Motion and wake structure of spherical particles

This paper presents results from a flow visualization study of the wake structures behind solid spheres rising or falling freely in liquids under the action of gravity. These show remarkable differences to the wake structures observed behind spheres held fixed. The two parameters controlling the rise or fall velocity (i.e., the Reynolds number) are the density ratio between sphere and liquid and the Galileo number.Comment: 9 pages, 8 figures. Higher resolution on demand. To appear in Nonlinearity January 200

A brief summary of L. van Wijngaarden's work up till his retirement

This paper attempts to provide an overview of Professor Leen van Wijngaarden's scientific work by briefly summarizing a number of his papers. The review is organized by topic and covers his work on pressure waves in bubbly liquids, bubble dynamics, two-phase flow, standing waves in resonant systems, and flow cavitation noise. A list of publications up till his retirement in March 1997 is provided in the Appendix

On the characteristics of the equations of motion for a bubbly flow and the related problem of critical flow

For the study of transients in gas-liquid flows, the equations of the so-called separated flow model are inadequate, because they possess, in the general case where gas and liquid move at different velocities, complex characteristics. This paper is concerned with the equations of motion for bubbly flow. The equations are discussed with emphasis on the aspects of relative motion and the characteristics are calculated. It is found that all characteristics are real. The results are used to establish a relation between gas velocity, liquid velocity, void fraction and sound velocity at critical flow. This relation agrees very well with experimental data for these quantities as measured by Muir and Eichhorn in the throat of a converging-diverging nozzle

The emission of sound by statistically homogeneous bubble layers

This paper is concerned with the flow of a bubbly fluid along a wavy wall, which is one Fourier component of a linearized hydrofoil. The bubbles are dispersed, not throughout the whole of the liquid, but only over a certain distance from the wall, as occurs in practice with cavitation bubbles. Outside the bubbly regime there is pure liquid. The interface between the bubbly fluid and pure liquid fluctuates for various reasons. One of these is the relative motion between bubbles and liquid. This is considered here in detail. A calculation is made of the sound emitted by the bubbly layer into pure liquid as a result of this stochastic motion of the interface

On the structure of shock waves in liquid-bubble mixtures

The structure of shock waves in liquids containing gas bubbles is investigated theoretically. The mechanisms taken into account are the steepening of compression waves in the mixture by convection and the effects due to the motion of the bubbles with respect to the surrounding fluid. This relative motion, radial and translational, gives rise to dissipation and to dispersion caused by the inertia of the radial flow associated with an expanding or compressed bubble. For not too thick shocks the dissipation by radial motion around the bubbles dominates over the dissipation by relative translational motion, in mixtures with low gas content. The overall thickness of the shock appears to be determined by the dispersion effect. Dissipation, however, is necessary to permit a steady shock wave. It is shown that, analogous to undular bores, a stationary wave train may exist behind the shock wave

Bubble interactions in liquid/gas flows

The system of equations, usually employed for unsteady liquid/gas flows, has complex characteristics. This as well as other facts have led to the search for a more accurate description of effects associated with relative motion. For liquid/bubble systems the fluctuations resulting from hydrodynamic interaction between the bubbles may be taken into account in the same way as particle interactions in the theory of viscous suspensions. This is illustrated for the pressure. In a description accurate up till the third power of the void fraction two-bubble interactions are of primary importance. Numerically obtained results for the relative motion in bubble pairs are presented and interpreted with help of simplified equations from which conclusions can be drawn in an analytic way

Evolving solitons in bubbly flows

At the end of the sixties, it was shown that pressure waves in a bubbly liquid obey the KdV equation, the nonlinear term coming from convective acceleration and the dispersive term from volume oscillations of the bubbles.\ud For a variableu, proportional to –p, wherep denotes pressure, the appropriate KdV equation can be casted in the formu t –6uu x +u xxx =0. The theory of this equation predicts that, under certain conditions, solitons evolve from an initial profileu(x,0). In particular, it can be shown that the numberN of those solitons can be found from solving the eigenvalue problem xx–u(x,0)=0, with(0)=1 and(0)=0.N is found from counting the zeros of the solution of this equation betweenx=0 andx=Q, say,Q being determined by the shape ofu(x,0). We took as an initial pressure profile a Shockwave, followed by an expansion wave. This can be realised in the laboratory and the problem, formulated above, can be solved exactly.\ud In this contribution the solution is outlined and it is shown from the experimental results that from the said initial disturbance, indeed solitons evolve in the predicated quantity.\u