Creeping motion of an assemblage of composite spheres relative to a fluid

The sedimentation of a homogeneous distribution of spherical composite particles and the fluid flow through a bed of these particles are investigated theoretically. Each composite particle is composed of a spherical solid core and a surrounding porous shell. In the fluid-permeable porous shell, idealized hydrodynamic frictional segments are assumed to distribute uniformly. The effect of interactions among the particles is taken into explicit account by employing a fundamental cell-model representation which is known to provide good predictions for the motion of a swarm of nonporous spheres within a fluid. In the limit of a small Reynolds number, the Stokes and Brinkman equations are solved for the flow field in a unit cell, and the drag force exerted by the fluid on the particle is obtained in a closed form. For a distribution of composite spheres, the normalized mobility of the particles decreases or the particle interactions increase monotonically with a decrease in the permeability of their porous shells. The effect of particle interactions on the creeping motion of composite spheres relative to a fluid can be quite significant in some situations. In the limiting cases, the analytical solutions describing the drag force or mobility for a suspension of composite spheres reduce to those for suspensions of solid spheres and of porous spheres. The hydrodynamic behavior for composite spheres may be approximated by that for permeable spheres when the porous layer is sufficiently thick, depending on the permeability.     

Time-dependent interaction across two conducting spheres in an applied electrostatic field

Charged particles exist widely in variety of technological areas as well as in nature. Even a weak charge on the particles can significantly influence their electric interaction. We investigated the phenomenon of time-dependent electric interaction between two conducting spheres in an electrostatic field. A mirror-image method was developed to analyze this system, and the fundamental role of the charges on the spheres was studied. We concluded that charges conducted to the lower sphere through the alumina tube used in our system play a main role in determining the time-dependent interaction, whereas the influence from air ions is negligible.     

Optimal lower eigenvalue estimates for Hodge-Laplacian and applications

We consider the eigenvalue problem for Hodge-Laplacian on a Riemannian manifold M isometrically immersed into another Riemannian manifold $\overline{M}$. We first assume the pull back Weitzenböck operator of $\overline{M}$ bounded from below, and obtain an extrinsic lower bound for the first eigenvalue of Hodge-Laplacian. As applications, we obtain some rigidity results. Second, when the pull back Weitzenböck operator of $\overline{M}$ bounded from both sides, we give a lower bound of the first eigenvalue by the Ricci curvature of M and some extrinsic geometry. As a consequence, we prove a weak Ejiri type theorem, that is, if the Ricci curvature bounded from below pointwisely by a function of the norm square of the mean curvature vector, then M is a homology sphere. In the end, we give an example to show that all the eigenvalue estimates are optimal when $\overline{M}$ is the space form.     

基于有序介孔碳的氯离子选择性电极的制备及其在手持传感系统中的应用

以有序介孔碳(OMC)球为离子-电子转换层,制备了固态氯离子选择性电极,构建了基于离子敏感的场效应晶体管(ISFET)的手持式传感系统,用于检测人体血清中的氯离子。优化了OMC前驱体的碳化温度,探究了OMC形貌结构对电极传感性能的影响;电极柔性化制备后考察了其在手持系统中对氯离子的检测效果。结果表明,最优条件下,电极在5.12×10^-4~1.02 mol/L的浓度范围呈现线性响应,响应斜率为60 mV/decade。该柔性电极在手持传感系统中展现出高灵敏度和重现性,可用于人体血清样品中氯离子的检测,其回收率为96.3%~104.9%。     

An overlapping additive Schwarz preconditioner for interpolation on the unit sphere with spherical radial basis functions

The problem of interpolation of scattered data on the unit sphere has many applications in geodesy and Earth science in which the sphere is taken as a model for the Earth. Spherical radial basis functions provide a convenient tool for constructing the interpolant. However, the underlying linear systems tend to be ill-conditioned. In this paper, we present an additive Schwarz preconditioner for accelerating the solution process. An estimate for the condition number of the preconditioned system will be discussed. Numerical experiments using MAGSAT satellite data will be presented.     

淀粉功能化Fe_3O_4纳米簇球的制备与表征

以淀粉为表面活性剂,利用乙二醇溶剂热法一步制备了Fe3O4纳米簇球.采用X射线衍射仪、傅立叶变换红外光谱仪、扫描电镜等分析了产物的结构;采用热重分析仪测定了其热稳定性.结果表明:所得产物为直径约为230nm的簇球结构,构成簇球的纳米粒子直径约为10nm;引入淀粉成功地改善了产物的纳米结构和表面性能.合成的Fe3O4纳米簇球具有独特的结构和表面性能,在生物领域具有潜在的应用前景.     

Synthesis of activated carbon foams with high specific surface area using polyurethane elastomer templates for effective removal of methylene blue

Carbon foams have gained significant attention due to their tuneable properties that enable a wide range of applications including catalysis, energy storage and wastewater treatment. Novel synthesis pathways enable novel applications via yielding complex, hierarchical material structure. In this work, activated carbon foams (ACFs) were produced from waste polyurethane elastomer templates using different synthesis pathways, including a novel one-step method. Uniquely, the produced foams exhibited complex structure and contained carbon microspheres. The ACFs were synthesized by impregnating the elastomers in an acidified sucrose solution followed by direct activation using CO₂ at 1000 ℃. Different pyrolysis and activation conditions were investigated. The ACFs were characterized by a high specific surface area (S_BET) of 2172 m²/g and an enhanced pore volume of 1.08 cm³/g. Computer tomography and morphological studies revealed an inhomogeneous porous structure and the presence of numerous carbon spheres of varying sizes embedded in the porous network of the three-dimensional carbon foam. X-ray diffraction (XRD) and Raman spectroscopy indicated that the obtained carbon foam was amorphous and of turbostratic structure. Moreover, the activation process enhanced the surface of the carbon foam, making it more hydrophilic via altering pore size distribution and introducing oxygen functional groups. In equilibrium, the adsorption of methylene blue on ACF followed the Langmuir isotherm model with a maximum adsorption capacity of 592 mg/g. Based on these results, the produced ACFs have potential applications as adsorbents, catalyst support and electrode material in energy storage systems.