Naturally occurring spore particles at planar fluid interfaces and in emulsions

We have investigated the potential of utilizing naturally occurring spore particles of Lycopodium clavatum as sole emulsifiers of oil and water mixtures. The preferred emulsions, prepared from either oil-borne or aqueous-borne dispersions of the monodispersed particles of diameter 30 microm, are oil-in-water. The particles act as efficient stabilizers for oils of different polarity. Droplets as large as several millimeters are stable to coalescence indefinitely, despite the low coverage of interfaces by particles observed microscopically. Consistent with the emulsion findings, we discover that particles spontaneously adsorb to bare oil-water interfaces of single drops from oil dispersions, whereas adsorption is less spontaneous and extensive from aqueous dispersions. Monolayers of the spore particles at both air-water and oil-water planar interfaces contain particles in an aggregated state forming clusters and chains. The influence of particle concentration, oil/water ratio, and additives in the aqueous phase is studied.     

Particle zips: vertical emulsion films with particle monolayers at their surfaces

Vertical emulsion films with particle monolayers at their surfaces have been studied by direct microscope observations. The effects of particle wettability and surface coverage on the structure and stability of water films in octane and octane films in water have been investigated. Monodisperse silica particles (3 microm in diameter) hydrophobized to different extents have been used. It is found that the structure and stability of emulsion films strongly depend on the film type (water-in-oil or oil-in-water), the particle contact angle, the interactions between particles from the same and the opposite monolayer, and the monolayer density. Stable films are observed only when the particle wettability fulfills the condition for stable particle bridges--in agreement with the concept that hydrophilic particles can give stable oil-in-water emulsions, whereas hydrophobic ones give water-in-oil emulsions. In the case of water films with dilute disordered monolayers at their surfaces, the hydrophilic particles are expelled from the film center toward its periphery, giving a dimple surrounded by a ring of particles bridging the film surfaces. In contrast, the thinning of octane films with dilute ordered monolayers at their surfaces finally leads to the spontaneous formation of a dense crystalline monolayer of hydrophobic particles bridging both surfaces at the center of the film. The behaviors of water and octane films with dense close-packed particle monolayers at their surfaces are very similar. In both cases, a transition from bilayer to bridging monolayer is observed at rather low capillary pressures. The implications of the above finding for particle stabilized emulsions are discussed.     

A scalable synthesis of (1R,3S,5R)-2-(tert-butoxycarbonyl)-2-azabicyclo[3.1.0]hexane-3-carboxylic acid

A stereoselective and scalable synthesis of (1R,3S,5R)-2-(tert-butoxycarbonyl)-2-azabicyclo[3.1.0]hexane-3-carboxylic acid (3a) is described. Key to the success of the devised route was the realization that the stereoselectivity of a cyclopropanation step could be controlled by the composition of the functional group at C-α.     

Estimation of Treatment Time for Microbial Preprocessing of Biomass

Biochemical conversion of lignocellulosic biomass to ethanol involves size reduction, preprocessing, pretreatment, enzyme hydrolysis, and fermentation. In recent years, microbial preprocessing has been gaining attention as a means to produce labile biomass for lessening the requirement of pretreatment severity. However, loss of sugars due to microbial consumption is a major consequence, suggesting its minimization through optimization of nutrients, temperature, and preprocessing time. In this work, we emphasized estimation of fungal preprocessing time, at which higher sugar yields can be achieved after preprocessing and enzyme hydrolysis. The estimation is based on the enzymatic activity profile obtained by treating switchgrass with Phanerochaete chrysosporium for 28 days. Enzyme assays were conducted once in every 7 days for 28 days, for activities of phenol oxidase, peroxidase, β-glucosidase, β-xylosidase, and cellobiohydrolase. We found no activity for phenol oxidase and peroxidase, but the greatest activities for cellulases on the seventh day. We then treated switchgrass for 7 days with P. chrysosporium and observed that the preprocessed switchgrass had higher glucan (39%), xylan (17.5%), and total sugar yields (25.5%) than the unpreprocessed switchgrass (34%, 37.5%, and 20.5%, respectively, p < 0.05). This verifies the utility of using enzyme assays for initial estimation of preprocessing time to enhance sugar yields.     

