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1.
Agrichemicals usually contaminate groundwater via preferential flow, therefore determination of the preferential flow characteristics of soil is needed. One model that predicts solute transport due to preferential flow is the mobile–immobile (MIM) solute-transport model, which partitions total water content (θ; m3 m?3) into mobile (θm) and immobile fractions (θim). In undisturbed soils, a method is proposed for determining the MIM model parameters, i.e. immobile water fraction (θim), mass transfer coefficient (α) and hydrodynamic dispersion coefficient (D h). Breakthrough curves were obtained for five different soil textures in three replicates, by miscible displacement of Cl? in undisturbed soil columns. Cl? breakthrough curves were evaluated in terms of the MIM model. Analysis suggests that the values of D h and α increased with lighter soil textures and θim increased with heavier soil textures. The values of θim ranged from 5.31 to 14.28% in different soil textures. Furthermore, values of θim were found to be related to soil clay content. Values of α ranged from 0.0257 to 0.32 h?1 and values of D h ranged from 0.36 to 11.2 cm2 h?1 in different soil textures. A significant linear correlation was obtained between α, θim, D h and soil saturated hydraulic conductivity (K s) and pore water velocity (v). A multivariate pedotransfer function was developed to estimate α, θim and D h based on the geometric mean (d g) and the standard deviation (σg) of the diameter of soil particles and soil organic matter content. The pedotransfer functions for D h, θim and α were validated by independent data sets from other investigators.  相似文献   

2.
In a well-structured soil at or close to pedal saturation, rainfall intensity in excess of pedal Ksat is predicted to result in by-passing flow through well connected structural voids. The depth of solute penetration (tracer dye and nitrate) under by-passing flow has been predicted by Df=(P-Cp)/θf, where Df is the depth of penetration of the leading edge of solute in by-passing flow, P is gross precipitation, Cp is the input volume transmitted through the soil peds and θf is the operational volumetric moisture content in by-passing. The timing of surface applied nitrate arrival at a channel bank is demonstrated to be related to by-passing flow rather than uniform displacement. The relationship between nitrate load in soil drainage waters (Y, mg s-1) and water discharge (X, dm3 s?1) was Y6X after nitrate fertilizer application but subsequently declined to Y 0.5X It is deduced that the decline resulted from inefficient leaching under by-passing conditions once surface applied nitrate had become relocated within the soil peds.  相似文献   

3.
Introduction

Springer1) used in his earlier work acetyl bromide for separating true humic substance from soil organic matter, and proposed to designate the degree of decomposition (Zersetzungsgrad) by such a numeral Ch Ct x 100, of which Ct, was total carbon, and Ch was carbon insoluble in acetyl bromide. In Germany this numeral, abbreviated as Z. G., has been widely applied.  相似文献   

4.
The dependence of runoff dissolved reactive phosphorus (DRP) loss on soil test P or rapid estimations of degree of P saturation (DPS) often varies with soil types. It is not clear whether the soil‐specific nature of runoff DRP versus DPS is due to the different sorption characteristics of individual soils or the inability of these rapid DPS estimates to accurately reflect the actual soil P saturation status. This study aimed to assess environmental measures of soil P that could serve as reliable predictors of runoff DRP concentration by using soils collected from Ontario, Canada, that cover a range of chemical and physical properties. A P sorption study was conducted using the Langmuir equation  to describe amount of P sorbed or desorbed by the soil (Qs, mg/kg) versus equilibrium P concentration (C, mg/L) in solution, where Qmax is P sorption maximum (mg/kg), k represents P sorption strength (L/mg), and Q0 (mg/kg) is the P sorbed to soil prior to analysis. Runoff DRP concentration increased linearly with increasing DPSsorp (i.e. the ratio of (Q0 + QD)/Qmax) following a common slope value amongst soil types, while the P buffering capacity (PBC0) at C = C0 yielded a common change point, below which runoff DRP concentration decreased greatly with increasing PBC0 compared to that above the change point, where C0 and QD represent the equilibrium P concentration and amount of P desorbed, respectively. Both DPSsorp and PBC0 showed great promises as indicators of runoff DRP concentration.  相似文献   

