An image system and surface singularity solutions for potential flow past an elliptical cylinder

The Milne-Thomson circle theorem is extended to give a simplegeneral expression for the image system in an elliptical cylinderintroduced into an otherwise specified unbounded potential flowwhich contains no singularities in the region to be occupiedby the ellipse. This image system is used to obtain an expressionfor the corresponding source-sink surface singularity distributionon the ellipse, thus providing new benchmark test cases forsource-sink solutions as obtained numerically by a panel method.Several typical examples are given to illustrate the generaltheoretical approach.     

Coulometric titration of copper(II) with electro-generated chromium(II)

The current efficiency for the electrogeneration of chromium(II) for use as a coulometric titrant was studied for several supporting electrolytes. With a mercury cathode and a 0.1 M chromic sulfate-0.1 M potassium chloride medium, 0.8 to 2.8 mg of copper (II) in 110 ml of solution can be titrated using potentiometric end-point detection.     

Optical vs. direct sorption and swelling measurements for the study of stiff-chain polymer-penetrant interactions

This work involves interferometric ‘optical thickness’ and refractive index measurements performed in an optical thickness meter (OTM), on supported cellulose acetate (CA) films equilibrated with various activities of methylene chloride (MC) vapor. The relevant equilibrium sorption and volume swelling isotherms were determined by application of the Claussius-Mossotti equation on the assumption that these films swell unidimensionally along the thickness direction, and were compared with corresponding direct equilibrium sorption (weight gain), elongation and thickness dilation measurements on similar free films performed in a vacuum sorption/swelling apparatus (VSA) and complemented with refractive index data. Combined elongation and thickness dilation data from the VSA showed that free glass-cast CA films exhibit pronounced swelling anisotropy. The said anisotropy, although it cannot be completely eliminated, by conditioning at high degrees of swelling, does not appear to affect the extent of volume swelling significantly, thus permitting quantitative comparison of sorption and swelling isotherms determined by the VSA and the OTM. Such comparison showed satisfactory agreement between these two sets of results up to an MC uptake of ca. 0.4 gMC/cm³ of dry CA corresponding to a degree of swelling of ca. 0.2. Increasing discrepancies are observed at higher MC concentrations, which are attributable to breakdown of the assumption used that the supported films swell unidimensionally along the thickness direction. The present CA-MC volume swelling data exhibit the negative deviation from volume additivity on mixing typical glassy polymers.