Godunov–mixed methods for immiscible displacement

The immiscible displacement problem in reservoir engineering can be formulated as a system of partial differential equations which includes an elliptic pressure–velocity equation and a degenerate parabolic saturation equation. We apply a sequential numerical scheme to this problem where time splitting is used to solve the saturation equation. In this procedure one approximates advection by a higher-order Godunov method and diffusion by a mixed finite element method. Numerical results for this scheme applied to gas–oil centrifuge experiments are given.     

Finite dimensional lie-poisson approximations to vlasov-poisson equations

Many of the basic equations of conservative continuum mechanics (Euler, Vlasov-Poisson, Vlasov-Maxwell, MHD, etc.) are Hamiltonian systems with respect to Lie-Poisson brackets on dual spaces of infinite dimensional Lie algebras. The development of Lie-Poisson integrators for finite dimensional Lie-Poisson systems has shown that they are superior in the numerical simulations of these systems, especially with regard to long term phenomena. This paper shows how to truncate one of these systems, the Vlasov-Poisson equation of plasma physics, to a finite dimensional Lie-Poisson system. This requires replacing the functions on single-particle phase space, with their Poisson bracket Lie algebra structure, by a finite dimensional Lie algebra. Replacing the densities by their moments of order up to k about a fixed reference point corresponds to replacing the functions by their Taylor expansions up to order k. Unfortunately, these truncated Taylor expansions do not form a Lie algebra, since the functions which vanish through order k do not form an ideal under Poisson bracket. Geometrically, this corresponds to the fact that canonical transformations which fix the reference point do not form a normal subgroup. Introducing the location of a reference point in phase space as an extra variable and truncating with respect to this moving point turns out to decouple the “location” from “shape” coordinates of a lump of density in phase space, as far as the Poisson bracket is concerned. One can then replace the shape coordinates by a finite number of moments. The central result of the paper is a construction of the decoupling map described above in the general context of the decomposition of a Lie group as a product of subgroups. The main theorem is first proved by the general theory of Poisson reduction, then by explicit calculation, and lastly by showing that the Poisson isomorphism follows from the lift of a natural groupoid isomorphism. The groupoid aspect of the theory also provides natural Poisson maps, useful in the application of Ruth-type integration techniques, which do not seem easily derivable from the general theory of Poisson reduction. © 1994 John Wiley & Sons, Inc.     

High resolution upwind-mixed finite element methods for advection-diffusion equations with variable time-stepping

Numerical methods for advection-diffusion equations are discussed based on approximating advection using a high-resolution upwind finite difference method, and incorporating diffusion using a mixed finite element method. In this approach, advection is approximated explicitly and diffusion implicitly. We first describe the basic procedure where each advection time-step is followed by a diffusion step. Because the explicit nature of the advective scheme requires a CFL time-step constraint, the basic procedure may be expensive, especially if the CFL constraint is severe. Two alternative time-stepping approaches are presented for improving computational efficiency while preserving accuracy. In the first approach, several advective time-steps are computed before taking a diffusion step. In the second approach, the advective time-steps are also allowed to vary spatially. Numerical results for these three procedures for a model problem arising in flow through porous media are given. © 1995 John Wiley & Sons, Inc.     

Modeling of in-situ biorestoration of organic compounds in groundwater

A convergent numerical method for modeling in situ biorestoration of contaminated groundwater is outlined. This method treats systems of transport-biodegradation equations by operator splitting in time. Transport is approximated by a finite element modified method of characteristics. The biodegradation terms are split from the transport terms and treated as a system of ordinary differential equations. Numerical results for vertical cross-sectional flow are presented. The effects of variable hydraulic conductivity and variable linear adsorption are studied.     

Fullerene-templated synthesis of a cyclic porphyrin trimer using olefin metathesis

An olefination approach to the construction of covalently linked cyclic metalloporphyrin trimers is presented using fullerenes such as C(60) or C(70) as a template. Yields of the trimer approach 60%. In the absence of a template, the major product is the cyclic dimer (50% yield) with only a small amount of trimer (<10%) formed, indicating this is a template-directed approach.