A derivation of the Mehrabadi-Cowin equations

An alternative derivation to that given by Mehrabadi and Cowin (1978) is presented here for a pair of kinematic equations governing a certain class of flows in the plastic deformation of dilatant granular materials. This class has been described by Spencer (1981) as double shearing flows. In their derivation Mehrabadi and Cowin (1978), prior to presenting the equations relative to rectangular Cartesian coordinates, obtained an intermediate pair of equations relative to a non-orthogonal network of characteristic coordinates. The essential difference between the original and present derivation is that here, the flow rule, expressed relative to rotating, rectangular Cartesian coordinates, is transformed directly to obtain the kinematic equations relative to fixed rectangular Cartesian coordinate axes, without the need to obtain the characteristic equations.     

A computer simulation of the oscillating cup experiment

Summary A digital computer simulation has been made of the oscillating cup experiment which was originally used byRichardson, also byRussell andWeissenberg to detect shear elasticity in liquids. In developing the theory the principle of a boundary layer to which viscous effects are confined is again applied as it has been previously byHarris and co-workers to the case of axial oscillatory flow. Pairs of quadrature displacement envelopes are given for a range of experimental conditions, for both viscous and viscoelastic fluids. The theoretical curves obtained correspond with certain observations byRichardson andRussell.

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Zusammenfassung Das Schwing-Zylinder-Experiment, welches zuerst vonRichardson sowie vonRussell undWeissenberg zum Nachweis der Scherelastizität von Flüssigkeiten ausgeführt worden ist, wird mit Hilfe eines Digital-Komputers simuliert. Bei der Entwicklung der Theorie wird das Konzept der rein-viskosen Grenzschicht in der gleichen Weise benutzt, wie es schon früher vonHarris und Mitarbeitern für den Fall der oszillierenden Axial-Strömung angewandt worden ist. So berechnete Paare von Verschiebungsenveloppen werden für den Bereich experimentell realisierbarer Bedingungen sowohl für rein-viskose als auch für viskoelastische Flüssigkeiten mitgeteilt. Die erhaltenen theoretischen Kurven entsprechen gewissen vonRichardson bzw. vonRussell erhaltenen Beobachtungsergebnissen.

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With 6 figures     

A reinvestigation of the rate constants for the reactions of ozone with cyclopentene and cyclohexene under atmospheric conditions

The rates of decay of ozone in a large excess of the cycloalkene have been re-measured by an improved experimental procedure, and the following second-order rate constants (cm³ molecule^?1 s^?1) have been determined in synthetic air at atmospheric pressure: The results are discussed in relation to existing literature data on the kinetics of ozonecycloalkene reactions.     

On the size of balls covered by analytic transformations

Two quantitative forms of the inverse function theorem giving estimates on the size of balls covered biholomorphically are proved for holomorphic mappings of a ball in a Banach space into the space. Also, a Bloch theorem forK-quasiconformal mappings on the open unit ball of a Banach space is given and some mapping properties ofK-quasiconformal mappings are deduced.Research supported by N. S. F. Grant GP-33117A-2.     

Direct numerical simulation of aerosol coagulation with van der Waals forces

The van der Waals interaction energy has been computed for a large number of silver and water particle pairs in the range of 1 to 15 nm radius by first calculating the exact, retarded Hamaker factor for semi-infinite bodies and then applying a geometric correction for sphericity. The enhancement of particle collision rates has been deduced from these calculations. These values for the collisional enhancement were used in a direct numerical simulation of the coagulation of silver and water aerosols. Despite the size dependence of the van der Waals enhancement factors, the aerosol size distributions quickly attained nearly self-preserving forms.