériques. Dans ce contexte, l'utilisation du traceur isotopique 15N permet de quantifier les différents mécanismes (assimilation et réorganisation, minéralisation, volatilisation, nitrification—dénitrification) et d'étudier les voies de transferts possibles. La technique développée consiste notamment à marquer la fraction azote ammoniacal du lisier par ajout direct de sulfate d'ammonium ou d'urée enrichis en 15N. Des essais en laboratoire illustrent les processus de nitrification - dénitrification ainsi que les transferts d'azote sous forme de protoxyde d'azote (N2O). Par ailleurs le suivi du devenir de l'azote après épandage de lisier au champ, permet d'établir un bilan sol—plante—air. Au travers de ces expériences, l'utilisation du marquage isotopique 15N de l'azote des déjections animales apparaît comme un outil de première importance.

Regional muscle and adipose tissue amino acid metabolism in lean and obese women.

The effect of obesity on regional skeletal muscle and adipose tissue amino acid metabolism is not known. We evaluated systemic and regional (forearm and abdominal subcutaneous adipose tissue) amino acid metabolism, by use of a combination of stable isotope tracer and arteriovenous balance methods, in five lean women [body mass index (BMI) <25 kg/m(2)] and five women with abdominal obesity (BMI 35.0-39.9 kg/m(2); waist circumference >100 cm) who were matched on fat-free mass (FFM). All subjects were studied at 22 h of fasting to ensure that the subjects were in net protein breakdown during this early phase of starvation. Leucine rate of appearance in plasma (an index of whole body proteolysis), expressed per unit of FFM, was not significantly different between lean and obese groups (2.05 +/- 0.18 and 2.34 +/- 0.04 micromol x kg FFM(-1) x min(-1), respectively). However, the rate of leucine release from forearm and adipose tissues in obese women (24.0 +/- 4.8 and 16.6 +/- 6.5 nmol x 100 g(-1) x min(-1), respectively) was lower than in lean women (66.8 +/- 10.6 and 38.6 +/- 7.0 nmol x 100 g(-1) x min(-1), respectively; P < 0.05). Approximately 5-10% of total whole body leucine release into plasma was derived from adipose tissue in lean and obese women. The results of this study demonstrate that the rate of release of amino acids per unit of forearm and adipose tissue at 22 h of fasting is lower in women with abdominal obesity than in lean women, which may help obese women decrease body protein losses during fasting. In addition, adipose tissue is a quantitatively important site for proteolysis in both lean and obese subjects.

Underestimation of gluconeogenesis by the [U-(13)C(6)]glucose method: effect of lack of isotope equilibrium.

Among the many tracer methods to indirectly estimate gluconeogenesis in humans, the [U-(13)C(6)]glucose method as proposed by Tayek and Katz (Am J Physiol Endocrinol Metab 270: E709-E717, 1996; Am J Physiol Endocrinol Metab 272: E476-E484, 1997) has the advantage of being able to simultaneously estimate hepatic glucose output and fractional gluconeogenesis. However, Landau et al. (Landau BR, J Wahren, K Ekberg, SF Previs, D Yang, and H Brunengraber. Am J Physiol Endocrinol Metab 274: E954-E961, 1998) have shown that this method underestimates the rate of gluconeogenesis. The underestimation has been attributed to tracer dilution by other three-carbon substrates and the lack of isotopic steady state. Using a computer simulation of [U-(13)C(6)]glucose infusion, we demonstrate that the lack of isotope equilibrium in both the lactate and glucose compartments contributes substantially to the underestimation of gluconeogenesis. [U-(13)C(6)]glucose experiments were performed with the addition of a primed constant infusion of [U-(13)C(3)]lactate and the delay in M3 glucose equilibrium estimated from the isotopic steady-state value determined by modeling M3 glucose to a single-exponential fit. We found that, even with the addition of [U-(13)C(3)]lactate infusion, the M3 glucose enrichment of the last timed sample was approximately 20% less than the isotopic steady-state value. Thus the lack of isotopic equilibrium of the glucose compartment potentially accounts for 20% of the underestimation of gluconeogenesis. The underestimation of gluconeogenesis using [U-(13)C(6)]glucose without the additional infusion of [U-(13)C(3)]lactate in previous publications is expected to be even greater because of the lack of isotope equilibrium in both the lactate and glucose compartments. These findings are consistent with the results from our computer simulation.

