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1.

Background

Riverine particles undergo a rapid transformation when they reach estuaries. The rapid succession of hydrodynamic and biogeochemical regimes forces the particles to flocculate, settle and enter the sediment pool. The rates and magnitudes of flocculation depend on the nature of the particles which are primarily affected by the types and quantities of organic matter (OM). Meanwhile, the OM characteristics vary widely between environments, as well as within a single environment due to seasonal climate and land use variability. We investigated the effect of the OM types and quantities through laboratory experiments using natural estuarine particles from the Mississippi Sound and Atchafalaya Bay as well as model mixtures of montmorillonite and organic molecules (i.e., biopolymers (guar/xanthan gums) and humic acid).

Results

Biopolymers promote flocculation but the magnitude depends on the types and quantities. Nonionic guar gum yields much larger flocs than anionic xanthan gum, while both of them exhibit a nonlinear behavior in which the flocculation is the most pronounced at the intermediate OM loading. Moreover, the effect of guar gum is independent of salinity whereas the effect of xanthan gum is pronounced at higher salinity. Meanwhile, humic acid does not affect flocculation at all salinity values tested in this study. These results are echoed in the laboratory manipulation of the natural estuarine particles. Flocculation of the humic acid-rich Mississippi Sound particles is unaffected by the OM, whereas that of biopolymer-rich Atchafalaya Bay particles is enhanced by the OM.

Conclusions

Flocculation is positively influenced by the presence of biopolymers that are produced as the result of marine primary production. Meanwhile, humic acid, which is abundant in the rivers that drain the agricultural soils of Southeastern United States, has little influence on flocculation. Thus, it is expected that humic acid-poor riverine particles (e.g., Mississippi River, and Atchafalaya River, to a lesser degree) may be prone to rapid flocculation and settling in the immediate vicinity of the river mouths when mixed with biopolymer-rich coastal waters. It is also expected that humic acid-rich riverine particles (e.g., Pearl River) may resist immediate flocculation and be transported further away from the river mouth.  相似文献   

2.
The laboratory tests for the use of sapogenic amphiphilic glycosides as a coagulation–flocculation aid are presented in this paper. These amphiphilic glycosides were obtained, through a natural fermentation process, of the juice, of fique (Furcraea sp.) leaves. Decantation allows for the separation of a supernatant denominated “supernatant fique juice” and a decanted fraction denominated “decanted fique juice.” The latter contains most of the sapogenic amphiphilic glycosides and was mixed with the chemical coagulant ferric chloride hexahydrate, at varying doses. Ferric chloride hexahydrate was also used as a control to ascertain the removal efficiency of persistent contaminants from samples of a textile industry effluent. The parameters of interest were typical indicators of water quality such as color, turbidity, chemical oxygen demand, pH and conductivity. The results indicate that the decanted fique juice, when used as a coagulation–flocculation aid, and upon comparison with the chemical coagulant alone, causes an additional color and turbidity reduction of 31 and 17 %, respectively. No significant differences were noted in the chemical oxygen demand values (α = 0.05; P < 0.001). Thus, there is a scope for further research about the commercial feasibility of DFJ as an industrial water treatment agent, which reduces the toxicity of raw fique juice and its detrimental environmental effects.  相似文献   

3.
In recent years, concerns about the occurrence and fate of active pharmaceutical ingredients, solvents, intermediates and raw materials that could be present in pharmaceutical industry effluents have gained increasing attention. Conventional treatment methods, such as activated sludge, are not sufficient enough to remove active pharmaceutical ingredients completely. As a result, complementary treatment methods like coagulation and flocculation are often used and play a critical role in industrial and municipal wastewater treatment. The primary goal of these methods is to destabilize and remove colloidal particles along with other organic/inorganic contaminants. Recently empirical works have considered ozone as the most promising oxidant for the removal of micro-pollutants. The current study examined the effectiveness of coagulation/flocculation process using ferric chloride, polyaluminum chloride, and aluminum sulfate as a reasonable approach to tackle the issue of treating pharmaceutical wastewater. In addition, the results were compared with the process using only ferric chloride that was the coagulant of an actual treatment plant. Then, improvement of the process performance was investigated using ozone as an oxidant. In conclusion, it was found out that polyaluminum chloride presented better performance among two other coagulants and also adding 200 mg/L of polyaluminum chloride can lead to 97–98 % turbidity removal efficiency. Moreover, polyaluminum chloride was capable of reducing most of the environmental parameters such as chemical oxygen demand and total dissolved solid with the removal efficiency of 70 and 68 %, respectively. Additionally, ozonation improved the coagulation process, especially iron ion removal, and dramatically decreased the concentration from 5.68 to 0.19 mg/L.  相似文献   