5.
The one-compartment C model Ct=C0ek2t+k1A/k2(1−ek2t) is being long used to simulate soil organic C (SOC) stocks. Ct is the SOC stock at the time t; C0, the initial SOC stock; k2, the annual rate of SOC loss (mainly mineralization and erosion); k1, the annual rate to which the added C is incorporated into SOC; and A, the annual C addition. The component C0ek2t expresses the decay of C0 and, for a time t, corresponds to the remains of C0 (C0 remains). The component k1A/k2(1−ek2t) refers, at time t, to the stock of SOC derived from C crops (Ccrop). We herein propose a simple method to estimate k1 and k2 coefficients for tillage systems conducted in long-term experiments under several cropping systems with a wide range of annual C additions (A) and SOC stocks. We estimated k1 and k2 for conventional tillage (CT) and no-till (NT), which has been conducted under three cropping systems (oat/maize −O/M, vetch/maize −V/M and oat + vetch/maize + cowpea −OV/MC) and two N-urea rates (0 kg N ha−1 −0 N and 180 kg N ha−1 −180 N) in a long-term experiment established in a subtropical Acrisol with C0 = 32.55 Mg C ha−1 in the 0–17.5 cm layer. A linear equation (Ct = a + bA) between the SOC stocks measured at the 13th year (0–17.5 cm) and the mean annual C additions was fitted for CT and NT. This equation is equivalent to the equation of the model Ct=C0ek2t+k1A/k2(1−ek2t), so that a=C0ek2t and bA=k1A/k2(1−ek2t). Such equivalences thus allow the calculation of k1 and k2. NT soil had a lower rate of C loss (k2 = 0.019 year−1) than CT soil (k2 = 0.040 year−1), while k1 was not affected by tillage (0.148 year−1 under CT and 0.146 year−1 under NT). Despite that only three treatments had lack of fit (LOFIT) value lower than the critical 5% F value, all treatments showed root mean square error (RMSE) lower than RMSE 95% indicating that simulated values fall within 95% confidence interval of the measurements. The estimated SOC stocks at steady state (Ce) in the 0–17.5 cm layer ranged from 15.65 Mg ha−1 in CT O/M 0 N to 60.17 Mg ha−1 in NT OV/MC 180 N. The SOC half-life (t1/2 = ln 2/k2) was 36 years in NT and 17 years in CT, reflecting the slower C turnover in NT. The effects of NT on the SOC stocks relates to the maintenance of the initial C stocks (higher C0 remais), while increments in Ccrop are imparted mainly by crop additions.  相似文献   

6.
If an exchangeable ion in soil diffuses along a liquid and solid pathway, its diffusion coefficient may be expressed as where D, v, f, C are diffusion coefficient, volume fraction, impedance factor, and concentration terms and the suffixes l,S refer to liquid and solid. The self-diffusion coefficient of the ion is then where D′, Dt, and Ds, are self-diffusion coefficients. D and D′ will vary with concentration. In diffusion out of the soil to a zero sink, the appropriate average diffusion coefficient is, approximately, the self-diffusion coefficient in the undisturbed soil. Diffusion of one ion species is influenced by other ions diffusing in the system through the diffusion potential set up. When ions are diffusing to plant roots, the diffusion potential is likely to be small. A more likely, though more complicated, expression for D than the first equation above is derived by assuming the ion to follow solid and liquid pathways in series as well as in parallel.  相似文献   

7.
Soil respiration and methane flux from adjacent forest, grassland, and cornfield were measured by using the closed chamber method from June to November, 1999 in Shizunai, Hokkaido, Japan, where the soil was an Aquic Humic Udivitrands derived from volcanic ash. The forest soil absorbed methane, at arate ranging from -0.12 to -0.02 mg C m-2 h-1, while the grassland soil emitted methane, at a rate ranging from undetectable levels to 0.18 mg C m-2 h-1. In the cornfield soil methane flux ranged from -0.01 to 0.04 mg C m-2 h-1. The soil respiration rate varied from 3 to 230 mg C m-2 h-1, 27 to 372 mg C m-2 h-1, and 29 to 156 mg C m-2 h-1 for the cornfield, grassland, and forest soils, respectively. Linear regression analysis demonstrated that the methane flux rate was positively correlated with the soil water-filled pore space (WFPS), and negatively correlated with the relative gas diffusion coefficient (D/D o) and air-filled pore space (AFPS). Soil respiration rates were positively correlated with the soil temperature at all the sites. The Q 10 value was 4.8, 3.3, and 1.9 for the cornfield, grassland, and forest soils, respectively.  相似文献   