Use of stable isotopically labeled tracers to measure very low density lipoprotein-triglyceride turnover

Tracer methods for VLDL-TG kinetics vary in their ability to account for the effect of tracer recycling, which can influence the calculation of VLDL-TG fractional catabolic rates (FCRs). We evaluated a novel approach, involving stable isotopically labeled glycerol or palmitate tracers in conjunction with compartmental modeling, for measuring VLDL-TG kinetics in normolipidemic human subjects. When administered as a bolus simultaneously, both tracers provided identical VLDL-TG FCRs when the data were analyzed by a compartmental model that accounted for hepatic lipid tracer recycling, but not by non-compartmental analysis. The model-derived FCR was greater than that determined using a non-compartmental approach, and was 2- to 3-fold higher than that usually reported by using a bolus of radioactive [3H]glycerol. When palmitate tracer was given as a constant infusion, VLDL-TG turnover appeared 5-fold slower, because tracer recycling through hepatic lipid pools could not be resolved with the infusion protocol. We conclude that accounting for tracer recycling, particularly the contribution of hepatic glycerolipid pools, is essential to accurately measure VLDL-TG kinetics, and that bolus injection of stable isotopically labeled glycerol or palmitate tracers in conjunction with compartmental modeling analysis offers a reliable approach for measuring VLDL-TG kinetics.—Patterson, B. W., B. Mittendorfer, N. Elias, R. Satyanarayana, and S. Klein. Use of stable isotopically labeled tracers to measure very low density lipoprotein-triglyceride turnover.

Elucidation of sulfidation state and hydrodesulfurization mechanism on Mo/TiO2 catalyst using [formula omitted] radioisotope tracer methods

In hydrodesulfurization (HDS) of dibenzothiophene (DBT) the activities on the Mo/TiO2 catalysts with various Mo contents were estimated under the typical HDS reaction conditions. The results show that the activities of the catalysts increased linearly with Mo content up to 6wt.% MoO3, which means that the monolayer dispersion of MoO3 on TiO2 support is maintained up to 6wt.% MoO3. The sulfidation states of MoO3/TiO2 catalysts were investigated using a 35S radioisotope pulse tracer method. The results showed that the sulfidation of TiO2 support would also occur. Moreover, the sulfur mobility on the sulfided 6% MoO3/TiO2 catalyst under the reaction conditions was elucidated by a 35S radioisotope tracer method using 35S-labeled DBT. The results suggested that, compared to Mo/Al2O3 catalyst, Mo/TiO2 catalyst showed a little higher amount of labile sulfur (S0) and about two times higher release rate constant of H2S (kRE), which indicated that higher mobility of sulfur was obtained on sulfided Mo/TiO2 catalyst.

A shuttlecock optical rotator-its design, fabrication and evaluation for a microfluidic mixer

An optically driven microrotator is proposed for fluidic mixing in future micrototal analysis systems (/spl mu/-TAS). The rotation mechanism, optical torque and microflow around the rotator are analyzed, and the rotator is fabricatied both by photolithography and photoforming methods. The microflow fields generated by the optical rotation are then experimentally visualized by both tracer and optical methods, and the velocity vectors and flux amount around the rotator are analyzed for the evaluation of the mixing performance of the microfluids.

Phosphoenolpyruvate carboxykinase revisited: Insights into its metabolic role

Phosphoenolpyruvate carboxykinase revisited: Insights into its metabolic role

Elucidation of Hydrogen Mobility in Functional Groups of Coals Using Tritium Tracer Methods

Hydrogen exchange reactions of coal with tritiated water and gaseous hydrogen were investigated to estimate the mobility of hydrogen in coal using not only a batch type reactor but also a flow type reactor. Specifically, the reactivities of functional groups were traced in these reactions. In the reaction of coal with tritiated water at 100 °C the hydrogen exchange of functional groups such as hydroxyl group in coals could be estimated. In the pressurized system using stainless batch type reactor aromatic hydrogen at ortho- and para-positions of a functional group could also be estimated by the hydrogen exchange reactions of coal and tritiated water at higher temperature. In hydrogen exchange reactions of coals with tritiated gaseous hydrogen using a flow reactor, reaction temperature was controlled exactly. The use of a Pt/Al2O3 catalyst promoted the generation of hydrogen radicals which reacted with coal. This method enables us to estimate the reactivity of a functional group with a hydrogen radical. Fu...

On the mound of Macrotermes michaelseni as an organ of respiratory gas exchange.

