一类Capillarity系统非平凡解的存在性研究

本文研究了一类capillarity系统解的存在性问题.采用在乘积空间中定义非线性映射的方法,把capillarity系统转化为非线性算子方程.借助于Sobolev嵌入定理等技巧证明非线性映射具有紧性,进而利用非线性映射值域的性质得到非线性算子方程解的存在性的结论.并由此获得在一定条件下capillarity系统在L^(P1)(Ω)×L^(P2)(Ω)×…×L^(PM)(Ω)空间中存在非平凡解的结论,其中Ω为R^N(N≥1)中有界锥形区域且2N/N+1<p_i<+∞,i=1,2,…,M.本文所研究的问题和所采用的方法推广和补充了以往的相关研究工作.

一类广义Capillarity方程的单调性方法

利用变分不等式解的存在性的结论,证明了具有Dirichlet边值条件的广义Capillarity方程解的存在唯一性.借助于挖掘具有Dirichlet边值条件的广义Capillarity方程和具有Neumann边值条件的广义Capillarity方程之间的关系并利用极大单调算子值域的扰动结果,得到了具有Neumann边值条件的广义Capillarity方程解的存在性的一个充分条件.文中采用了一些新的证明技巧,推广和补充了笔者以往的一些研究工作.

INFLUENCE OF CAPILLARITY ON NANO-LITER FLOWRATE MEASUREMET WITH DISPLACEMET METHOD

Nanoqiter flowrate measurements in micro-tubes with displacement method were performed and the effect of capillarity force on the accuracy was investigated through lab experiments and theoretical analysis in this article. The experiments were conducted under the pressure drops ranging from 1 kPa to 10 kPa in a circular pipe with a diameter of 50 pm, to give the pressure-flowrate （P-Q） relation and verify the applicability of the classical Hagen-Poiseuille （HP） formula. The experimental results showed that there existed a discrepancy between the experimental data and the theoretical values predicted by the HP formula if the capillary effect was not considered, which exceeded obviously the limit of the system error. And hence a modified formula for the relation, taking the capillary effect into account, was presented through theoretical deduction, and after the HP formula had been modified the error was proved to be less than 3%, which was permitted in comparison with the system error. It was also concluded that only by eliminating the effect of the capillary force in experiments could the original HP formula be employed to predict the pressure-flowrate relation in the Hagen-Poiseuille flow in the micro-tube.

Existence and Nonexistence of Nontrivial Weak Solution for a Class of General Capillarity Systems

The aim of this paper is to study the nonexistence and existence of nonnegative, nontrivial weak solution for a class of general capillarity systems. The proofs rely essentially on the minimum principle combined with the mountain pass theorem.

Nano-capillary induced assemble of quantum dots on perovskite grain boundaries for efficient and stable perovskite solar cells

In recent years, perovskite solar cells(PSCs) have propelled into the limelight owing to rapid development of efficiency;however, the abundant defects at the perovskite grain boundaries result in unwanted energy loss and structural degradation. Here, the grain boundaries of perovskite polycrystalline films have been found to act as nanocapillaries for capturing perovskite quantum dots(PQDs), which enable the conformal assemble of PQDs at the top interspace between perovskite grains. The existence of PQDs passivated the surface defects, optimized the interfacial band alignments, and ultimately improved the power conversion efficiency from 19.27% to 22.47% in inverted PSCs. Our findings open up the possibility of selective assembly and structural modulation of the perovskite nanostructures towards efficient and stable PSCs.

Spontaneous imbibition characteristics of shale oil reservoir under the influence of osmosis

The spontaneous imbibition(SI)process in shale oil reservoirs is not only infuenced by capillary force,but also by the osmotic pressure between the fracturing fuid and formation water in the nanopores media.In this study,experimental methods are used to investigate the mechanisms of osmosis in the SI,taking into account the presence of initial formation water in shale oil reservoirs.To investigate the efect of osmosis,SI experiments were performed on the fne-grained felsic shale of the Qikou sag of Dagang oilfeld.Low-feld NMR testers and high-precision electronic balances are utilized for the measuring of oil–water migration.The results show that,when Sw≠0,high-salinity fuid SI can be divided into four stages:initial imbibition stage,drainage stage,secondary imbibition stage and stationary stage;when Sw=0,there is no drainage stage of high-salinity fuid SI;when Sw≠0 or Sw=0,low-salinity fuid SI can be called the“osmosis-enhanced SI”;and we have found that“newly formed pores or microfractures”as well as reducing salinity can promote SI.This article presents a systematic study of SI of shale oil reservoirs under the infuence of osmosis,which provide useful information for reservoir numerical simulation and development program design.

