Statistical mechanics of bubbly liquids

The dynamics of bubbles at high Reynolds numbers is studied from the viewpoint of statistical mechanics. Individual bubbles are treated as dipoles in potential flow. A virtual mass matrix of the system of bubbles is introduced, which depends on the instantaneous positions of the bubbles, and is used to calculate the energy of the bubbly flow as a quadratic form of the bubbles' velocities. The energy is shown to be the system's Hamiltonian and is used to construct a canonical ensemble partition function, which explicitly includes the total impulse of the suspension along with its energy. The Hamiltonian is decomposed into an effective potential due to the bubbles' collective motion and a kinetic term due to the random motion about the mean. An effective bubble temperature-a measure of the relative importance of the bubbles' relative to collective motion-is derived with the help of the impulse-dependent partition function. Two effective potentials are shown to operate: one due to the mean motion of the bubbles, dominates at low bubble temperatures, where it leads to their grouping in flat clusters normal to the direction of the collective motion, while the other, temperature-invariant, is due to the bubbles' position-dependent virtual mass and results in their mutual repulsion. Numerical evidence is presented for the existence of the effective potentials, the condensed and dispersed phases, and a phase transition

Virtual mass of an oscillating sphere within a fixed concentric shell

CER62AA84.July 30, 1962.Includes bibliographical references.The virtual mass of a sphere oscillating within a fixed concentric spherical shell filled with water was determined experimentally for seven sphere-to-shell diameter ratios between 0 and 0.865. Laboratory measurements of the virtual mass for diameter ratios less than 0.520 agreed closely with the theoretically predicted values based on a potential flow analysis. For ratios greater than 0.520 the virtual mass increased more rapidly than the potential flow theory indicated with an increase of 33% for a diameter ratio of 0.865

Virtual mass of regular polygon at angle of attack

In case of the accelerating motion like a sinusoidal motion, the virtual mass effect should be taken into account in equation of motion. Generally speaking we should find the appropriate mapping functions while they are restricted in some functions. To the author’s knowledge, the virtual mass of the regular polygon is not shown by the exact solution, while the regular polygon is used as a sectional shape of the structure like a building, a membrance of a structure and so on. It is shown that the virtual mass of an regular polygon has been calculated by using the exact conformal mapping, in which the angle of attack is taken into account. Results show that it is not dependent from the angle of attack except the flat plat (n=2). It means, although the body shape is not a point symmetry, there is no dependence of angle of attack on virtual mass except the flat plate

The effects of virtual mass force and particle aspect ratio on orientation of slender particles in a stirred tank

Fundamental knowledge on particle orientation is important for processing and utilizing irregular shape particles. The orientation of slender particles influences the application of slender particles in many fluidization processes, such as pulp and paper, catalytic reaction, air pollution control. In this paper, the effects of virtual mass force and aspect ratio on the orientation of a slender particle in a particle cloud are studied. Virtual mass force, also called added mass force, apparent mass force, is a force due to the relative acceleration of the phases. The definition of virtual mass force is defined by Kuo and Wallis (1): Please click Additional Files below to see the full abstract

Free vibration of transversely isotropic magneto-electro-elastic plates in contact with fluid

In this study, one investigates the free vibration behaviors of transversely isotropic Magneto-electro-elastic (MEE) rectangular plates in contact with fluid. In particular, one derives the mathematical formulation on the determination of added virtual mass for MEE rectangular plates with uniform thickness, which is in contact with fluid. A fluid-structure interaction model is constructed and analyzed on the basis of the recently derived differential equation governing the dynamical responses of the MEE rectangular plates. The added virtual mass incremental (AVMI) factor of the system is computed by adopting the proposed method and the added virtual mass can then be estimated. The natural frequencies based on the proposed approach play an important role in the vibration analysis and design of the fluidcontacting MEE plate

Hydromechanics of swimming propulsion. Part 3. Swimming and optimum movements of slender fish with side fins

This paper seeks to evaluate the swimming flow around a typical slender fish whose transverse cross-section to the rear of its maximum span section is of a lenticular shape with pointed edges, such as those of spiny fins, so that these side edges are sharp trailing edges, from which an oscillating vortex sheet is shed to trail the body in swimming. The additional feature of shedding of vortex sheet makes this problem a moderate generalization of the paper on the swimming of slender fish treated by Lighthill (1960a). It is found here that the thrust depends not only on the virtual mass of the tail-end section, but also on an integral effect of variations of the virtual mass along the entire body segment containing the trailing side edges, and that this latter effect can greatly enhance the thrust-making. The optimum shape problem considered here is to determine the transverse oscillatory movements a slender fish can make which will produce a prescribed thrust, so as to overcome the frictional drag, at the expense of the minimum work done in maintaining the motion. The solution is for the fish to send a wave down its body at a phase velocity c somewhat greater than the desired swimming speed U, with an amplitude nearly uniform from the maximum span section to the tail. Both the ratio U/c and the optimum efficiency are found to depend upon two parameters: the reduced wave frequency and a 'proportional-loading parameter', the latter being proportional to the thrust coefficient and to the inverse square of the wave amplitude. The basic mechanism of swimming is examined in the light of the principle of action and reaction by studying the vortex wake generated by the optimum movement