Patterns and rates of air movements in the mounds and nests of Macrotermes michaelseni were studied using tracer methods. Wind is a significant source of energy for powering nest ventilation, despite the mound being a completely enclosed structure. Nests are ventilated by a tidal movement of air driven by temporal variation in wind speed and wind direction. Density gradients sufficiently steep to drive bulk flow by natural convection will be rare. However, metabolism-induced buoyant forces may interact with wind energy in a way that promotes homeostasis of the mound atmosphere.

Photosynthesis controls of rhizosphere respiration and organic matter decomposition

The effects of shading wheat plants on rhizosphere respiration and rhizosphere priming of soil organic matter decomposition were investigated by using a natural abundance 13C tracer method and 14C pulse labeling simultaneously. Seven days with strongly reduced photosynthesis (12/60 h day/night period) resulted in only half of the total CO 2 efflux from soil compared to the treatment with a 12/12 h day/night period. The CO 2 efflux from unplanted soil amounted to only 12 and 20% of the total CO 2 efflux from the soil with non-shaded and shaded plants, respectively. On average 75% of total CO 2 efflux from the planted soil with prolonged night periods was root-derived. Rhizosphere respiration was tightly coupled with plant photosynthetic activity. Any factor affecting photosynthesis, or substrate supply to roots and rhizosphere microorganisms, is an important determinant of root-derived CO 2 efflux, and thereby, total CO 2 efflux from soils. Clear diurnal dynamics of the total CO 2 efflux intensity indicate the existence of an endogenous control mechanism of rhizosphere respiration. The light-on events after prolonged dark periods lead to strong increases of root-derived and therefore of total CO 2 efflux from soil. After 14C pulse labeling, two maxima of the root-derived 14CO 2 efflux were measured (6 and 24 h). This result demonstrated the diurnal dynamics of the rhizosphere respiration of recently-assimilated C in both the normal light conditions and shaded plants as well. The total amount of root-derived C respired in the rhizosphere was 17.3 and 20.6% of the total assimilated C for non-shaded and shaded plants, respectively. Both methods used, 13C natural abundance and 14C pulse labeling, gave similar estimates of root-derived CO 2 during the whole observation period: 1.80±0.27 and 1.67±0.37 mg C kg −1 h −1 (±SD), respectively. Both tracer methods show that the cultivation of wheat led to the increasing decomposition intensity of soil organic matter (priming effect). Additionally, 13C natural abundance allows tracing of the dynamics of the priming effect depending on the light-on events.

Elucidation of Sulfidation State and Hydrodesulfurization Mechanism on TiO2 Catalysts Using 35S Radioisotope Tracer Methods

The hydrodesulfurization (HDS) activities of sulfided TiO2 with various surface areas were characterized under the typical HDS reaction conditions. The results showed that HDS activities increased linearly with increasing surface area of TiO2, suggesting that the surface sulfide TiS2 is the active phase of the HDS reaction on sulfided TiO2 catalyst. The sulfidation states of TiO2 with various surface areas were investigated using a 35S radioisotope pulse tracer method. The results showed that the Ti atoms on the surface of TiO2 could be completely sulfided to TiS2 at 400°C, whereas the sulfidation of Ti atoms in the bulk of TiO2 would occur slowly at 500°C. When the sulfided TiO2 was reduced in H2 at 400°C, TiS2 was reduced to the sulfidation state TiS1.5, leading to the formation of Ti3+ ions and sulfur anion vacancies. Moreover, HDS reaction mechanisms on sulfided TiO2 catalysts under the reaction conditions were elucidated by a 35S radioisotope tracer method using 35S-labeled dibenzothiophene (DBT). The results showed that less labile sulfur was detected on the sulfided TiO2 catalysts, suggesting that the HDS mechanism on TiO2 catalysts was very different from that on Mo-based catalysts.

NMR imaging of falling water drops.

The falling water drop is a simple model for studying phenomena related to chemical extraction, where two immiscible phases are dynamically blended to promote the transport of solute molecules from one phase to the other. Convective motion inside the drop significantly influences the extraction efficiency. Whereas optical and tracer methods are model bound or invasive, NMR imaging is noninvasive, direct, and applicable to nontransparent media. The first NMR measurements of a water drop falling through air are reported. It is shown that, in drops from pure water, large-scale convection rolls are observed in contrast to drops with the surface tension lowered by surfactants.

