Transient Erosion Research Articles

Eulerian approach for erosion induced by particle-laden impinging jets

Particle dispersion and erosion play an important role in various engineering applications, particularly in impinging jet flows. This study presents a new Eulerian method for characterizing these phenomena in axisymmetric, laminar, and turbulent jets, impinging and transiently eroding a flat wall. The Eulerian mass and momentum conservation equations are solved assuming a one-way coupling between the flow and the particles. The carrier flow boundary layer velocity profiles in the laminar case are validated with analytical solutions. The particle calculation involves two stages, incident and reflected particles, connected via a restitution model. The reflected particles’ results offer insights into secondary erosion areas but are not used for the main erosion calculations. Subsequently, erosion at the eroded surface is computed using an empirical erosion model, followed by the displacement of computational nodes using the linear-elastic, small-strain deformation equations, all of which are solved transiently. The solutions reveal the spatial particle concentrations and momentum for different Stokes numbers: smaller Stokes particles follow the carrier flow streamlines, medium Stokes particles deviate, forming a W-shaped erosion profile, while the largest Stokes particles create a U-shaped profile. This numerical model offers a computationally efficient framework for CFD-based transient erosion calculation due to its Eulerian implementation.

Half of the soil erosion in the Alps during the Holocene is explained by transient erosion crises as a consequence of rapid human land clearing

Human land use changes have altered soil erosion for millennia with extensive consequences on terrestrial and aquatic ecosystems as well as on biogeochemical cycles along the land-ocean continuum. Despite their great importance, past erosion trends have high uncertainties limiting quantitative estimates of long-term erosion dynamics. Here, we applied a new approach combining well-dated paleo-records of soil erosion from lake sediments and a spatially distributed semi-empirical model to simulate annual soil erosion in six lake watershed systems in the Northwestern Alps during the Holocene. Progressive and abrupt changes in soil erosion are detected in the six watersheds. Progressive erosion explains most of the soil exports observed during the Early to Mid-Holocene period (from 11,700 to 3000 cal. yr. BP), while transient erosion crises (i.e., periods of abrupt increase in the erosion rates spanning approximately 1000 ± 500 years) led to massive soil losses during the Late-Holocene period (from 3000 to 1000 cal. yr. BP). Our coupled approach of proxy-model reconstruction shows that the transient erosion crises represent the half of the total soil erosion exports during the Holocene. These estimates defy current representations of large-scale soil erosion during the Holocene that do not consider transient erosion crises, hence potentially underestimating the anthropogenic perturbation of lateral fluxes and fate along the land-ocean continuum. Our results further suggest that erosion and/or land cover proxies need to be consistently integrated into model approaches when attempting to estimate past variations in mass exports from terrestrial to aquatic ecosystems over centennial to millennial timescales.

Modeling of particle erosion of high-pressure turbine based on dynamic mesh method

In this work, we investigate erosion characteristics of a high-pressure turbine by using Oka erosion model coupled with the dynamic mesh method, which allows for the dynamic change of blade profile. The variation of blade profile, material removal and performance degradation during erosion are quantified for the original blade, and the results are compared with those of an optimized blade previously obtained through multi-objective optimization of aerodynamic and erosion resistance performances. It is found that compared with the original blade, the optimized blade is of higher efficiency and lower erosion, suggesting that the previous multi-objective optimization, albeit ignoring the dynamic change of blade profile, still works for the dynamic erosion process. For either blade, the efficiency decreases slowly at first and drops sharply after a period of erosion, because as the erosion proceeds, the regions occupied by the vortex rapidly expand, leading to the blockage of blade passage. The transient erosion characteristics and particle trajectories indicate that the erosion is initially located near the middle and rear of blade on pressure side and the leading edge on suction side; as the erosion progresses, the erosion mainly occurs near the leading edge on pressure side but almost disappears on suction side.

