Long-time asymptotics for the porous medium equation: The spectrum of the linearized operator

We compute the complete spectrum of the displacement Hessian operator, which is obtained from the confined porous medium equation by linearization around its stationary attractor, the Barenblatt profile. On a formal level, the operator is conjugate to the Hessian of the entropy via similarity transformation. We show that the displacement Hessian can be understood as a self-adjoint operator and find that its spectrum is purely discrete. The knowledge of the complete spectrum and the explicit information about the corresponding eigenfunctions give new insights on the convergence and higher order asymptotics of solutions to the porous medium equation towards its attractor. More precisely, the inspection of the eigenfunctions allows to identify symmetries in R^N${\mathbb{R}}^N$ with flows whose rates of convergence are faster than the uniform, translation-governed bound. The present work complements the analogous study of Denzler & McCann for the fast-diffusion equation.     

Optical ammonia gas sensor based on a porous silicon rugate filter coated with polymer-supported dye

An ammonia gas sensor chip was prepared by coating an electrochemically-etched porous Si rugate filter with a chitosan film that is crosslinked by glycidoxypropyltrimethoxysilane (GPTMS). The bromothylmol blue (BTB), a pH indicator, was loaded in the film as ammonia-sensing molecules. White light reflected from the porous Si has a narrow bandwidth spectrum with a peak at 610 nm. Monitoring reflective optical intensity at the peak position allows for direct, real-time observation of changes in the concentration of ammonia gas in air samples. The reflective optical intensity decreased linearly with increasing concentrations of ammonia gas over the range of 0–100 ppm. The lowest detection limit was 0.5 ppm for ammonia gas. At optimum conditions, the full response time of the ammonia gas sensor was less than 15 s. The sensor chip also exhibited a good long-term stability over 1 year. Therefore, the simple sensor design has potential application in miniaturized optical measurement for online ammonia gas detection.     

含氧煤层气流化床催化燃烧脱氧特性研究

利用自制的铜基球形甲烷催化燃烧催化剂,在小型流化床反应器中对模拟含氧煤层气进行了流化床催化燃烧脱氧的实验研究,考察了床层温度、催化剂粒径、空速对脱氧效率和CO₂选择性的影响。结果表明,较高的反应床层温度使催化剂活性增强,进而提高催化脱氧效率。床层温度在450 ℃以上,脱氧效率可稳定保持在95%以上。较小的催化剂粒径降低了内扩散阻力对催化反应的影响,提高催化反应的CO₂选择性。床层温度在450 ℃以下时,降低空速可提高氧气转化率,但温度高于450 ℃时,脱氧反应速率加快,空速变化对脱氧效率影响不明显。此外,通过调节CH₄/Air比例模拟不同含氧量的煤层气,考察流化床反应器及催化剂对含氧煤层气中O₂浓度变化的适应性。模拟含氧煤层气中氧气体积分数在5%~15%,该催化剂均表现出高的脱氧活性和选择性,反应器出口气体中氧气体积分数低于0.2%,CO₂选择性高于98%。     

微型流化床与热重测定煤焦-CO2气化反应动力学的对比研究

对微型流化床反应分析仪(MFBRA)和热重分析仪(TGA)测定煤焦与CO₂的等温气化反应动力学进行了比较.在最小化气体扩散影响的条件下,半焦在MFBRA中的气化反应速率比TGA中大,且在转化率为0.15时有最大值.缩核模型能很好地描述半焦的气化行为.在760~1 000 ℃,半焦气化分两个阶段:在低温段,利用MFBRA和TGA求取的反应活化能基本相同,验证了MFBRA在求取反应动力学数据方面的有效性和可靠性;在高温段,MFBRA测定的反应活化能较大,说明其受扩散的抑制作用较小.相同温度下通过MFBRA求取的效率因子明显较大,这同其较快的反应速率相一致.上述差异充分说明了反应器类型对测试的(表观)反应动力学有显著影响.     

半焦的多循环气化活性及微观结构分析

为了研究工业流化床气化条件下多循环过程中半焦的气化活性及微观结构变化规律,在快速反应固定床装置上,对三种不同煤阶的半焦进行了模拟多循环气化.通过残焦质量计算得到了循环次数对半焦碳转化率的影响,并利用孔隙分析仪和XRD分析仪考察了半焦的微观结构变化.结果表明,随循环次数的增加,低阶霍林河褐煤半焦的转化率增加,而神木烟煤和晋城无烟煤半焦的转化率降低.多循环过程中"冷淬"效应的存在使得半焦的BET比表面积和微孔比表面积随循环次数呈"山形"趋势变化,而石墨化结构与转化率的变化趋势一致,是决定碳转化率变化的决定性因素.     

