Effect of Vibrations on the Motion of Small Gas Bubbles in a Liquid

Abstract

If a transparent test tank partially filled with water is strongly vibrated, small gas bubbles originated by surface disturbances appear in the lower parts of the vessel. These bubbles do not rise to the surface as would be expected from their buoyancy, but perform vibratory motions at the bottom or at the sides of the tank. As the rocket engine of a missile causes heavy vibrations, the possibility of the occurrence of similar bubble phenomena in fuel tanks is worth consideration. The present paper is a step toward an explanation of the complicated phenomena observed in the test tank. The basic equations for the motion of small gas bubbles in an inviscid liquid in the presence of harmonic vibrations are derived, and the mechanism which may make bubbles move contrary to gravity forces is explained. Applying the theory to cylindrical tanks, it is found that for sufficiently strong vibrations there are regions in the tank in which bubbles move downward and, further, that there are points where bubbles will collect. The paper does not treat all the phenomena observed in the test tank; e.g., the important question of the creation of the bubbles at the surface is left for future work. Nomenclature a = reference (nominal) radius of bubble C, C = coefficients in Equations [39, 41] defining the acceleration in an elastic vessel / = f(h,r) = distribution of the applied dynamic pressure (Eqs. [29,39]) g = gravitational constant h = depth of bubble below surface; specifically, depth at which bubble oscillates without rising IQ = modified Bessel function M = total mass of fluid in vessel N = number defining the applied acceleration x = Ng cos cot p = gas pressure in bubble p 0 -ullage pressure in vessel Pi = p 0 -f hg static pressure at depth h p -dynamic pressure due to vibration P = potential energy r = radial coordinate (Fig. 4) R = radius of cylindrical tank t = time T -kinetic energy u = vertical component of fluid velocity U ~v = velocity (vector) of a fluid particle v = volume; specifically, volume of bubble x(t)= displacement of vessel with respect to a reference line z(t) -relative depth of bubble below the surface which moves with the velocity x(t)

Motion of a gas bubble in fluid under vibration

“…The present study appreciably supplements results of the papers [13] and [4]. The supposition that the effect of gas bubble sinking in a vertically oscillating fluid-filled volume can occur in the absence of the standing wave, which is conditional on the gasfluid medium compressibility, i.e.…”

“…In expression (13) μ is the dynamic viscosity of the fluid, and V is the velocity of the gas bubble motion. Formulas (12) and (13), strictly speaking, correspond to the case of motion with constant velocity.…”

“…The motion of small ("before resonant") bubbles in an oscillating incompressible fluid was examined by Bleich [13], who obtained an expression for the critical depth, which does not allow for fluid viscosity, and experimentally confirmed the possibility of gas bubble sinking starting from this depth. However, Bleich did not solve the rather complicated differential equation of gas bubble motion considering resistance forces, and so he did not obtain an expression for its average velocity; the experimental part of the research is also rather partial.…”

Research of process of filtration of salt water by bulk filters with the use of vibration

“…Тяжелые крупные частицы перемещаются в верхние слои, тогда как «мелочь» формирует уплотненный слой в нижней части. Эти и подобные явления рассматривались во многих публика-циях, принадлежащих, в том числе, выдающимся учёным [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Настоящая работа развивает и дополняет эти исследования.…”

Surface and volumetric effects in a fluid subjected to high-frequency vibration

“…Up to now, two different mechanisms explaining the effect of gas bubble sinking have been proposed: 'wave' [11][12][13][14] and 'nonwave', 'vibrational'. 15,16 The first explanation brings forward the wave amplitude gradient as a determining factor, while the second one is apt to explain the phenomenon by bubble compressibility. The authors of this article endeavor to consider both the mechanisms in their joint interaction by studying gas bubble motion in an oscillating fluid-filled vessel while taking into account compressibility both of the bubble and of the surrounding gas-saturated turbulent layer.…”