4.
水流紊动对泥沙絮凝的影响   总被引:7,自引:0,他引:7       下载免费PDF全文
主要研究水流紊动对泥沙絮凝的影响。认为水处理方面的絮凝动力学理论可用于研究泥沙絮凝问题。根据试验实测资料及国外有关试验结果研究表明,在紊动状态下,泥沙絮凝存在两个阶段,每个阶段中紊动对泥沙絮凝的影响也有所不同。  相似文献   

5.
A simple theoretical model of magnetic–hydrophobic coagulation considering the total interaction potential energy between two spheres exposed to an external magnetic field as a sum of the van der Waals, electrostatic, magnetic, and hydrophobic components is proposed. The model was used to interpret experiments on coagulation of fine siderite particles in distilled water and 10−2 M KCl, hydrophobized by sodium oleate. In the experiments, a relative extent of the coagulation/stability equilibrium of the siderite suspension was evaluated photoelectrically. To estimate the model parameters, the ζ-potential and hydrophobicity of siderite particles were measured.A qualitative agreement was obtained between the model predictions (energy maximum and secondary minimum) and the experimental results (voltage changes after a selected interval of sedimentation) of the siderite suspensions. Moreover, a statistically significant correlation was found between the experimental voltages and the calculated energy maximum (a crucial factor of theories on the fine particle coagulation kinetics), which can be represented by a linear regression equation with the correlation coefficient of 0.979.  相似文献   

6.
Recent studies have suggested that rivers may present an isotopically light Fe source to the oceans. Since the input of dissolved iron from river water is generally controlled by flocculation processes that occur during estuarine mixing, it is important to investigate potential fractionation of Fe-isotopes during this process. In this study, we investigate the influence of the flocculation of Fe-rich colloids on the iron isotope composition of pristine estuarine waters and suspended particles. The samples were collected along a salinity gradient from the fresh water to the ocean in the North River estuary (MA, USA). Estuarine samples were filtered at 0.22 μm and the iron isotope composition of the two fractions (dissolved and particles) were analyzed using high-resolution MC-ICP-MS after chemical purification. Dissolved iron results show positive δ56Fe values (with an average of 0.43 ± 0.04‰) relative to the IRMM-14 standard and do not display any relationships with salinity or with percentage of colloid flocculation. The iron isotopic composition of the particles suspended in fresh water is characterized by more negative δ56Fe values than for dissolved Fe and correlate with the percentage of Fe flocculation. Particulate δ56Fe values vary from −0.09‰ at no flocculation to ∼0.1‰ at the flocculation maximum, which reflect mixing effects between river-borne particles, lithogenic particles derived from coastal seawaters and newly precipitated colloids. Since the process of flocculation produces minimal Fe-isotope fractionation in the dissolved Fe pool, we suggest that the pristine iron isotope composition of fresh water is preserved during estuarine mixing and that the value of the global riverine source into the ocean can be identified from the fresh water values. However, this study also suggests that δ56Fe composition of rivers can also be characterized by more positive δ56Fe values (up to 0.3‰) relative to the crust than previously reported. In order to improve our current understanding of the oceanic iron isotope cycling, further work is now required to determine the processes controlling the fractionation of Fe-isotopes during continental run-off.  相似文献   

