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The instability of small gas bubbles moving uniformly in various liquids is investigated experimentally and theoretically.The experiments consist of the measurement of the size and terminal velocity of bubbles at the threshold of instability in various liquids, together with the physical properties of the liquids. The results of the experiments indicate the existence of a universal stability curve. The nature of this curve strongly suggests that there are two separate criteria for predicting the onset of instability, namely, a critical Reynolds number (202) and a critical Weber number (1.26). The former criterion appears to be valid for bubbles moving uniformly in liquids containing impurities and in the somewhat more viscous liquids, whereas the latter criterion is for bubbles moving in pure, relatively inviscid liquids.The theoretical analysis is directed towards an investigation of the possibility of the interaction of surface tension and hydrodynamic pressure leading to unstable motions of the bubble, i.e. the existence of a critical Weber number. Accordingly, the theoretical model assumes the form of a general perturbation in the shape of a deformable sphere moving with uniform velocity in an inviscid, incompressible fluid medium of infinite extent. The calculations lead to divergent solutions above a certain Weber number, indicating, at least qualitatively, that the interaction of surface tension and hydrodynamic pressure can result in instabilities of the bubble motion.A subsequent investigation of the time-independent equations, however, shows the presence of large deformations in shape of the bubble prior to the onset of unstable motion, which is not compatible with the approximation of perturbing an essentially spherical bubble. This deformation and its possible effects on the stability calculation are therefore determined by approximate methods. From this it is concluded that the deformation of the bubble serves to introduce quantitative, but not qualitative, changes in the stability calculation.

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Measurements have been made of the heat-transfer rate to the stagnation point of catalytic spheres and cylinders placed in the slow flow of dissociated oxygen produced in a glow-discharge tube. The use of a rapid-response thin-film heat-transfer gauge permitted operation in a transient mode; that is, a step function of atoms was produced by suddenly turning on the rf discharge. Use of this technique leads to small error in the measurement of heat transfer. Operating conditions, range of pertinent parameters, as well as flow tube and probe diameters were selected to conform with the results of the theoretical analysis for this flow. Specifically, the Reynolds number based on diffusion Ua/D, where U is the flow velocity, a is the probe radius, and D the diffusion coefficient, was varied from about 0.2–0.8, and the catalytic parameter K = kwa/D, where kw is the effective speed of the surface reaction, took on values from about 0.3–1.7. The freestream atom concentration was determined by the familiar NO titration technique. Comparison of the measurements with the theoretical results has led to the determination of surface catalytic efficiency of silver oxide and oxygen atoms and the O–O2 diffusion coefficient. These values are γ = 0.15±15% and Dp = 200 cm2/sec·mm Hg±30%. Preliminary measurements of catalytic efficiency of other metals are also presented.

Measurements of the heat transfer from dissociated oxygen to the sidewall of a shock tube have been made over a wide range of operating conditions using the methods of thin-film thermometry. Numerical solutions of the equilibrium shock-tube wall boundary layer equations for several values of the Lewis number have been obtained. The results show the heat transfer to be very weakly dependent upon the Lewis number. This fact indicates the shock-tube wall boundary layer to be a source for experimental determinations of the viscosity coefficient of dissociated gases. Experimental data obtained in the equilibrium boundary layer regime agree with the theory at the low temperatures, and rise above the theoretical curves at the higher temperatures. This difference between theory and experiment is attributed to the uncertainty in the calculated viscosity coefficient used in the theory. The experiments were then used to determine new values for the viscosity coefficient of high temperature, dissociated oxygen. These values are considerably higher than those predicted theoretically using a Lennard-Jones potential or Sutherland's formula.