Drag of a rotating sphere

We consider the problem of steady incompressible viscous fluid flow about a rotating sphere, with the flow specified on a sphere of finite radius, which reduces to the solution of the complete Navier-Stokes equations.The dimensionless stream functions and circulai velocity are sought in the form of series in powers of the Reynolds numbers, which converge for small values of this number. Recurrence formulas are derived for determining the coefficients of these series. The pressure, rotational resistance torque, and drag are determined. It is established that the rotating sphere has higher drag than a stationary sphere. The leading term of the series in powers of the Reynolds number for the drag and resistive torque is calculated.     

Synthesis and Structure of Octahedral Bis-Chelate Tin(IV) Derivative of the Ruthenocene Series

Cyclopalladated -(p-tolylimino)benzylruthenocene reacts with metallic tin in a way similar to ferrocene analogs, yielding bis-chelate diruthenocenyl tin(IV) compound as a result of transmetalation.     

Diastereoselectivity of the formation of planar chiral ruthenocenol in reactions of chiral tertiary phosphines with the (η4-cyclopentadienone)(η5-cyclopentadienyl)ruthenium cation

The reactions of chiral benzyl- and ethyl(phenyl)ferrocenylphosphines with (acetonitrile)(⁴-cyclopentadienone)(⁵-cyclopentadienyl)ruthenium trifluoromethylsulfonate proceed diastereoselectively through the attack on the cyclopentadienone ring to form planar chiral 2-phosphonioruthenocenols as mixtures of two diastereomers in ratios of 1.7 : 1 and 2 : 1, respectively.     

Motion of a viscous liquid between two rotating spheres

An analysis is presented of the steady-state asymmetric motion of an incompressible viscous liquid between two concentric spheres rotating with constant angular velocities about various axes passing through their common center. The reaction force of the liquid on the inner sphere is determined; this force reduces to a resistive torque.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 179–180, May–June, 1974.     

Cyclopalladation of Schiff's bases in the ruthenocene series. The possibility of application of the asymmetric version of the reaction to metalloceneimines

p-Tolyliminoalkylruthenocenes—Schiff's bases of the ruthenocene series—react with sodium tetrachloropalladate in the presence of carboxylate anion similarly to their ferrocenyl analogs to give cyclopalladation products. The optical rotation values of the products resulting from carbonylation of palladated ferrocene and ruthenocene aldimines, prepared under conditions of asymmetric catalysis, followed by liberation of the aldehyde group were used to determine the stereochemistry and enantiomeric purity of the cyclopalladation products. Centre Nationale de Recherches Scientifiques, URA 419 4, pl. Jussieu, Bat. F, 75252 Paris, France. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1421–1424, July, 1998.     

Flow of a viscous fluid around a sphere of finite radius

We consider the stead y flow of a viscous fluid around a sphere of finiteradius in non-linear formulation. The equations of motion are written in non-dimensional terms. We seek their solution as the expansion of the unknown stream function in a series of powers of the Reynolds number, the coefficients of which are polynomials in associated Legendre functions of the first kind. Recurrence relations are given for the sequential determination of all coefficients. The velocity and pressure fields are determined. The drag is calculated. Numerical calculations are carried out.     

Stereochemical control in reactions of chiral ketone with 2-lithiated substituted ferrocene derivatives

The formation of a new chiral center in the reactions of ketone 4-MeOC₆H₄CH(Et)C(O)Et with planar-chiral 2-lithio-1-methyl- and 1-chloro-2-lithioferrocenes proceeded stereoselectively to give two diastereomers in a ratio of 3 : 2 or a single diastereomer, respectively, out of four possible diastereomeric 4-aryl-3-ferrocenylhexan-3-ols. The replacement of the hydroxy group in the resulting compounds by hydrogen under the conditions of ionic hydrogenation was studied. The configurations of the reaction products were established by X-ray diffraction analysis and ¹H NMR spectroscopy.