7.
Placer gold particles derived from epithermal deposits display distinct morphological and compositional features compared with particles from mesothermal systems. Here, it is hypothesized that the chemical composition of primary gold derived from different deposit types is a principle factor affecting the composition of resident biofilm communities as well as the transformation of placer particles. Gold particles were collected from placers originating from the epithermal system at the Eisenberg, Germany's largest primary gold deposit. For comparison, placer gold from mesothermal sources was studied. Morphological differences due to mechanical transport and physical reshaping were not observed. Biogeochemical gold/silver dissolution and gold re-precipitation were evident on epithermal particles and they accentuate the silver-fabrics and gold-rich clusters. In contrast, on mesothermally derived gold particles these processes led to the development of gold-rich rims via the formation of nano-porous secondary gold. Microprobe- and laser ablation mass spectrometric analyses of polished whole particle mounts confirmed differences in gold/silver content/distribution and trace metal content between particles from epi- and mesothermal sources, respectively. On particles from all sites nano- and micro-particulate gold is associated with polymorphic layers. These are composed of microbial cells, extracellular polymeric substances (EPS) and clay-sized minerals. Multivariate statistical analyses shows a significant difference between biofilm communities from epi- vs. mesothermally derived particles, which is linked to the chemical composition of the primary gold. While a number of key-species capable of gold transformation, e.g., Cupriavidus sp., Geobacter sp. and Rhodoferax sp., were detected on particles from both sources, higher numbers of organisms with the potential for gold solubilization, precipitation and detoxification were associated with particles from the epithermal sources. A range of species involved in gold transformation, i.e., Arthrobacter spp., Delftia sp., Shewanella sp., and Stenotrophomonas spp., were detected only on epithermally derived placer gold. This indicates the communities are sensitive to differences in gold/silver and possibly trace metal-cycling, resulting from differences in their content, distribution and mobilization behaviour in epi- vs. mesothermally derived particles. Ultimately, this study shows that the chemical composition of the primary deposit strongly influences the biogeochemical transformation of placer gold and the composition of associated biofilms, whereas physical transformations appear to be largely unaffected.  相似文献   

8.
The influences of solids concentration, molecular weight of dispersant, particle size and distribution, and temperature on the rheological behaviour of limestone slurries have been investigated. The results reveal that when the solids concentration of a limestone slurry (< 100 μm) is increased from 60 wt.% (35.71 vol.%) to 78.5 wt.% (57.49 vol.%), the rheological behaviour of the slurry is transformed from a weakly dilatant characteristic to a pseudoplastic one with a yield stress, which is in combination with a thixotropic property at a higher solids concentration (i.e., ≥ 75 wt.% or 52.63 vol.%). At a certain shear rate, the apparent viscosity and the relative viscosity of the slurry increase exponentially with solids concentration. The extrapolated Bingham yield stress increases rather sharply in a power-law form with increasing solids concentration when the solids concentration of the slurry is larger than 70 wt.% (i.e., 46.36 vol.%). An attainable maximum packing solids fraction (?m) is predicted as ?m = 64.6 vol.% at the certain limestone–water suspension system. A polymeric dispersant named Dispersant S40 with a molecular weight of 5500 appears most effective for the reduction of the apparent viscosity of limestone slurry due to its good electrosteric stabilization and effective avoidance of depletion flocculation. The smaller the particle size and the narrower the size distribution, the more evident the pseudoplastic property of limestone slurry is with a larger yield stress and a larger apparent viscosity at a given shear rate in the range of 12 to 1200 s− 1. Also, a statistic model describes a relationship between the particle size and distribution and the apparent viscosity of the slurries at a given solids concentration (i.e., 70 wt.% or 46.36 vol.%). However, a sufficient additive dosage of Dispersant S40 (i.e., ≥ 0.1 wt.%) significantly decreases or even eliminates the rheological differences of limestone slurries (apparent viscosities and extrapolated yield stresses) resulting from the difference in particle size and distribution. Besides, the apparent viscosity of limestone slurries decreases with increasing temperature in the range of 13 to 55 °C, regardless of the absence or the presence of Dispersant S40.  相似文献   

9.
The microstructural evolution of polymineralic contact metamorphic calcite marbles (Adamello contact aureole) with variable volume fractions of second-phase minerals were quantitatively analyzed in terms of changes in grain size and nearest neighbor relations, as well as the volume fractions, dispersion and occurrences of the second phases as a function of changing metamorphic conditions. In all samples, the calcite grain size is controlled by pinning of grain boundaries by second phases, which can be expressed by the Zener parameter (Z), i.e., the ratio between size and volume fraction of the second phases. With increasing peak metamorphic temperature, both the sizes of matrix grains and second phases increase in dependence on the second-phase volume fraction. Two distinct coarsening trends are revealed: trend I with coupled grain coarsening limited by the growth of the second phases is either characterized by large-sized or a large number of closely spaced-second phase particles, and results finally in a dramatic increase in the calcite grain size with Z. Trend II is manifest by matrix controlled grain growth, which is retarded by the presence of single second-phase particles that are located on calcite grain boundaries. It is supported by grain boundary pinning induced by triple junctions, and the calcite grain size increases moderately with Z. The two different grain coarsening trends manifest the transition between relatively pure polymineralic aggregates (trend II) and microstructures with considerable second-phase volume fractions of up to 0.5. The variations might be of general validity for any polymineralic rock, which undergoes grain coarsening during metamorphism. The new findings are important for a better understanding of the initiation of strain localization based on the activation of grain size dependent deformation mechanisms.  相似文献   

