Water waves in a suspended container

Analysis and experiments are carried out on a horizontal rectangular wave tank which swings at the lower end of a pendulum. The walls of the tank generate waves which affect the motion of the pendulum. For small displacements of the tank, linearised shallow water equations are used to model the motion, and there exist time-periodic solutions for the system whose periods are governed by a transcendental relation. Numerical and analytic solutions of this relation show that the fundamental period is greater than both the period of the empty tank (moving like a simple pendulum) and the fundamental period of the standing wave which occurs when the tank is removed from its supports and held fixed. For a rectangular tank the theory compares well with some experimental measurements. Qualitative observations are also made of the effect of breaking waves on the tank motion: for a tank which has a mass small compared with its load the energy dissipated by breaking waves can rapidly reduce the amplitude of swing of the tank. Potential flow theory is used with linearised free-surface boundary conditions to find time periodic motions for a tank with a hyperbolic cross section.     

The direct synthesis of methyldichlorosilane and dimethylchlorosilane

The synthesis of methylchlorosilanes with a siliconhydrogen bond, based on the reaction of silicon and methyl chloride with copper as a catalyst, has been investigated at a temperature of 332°C and a pressure of 1 atmosphere. By adding hydrogen to the gas phase, an overall selectivity of methyldichlorosilane and dimethylchlorosilane of over 80 mol% has been achieved together with a small quantity of by-products. The action of hydrogen consists of a reaction with the CuCl reaction intermediates; reaction of hydrogen with CuCl and silicon or with CuCl and chemisorbed methyl chloride also takes place. Metal chlorides such as CdCl₂ and ZnCl₂, which usually are promoters in the synthesis of methylchlorosilanes, do not promote the formation of the hydrogen-containing products.     

The influence of oxygen on the direct synthesis of methylchlorosilanes

The influence of oxygen on the direct synthesis of methylchlorosilanes in a fluidised bed with copper as a catalyst has been studied. At 320° C and a pressure of 1 atmosphere the oxygen content in the feed gas was varied from 1 to 5000 ppm. It was found that the oxygen sharply reduces the rate of reaction but hardly influences the product composition. The maximum degree of conversion of the silicon is about 70% if no oxygen is present; at an oxygen concentration of 2000 ppm the conversion decreases to 50 percent.     

Breaking Water Waves: Unsteady 2D Free-Surface Computations

Some numerical methods for the full Euler equations in two space dimensions are reviewed. Efficient computations can be carried out using a boundary-integral method described, (originally due to J. W. Dold and D. H. Peregrine) which is able to track the unsteady evolution of the free surface of overturning waves. The method is fifth-order in time and tenth order in space. It has been used to compute violent water motions when a wave collides with a vertical wall, for which high accelerations and large pressure gradients are found. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)