8.
The composition of the soil atmosphere is an indicator of biological processes, and soil CO2 gradients have been used to estimate CO2 efflux from the surface. Soil atmosphere samplers, constructed with gas-permeable materials, have been used to quantify soil CO2 concentrations. The type of material used can influence the perceived real-time concentrations of CO2 in the soil. Previous works have not directly compared different types of materials under the same conditions. The objective of this study was to determine the diffusion coefficient (D) and time of 95% equilibrium (teq) of CO2 through several materials, and to evaluate the effect of long-term soil burial (183 days) on diffusion characteristics. Materials tested included silicone, expanded Teflon (ePTFE), and ultra high molecular weight polyethylene (PE) tubing. The D of each material was determined using a closed-loop system consisting of a CO2-enriched (7800 ppm) chamber, a CO2 analyzer and an inner tube (experimental tubing) placed inside the chamber. Air was re-circulated through the inner tube, and as CO2 diffused from the chamber into the tubing, the analyzer recorded the increase in concentration. The silicone tubes had values of D ranging from 8.64 to 5.80×10−6 cm2 s−1 with corresponding teq between 3.9 and 9.7 h. Diffusion coefficients of the ePTFE (1.25×10−4 cm2 s−1) and PE (7.70×10−4 cm2 s−1) materials were 2 orders of magnitude greater, with teq<6 min. Exposure to the soil environment for 183 days did not visibly deteriorate the materials or significantly affect the D or teq values. Use of the ePTFE or PE materials, over the silicone materials, may allow for better characterization of dynamic CO2 concentrations in the soil based on the greater D and lesser teq values of these materials.  相似文献   

9.
Phosphate diffusion coefficients (De) were determined by the quantity of P that diffused from a soil block with P addition into a soil block without P addition. To compare the results with theoretical concepts and to quantify the influencing factors, De was also calculated using the equation of Nye (1968). This equation takes into account the P diffusion coefficient in water, D1, the volumetric water content, θ, the impedance factor, f, and the buffer power, b, of the soil. The results show that De strongly depends on volumetric water content whereas the effect of bulk density on De values was relatively small. If the weighted average buffer power was used, calculated De values were in good agreement with measured values at higher soil moisture contents. At θ < 0.22 g cm?3 the measured values for De were smaller than the calculated. This effect is attributed to incomplete contact between the two soil blocks. The only small influence of bulk density on De is caused by the fact that bulk density affects both θ and b in a way which compensates each other.  相似文献   

10.
In the range of volumetric water content, θ, from about 0.12 cm3 cm–3 to saturation the relation between bulk electrical conductivity, Cb, and bulk electrical permittivity, ε, of mineral soils was observed to be linear. The partial derivative ?Cb/?ε appeared independent of the moisture content and directly proportional to soil salinity. We found that the variable Xs = ?Cb/?ε determined from in situ measurements of Cb(θ > 0.2) and ε(θ > 0.2) can be considered as an index of soil salinity, and we call it the ‘salinity index’. Knowing the index and sand content for a given soil we could calculate the electrical conductivity of the soil water, Cw, which is a widely accepted measure of soil salinity. The two variables from which the salinity index can be calculated, i.e. Cb and ε, can be read simultaneously from the same sensor by time-domain reflectometry. Quantities and symbols a constant /dS m–1 b constant c constant /dS m–1 C b electrical conductivity of bulk soil /dS m–1 C b′ constant equal to 0.08 dS m–1 C s electrical conductivity of a solution used to moisten soil samples /dS m–1 C w electrical conductivity of soil water defined as the soil salinity /dS m–1 C wref reference salinity (that truly existing) resulting from the procedure of moistening samples, expressed as Cs + Cr/dS m–1 C r baseline value of Cs due to residual soluble salts present in the soil /dS m–1 d constant D dry soil bulk density /g cm–3 l slope r ratio S sand content /% by weight t time /s X s salinity index /dS m–1 X si initial salinity index when distilled water is used to moisten soil samples /dS m–1 Y a moisture-independent salinity-dependent variable /dS m–1 z coordinate along direction of flow of the soil solution ε′ constant equal to 6.2 ε relative bulk electrical permittivity (dielectric constant) of the soil θ volumetric water content determined thermogravimetrically using oven-drying /cm3 cm–3  相似文献   