10.
11.
Information on the particle size and reactive surface area of natural samples is essential for the application of surface complexation models (SCM) to predict bioavailability, toxicity, and transport of elements in the natural environment. In addition, this information will be of great help to enlighten views on the formation, stability, and structure of nanoparticle associations of natural organic matter (NOM) and natural oxide particles.Phosphate is proposed as a natively present probe ion to derive the effective reactive surface area of natural samples. In the suggested method, natural samples are equilibrated (?10 days) with 0.5 M NaHCO3 (pH = 8.5) at various solid-solution ratios. This matrix fixes the pH and ionic strength, suppresses the influence of Ca2+ and Mg2+ ions by precipitation these in solid carbonates, and removes NOM due to the addition of activated carbon in excess, collectively leading to the dominance of the PO4-CO3 interaction in the system. The data have been interpreted with the charge distribution (CD) model, calibrated for goethite, and the analysis results in an effective reactive surface area (SA) and a reversibly bound phosphate loading Γ for a series of top soils.The oxidic SA varies between about 3-30 m2/g sample for a large series of representative agricultural top soils. Scaling of our data to the total iron and aluminum oxide content (dithionite-citrate-bicarbonate extractable), results in the specific surface area between about 200-1200 m2/g oxide for most soils, i.e. the oxide particles are nano-sized with an equivalent diameter in the order of ∼1-10 nm if considered as non-porous spheres. For the top soils, the effective surface area and the soil organic carbon fraction are strongly correlated. The oxide particles are embedded in a matrix of organic carbon (OC), equivalent to ∼1.4 ± 0.2 mg OC/m2 oxide for many soils of the collection, forming a NOM-mineral nanoparticle association with an average NOM volume fraction of ∼80%. The average mass density of such a NOM-mineral association is ∼1700 ± 100 kg/m3 (i.e. high-density NOM). The amount of reversibly bound phosphate is rather close to the amount of phosphate that is extractable with oxalate. The phosphate loading varies remarkably (Γ ≈ 1-3 μmol/m2 oxide) in the samples. As discussed in part II of this paper series (Hiemstra et al., 2010), the phosphate loading (Γ) of field samples is suppressed by surface complexation of NOM, where hydrophilic, fulvic, and humic acids act as a competitor for (an)ions via site competition and electrostatic interaction.  相似文献   

12.
Boulders moving in flash floods cause considerable damage and casualties. More and bigger boulders move in flash floods than predicted from published theory. The interpretation of flow conditions from the size of large particles within flash flood deposits has, until now, generally assumed that the velocity (or discharge) is unchanging in time (i.e. flow is steady), or changes instantaneously between periods of constant conditions. Standard practice is to apply theories developed for steady flow conditions to flash floods, which are however inherently very unsteady flows. This is likely to lead to overestimates of peak flow velocity (or discharge). Flash floods are characterised by extremely rapid variations in flow that generate significant transient forces in addition to the mean‐flow drag. These transient forces, generated by rapid velocity changes, are generally ignored in published theories, but they are briefly so large that they could initiate the motion of boulders. This paper develops a theory for the initiation of boulder movement due to the additional impulsive force generated by unsteady flow, and discusses the implications.  相似文献   

13.
Freshwater inflow is a driver of the functioning of estuaries, and average salinity is usually measured to identify the effects of inflow in salinity-zone habitats. However, salinity variability could act as a disturbance by producing unstable habitats, leading to the question: is salinity variance an indicator of benthic disturbance, and therefore a driver of community stability? The macrofauna communities of five estuaries that lie in a climatic gradient on the Texas coastline were analyzed using a 26-year data set. Comparisons within and between estuaries with different inflow regimes were used as a natural experiment to simulate press disturbance events (i.e., climatic inflow) and pulse disturbance (i.e., floods) in maintaining community stability. Salinity average and variance was compared with benthic community diversity, evenness, and species richness. Salinity variance was more correlated to benthic diversity for each estuarine system (r?=??0.6610; p?=?0.0015) than average salinity (r?=?0.3818; p?=?0.0967). As salinity variance decreased (i.e., stability increased), diversity levels of benthic communities increased, and areas with mgore freshwater inflow displayed lower levels of benthic diversity. These findings advance a component of the general theory of diversity maintenance that persistent stressors, such as salinity variability, can influence diversity.  相似文献   