Development of scaling approach based on experimental and CFD data for thermal stratification and mixing induced by steam injection through spargers

Advanced Pressurized Water Reactors (APWRs) and Boiling Water Reactors (BWRs) employ a suppression pool as a heat sink to prevent containment overpressure. Steam can be discharged into the pool through multi-hole spargers or blowdown pipes in both normal and accident conditions. Direct Contact Condensation (DCC) creates sources of momentum and heat. The competition between these two sources determines the development of thermal stratification or mixing of the pool. Thermal stratification is of safety concern as it reduces the cooling capability compared to a completely mixed pool condition. In this work we develop a scaling approach to prediction of the thermal stratification in a water pool induced by steam injection through spargers. Experimental data obtained from large-scale pool tests conducted in the PPOOLEX and PANDA facilities, as well as simulation results obtained using validated codes are used to develop the scaling. Two injection orientations, namely radial injection through multi-hole Sparger Head (SH) and vertical injection through Load Reduction Ring (LRR), are considered. We show that the erosion rate of the cold layer can be estimated using the Richardson number. In this work, scaling laws are proposed to estimate both the (i) transient erosion velocity and (ii) the stable position of the thermocline. These scaling laws are then implemented into a 1D model to simulate the thermal behavior of the pool during steam injection through the sparger.

Image-based machine learning for monitoring the dynamics of deltaic islands in the Atchafalaya River Delta Complex between 1991 and 2019

Deltaic islands are distinct hydro-environmental zones with global significance in food security, biodiversity conservation, and fishery industry. These islands are the fundamental building blocks of many river deltas. However, deltaic islands are facing severe challenges due to intensive anthropogenic activities, sea level rise, and climate change. In this study, dynamic changes of deltaic islands in Wax Lake Delta (WLD) and Atchafalaya Delta (AD), part of the Atchafalaya River Delta Complex (ARDC) in Louisiana, USA, were quantified based on remote sensing images from 1991 to 2019 through a machine learning method. Results indicate a significant increase in deltaic islands area for the whole ARDC at a rate of 1.29 km2/yr, with local expansion rates of 0.60 km2/yr for WLD and 0.69 km2/yr for AD. All three parts of the WLD naturally prograded seaward, with the western part (WP) and central part (CP) expanding southwestward to the sea, while the eastern part (EP) prograding southeastwards. Differently from WLD, the three parts of AD irregularly expanded seaward under the impacts of anthropogenic activities. The WP and CP of the AD expanded respectively northwestwards and southwestwards, while the EP remained stable. Different drivers dominate the growth of deltaic islands in the WLD and AD. Specifically, fluvial suspended sediment discharge and peak flow events were responsible for the shift in the spatial evolution of WLD, while dredging and sediment disposal contributed to the expansion of AD. Tropical storms with different intensity and landing locations caused short-term deltaic island erosion or expansion. Tropical storms mainly generated erosion on the deltaic islands of the WLD, while causing transient erosion or siltation on the deltaic islands of the AD. In addition, high-intensity hurricanes that made landfall east of the deltas caused more erosion in the AD. Finally, sea level rise, at the current rate of 8.17 mm/yr, will not pose a threat to the deltaic island of WLD, while the eastern part of AD may be at risk of drowning. This study recognizes the complexity of factors influencing the growth of deltaic islands, suggesting that quantitative studies on the deltaic island extent are of critical for the restoration and sustainable management of the Mississippi River Delta and other deltas around the world.

How is a turbidite actually deposited?

The deposition of a classic turbidite by a surge-type turbidity current, as envisaged by conceptual models, is widely considered a discrete event of continuous sediment accumulation at a falling rate by the gradually waning density flow. Here, we demonstrate, on the basis of a high-resolution advanced numerical CFD (computational fluid dynamics) simulation and rock-record examples, that the depositional event in reality involves many brief episodes of nondeposition. The reason is inherent hydraulic fluctuations of turbidity current energy driven by interfacial Kelvin-Helmholtz waves. The experimental turbidity current, with realistic grain-size composition of a natural turbidite, used only 26 to 33% of its in-place flow time for deposition, while the remaining time went to the numerous episodes of sediment bypass and transient erosion. The general stratigraphic notion of a gross incompleteness of sedimentary record may then extend down to the deposition time scale of a single turbidite.