Fiber Traction Printing:A 3D Printing Method of Continuous Fiber Reinforced Metal Matrix Composite

A novel metal matrix composite freeform fabrication approach,fiber traction printing(FTP),is demonstrated through controlling the wetting behavior between fibers and the matrix.This process utilizes the fiber bundle to control the cross-sectional shape of the liquid metal,shaping it from circular to rectangular which is more precise.The FTP process could resolve manufacturing difficulties in the complex structure of continuous fiber reinforced metal matrix composites.The printing of the first layer monofilament is discussed in detail,and the effects of the fibrous coating thickness on the mechanical properties and microstructures of the composite are also investigated in this paper.The composite material prepared by the FTP process has a tensile strength of 235.2 MPa,which is close to that of composites fabricated by conventional processes.The complex structures are printed to demonstrate the advantages and innovations of this approach.Moreover,the FTP method is suited to other material systems with good wettability,such as modified carbon fiber,surfactants,and aluminum alloys.

Analytical Methods for Prediction of Water Absorption in Cement-Based Material

The capillary absorption of water by unsaturated cement-based material is the main reason of degradation of the structures subjected to an aggressive environment since water often acts as the transporting medium for damaging contaminants. It is well known that the capillarity coefficient and sorptivity are two important parameters to characterize the water absorption of porous materials. Generally, the former is used to describe the penetration depth or height of water transport, which must be measured by special and advanced equipment. In contrast, the sorptivity represents the relationship between cumulative volume of water uptake and the squareroot of the elapsed time, which can be easily measured by the gravimetric method in a normal laboratory condition. In the present study, an analytical method is developed to build up a bridge between these two parameters, with the purpose that the sorptivity or the gravimetric method can be used to predict the penetration depth of water absorption. Additionally, a new model to explain the dependence of sorptivity on initial water content of the material is developed in order to fit the in situ condition. The comparison of predicted results by the analytical method with experimental data or numerical calculation results, as well as some previous models, validates the feasibility of the methods presented in this paper.

A Remark on Global Existence,Uniqueness and Exponential Stability of Solutions for the 1D Navier-Stokes-Korteweg Equations

In this paper, we investigate non-isothermal one-dimensional model of capillary compressible fluids as derived by M Slemrod(1984) and J E Dunn and J Serrin(1985). We establish the existence, uniqueness and exponential stability of global solutions in H^2×H^1× H^1 for the one-dimensional Navier-Stokes-Korteweg equations by a priori estimates,which implies the existence and exponential stability of the nonlinear C_0-semigroups S(t) on H^2× H^1× H^1.

Characterization of Fired Clay Bricks for an Economic Contribution of the Exploitation of Thicky Clay Deposit

Clay materials from Thicky in Thiès district (Senegal) are very abundant and could be used for the production of clay brick for the construction industry in Senegal and the surrounding countries. The geophysical, geotechnical, and thermal studies carried out did lead to a better comprehension of the potential of the area for clay production. It also allowed determining the physical and chemical characteristics of the clays for their use in order to make fired clay bricks. Different types of fired clay brick were produced with Thicky’s clays. The study of the physical, mechanical and thermal parameters of these raw materials and bricks has given very satisfactory results compared to the standards in use. It is noted a good ceramic behavior, and there is no deterioration observed after firing at 900°C until low residual moisture of about 3% (on a dry basis), a smooth texture with a beautiful appearance, a low loss on ignition, a low shrinkage value of less than 1% (dry), moderate water absorption and also good compressive strength. The study of thermal properties on a brick wall by the asymmetric lime plane method gives satisfactory effusivity and thermal conductivity values which are respectively equal to 746.48 J·K-1·m-2·s-1/2 and 0.42 W·m-1·k-1 with a thermal resistance of 0.0028 m2·K·W-1.