11.
The relationships of soil microbial biomass C (Cmic) or N (Nmic) with mean annual precipitation and temperature were studied along a climatic transect in the Mongolian steppe. Soil organic C (Corg) and total N (Nt), respiration rate, Cmic and Nmic at depths of 0–5 and 5–10 cm decreased with increasing aridity. The contents of Corg and Nt in the 0- to 5-cm soil layers decreased linearly with precipitation reduction along the transect. Cmic and Nmic changes with precipitation were not linear, with higher changes between 330 and 128 mm mean annual precipitation. Cmic/Corg and Nmic/Nt increased with increasing aridity. The metabolic quotient qCO2 of 0- to 5-cm soil layers was low between 330 and 273 mm precipitation. The relationship between the qCO2 of the 0- to 5-cm soil layers and the mean annual precipitation was well fitted with a quadratic function y =0.0006x2 –0.40x +86.0, where y is the qCO2 (µmol CO2-C mmol–1 Cmic) and x is the mean annual precipitation (mm). Corg, Nt, Cmic, Nmic and respiration rate decreased exponentially with increasing mean annual temperature in both the 0- to 5- and 5- to 10-cm soil layers, and change rate was lower when the mean annual temperature was higher than 2.6°C. The close relationships of the mean annual precipitation or temperature with soil Corg, Nt, Cmic, Nmic, Cmic/Corg and qCO2 indicate that each parameter can be calculated by determining the other parameters in this specific climatic range.  相似文献   

12.
植物篱枝叶有机碳分解研究   总被引:7,自引:0,他引:7  
孙辉  唐亚  赵其国  张炎周 《土壤学报》2002,39(3):361-367
研究植物篱枝叶的分解和养分矿化过程对该模式下养分的有效利用具有重要意义。在金沙江干热河谷坡耕地上利用分解袋法对新银合欢、山蚂蝗等 6个植物篱树种枝叶的分解进行了研究 ,结果显示山蚂蝗和新银合欢分解最快 ,前 2个星期有机碳分解了48 6 %和 5 0 0 % ;山毛豆和云南合欢次之 ,前 4星期有机碳累积分解量为 5 1 5 %和 45 6 % ;圣诞树和黑荆树分解最慢 ;将枝叶埋入土壤中比覆盖地表分解快。有机碳的分解规律可以用单指数模型Ct=C0 (1 e kt)和双指数模型Ct=C0 1 (1 e k1t) C0 2 (1 e k2 t)拟合 (式中 ,Ct 为有机碳累积分解量占全碳百分数 ,C0 、C0 1 和C0 2 分别为易分解有机碳和难分解有机碳百分数 ,k和k1分别为易分解有机碳分解常数 ,k2 为难分解有机碳分解常数 ) ,双指数模型更具合理性。研究表明有机碳的累积分解量与枝叶初始C/N比呈负相关 ,枝叶分解速度可用有机碳 (或易分解有机碳 )半减期来衡量。  相似文献   

13.
土壤微生物对苯乙烯的降解   总被引:1,自引:0,他引:1       下载免费PDF全文
本文用实验室模拟的方法研究了苯乙烯在江苏常州大通河灌区水田、旱地中的微生物降解。实验表明,30℃条件下苯乙烯在上述两种农田中均能被土壤微生物降解,其降解动力学均符合一级反应方程。在统计学基础上对二者的降解速率常数进行了比较,经检验,确有差异,旱地中微生物降解速率常数约为水田中的6.7倍。与三种氯代苯共存时,苯乙烯在水田中的微生物降解速率常数约为单独存在时的1.5倍。作者用土壤环流的方法从供试土壤中分离、鉴定了4株以苯乙烯为唯一碳源的细菌,经试验,均具降解苯乙烯能力。进一步确证了土壤微生物可以降解苯乙烯。  相似文献   