Analysis on the effect of discharge energy on machining characteristics of wire electrical discharge turning process

Energy conservation is one of the most important aspects of electrical discharge machining process in which the material removal is by means of spark erosion. Metal removal in wire electrical discharge turning is a complex erosion mechanism which involves melting, vaporization and rapid cooling of molten material. In this work, the significance of discharge energy on the performance of wire electrical discharge turning process, namely, material removal rate, surface finish, thickness of recast layer and surface crack, is analyzed. New model to estimate material removal rate and surface finish in wire electrical discharge turning process have been proposed. Erosion energy and kinetic energy imparted by electrons and average physio-thermal properties of work material are utilized for the modeling. Proposed models are validated by conducting experiments on AISI 4340 steel material. The results obtained from the model are well in agreement with the experimental values. The influence of discharge energy on surface crack and recast layer thickness is analyzed using scanning electron microscope micrographs and energy-dispersive x-ray spectroscopy analysis. Surface crack is observed at higher discharge energy. The thickness of recast layer increases with the increase in discharge energy. Three-dimensional surface topography reveals the turbulent nature of machining process resulted from transient erosion phenomena of wire electrical discharge turning process. Higher material removal rates of the order of about 0.06 g/min with consistent average roughness in the range of 4.5–5.5 µm at the expense of 1.6–2.6 J of discharge energy are achieved in this work. The proposed models can be utilized for machining of difficult to machine material by effective utilization of energy that leads to energy conservation in wire electrical discharge turning process.

Interaction between Molten Steel, Alumina Lining Refractory and Slag Phase

AbstractLaboratory experiments exploring the interaction between molten steel, slag and lining refractory were performed. The transient erosion and reaction over time were investigated, and the transient change of the reaction layer and inclusions generated in the molten steel were evaluated using optical microscopy and SEM-EDS. Without slag addition before remelting, the FeO from reoxidation entered the space between the lining refractory and the steel and strengthened the erosion of the lining refractory. Several layers were found from the steel to the original lining refractory layer: steel phase, FeO layer, a FeO-rich lining layer and an Original Lining (OL)-rich lining layer. The thickness of the reaction layer increased nearly linearly with the reaction time at an erosion rate of 4.2 µm/min. With slag addition before remelting, the reaction layer between the steel and the original lining materials included several sub-layers: a gap, a slag layer, an FeO-rich lining layer and an Original Lining (OL)-rich lining layer. The thickness of the reaction layer nearly linearly increased with the reaction time and with an erosion rate of 5.7 µm/min. Slags were entrained into the steel occasionally.

Transient erosion in the Valencia Trough turbidite systems, NW Mediterranean Basin

Submarine canyons can efficiently drain sediments from continental margins just as river systems do in subaerial catchments. Like in river systems, submarine canyons are often arranged as complex drainage networks that evolve from patterns of erosion and deposition. In the present paper we use a morphometric analysis of submarine canyon-channel long-profiles to study the recent sedimentary history of the Valencia Trough turbidite system (VTTS) in the NW Mediterranean Sea. The VTTS is unique in that it drains sediment from margins with contrasting morphologies through a single “trunk” conduit, the Valencia Channel. The Valencia Channel has been active since the late Miocene, evolving in response to Plio-Quaternary episodes of erosion and deposition. The integrated analysis of long-profiles obtained from high-resolution bathymetric data across the entire turbidite system shows evidence for transient canyon incision in the form of knickpoints and hanging tributaries. Multiple factors appear to have triggered these periods of incision. These include a large debris flow at 11,500yrBP that disrupted the upper reaches of the VTTS and glacio-eustatic lowstands that forced shifting of sediment input to the VTTS. Based on these inferences, long-term time-averaged incision rates for the Valencia Channel have been estimated. The evidence we present strongly suggests that Foix Canyon has played a key role in the drainage dynamics of the VTTS in the past.This study builds conceptually on a recent modeling study that provides a morphodynamic explanation for the long-term evolution of submarine canyon thalweg profiles. The procedure and results from this work are of potential application to other submarine sediment drainage systems, past and present, including those containing mid-ocean type valleys like the Valencia Channel.