Full filling of mesoporous carbon nanotubes by aqueous solution at room temperature

Carbon nanotubes(CNTs) have the ideal structure to be used as templates for nanomaterials, especially for nanowires,and the tungsten nanowire is an important nanomaterial that is used as a strengthening phase. Therefore, we have proposed to apply mesoporous CNT(mCNT) as a template to prepare tungsten nanowires. However, the tungsten precursor should fill the hollow tube of mCNT firstly, and very few related studies have been reported. In this paper, we have systematically studied the filling process of ammonium metatungstate(AMT) aqueous solution. The results reveal that owing to the mesopores in the mCNT sidewall, the AMT can be encapsulated into the tube at room temperature(RT) and we can fully fill it without destroying the structure. In addition, vibration and solute concentration are also important factors. Besides,the mesoporous sidewall and hollow tubular core structure of mCNT are prerequisites to realize full filling. Furthermore,tungsten nanowires have been obtained after reduction of AMT in mCNTs.

Proactive control of cresting in homogeneous oil reservoirs:an experimental study

This paper sets out to investigate experimentally the use of electromagnetic valves in controlling production of water during cresting from homogeneous non-fractured thick-oil and thin-oil reservoirs, based on the principle of capillarity and breakthrough time. A time half the initial breakthrough times was preset for the electromagnetic valve to close. The valve closed almost immediately at the set time thereby shutting oil production temporarily,causing the water and gas height levels to recede by gravity and capillarity with receding reservoir pressure. The efficiency of this technique was compared with an uncontrolled simulation case, in terms of cumulative oil, oil recovery and water produced at the same overall production time. From the results obtained, higher percentages in oil produced and water reduction were observed in the cases controlled proactively, with a 3.6% increase in oil produced and water reduction of 10.0% for thick-oil rim reservoirs, whereas only a small increment in oil produced(0.7%) and a lower water reduction of 1.03% were observed for the thin-oil rim reservoirs. Hence, the effectiveness of the cresting control procedure depends on the oil column height of the reservoir.

Modeling Water Adsorption and Retention of Building Materials From Pore Size Distribution

Water adsorption and capillarity are key phenomena involved during heat and moisture transfer in porous building materials.They account for interaction between solid matrix,liquid water and moist air.They are considered through Water Vapor Adsorption Isotherm(WVAI)and Retention Curve(RC)functions which are constitutive laws characterizing water activity within a porous medium.The objective of this paper is to present a water vapor adsorption and retention models built from multimodal Pore Size Distribution Function(PSDF)and to see how its parameters modify moisture storage for hygroscopic and near saturation ranges.The microstructure of the porous medium is represented statistically by a bundle of tortuous parallel pores through its PSDF.Firstly,the influence of contact angle and temperature on storage properties were investigated.Secondly,a parametric study was performed to see the influence of the PSDF shape on storage properties.Three cases were studied considering the number of modalities,the weight of each modality and the dispersion around mean radius.Finally,as a validation,the proposed model for WVAI were compared to existing model from literature showing a good agreement.This study showed that the proposed models are capable to reproduce various shapes of storage functions.It also highlighted the link between microstructure and adsorption-retention phenomena.

Effect of Heterogeneity of Porous Media on Gas Permeation and Entrapment

Capillary trapping prevents the migration of CO2 in reservoirs due to buoyancy. The residual gas saturation is strongly influenced by the gas saturation after gas injection. In this study, we have investigated the effect of stratified structure of heterogeneous porous media on gas permeation and entrapment. Experiments were carried out at a laboratory condition for a nitrogen-water system with the packed beds of glass beads with various diameters which modeled stratified porous media. In the case of parallel structure, the injected gas selectively percolated into permeable layers. The gas permeation can hardly occur for the less permeable layers because of the capillary entrance pressure. In the case of serial structure, the interface of porous structure hindered the migration of gas across it, because of the capillary entrance pressure. When the gas percolated in the permeable layers, capillary fingering was developed in the layers. However, when the tip of finger reached the interface, fingers grew in tangential directions until the pressure built up to overcome the capillary entrance pressure. As a result, high gas saturation was achieved in the permeable layers of both upward and downward gas injections.

