Numerical analysis of a mixed finite element method for a flow-transport problem

We consider a generic flow-transport system of partial differential equations, which has wide application in the waste disposal industry. The approximation of this system, using a finite element method for the brine, radionuclides, and heat combined with a mixed finite element method for the pressure and velocity, is analyzed. Optimal order error estimates in H¹ and L² are derived. The error analysis is given with no restriction on the diffusion tensor. That is, we have included the effects of molecular diffusion and dispersion. © 1996 John Wiley & Sons, Inc.     

Numerical study of vortex shedding from a rotating cylinder immersed in a uniform flow field

A numerical study is made of the unsteady two‐dimensional, incompressible flow past an impulsively started translating and rotating circular cylinder. The Reynolds number (Re) and the rotating‐to‐translating speed ratio (α) are two controlled parameters, and the influence of their different combinations on vortex shedding from the cylinder is investigated by the numerical scheme sketched below. Associated with the streamfunction (ψ)–vorticity (ω) formulation of the Navier–Stokes equations, the Poisson equation for ψ is solved by a Fourier/finite‐analytic, separation of variable approach. This approach allows one to attenuate the artificial far‐field boundary, and also yields a global conditioning on the wall vorticity in response to the no‐slip condition. As for the vorticity transport equation, spatial discretization is done by means of finite difference in which the convection terms are handled with the aid of an ENO (essentially non‐oscillatory)‐like data reconstruction process. Finally, the interior vorticity is updated by an explicit, second‐order Runge–Kutta method. Present computations fall into two categories. One with Re=10³ and α≤3; the other with Re=10⁴ and α≤2. Comparisons with other numerical or physical experiments are included. Copyright © 2000 John Wiley & Sons, Ltd.     

Collision dynamics of high-speed droplets upon layers of variable thickness

The collision dynamics between a droplet and a film has been studied with high-impact energy that can be grouped in a dimensionless Weber number, We, as normalized by surface energy. To accomplish this, we have developed a technique based on cutting of a high-speed jet, which can generate a single droplet with speed up to 23 m/s and We on the order of thousands. It was found that the boundaries indicating the occurrence of a central jet and that of a secondary droplet disintegrated from the jet decreased monotonically with increased dimensionless film thickness, H, and remained constant when the film thickness was larger than the crater depth. However, the transition designating multiple droplets that are originated from a central jet shows a non-monotonic trend with the variation of H, with a minimum We being at H ≈ 3, which is about the maximum crater depth, owing to a tuning behavior. The critical We for splashing that occurs at an early phase immediately after the impact is relatively sensitive to the film thickness only when H is between 1 and 2, which increases with reduced H. At large We (≳2,570 for high H), the ejected crown is closed to form a bubble and the transition boundary reveals a similar dependence on H as that for creation of a central jet.     

Mixing of cohesive particles in a shear cell

This paper discusses two series of experiments performed in a shear cell device with six different amounts of silicone oils and using 2-mm soda lime beads as the granular materials. The first series of experiments were mixing experiments, and the developments of mixing layer thicknesses were measured. The second series of experiments had the same experimental conditions as the first series but used different combinations of colored particles. In the second series of experiments, the motions of granular materials were recorded by a high-speed camera. Using the image processing technology and particle tracking method, the positions and velocities of particles were measured. The self-diffusion coefficient could be found from the history of the particle displacements.     

C2, Symmetric Dibenzosuberanes as Templates for the Chirality Determination of Helicenes and Their Applications as Optically Switchable Memory Device

We have recently developed a new type of chiral templates, dibenzosuberanes. Thess C₂, symmetric diaryl modifiers have been successfully applied to the synthesis of chiral triarylcarbenium ions. They can serve as catalysts in the asymmetric Mukaiyama aldol reactions with moderate enantioselectivities of up to 50% [1]. We have subsequently found that one major side reaction between the catalyst and the substrate-silyl ketene acetal which releases extra silyl-X species is responsible for the erosion of asymmetric induction. The dibenzosuberane scaffold was found essential to prevent this type of side reaction. For the selection of carbenium counter ions, we have resorted to the chloride in order to completely suppress the undesired silyl catalysis [2].     

Critical Conformational Change of Poly(oxypropylene)diamines in Layered Aluminosilicate Confinement

The intercalation of aluminosilicate clays proceeds via a critical conformation change. Ion exchange of the poly(oxypropylene)diamine salts allows widening of the clay layers from 12 Å to 20 Å and then a sharp increase to 58 Å. The data indicate a critical conformation change of the intercalated amines, thus providing a new way for manipulating nanomaterials and control of polymer conformations in layered silicate confinement.

Schematic illustration of POP‐amine self‐assembly in silicate confinements.     

Recent advances in heterostructured cathodic electrocatalysts for non-aqueous Li–O2 batteries

Developing efficient energy storage and conversion applications is vital to address fossil energy depletion and global warming. Li–O₂ batteries are one of the most promising devices because of their ultra-high energy density. To overcome their practical difficulties including low specific capacities, high overpotentials, limited rate capability and poor cycle stability, an intensive search for highly efficient electrocatalysts has been performed. Recently, it has been reported that heterostructured catalysts exhibit significantly enhanced activities toward the oxygen reduction reaction and oxygen evolution reaction, and their excellent performance is not only related to the catalyst materials themselves but also the special hetero-interfaces. Herein, an overview focused on the electrocatalytic functions of heterostructured catalysts for non-aqueous Li–O₂ batteries is presented by summarizing recent research progress. Reduction mechanisms of Li–O₂ batteries are first introduced, followed by a detailed discussion on the typical performance enhancement mechanisms of the heterostructured catalysts with different phases and heterointerfaces, and the various heterostructured catalysts applied in Li–O₂ batteries are also intensively discussed. Finally, the existing problems and development perspectives on the heterostructure applications are presented.

The structure–function relationships between heterostructures and their catalytic properties were discussed in detail, and the challenges and improvement strategies for heterostructure based cathodes towards Li–O₂ catalysis were also summarized.