Comparison of non-tracer and tracer methods for determination of volatile fatty acid production rate in the rumen of sheep fed on two levels of intake

The aim of the present work was to estimate volatile fatty acid (VFA) production rate in the rumen of sheep fed two levels of intake using both a tracer (TM; by isotope dilution) and a non-tracer method (NTM; by supplementary infusion) in steady-state conditions. Six wethers received a diet containing 700 g lucerne hay and 300 g ground maize/kg in eight equal meals at 3 h intervals per d. The diet (9.8 MJ metabolizable energy (ME)/kg DM) was offered at 90 % ad libitum consumption (high intake, HI) or 45 % ad libitum consumption (low intake, LI) in a crossover design. Each sheep received five intrarumen VFA solutions infused continuously for 24 h at rates of 250 ml and 165 ml/h for the HI and LI respectively. The first infusion, considered as a control treatment (Con), consisted of a solution of [1-(13)C]propionate (7 mmol/d). The four other solutions were isoenergetic (1.9 MJ ME/kg DM intake) mixtures of unlabelled propionate (C(3)) and butyrate (C(4)) at different levels: 0.90 mol C(4)/kg DM intake; 0.60 mol C(3)/kg DM intake; 0.30 mol C(3)/kg DM intake; 1.35 mol C(3)/kg DM intake. The VFA infusions did not affect rumen fermentation of the basal diet (pH, osmotic pressure, protozoa numbers), and comparable DM digestibility of the diet among the different treatments was observed. Both estimation methods demonstrated a similar increase (1.7-fold) in the rumen VFA production rate of sheep fed at intakes varying between 0.9 to 1.7 times maintenance. Irrespective of the intake level, the rumen production rate of individual VFA was on average 1.5-fold higher when estimated by the TM compared with the NTM. Rumen VFA production rates estimated by the NTM and TM represented 80 % and 120 % ME intake respectively. The difference between NTM and TM estimates seems likely to be caused mainly by overestimation of the VFA production rates by the TM.

Stable isotope approaches, applications, and issues related to polyunsaturated fatty acid metabolism studies.

The use of stable isotope tracers for investigating fatty acid metabolism in human subjects has increased substantially over the last decade. Advances in analytical instrumentation, commercial availability of labeled substrates, and safety considerations are major reasons for this increased use of stable isotope tracers. Several experimental design options are available for using either deuterium or carbon-13 as tracers for fatty acid and lipid studies. Options include feeding a pulse dose of labeled fat or a mixture containing two or more labeled fats. Multiple doses of the labeled fat can be fed at timed intervals to increase enrichments. Administration by injection or continuous intravenous infusion is an alternative. Another option is to use diets containing foods from plants that have slightly higher natural carbon-13 enrichment. Each basic experimental design has its specific strengths, and the best choice of experimental design depends on the study objectives. Stable isotope studies have been used to address a variety of questions related to unsaturated fatty acid metabolism in humans. Examples are provided that illustrate the use of stable isotopes to investigate oxidation of docosahexaenoic acid, desaturation of linoleic and linolenic acids in infants and adults, incorporation of long-chain n-6 and n-3 fatty acids, bioequivalency of linolenic acid in primates, 13C nuclear magnetic resonance spectra of arachidonic acid in living rat brain, and effect of triacylglycerol structure on absorption. Radioisotope and stable isotope tracer studies in animals and humans are responsible for much of our understanding of fatty acid and lipid metabolism. However, tracer studies have limitations, and there are some unresolved issues associated with isotope studies. Examples of unresolved issues are quantification of isotope data, validity of in vivo fatty acid metabolite results, kinetic modeling, subject variability, and use of blood lipid data as a reflection of tissue lipid metabolism. Resolving these issues, developing novel methodology, and applying stable isotope tracer methods to questions related to PUFA metabolism are broad areas of interesting and challenging research opportunities.

On the advection of sharp material interfaces in geodynamic problems: entrainment of the D″ layer

The D″ layer is a dense and chemically distinct layer at the base of the convecting mantle. Numerical modeling of the entrainment of this layer by mantle convection requires the solution of the advective transport equation without introducing numerical diffusion across sharp material boundaries. We use our improved second moment numerical method to solve the equation. The method conserves the amount of material and the first and second moments of material distribution in each control volume. We first consider two examples of isothermal Rayleigh–Taylor instability to illustrate the performance of our method by comparing our results with those of a number of field, tracer and marker chain methods. We show that the performance of our method in minimizing the numerical diffusion is better than the field methods and comparable to the tracer and marker chain methods. We then study the instability of the dense D″ layer and its interaction with the overlying mantle. A range of density contrast between the D″ layer and the mantle, layer thickness, and the Rayleigh number, Ra, is examined. We show that for higher values of these parameters, the amount of entrainment decreases and the layer remains stable over longer periods of time. For very thick D″ layers and high Ra values, internal convection can take place within the layer.