14.
This study was to determine if diffusion of soil ammonium may explain why many sandy soils have greater nitrogen (N)–supplying capacity to rice than clay soils. A laboratory procedure using transient-state methods measured the linear movement of soil ammonium (NH4) in tubes packed with five field soils under aerobic conditions. Ammonium diffusion was measured by sectioning tubes after 48 h of equilibration and then measuring NH4 by steam distillation. Effective diffusion coefficients, De, and NH4 diffusion distance, d, per day ranged from De = 4.6 × 10?5 cm2 d?1 and 1.5 cm d?1 for Katy sandy loam to De = 2.9 × 10?7 cm2 d?1 and 0.11 cm d?1 for League clay. Ammonium diffusion distance d was strongly related to soil clay content and hence was predicted by d = Y × {[100/(% clay)] ? 1}, where Y is set to 0.1. Predicted d and measured d were highly related (R2 = 0.99).  相似文献   

15.
The variability of gas diffusion in soil is not well known, but is important for assessing greenhouse gas emissions, soil decontamination, oxidation in soil and plant and root respiration. The goal of this study was to assess small‐scale variability of the relative soil‐gas diffusivity (Ds / Do, msoil air) using large intact soil monoliths and to compare Ds / Do calculation methods. Neon (Ne) was maintained constant at the lower boundary of three monoliths of two soils (a sand and an organic soil). Ne concentration was measured at large spatial and temporal frequencies. Calculation methods included the use of average concentration, and average Ds / Do per horizon, per section, or for the entire soil profile. Considering all sections of the monoliths, Ds / Do varied from 3.5 × 10−3 to 1.2 × 10−1 for the Ap horizon and from 4.8 × 10−3 to 8.3 × 10−1 for the Bf horizon in the sand and from 1.0 × 10−3 to 7.9 × 10−3 for the Ohp horizon and from 2.4 × 10−4 to 7.7 × 10−2 for the Of horizon in the organic soil. For the entire soil profile, variations in Ds / Do between monoliths reached 125% in the sand and 56% in the organic soil. The Ds / Do calculation method influenced the apparent variability (CV) of Ds / Do and, to a lesser extent, Ds / Do values of the overall soil profile. Differences in Ds / Do between monoliths could not be explained solely by the variability of total soil porosity and air‐filled porosity. Soil macroporosity (cracks and earthworm burrows) and layering greatly influenced variability of gas movement. Thus, the choice of sampling procedure, calculation method and modelling must be governed by the scale of the processes of interest and soil variability attributes.  相似文献   

16.
Investigation of the soil gas regime in a tillage experiment: 2. Apparent diffusion coefficients as a measure of soil structure In a soil tillage experiment with nursery stock on three different soils the apparent diffusion coefficients for CO2 were measured using soil cores of different depths at different times. Not-tilled, herbicide treated plots were compared with rototilled plots. The relationship between the relative apparent diffusion coefficient and the air content may be described by an exponential regression function Ds/Da = 0.0085 · e6.8EL, if all measurements are taken into the calculation. By dividing into different soil textures different regressions are obtained for the three studied soils: a sand, a silt and a clay loam. In many cases it is possible to show by the changing Ds(EL) regression changes of the soil structure with depth or as a result of tillage. In all these cases the soil of the not tilled plots turns out to be better structurized than that of the tilled ones, demonstrated by higher Ds-values at equal EL. The interpretation of the differences is being tried with the aid of soil pore tortuousity and continuity. Finally the measured Ds(EL) relationships are applied to characterize the soil gas regime for two seasons, using CO2 concentration profiles of the soil air on a day in summer and fall, respectively. It is shown, that CO2 production reaches farther down in summer than in fall.  相似文献   

17.
Gas diffusion through soil crumbs: the effects of compaction and wetting   总被引:3,自引:0,他引:3  
Samples of 1–2 mm crumbs from a clay loam under permanent pasture were equilibrated at -5 kPa water potential then compacted to varying degrees. Gas diffusion coefficients D, (hydrogen through air), were measured immediately on compaction, again after re-equilibration at -5 kPa, then at other water contents between saturation and dryness. The relationship between diffusion coefficient and air content, was, as elsewhere, in two parts (dD/d small for drainage of pores within crumbs; large for pores between crumbs), but the transition from one part to the other occurred at smaller air contents with increased compaction. The air content at which D approached zero as the samples wetted was greatest in the loosest soil. Compaction from a bulk density of 0.86–1.29 g cm?3 decreased the relative diffusion coefficient, D/D0 (D0 is the diffusion coefficient without impedance), from 0.35 to 0.22 (by 38%) at complete dryness, but from 0.19 to 0.035 (by 82%) in the soil initially at -5 kPa. On re-wetting and re-equilibrating at ?5 kPa, D/D0 decreased further to 0.008 (total 97%) because of extra water held in the now smaller pores of the compacted soil. No single relationship between D/D0 and fitted the results for even this one soil.  相似文献   