Contrasting bedrock incision rates from snowmelt and flash floods in the Henry Mountains, Utah

Hydrograph variability and channel morphology influence rates of fluvial bedrock incision, but little data exist on these controls in natural channels. Through field monitoring we demonstrate that (1) short-term bedrock channel incision can be rapid, (2) sustained floods with smaller peak discharges can be more erosive than flash floods with higher peak discharges, due to changes in bed alluviation, and (3) bedrock channel morphology varies with local bed slope and controls the spatial distribution of erosion. We present a three-year record of flow depths and bedrock erosion for a human-perturbed channel reach that drains the Henry Mountains of Utah, USA. Starting from a small and steep (∼30% slope), engineered knickpoint in Navajo sandstone, erosion has cut a narrow, deep, and tortuous inner channel in ∼35–40 years. Along the inner channel, we measured up to 1/2 m of vertical incision into Navajo sandstone over ∼23 days, caused by the 2005 season of exceptional snowmelt flow. In contrast, flash floods caused little bedrock incision even when peak discharges were much higher than the peak snowmelt flow. Flash floods were net depositors of coarse sediment while snowmelt flow cleared alluvial cover. We document the formation of a pothole and interpret that it was abraded by bedload rather than fine suspended sediment. Finally, several slot canyons (Peek-a-boo, Spooky, and Coyote Gulch narrows) in the nearby Escalante River drainage basin have erosional morphologies similar to the monitored channel reach. Feedbacks between flow, sediment transport, and transient erosion provide a plausible explanation for the evolution of channel slope, width, and bed roughness of these natural bedrock channels.

Seasonal variations of physical and chemical erosion: A three-year survey of the Rhone River (France)

Numerous studies of weathering fluxes have been carried out on major world rivers during the last decade, to estimate CO 2 consumption rates, landscape evolution and global erosion rates. For obvious logistical reasons, most of these studies were based on large scale investigations carried out on short timescales. By comparison, much less effort has been devoted to long term monitoring, as a means to verify the temporal variability of the average characteristics, their trends, and the representativeness of short-term investigations. Here we report the results of a three-year survey (November 2000 to December 2003) of the major and trace element composition of dissolved and suspended matter in the lower Rhone River (France), the largest river of the Mediterranean area. Subsurface water samples were collected in Arles, about 48 km upstream of the estuary, twice a month routinely, and at higher frequency during flood events. During each flood event, the suspended particulate matter (SPM) show the usual trend of clockwise hysteresis with higher SPM concentrations on the rising limb of the flood than at the same discharge on the falling limb. We show that the annual average SPM flux of the Rhone River to the Mediterranean Sea (7.3 ± 0.6 × 10 6 tons yr −1) was largely controlled by the flood events (83% of the solid discharge occurred in less than 12% of the time), and that the precision on the total output flux depends strongly on the precise monitoring of SPM variations during the floods. The chemical composition of water and SPM are characterized by the predominance of Ca 2+ due to the abundance of carbonate rocks in the Rhone watershed. Chemical budgets have been calculated to derive the contributions of atmospheric deposition, carbonate, silicate and evaporite weathering, and anthropogenic inputs. The chemical weathering rate of carbonates is estimated to be 89 ± 5 t km −2 yr −1 compared to 14.4 ± 3 t km −2 yr −1 from silicates. By contrast, the physical erosion rate of silicates is about 51 t km −2 yr −1 against 19 t km −2 yr −1 for carbonates. The steady-state model of Gaillardet et al. (1995) has been applied to the chemical composition of dissolved and solid products. The results show that the Rhone River currently exports much less material than produced at steady-state by weathering in its watershed. The sediment flux inferred from the steady-state calculation (21–56 × 10 6 t yr −1) is on the same order as that estimated in literature for the 19th and the beginning of the 20th centuries. This imbalance may suggest that the Rhone is under a transient erosion regime following climate change (i.e. significant decrease of the flooding frequency since the beginning of the 19th century). On the other hand, the imbalance may also be due to the trapping of alluvion by the numerous dams on the river and its tributaries. Our data corroborate with previous studies that suggest a strong coupling between chemical and physical erosion fluxes, during the hydrological seasonal cycle of the Rhone River. The correlation between physical and chemical transport rates is, however, clearly different from that reported for global annual averages in large world rivers.