无烟煤流化床气化飞灰的结渣特性

通过烧结特性实验研究了无烟煤流化床气化飞灰在"近灰熔点"处的烧结特性,并利用X射线衍射分析(XRD)进行了结晶矿物质和玻璃相的定量分析以研究其烧结机制。结果表明,飞灰中矿物质间的相互转化控制着其结渣特性。由于铁、钙和镁等碱性组分的部分富集,飞灰的灰熔点与原煤相比要低;在低于灰熔点DT 100~200℃附近,由于长石类矿物质的转变熔融形成了具有黏结性的液相,灰样发生液相烧结导致收缩变形而结块;大部分的钙和铁等助熔组分赋存于玻璃相中提高了其浓度,且在热处理过程中它们并未发生析晶行为,从而促进灰样的烧结致密化过程,进一步使得飞灰的结渣倾向增强。     

多孔金属有机骨架材料储氢性能分子模拟

采用优化的DREIDING力场参数, 通过巨正则系综蒙特卡洛(GCMC)模拟方法对H₂在IRMOF-1、IRMOF-61和IRMOF-62共3种金属有机骨架(MOFs)材料中的吸附平衡性能进行了比较研究. 结果表明, 该力场能够在全压力范围内很好地复制H₂在IRMOF-62材料中的等温吸附曲线; 但对低压下H₂在IRMOF-61中的等温吸附曲线预测出现低估. 与IRMOF-1相比, 具有互穿骨架结构的IRMOF-61和IRMOF-62材料在常温下的储氢能力并无明显提高. 进一步比较77 K时100 kPa、3.0 MPa下H₂在上述MOFs材料中达到吸附平衡时的几率密度分布发现, H₂会优先吸附在Zn₄O骨架附近靠近苯环的位置;对具有互穿结构的MOFs材料而言,由于其孔腔尺寸缩小, 使得H₂优先吸附位区域零散化. 适当长度的有机配体形成的互穿骨架结构能增强与H₂分子之间的相互作用, 具备较高的储氢能力; 而有机配体尺寸过长则会增加骨架结构中H₂吸附死角, 对H₂的吸附能力反而出现下降.     

A study on the system of nonaqueous microchip electrophoresis with on‐line peroxyoxalate chemiluminescence detection

This article describes a further development of our previously reported miniaturized analysis system of microchip electrophoresis with on‐line chemiluminescence detection. The system, developed first time for nonaqueous microchip electrophoresis with peroxyoxalate chemiluminescence detection, consists of a suction pressure device for sample or reagent introduction, a constant voltage supplied for electrophoretic separation, an either hydrophilic or hydrophobic porous polymer plug for preventing chemiluminescence reagent flowing upstream and a spiral detection channel for enhancement of both detection sensitivity and reproducibility. Especially, by using organic solvent as BGE medium, the developed system avoided the interface problem between aqueous running buffer and low‐water‐content chemiluminescence solvent in previous reports. The influencing factors on chemiluminescence signal were optimized using rhodamine 6G as model molecule. The system performance was further investigated in the experiment of separation of hydrophilic rhodamine dyes and analysis of hydrophobic polycyclic aromatic hydrocarbon, providing the detection limit (S/N = 3) of 3.5 nmol/L for rhodamine 123, 6.8 nmol/L for rhodamine 6G, and 60 nmol/L for 1‐aminopyrene, respectively. The experimental results showed the system offered a number of benefits, including compact structure, high sensitivity, good reproducibility, and a wide range of application prospect.     

Photoluminescence properties of heat-treated porous alumina films formed in oxalic acid

Photoluminescence and optical properties of as-anodized and heat-treated at 500 °C porous alumina films formed in a 0.3 M oxalic acid at 40 V have been studied. The FTIR indicates that the oxalate ions are embedded in the anodic alumina as chelating bidentate structures and further heating up to 500 °C does not cause any change in ion coordination. The results of time-resolved spectroscopy show the presence of two luminescence centers both in the as-anodized and heat-treated anodic alumina films with lifetimes of about 0.25 and 4.0 ns. The F⁺-centers in anodic alumina are responsible for the luminescence peak at about 420 nm, with a lifetime of about 4.0 ns. The luminescence peak at about 480 nm, with lifetime of about 0.25 ns, can be attributed to the luminescence of carboxylate ions existing in bulk of anodic alumina.