14.
Estuarine systems are complex environments where seasonal and spatial variations occur in concentrations of suspended particulate matter, in primary constituents, and in organic matter content. This study investigated in the laboratory the flocculation potential of estuarine-suspended particulate matter throughout the year in order to better identify the controlling factors and their hierarchy. Kinetic experiments were performed in the lab with a “video in lab” device, based on a jar test technique, using suspended sediments sampled every 2 months over a 14-month period at three stations in the Seine estuary (France). These sampling stations are representative of (1) the upper estuary, dominated by freshwater, and (2) the middle estuary, characterized by a strong salinity gradient and the presence of an estuarine turbidity maximum. Experiments were performed at a constant low turbulent shear stress characteristic of slack water periods (i.e., a Kolmogorov microscale >1,000 μm). Flocculation processes were estimated using three parameters: flocculation efficiency, flocculation speed, and flocculation time. Results showed that the flocculation that occurred at the three stations was mainly influenced by the concentration of the suspended particulate matter: maximum floc size was observed for concentrations above 0.1 g l−1 while no flocculation was observed for concentrations below 0.004 g l−1. Diatom blooms strongly enhanced flocculation speed and, to a lesser extent, flocculation efficiency. During this period, the maximum flocculation speed of 6 μm min−1 corresponded to a flocculation time of less than 20 min. Salinity did not appear to automatically enhance flocculation, which depended on the constituents of suspended sediments and on the content and concentration of organic matter. Examination of the variability of 2D fractal dimension during flocculation experiments revealed restructuring of flocs during aggregation. This was observed as a rapid decrease in the floc fractal dimension from 2 to 1.4 during the first minutes of the flocculation stage, followed by a slight increase up to 1.8. Deflocculation experiments enabled determination of the influence of turbulent structures on flocculation processes and confirmed that turbulent intensity is one of the main determining factors of maximum floc size.  相似文献   

15.
In this paper, a local non-equilibrium diffuse interface model is introduced for describing solid–liquid dissolution problems. The model is developed based on the analysis of Golfier et al. (J Fluid Mech 457:213–254, 2002) upon the dissolution of a porous domain, with the additional requirement that density variations with the mass fraction are taken into account. The control equations are generated by the upscaling of the balance equations for a solid–liquid dissolution using a volume averaging theory. This results into a diffuse interface model (DIM) that does not require an explicit treatment of the dissolving interface, e.g., the use of arbitrary Lagrangian–Eulerian (ALE) methods, for instance. Test cases were performed to study the features and influences of the effective coefficients inside the DIM. In particular, an optimum expression for the solid–liquid exchange coefficient is obtained from a comparison with the referenced solution by ALE simulations. Finally, a Ra–Pe diagram illustrates the interaction of natural convection and forced convection in the dissolution problem.  相似文献   

16.
Zhang  Rong-jun  Zheng  Yao-lin  Zheng  Jun-Jie  Dong  Chao-qiang  Lu  Zhan 《Acta Geotechnica》2020,15(6):1685-1698

A new method, i.e., flocculation–solidification combined method (FSCM), is proposed for building a working platform efficiently and economically at the surface of newly reclaimed ground filled with hydraulically dredged mud slurry at extra high water content (EHW-MS). A number of laboratory experiments are performed in this paper to identify the feasibility and mechanism of the proposed FSCM. First, the reasonable flocculant dosage range suitable for FSCM is determined by the simple sedimentation tests. Second, the engineering properties of FSCM, pure cement solidification method (PCSM) and pure flocculation conditioning method (PFCM) treated EHW-MS are compared in detail via a series of model tests, to demonstrate the superiority of FSCM over PCSM and the influence of flocculant dosage on FSCM efficiency. Third, the superiority of FSCM over PCSM is rationalized from the perspective of intrinsic working mechanism of flocculant and PCSM. Results demonstrate well that FSCM shows substantial superiority over PCSM, and at the reasonable flocculant dosage, the strength of FSCM-treated EHW-MS is at least 5.7 times larger than that of the corresponding PCSM-treated EHW-MS. The superiority of FSCM over PCSM can be attributed to two aspects, i.e., the dewatering effect and the other detrimental effect. The former is predominant and primarily governs the strength gain of FSCM-treated EHW-MS, while the latter is less significant but not negligible.

