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.     

On air entrainment in coatings

A series of experiments that clarify how air bubbles become entrained into coatings are described. The contact line dynamics at the air-liquid interface surrounding a fiber is characterized for a typical coating die operating under atmospheric and pressurized conditions. Glycerin and other viscous liquids are used to reveal that a critical fiber speed exists at which air entrainment begins. The observations confirm that the critical capillary number Ca(c) depends on the physical properties of the coating material, in the form of the Morton number. When the liquid supply is pressurized, the experiments show that adjusting the pressure can stabilize the displaced free surface interface at a prescribed location. Controlling the meniscus location in this way eliminates air entrainment. The threshold occurs when the applied pressure balances the shear exerted on the coating by the moving fiber. Using this approach it is possible to eliminate air entrainment and attain stable wetting at very large values of the capillary number, e.g., Ca congruent with 50.     

A novel regiodivergent resolution reaction mediated by a homochiral lithium amide base

The reaction of a racemic perhydroisoquinolene derivative 9 with the homochiral lithium amide basse 3 in the presence of Me₃SiCl in an regiodivergent fashion to give the two non-racemic regioisomeric enol silanes 10 and 11. Conversion of 10 into enone 15, an intermediate useful in the synthesis of the alkaloid (+)-yohimbine, was also possible.     

Stereoselective synthesis of beta-(chloro)vinylsilanes using a regio- and (E)-stereoselective bis-stannylation of unsymmetrically substituted butadiynes: application to the synthesis of a masked triyne

[reaction: see text] A highly regio- and stereoselective bis-stannylation of unsymmetrically substituted butadiyne 3 provides bis-stannane 4. Selective lithiation of the internal tin residue effects a 1,4-retro-Brook rearrangement to afford vinylsilane 5. This was elaborated into the novel diethynylethene 1, which also functions as a masked triyne.