Quantifying transient erosion of orogens with detrital thermochronology from syntectonic basin deposits

The evolution of an orogen is marked by phases of topographic growth, equilibrium, and decay. During these phases erosion rates vary in response to temporal and spatial changes in climate, topographic relief and slope, and deformation. Detrital thermochronometer cooling-age data collected from syntectonic basin deposits are a promising tool for quantifying erosion histories during orogenic evolution. Previous studies typically assume steady-state erosion for interpreting detrital data, although in many situations this assumption is not justified. Here we present a new numerical modeling approach that predicts thermochronometer cooling ages in a stratigraphic section where sediment is sourced from a region with a temporally variable erosion history. Multiple thermochronometer cooling ages are predicted at different stratigraphic horizons as a function of variable erosion histories, rock cooling rates in the hinterland, and thermophysical material properties and boundary conditions. The modeling approach provides the context for the interpretation of natural data, including geologically realistic situations with a temporally varying erosion rate. The results of three end-member hinterland erosion histories are explored: (1) steady-state erosion; (2) increasing erosion rate with time; and (3) decreasing erosion rate with time. Results indicate that for steady erosion rates between 0.2 and 1.0 mm/yr, up to 30 m.y. will pass following a change in erosion rate before the detrital ages have adjusted to reflect a new erosion regime. In simulations with transient erosion, the estimation of erosion rates from a detrital record using assumption of thermal steady-state will generally be in error, often by as much as − 25 to 100%. These results highlight that assumptions of steady erosion in mountain belts should be used with caution. Application of the model to thermochronometer cooling ages preserved in syntectonic sediments sourced from the Nanga Parbat region, Himalaya, illustrates how the transient catchment averaged erosion history can be quantified with detrital thermochronology. In this example, we found that erosion rates increased over the past 20 Ma, from about 1.0 mm/yr to modern rates in the range of 1.5 to 2.0 mm/yr.

The use of detrital mineral cooling ages to evaluate steady state assumptions in active orogens: An example from the central Nepalese Himalaya

The distribution of detrital mineral cooling ages in modern sediments has been proposed as a proxy for long‐term, catchment‐averaged erosion rates in developing orogens. However, the applicability of this potentially valuable tool hinges on restrictive assumptions regarding a catchment's steady state thermal and topographic evolution. In this paper, we outline a method by which these assumptions can be tested through statistical comparisons of cooling age distributions for detrital minerals and the hypsometric curves for their source regions using cumulative synoptic probability density functions. Our approach is illustrated with new detrital muscovite 40Ar/39Ar dates from the Marsyandi River valley, in the central Nepalese Himalaya. One of three studied catchments (Nyadi Khola) showed the strong correlation of hypsometry and cooling ages expected for steady state conditions over the 11 to 2.5 Ma time frame. The pattern of mismatch between hypsometry and cooling age distribution in the other catchments suggests that spatially nonuniform and transient erosional processes may be responsible for departure from steady state. Cooling age distribution comparisons for samples collected from nearby localities, samples collected in different years, and different grain size fractions from the same sample were used to evaluate sampling fidelity over a range of spatial scales (200 to 2590 km2). We found that approximately 50 analyses from a single sediment sample adequately characterize the cooling age signal for tributary catchments with simple erosional histories. However, because of temporally and spatially transient erosion, a specific detrital sample is unlikely to adequately characterize the complex signal in trunk stream sediments that integrate information from several large tributaries.

