Spherical Air Bubbles Research Articles

Motion of Air Bubbles in Mineral Oils Subject to Sudden Change in Chamber Pressure : 1st Report, Experimental Analysis of Single Spherical Bubbles

This paper deals with an experimental and a theoretical analysis of growth and decay of a spherical air bubble rising in a stationary oil closed in a chamber subject to such a rapid rate of pressure variation as one bar during two or several milliseconds. The oils used were two kinds of base oils for hydraulic fluids with low and high viscosities, and base oils including a small quantity of silicon-type deforming agent were also used. The following are discussed from the comparison of the measured bubble motion with the numerical analysis: (1) mass transfer effect on expansion or compression of the bubble boundary. (2) effect of deforming agents added to the oil on the mass transfer through the bubble boundary, and (3) effect of surface dilational viscosity on violent bubble oscillation in a low viscosity oil.

A new fenestration material for heat protection

This work applies the Mie scattering theory to the case of polydisperse spherical air bubbles embedded in a transparent medium. It calculates the attenuation through such medium of normally incident solar radiation. The attenuation depends on the size parameter, x; where x is 2 π times the ratio of bubble radius to the incident wavelength. By proper choice of the bubble size the attenuation can be made skew with respect to the wavelengths of incident solar radiation. A practical application of this theory has been made in the design of fenestration material. The bubble size can be so chosen as to attenuate the larger wavelengths considerably more than the shorter ones. This will suit the fenestration requirements of the tropical climate, insofar as the elimination of heat is desirable. A fenestration material (a Perspex sheet with air bubbles embedded in it) based on these considerations has been prepared and attenuation of normally incident radiation from an artificial source, simulating solar radiation, through it has been measured experimentally. The results are in good agreement with the theoretical calculations obtained for such case. The cut-off is about 14%.

The collision efficiency of small particles with spherical air bubbles

Trajectories are calculated for particles in the path of a spherical bubble rising in an infinite pool of liquid. From grazing trajectories, collision efficiences are calculated corresponding to values of a particle inertia parameter K down to 0·001 and a particle gravity parameter G up to 0·3 for both Stokes and potential flow fields around the bubble. Limiting values of collision efficiency corresponding to K → 0 are derived and are shown to be the same for both potential and Stokes solutions. The solutions of the equations of motion are verified experimentally and the existence of an optimum bubble size for recovering an ore particle by flotation is demonstrated. From a simplified description of a bubble assemblage, it is shown that the collision efficiency of particles with bubbles in a swarm can be several times as large as those calculated from a single sphere model even at large bubble separations.

A Method for Calculating the Output Pressure Waveform from an Air Gun

The signal from an air gun is assumed to behave as if it were derived from an oscillating spherical air bubble in water. The theory of the oscillations of spherical bubbles according to Gilmore is used in conjunction with experimental evidence to derive the complete set of equations necessary to calculate the shape of the radiated pressure waveform anywhere in the water. It is believed that this method will be useful in the design of signal processing techniques and also to improve the design of existing air gun profiling systems.

Motion of Spherical Gas Bubbles in a Viscous Liquid at Large Reynolds Numbers

An analysis is made for the motion of a gas bubble rising steadily in a quiescent liquid of infinite extent. The disturbed layer of the fluid, due to viscosity, on either side of the interface is thin when the Reynolds number is sufficiently large and thus makes possible a considerable simplification of the governing equations of motion. Simultaneous solutions of the boundary-layer equations for the flow outside and inside of the bubble are obtained by considering that the tangential velocity components and the shear stresses on both sides of the interface are equal. From the calculated external stress field, the drag of a spherical bubble with negligible flow separation is evaluated. Good agreement is obtained with published data for spherical air bubbles in four different organic liquids. The experimental drag curve due to Haberman and Morton for air bubbles rising in filtered water deviates from that predicted from the present theory. The theoretical results are applicable to any fluid sphere moving steadily in a substantially immiscible, viscous liquid provided that the internal circulation is complete, the flow separation is negligible, and the Reynolds number is sufficiently large.

Scattering of Light by an Air Bubble in Water

The angular distribution of intensity of light scattered from a collimated beam incident upon a spherical air bubble in water is determined for any bubble with radius greater than a few wavelengths of the incident light. The computations are for wavelength 5893 A and n=1.3334, the relative index of refraction of water at 15°C. One external reflection, five internal reflections, and six refractions are considered. A general equation for the geometric attenuation factor is developed, with special forms for external reflection and for zero angle of incidence. The limits of accuracy of the equations for angles of scattering in the neighborhood of 0° and 180° are evaluated. The effects of diffraction and interference are assumed to be negligible. The fractions of the incident light scattered from each of the six “surfaces” (successive points of incidence of any ray on the spherical surface) are shown by accurate curves for all angles of deviation. The corresponding geometric attenutation factors are similarly shown. Final intensity values are tabulated and are plotted both with rectangular and with polar coordinates.

The effect of the aeration of the water used in the determination of the mechanical equivalent of heat

In relation to Dr Jessel's experiments two matters are discussed. (i) The effects of the liberation of dissolved air on the specific heat of water. It is shown that heat of solution, surface energy, and latent heat of vaporization contribute negligible amounts to the specific heat of water. A theory of the equilibrium of spherical air bubbles in fully aerated water is developed. (ii) The reliability of the existing evidence as to the value of the mechanical equivalent of heat. The conclusion is reached that Dr Jessel's experiments do not invalidate the work of Jaeger and Steinwehr or of the writers on the mechanical equivalent of heat, and that the value as calculated by Birge, viz. 4.1852 × 107 erg/cal. at 15° C., is to be accepted.