18.
The direct application of Sokoto phosphate rock to restore phosphorus in the savanna soil of Nigeria has not been very successful. The dissolution of Sokoto phosphate rock was investigated in three electrolyte solutions – 0.01 m CaCl2, NaCl and KCl – at pH range 3.5–7.0 under laboratory conditions to provide solubility and kinetic data that are required to develop guidelines for direct application in the field. The phosphate rock dissolved in the salt solutions in the order KCl > NaCl > CaCl2. Particle size and ionic strength had no significant effect on the dissolution. The standard free energy of reaction ΔG°R in an acidic solution with no basic cations was ?38 kJ mol?1. If Ca2+ ions were in the acidic solution, then ΔG°R increased to 210 kJ mol?1, 170 kJ mol?1 for Na+ ions, and 107 kJ mol?1 for K+ ions in the solution. The theoretical solubility constant (Ks) calculated from the relation ΔG° = ?RT ln Ks gave Ks = 106.7 in an acidic solution without basic cations, but decreased to 10?36.8 with Ca2+ ions in solution, 10?29.8 with Na+ ions, and 10?18.8 with K+ ions in solution. At pH ≥ 5.5, the dissolution was more constrained by Ca2+ ions or basic cations in solution than by availability of protons. The kinetics of the dissolution reaction was best described by a power function: Ct = atb, where Ct is the amount of P released from the rock phosphate at time t, and a and b are fitting parameters. An Elovich and a parabolic diffusion expression equally gave satisfactory fits to the dissolution data, suggesting that the rate of dissolution was limited by a combination of film‐ and intra‐particle diffusion. To utilize this rock phosphate as an effective source of P, management practices that increase Ca sinks and the supply of protons to the soil are necessary. In the savanna, increasing the soil's organic matter greatly enhances cation exchange capacity and availability of protons. The practice should provide adequate sinks for Ca2+ and the acidic environment required for the release of P from rock phosphate.  相似文献   

19.
In 11 rain‐fed arable soils of the Potohar plateau, Pakistan, the amounts of microbial‐biomass C (Cmic), biomass N (Nmic), and biomass P (Pmic) were analyzed in relation to the element‐specific total storage compartment, i.e., soil Corg, Nt, and Pt. The effects of climatic conditions and soil physico‐chemical properties on these relationships were highlighted with special respect to crop yield levels. Average contents of soil Corg, Nt, and Pt were 3.9, 0.32, and 0.61 mg (g soil)–1, respectively. Less than 1% of Pt was extractable with 0.5 M NaHCO3. Mean contents of Cmic, Nmic, and Pmic were 118.4, 12.0, and 3.9 µg (g soil)–1. Values of Cmic, Nmic, Pmic, soil Corg, and Nt were all highly significantly interrelated. The mean crop yield level was closely connected with all soil organic matter– and microbial biomass–related properties, but showed also some influence by the amount of precipitation from September to June. Also the fraction of NaHCO3‐extractable P was closely related to soil organic matter, soil microbial biomass, and crop yield level. This reveals the overwhelming importance of biological processes for P turnover in alkaline soils.  相似文献   

20.
Molecular diffusion is an important mechanism for gas transport in various natural and man-made systems. This is particularly the case with soil covers installed on acid-generating mine tailings, where oxygen availability has to be controlled. One of the most important roles of such covers is to limit gas flux, which depends on the effective diffusion coefficient D e of the cover materials. This paper presents an experimental procedure and results from oxygen diffusion tests performed on different types of materials, at various degrees of saturation. The determination of D e in the laboratory from the test data is based on analytical and numerical solutions to Ficks laws. The ensuing values of D e are compared to values calculated from available models that relate D e to basic material properties, including porosity and degree of saturation. Statistical indicators are used to evaluate the accuracy of selected models, individually and on a comparative basis. It is shown that modified versions of the Millington–Quirk (M-Q) and Millington–Shearer (M-S) models provide D e values close to the measured data. A semi-empirical expression, ensuing from these models and measurements, is proposed as a simple means of estimating D e.  相似文献   

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