Response function during oxygen sputter profiling and its application to deconvolution of ultrashallow B depth profiles in Si

The secondary ion mass spectrometry (SIMS) response function to a B “δ surface layer” has been investigated. Using electron-gun evaporation combined with liquid nitrogen cooling of target, we are able to deposit an ultrathin B layer without detectable island formation. The B spatial distribution obtained from SIMS is exponentially decaying with a decay length approximately a linear function of the incident energy of the oxygen during the SIMS analysis. Deconvolution with the response function has been applied to reconstruct the spatial distribution of ultra-low-energy B implants. A correction to depth and yield scales due to transient sputtering near the Si surface region was also applied. Transient erosion shifts the profile shallower, but beam mixing shifts it deeper. These mutually compensating effects make the adjusted distribution almost the same as original data. The one significant difference is a buried B peak observed near the surface region.

Coordinated Cluster and ground-based instrument observations of transient changes in the magnetopause boundary layer during an interval of predominantly northward IMF: relation to reconnection pulses and FTE signatures

Abstract. We study a series of transient entries into the low-latitude boundary layer (LLBL) of all four Cluster spacecraft during an outbound pass through the mid-afternoon magnetopause ( [ XGSM, YGSM, ZGSM ] ≈ [ 2, 7, 9 ] RE). The events take place during an interval of northward IMF, as seen in the data from the ACE satellite and lagged by a propagation delay of 75 min that is welldefined by two separate studies: (1) the magnetospheric variations prior to the northward turning (Lockwood et al., 2001, this issue) and (2) the field clock angle seen by Cluster after it had emerged into the magnetosheath (Opgenoorth et al., 2001, this issue). With an additional lag of 16.5 min, the transient LLBL events correlate well with swings of the IMF clock angle (in GSM) to near 90°. Most of this additional lag is explained by ground-based observations, which reveal signatures of transient reconnection in the pre-noon sector that then take 10–15 min to propagate eastward to 15 MLT, where they are observed by Cluster. The eastward phase speed of these signatures agrees very well with the motion deduced by the cross-correlation of the signatures seen on the four Cluster spacecraft. The evidence that these events are reconnection pulses includes: transient erosion of the noon 630 nm (cusp/cleft) aurora to lower latitudes; transient and travelling enhancements of the flow into the polar cap, imaged by the AMIE technique; and poleward-moving events moving into the polar cap, seen by the EISCAT Svalbard Radar (ESR). A pass of the DMSP-F15 satellite reveals that the open field lines near noon have been opened for some time: the more recently opened field lines were found closer to dusk where the flow transient and the poleward-moving event intersected the satellite pass. The events at Cluster have ion and electron characteristics predicted and observed by Lockwood and Hapgood (1998) for a Flux Transfer Event (FTE), with allowance for magnetospheric ion reflection at Alfvénic disturbances in the magnetopause reconnection layer. Like FTEs, the events are about 1 RE in their direction of motion and show a rise in the magnetic field strength, but unlike FTEs, in general, they show no pressure excess in their core and hence, no characteristic bipolar signature in the boundary-normal component. However, most of the events were observed when the magnetic field was southward, i.e. on the edge of the interior magnetic cusp, or when the field was parallel to the magnetic equatorial plane. Only when the satellite begins to emerge from the exterior boundary (when the field was northward), do the events start to show a pressure excess in their core and the consequent bipolar signature. We identify the events as the first observations of FTEs at middle altitudes.Key words. Magnetospheric physics (magnetopause, cusp and boundary layers; magnetosphere-ionosphere interactions; solar wind-magnetosphere interactions)

Mathematical Modeling of Iron and Steel Making Processes. Mathematical Model for Transient Erosion Process of Blast Furnace Hearth.

