An experimental realization of an unstrained, planar diffusion flame

A unique burner was constructed to experimentally realize a one-dimensional unstrained planar non-premixed flame, previously considered only in idealized theoretical models. One reactant, the fuel mixture in the current experiments, is supplied through a porous plug at the bottom of the combustion chamber and flows vertically up towards the horizontal flame. The crux of the design is the introduction of the oxidizer from above in such a way that its diffusion against the upward product flow is essentially one-dimensional, i.e., uniform over the burner cross-section. This feature was implemented by introducing the oxidizer into the burner chamber from the top through an array of 625 closely spaced hypodermic needles, and allowing the hot products to escape vertically up through the space between the needles. Due to the injection of oxidizer through discrete tubes, a three-dimensional “injection layer” exists below the exit plane of the oxidizer supply tubes. Experimental evidence suggests that this layer is thin and that oxidizer is supplied to the flame by 1-D counterdiffusion, producing a nearly unstrained flame. To characterize the burner, flame position measurements were conducted for different compositions and flowrates of H₂–CO₂ and O₂–CO₂ mixtures. The measured flame locations are compared to an idealized one-dimensional model in which only diffusion of oxidizer against the product flow is considered. The potential of the new burner is demonstrated by a study of cellular structures forming near the extinction limit. Consistent with previous investigations, cellular instabilities are shown to become more prevalent as the initial mixture strength and/or the Damköhler number are decreased. As the extinction limit is approached, the number of cells was observed to decrease progressively.     

Angular gaps in radial diffusion-limited aggregation: two fractal dimensions and nontransient deviations from linear self-similarity

When suitably rescaled, the distribution of the angular gaps between branches of off-lattice radial diffusion-limited aggregation is shown to approach a size-independent limit. The power-law expected from an asymptotic fractal dimension D = 1.71 arises only for very small angular gaps, which occur only for clusters significantly larger than M = 10(6) particles. Intermediate size gaps exhibit an effective dimension around 1.67, even for M--> infinity. They dominate the distribution for clusters with M<10(6). The largest gap approaches a finite limit extremely slowly, with a correction of order M(-0.17).     

Imaging microscopic viscosity with confocal scanning optical tweezers

The techniques of confocal microscopy and optical tweezers have shown themselves to be powerful tools in biological and medical research. We combine these methods to develop a minimally invasive instrument that is capable of making hydrodynamic measurements more rapidly than is possible with other devices. This result leads to the possibility of making scanning images of the viscosity distribution of materials around biopolymer-producing cells. 100 x 100 images can be taken with 0.5-microm spatial resolution in 3 min. An image of the viscosity distribution around a pullulan-producing cell of Aureobasidium pullulans is shown as an example.     

The role of template in the synthesis of meso-hexamethyl-meso-hexaphenyl-calix[6]pyrrole: trihalogenated compounds as templates for the assembly of a host with a trigonal cavity

Trihalogenated compounds act as effective and selective templates in the template-assisted synthesis of meso-hexaphenyl-calix[6]pyrrole.     

Combustion theory and modeling

In honor of the fiftieth anniversary of the Combustion Institute, we are asked to assess accomplishments of theory in combustion over the past fifty years and prospects for the future. The title of our article is chosen to emphasize that development of theory necessarily goes hand-in-hand with specification of a model. Good conceptual models underlie successful mathematical theories. Models and theories are discussed here for deflagrations, detonations, diffusion flames, ignition, propellant combustion, and turbulent combustion. In many of these areas, the genesis of mathematical theories occurred during the past fifty years, and in all of them significant advances are anticipated in the future. Increasing interaction between theory and computation will aid this progress. We hope that, although certainly not complete in topical coverage or reference citation, the presentation may suggest useful directions for future research in combustion theory.     

Strong γ-sets and other singular spaces

Whereas the Gerlits-Nagy γ property is strictly weaker than the Galvin-Miller strong γ property, the corresponding strong notions for the Menger, Hurewicz, Rothberger, Gerlits-Nagy (∗), Arkhangel'ski?ˇ and Sakai properties are equivalent to the original ones. The main result is that almost each of these properties admits the game theoretic characterization suggested by the stronger notion. We also solve a related problem of Ko?inac and Scheepers, and answer a question of Iliadis.     

Hurewicz sets of reals without perfect subsets

We show that even for subsets of the real line that do not contain perfect sets, the Hurewicz property does not imply the property , asserting that for each countable family of open -covers of , there is a choice function whose image is a -cover of . This settles a problem of Just, Miller, Scheepers, and Szeptycki. Our main result also answers a question of Bartoszyński and the second author, and implies that for , the conjunction of Sakai's strong countable fan tightness and the Reznichenko property does not imply Arhangelskiı's property .

     

Diffusivity fractionations of H2(16)O/H2(17)O and H2(16)O/H2(18)O in air and their implications for isotope hydrology

We have determined the isotope effects of (17)O and (18)O substitution of (16)O in H(2)O on molecular diffusivities of water vapor in air by the use of evaporation experiments. The derived diffusion fractionation coefficients (17)alpha(diff) and (18)alpha(diff) are 1.0146 +/- 0.0002 and 1.0283 +/- 0.0003, respectively. We also determined, for the first time, the ratio ln((17)alpha(diff))/ln((18)alpha(diff)) as 0.5185 +/- 0.0002. This ratio, which is in excellent agreement with the theoretical value of 0.5184, is significantly smaller than the ratio in vapor-liquid equilibrium (0.529). We show how this new experimental information gives rise to (17)O excess in meteoric water, and how it can be applied in isotope hydrology.     

Light‐triggered antifouling coatings for porous silicon optical transducers

Nanostructured porous silicon (PSi) is an attractive platform for the design of biosensors because of its high sensitivity and selectivity towards various biological targets. Its use for biosensing applications, however, is compromised as a result of interfacial interactions with biological molecules that may accumulate on their surfaces and degrade their performance. We describe a new hybrid system comprising an oxidized PSi (PSiO₂) nanostructure and antifouling (anti‐adsorption), light‐triggered pre‐polymers that promote crosslinking and surface anchoring to Si walls. The incorporation of the pre‐polymers allowed the production of a thick hydrogel layer on the inorganic nanostructure. Coating completely prevents fouling of proteins on the surface without compromising biosensor performance in terms of sensitivity. The strategy developed here provides a convenient means to combine two distinct features of crosslinking and organic–inorganic hybrid fabrication in a “one‐pot” process. Copyright © 2017 John Wiley & Sons, Ltd.