We developed a capillary chromatography system by using an open capillary tube made of fused-silica, polyethylene, or polytetrafluoroethylene, and a water-hydrophilic/hydrophobic organic mixture carrier solution, called tube radial distribution chromatography (TRDC) system. By comparing with chromatograms obtained via the TRDC system, fluorescence photographs and profiles of the fluorescent dyes dissolved in the carrier solvents in capillary tubes were observed under laminar flow conditions. The chromatograms were obtained for a model mixture analyte consisting of 1-naphthol and 2,6-naphthalenedisulfonic acid with the TRDC system, by using a fused-silica capillary tube and a water-acetonitrile-ethyl acetate carrier solution. By altering the carrier flow rates, we examined the fluorescence photographs and profiles of the dyes, perylene and Eosin Y, dissolved in the carrier solvents in the capillary tube by using a fluorescence microscope equipped with a CCD camera. As confirmed by fluorescence observations, the major inner and minor outer phases generated in the capillary tube were based on the tube's radial distribution of the carrier solvents. We designed and manufactured a microreactor incorporating microchannels in which three narrow channels combined to form one wide channel. When the carrier solvents containing the dyes were fed into the channels, the inner and outer phase generations were also observed in the narrow and wide channels, strongly supporting the conclusions concerning the tube radial distribution phenomenon of the solvents.
We shall study the compressible Euler equation wtnch describes the motion of an isentropic gas. Many global existence theorems have been obtained for the one dimensional case. On the other hand, little is known for the case n _> 2. No global weak solutions have been known to exist, but only local classical solutions. In this paper, we will present global weak solutions first for the case n > 2. We will do this, however, only for the case of spherical symmetry with ~/----1, by using a modified Glimm's method.
We study the spherically symmetric motion of isothermal gas surrounding a ball. Recently we constructed global weak solutions for the initial boundary value problem in [2], but the class of the initial data considered there was not wide enough to include the stationary solutions for which the density is constant on the whole space. In this paper we will extend our preceding result to a wider class of the initial data so that ir includes such stationary solutions. To do this, we will presenta modification of Glimm's method in which the mesh lengths for approximate solutions are not uniform.
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