  相似文献   

17.
The chemical status of major and trace elements (TE) in various boreal small rivers and watershed has been investigated along a 1500-km transect of NW Russia. Samples were filtered in the field through a progressively decreasing pore size (5, 0.8 and 0.22 μm; 100, 10, and 1 kD) using a frontal filtration technique. All major and trace elements and organic carbon (OC) were measured in filtrates and ultrafiltrates. Most rivers exhibit high concentration of dissolved iron (0.2–4 mg/l), OC (10–30 mg/l) and significant amounts of trace elements usually considered as immobile in weathering processes (Ti, Zr, Th, Al, Ga, Y, REE, V, Pb). In (ultra)filtrates, Fe and OC are poorly correlated: iron concentration gradually decreases upon filtration from 5 μm to 1 kD whereas the major part of OC is concentrated in the <1–10 kD fraction. This reveals the presence of two pools of colloids composed of organic-rich and Fe-rich particles. According to their behavior during filtration and association with these two types of colloids, three groups of elements can be distinguished: (i) species that are not affected by ultrafiltration and are present in the form of true dissolved inorganic species (Ca, Mg, Li, Na, K, Sr, Ba, Rb, Cs, Si, B, As, Sb, Mo) or weak organic complexes (Ca, Mg, Sr, Ba), (ii) elements present in the fraction smaller than 1–10 kD prone to form inorganic or organic complexes (Mn, Co, Ni, Zn, Cu, Cd, and, for some rivers, Pb, Cr, Y, HREE, U), and (iii) elements strongly associated with colloidal iron in all ultrafiltrates (P, Al, Ga, REE, Pb, V, Cr, W, Ti, Ge, Zr, Th, U). Based on size fractionation results and taking into account the nominal pore size for membranes, an estimation of the effective surface area of Fe colloids was performed. Although the total amount of available surface sites on iron colloids (i.e., 1–10 μM) is enough to accommodate the nanomolar concentrations of dissolved trace elements, very poor correlation between TE and surface sites concentrations was observed in filtrates and ultrafiltrates. This strongly suggests a preferential transport of TE as coprecipitates with iron oxy(hydr)oxides. These colloids can be formed on redox boundaries by precipitation of Fe(III) from inflowing Fe(II)/TE-rich anoxic ground waters when they meet well-oxygenated surface waters. Dissolved organic matter stabilizes these colloids and prevents their aggregation and coagulation. Estuarine behavior of several trace elements was studied for two small iron- and organic-rich rivers. While Si, Sr, Ba, Rb, and Cs show a clear conservative behavior during mixing of freshwaters with the White sea, Al, Pb and REE are scavenged with iron during coagulation of Fe hydroxide colloids.  相似文献   

18.
Image-based soil particle size and shape characterization relies on computer methods to process and analyze the images. For contacting particles spread on a flat surface this requires delineation of particle boundaries through shape-based image segmentation. The traditional method using watershed analysis fails for particles that have constrictions (are peanut-shaped). The oversegmentation interprets such particles as being two, thereby underestimating the long particle dimension by about 50% and overestimating particle sphericity by about a factor of two. This paper presents a solution to the problem of oversegmentation through morphologic reconstruction. The key to this improvement is distinguishing the necks in peanut shaped particles from actual contacts between particles. A parameter α is defined to quantify the necks and contacts. Approximately 220,000 particles in a range of 2.0–35.0 mm having various shapes and angularities were studied to find typical α values for necks and contacts. An algorithm is proposed to correct the oversegmentation based on α. The results show that this improved watershed analysis accurately segments sand particles at contacts while preserving the continuity of peanut shaped particles. Example lab tests demonstrate the significance of the problem and its solution.  相似文献   

19.
According to Litwiniszyn's theory, subsidence over a yielding underground geo‐structure is seen as a stochastic (Markov) process. This theory leads to a single, linear parabolic differential equation of diffusion–convection type (D–C equation) in the plane‐field of displacements. If the boundary conditions for the governing D–C equation are prescribed along the shear bands, i.e. at ‘moving’ boundaries—it has been observed from small‐scale model experiments that the subsiding process is always confined between a set of inclined shear bands—then the resulting equation is nonlinear. The inverse problem for this nonlinear equation, i.e. the problem of determining the base displacement using the surface subsidence as ‘initial’ condition, is ill‐posed and estimation of the base displacement from a given surface subsidence profile is not possible. In the present paper the domain of integration of the governing D–C equation is fixed (and bounded)—the boundaries are not evolving. Hence, the governing equation remains linear parabolic. The advantage is that this linear differential equation admits an analytical solution, under the trap‐door mechanism assumption, that enables a direct solution to the inverse problem. Copyright © 2008 John Wiley & Sons, Ltd.  相似文献   

20.
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