Behaviour of Rendering Mortar for Rehabilitation of Buildings Subjected to Rising Damp

This paper presents an experimental study on the behaviour of rendering mortars used to rehabilitate buildings subjected to rising damp and consequently affected by efflorescence. This study was initiated by the characterization, ＂in situ＂ and in laboratory, of rendering mortar used as walls coating of an old building affected by efflorescence. Temperature, superficial humidity, mortar water content and salts content were used as characterization tests. Taking into account the reconstitution of old building rendering mortar composition, four different proportions were proposed to simulate different mortars skeletons and porosities. The mortars binders were composed by cement and three additions, such as hydrated lime, artificial hydraulic lime and quicklime paste. The results of capillary water absorption, soluble salts content and permeability test on masonry panels allowed analyzing the performance of mortars compared to the susceptibility of water rise and formation of salts. From this analysis, it was possible to draw some practical recommendations for design coating repair mortar in buildings subject to the problem of rising damp.

Influence of Temperature and Water Vapour Pressure on Drying Kinetics and Colloidal Microstructure of Dried Sodium Water Glass

Industrially produced sodium water glasses were dried in climates with controlled temperature and humidity to transparent amorphous water containing sodium silicate materials. The water glasses had molar SiO2:Na2O ratios of 2.2, 3.3 and 3.9 and were dried up to 84 days at temperatures between 40&degC and 95&degC and water vapour pressures between 5 and 40 kPa. The materials approached final water concentrations which are equilibrium values and are controlled by the water vapour pressure of the atmosphere and the microstructure of the solids. The microstructure of the dried water glasses was characterized by atomic force microscopy. It has a nanosized substructure built up by the silicate colloids of the educts but deformed by capillary forces. In the final drying equilibrium, the water vapour pressure of the atmosphere in the drying cabinet is equal to the reduced vapour pressure of the capillary system built up by the silicate colloids. Their size scale can be explained by the deformation of colloidal aggregates due to capillary forces.

Examples of Non-Uniqueness of the Equilibrium States for a Floating Ball

We provide a numerical algorithm for numerically approximating a centrally located floating ball. We give examples of equilibria, and we present non-unique cases for the same physical parameters when the density of the ball is either greater than the supporting liquid (heavy) or lighter than the density of the vapor above (light). We classify the non-uniqueness by analyzing a function related to the force balance. We derive the potential energy of these states, and make comparisons of the non-unique cases. In the cases of both the light and heavy floating balls, the evidence presented supports the conjecture that when there are two equilibria, the one with lower energy corresponds to the location of triple junction (between the ball, the vapor and the liquid) that is closer to the equator of the ball.

Effects of ethanol on liver sinusoidal endothelial cells-fenestrae of rats

Important advances have been made in research into the mechanism of alcoholic liver disease (ALD) over the past few years,but the role of liver sinusoidal endothelial cell (LSEC) in ALD has not been elucidated adequately. This study was undertaken to investigate the effect of ethanol on fenestrae of LSECs in rats. METHODS: A rat model of alcoholic liver disease was established by means of direct intragastric instillation of ethanol. Fifty-five rats of experimental (35 rats) and control (20) groups were sacrificed at the end of 4,8,12 weeks respectively, and also at the end of 12-week abstinence. After heart perfusion, the liver tissue was fixed and stained with hematoxylin and eosin for observation of serial changes of LSEC-fenestrae under a transmission electron microscope. RESULTS: Normal LESC was flat with a nucleus and organelles arranged regularly. The distal cytoplasm displayed as a lamina with many fenestrae, lacking the basement membrane(BM) underneath the endothelium. At the end of 4-week alcohol feeding, the number of fenestrae decreased at the distal cytoplasm in some LSECs, without the formation of the BM underneath the endothelium. At the end of 8 weeks, the number of fenestrae decreased significantly or even disappeared. The BM began to develop incompletely underneath the endothelium, while the active fibroblast appeared. At the end of 12 weeks, the number of fenestrae decreased more significantly and the complete BM could even be seen. But the changes were mostly limited in the single or adjoining sinus, and fibrosis was scarcely formed. At the end of 12-week abstinence, defenestration and formation of the endothelial BM lightened significantly. CONCLUSIONS:Defenestration and formation of the BM in LSECs develop gradually with the chronic stimulation of ethanol. Hepatic sinusoidal capillarization and fibrosis will be seen if their state is more serious. These early changes, i. e., limited and regional defenestration and capillarization may be the basis of alcoholic peri-fibrosis. This kind of he- patic fibrosis is reversible after removal of etiological factors.