A mathematical model that can estimate the transient erosion process of the blast furnace hearth has been developed. This mathematical model can treat the molten iron flow, heat transfer and the brick/refractory erosion at the hearth. To verify the availability of the mathematical model, comparisons of computational final erosion profile of the hearth were made with the investigation results of the dissection blast furnace and computational results gave good agreement with the measured one. The effects of the distribution profile of the dripping molten iron flow rate into the hearth, the coke free layer size, production rate of the molten iron, thermal conductivity of the carbon brick and the fluid flow resistance through the coke packed bed were examined by using this mathematical model.

Application of isotope tracer techniques for assessing the seepage of the hydropower dam at Tri An, South Vietnam

Some symptoms of excessive seepage of water were observed at the earthfill dam of the 400 MW Tri An hydropower plant in South Viet Nam. To provide experimental information for assessing the situation, isotope tracer experiments were performed using 24 existing piezometric boreholes encompassing a 1100 m long middle section of the dam. Filtration velocities measured were in the ranges (0.2–30) cm d−1 in the dam body and (0.5–75) cm d−1 in subsurface strata. No abnormally permeable horizons were detected. Permeability coefficients were calculated and compared with that obtained in pre-project hydrogeological surveys and by field tests during dam construction. Tracer experiments yielded permeability of the same range for the subsurface aquifer but from one to two orders of magnitude higher for the dam body. Such a dramatic change of permeability of the dam body me dia is interpreted as a result of interaction with seeping water after reservoir impoundment. A transient erosion process took place during several years. The losses of water by seepage through the dam body and infiltration to underground water were estimated as 1100 m3 d−1 and 15,000 m3 d−1 respectively, less than 1/2000 of the quantity of water consumed for power generation. A multi-well interconnection experiment was performed to determine the velocity and direction of subsurface flows.

Development and temporal evolution of erosion fronts in bioerodible controlled release devices

Cellular automata and discrete iterations are used to model and simulate the release of bioactive agents (drugs) from bioerodible pellets used as controlled release devices. The presented discrete simulation approach is a computationally efficient tool for designing delivery systems with optimal release properties, since it can accurately treat the transient erosion processes in multicomponent release systems of arbitrary geometry and with different dissolution rates for each component. Results from two-dimensional simulations are presented to show how the intrinsic dissolution rates, drug loadings, matrix porosities etc. affect the overall release rates and to establish the relationship between the ratio of dissolution rates and the fractal dimension of the erosion front.

Direct measurement of small diffusion coefficients with secondary ion mass spectroscopy

Sputter sectioning in combination with secondary ion mass spectroscopy enables the determination of very small diffusion coefficients which are not attainable with classical sectioning techniques. The exceedingly good depth resolution of the sputter sectioning and the high sensitivity of the mass spectroscopy allow to resolve penetration profiles of solutes in the 10-nm range at the ppm level. Two perturbing effects, inherent to the method and limiting its sensitivity are discussed: degradation of depth resolution by surface roughening and atomic mixing, and near surface distortion of profiles by transient erosion effects. Degradation of depth resolution was minimized by use of single crystalline specimens and low energy sputtering with reactive ions. To overcome the near surface distortions a special sample preparation technique has been developed, resulting in single crystalline specimens with one or more inserted layers of the solutes to be diffused. The application of the method is demonstrated by examples of thermal- and irradiation-induced diffusion of nickel in copper, and the main errors are discussed.