Pathological mechanisms of alcohol-induced hepatic portal hypertension in early stage fibrosis rat model

AIM： To study the role of hepatic sinusoidal capillarization and perisinusoidal fibrosis in rats with alcohol-induced portal hypertension and to discuss the pathological mechanisms of alcohol-induced hepatic portal hypertension. METHODS： Fifty SD rats were divided into control group （n=20） and model group （n=30）. Alcoholic liver fibrosis rat model was induced by intragastric infusion of a mixture containing alcohol, corn oil and pyrazole （1 000：250：3）. Fifteen rats in each group were killed at wk 16. The diameter and pressure of portal vein were measured. Plasma hyaluronic acid （HA）, type IV collagen （COW） and laminin （LN） were determined by radioimmunoassay. Liver tissue was fixed in formalin （10%） and 6-μm thick sections were routinely stained with Mallory and Sirius Red. Liver tissue was treated with rabbit polydonal antibody against LN and ColⅣ. Hepatic non-parenchymal cells were isolated, total protein was extracted and separated by SDS-PAGE. MMP-2 and TIMP-1 protein expression was estimated by Western blotting. RESULTS： The diameter （2.207 ± 0.096 vs 1.528±0.054 mm, P〈0.01） and pressure （11.014±0.395 vs 8.533±0.274 mmHg, P〈0.01） of portal vein were significantly higher in model group than those in the control group. Plasma HA （129.97±16.10 vs 73.09±2.38 ng/mL, P〈0.01）, ColⅣ （210.49±4.36 vs 89.65±4.42 ng/mL, P〈0.01） and LN （105.00±7.29 vs 55.70±4.32 ng/mL, P〈0.01） were upregulated in model group. Abundant collagen deposited around the central vein of Iobules, hepatic sinusoids and hepatocytes in model group. ColⅠ and ColⅢ increased remarkably and perisinusoids were almost surrounded by ColⅢ. Immunohistochemical staining showed that ColⅣ protein level （0.130±0.007 vs 0.032±0.004, P〈0.01） and LN protein level （0.152±0.005 vs 0.029±0.005, P〈0.01） were up-regulated remarkably in model group. MMP-2 protein expression （2.306±1.089 vs 0.612±0.081, P〈0.01） and TIMP-1 protein expression （3.015±1.364 vs 0.446±0.009, P〈0.01） in freshly isolated hepatic nonparenchymal cells were up-regulated in model group and TIMP-1 protein expression was evidently higher than MMP-2 protein expression （2.669±0.170 vs 1.695±0.008, P〈0.05）. CONCLUSION： Hepatic sinusoidal capillarization and peri-sinusoidal fibrosis are responsible for alcoholinduced portal hypertension in rats,

Hepatic Sinusoidal Obstruction Syndrome without Preceding Medical Events

Sinusoidal obstruction syndrome (SOS) is one of the severe complications of radiation, anticancer chemotherapy and immunosuppressive agents for transplantation. Autopsy of a case of rapidly progressive, uncontrollable severe ascites, without apparent signs of preceding drug toxicity, revealed a tensely enlarged liver and spleen, and 3000 ml of ascites attributed to secondary portal hypertension. Histopathological analysis disclosed sinusoidal endothelial damage and fibrous expansion from central veins. All the foregoing indicated hepatic SOS that needs to be included in the differential diagnosis of progressive ascites in patients without an apparent history of malignancy or transplantation.