CaltechAUTHORS: Combined
https://feeds.library.caltech.edu/people/Plesset-M-S/combined.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 26 Jun 2024 13:17:46 -0700Relativistic Wave Mechanics of Electrons Deflected by a Magnetic Field
https://resolver.caltech.edu/CaltechAUTHORS:PLEpr30
Year: 1930
It is shown that the relativistic wave equation for electrons in a uniform magnetic field leads to the same wave function as that already deduced by Page from the non-relativistic equation. As in the latter case the motion at right angles to the field is quantized.An expression is found for the current density from the relativistic wave equation. The relativistic expression differs from the non-relativistic only by a constant factor which does not affect the calculation of the mean radii of curvature of the electron current. Hence, for the relativistic case, as for the non-relativistic, the mean radius of curvature is less than that expected on the classical theory. It follows that the classical relativistic relation between ((epsilon)/(mu)) and the mean radius of curvature upon deflection gives a value of ((epsilon)/(mu)) which is too large.https://resolver.caltech.edu/CaltechAUTHORS:PLEpr30The Dirac Electron in Simple Fields
https://resolver.caltech.edu/CaltechAUTHORS:PLEpr32
Year: 1932
DOI: 10.1103/PhysRev.41.278
The relativity wave equations for the Dirac electron are transformed in a simple manner into a symmetric canonical form. This canonical form makes readily possible the investigation of the characteristics of the solutions of these relativity equations for simple potential fields. If the potential is a polynomial of any degree in x, a continuous energy spectrum characterizes the solutions. If the potential is a polynomial of any degree in 1/x, the solutions possess a continuous energy spectrum when the energy is numerically greater than the rest-energy of the electron; values of the energy numerically less than the rest-energy are barred. When the potential is a polynomial of any degree in r, all values of the energy are allowed. For potentials which are polynomials in 1/r of degree higher than the first, the energy spectrum is again continuous. The quantization arising for the Coulomb potential is an exceptional case.https://resolver.caltech.edu/CaltechAUTHORS:PLEpr32On the Production of the Positive Electron
https://resolver.caltech.edu/CaltechAUTHORS:OPPpr33
Year: 1933
DOI: 10.1103/PhysRev.44.53.2
The experimental discovery of the positive electron gives us a striking confirmation of Dirac's theory od the electron, and of his most recent attempts to gice a consistent interpretation of the formalism of that theory. As is well know, and quite apart from the difficulties connected with the existence and stability of the electron itself, the theory in its original form led to very grave difficulties in all problems involving length sof the order of the Compton wavelength, in that it predicted the occurrence of electrons of negative kinetic energy, in gross conflict with experience. Dirac has pointed out that we might obtain a consistent theory by assuming that it is only the absence of electrons of negative kinetic energy that has a physical meaning; in this way one could avoid the occurrence of the critical transitions, and yet understand the validity of many correct predictions of the theory, such as the formula for relativistic fine structure, and the Thomson and Klein-Nishina scattering formulae: only the physical interpretation of the formalism was changed, and involved in many cases the appearance pairs of electrons and "antielectrons" -- particles of electronic mass and of positive charge numerically equal to that of the electron. It was this aspect of the theory which remained dubious; and the discovery of the positive electron appears to settle that doubt.https://resolver.caltech.edu/CaltechAUTHORS:OPPpr33Note on an Approximation Treatment for Many-Electron Systems
https://resolver.caltech.edu/CaltechAUTHORS:MOLpr34
Year: 1934
DOI: 10.1103/PhysRev.46.618
A perturbation theory is developed for treating a system of n electrons in which the Hartree-Fock solution appears as the zero-order approximation. It is shown by this development that the first order correction for the energy and the charge density of the system is zero. The expression for the second-order correction for the energy greatly simplifies because of the special property of the zero-order solution. It is pointed out that the development of the higher approximation involves only calculations based on a definite one-body problem.https://resolver.caltech.edu/CaltechAUTHORS:MOLpr34Inelastic Scattering of Quanta with Production of Pairs
https://resolver.caltech.edu/CaltechAUTHORS:PLEpr35
Year: 1935
DOI: 10.1103/PhysRev.48.302
The problem of accounting for the anomalous scattering of gamma-rays suggests the importance of investigating the probability of processes in which an incoming quantum produces an electron-positron pair in the field of a nucleus, going on in a new direction with diminished energy. To determine the cross section in the general case is difficult, but an estimate of the total magnitude of the effect in the energy range of interest is obtained by a calculation of the cross section as a function of the energies of the incident and scattered quanta and the angle between them in the limit where the electron-positron pair is produced with small kinetic energy.
While there exists a possibility of observing the process under suitable experimental conditions, the cross section is found to be too small to contribute appreciably to the production of the hard component in the radiation from heavy elements exposed to penetrating gamma-rays.https://resolver.caltech.edu/CaltechAUTHORS:PLEpr35Note on Neutron-Proton Exchange Interaction
https://resolver.caltech.edu/CaltechAUTHORS:PLEpr36
Year: 1936
DOI: 10.1103/PhysRev.49.551
The matrix elements of the interaction between a proteon with coordinates x1 and a neutron with coordinates x2 as proposed by Majorana 2 may be written as ....https://resolver.caltech.edu/CaltechAUTHORS:PLEpr36On the Equality of the Proton-Proton and Proton-Neutron Interactions
https://resolver.caltech.edu/CaltechAUTHORS:BROpr39
Year: 1939
DOI: 10.1103/PhysRev.56.841.2
A comparison of the 1S proton-proton interaction and the 1S proton-neutron interaction has been made recently by Breit, Hoisington, Share, and Thaxton. It is the purpose of this letter to add a remark to the subject. With the meson type of potential, [C x e^(-lambda x r)]/r x lambda, a variational calculation has been made of the binding energy of H3 of high accuracy (error <0.1 percent).https://resolver.caltech.edu/CaltechAUTHORS:BROpr39On the Classical Model of Nuclear Fission
https://resolver.caltech.edu/CaltechAUTHORS:20140805-142755745
Year: 1941
DOI: 10.1119/1.1991623
The first experiments on neutron bombardment
of various elements carried out by
Fermi and his collaborators included the study
of the group of activities observed in uranium
which were at that time ascribed to transuranic
elements. The great number of studies following
this first work led finally to the results of Hahn
and Strassmann which showed clearly that many
of the activities ascribed to transuranic elements
came, instead, from nuclei of approximately
half the mass of uranium. The startling conclusion
that these activities must arise from the
splitting of the uranium nucleus under neutron
bombardment into two fragment nuclei was
pointed out by Meitner and Frisch, and was
quickly confirmed by subsequent experiments. In
the first theoretical discussion of this new type of
nuclear reaction, Meitner and Frisch proposed
the name fission for the process, and compared it
with the splitting that may take place in a liquid
drop in oscillation. This model was supported by
Bohr who correlated it with other nuclear
properties and, at the same time, emphasized
how far the phenomenon of nuclear fission may
be described classically. A very complete theoretical
discussion of both the classical and
quantum aspects of fission was given by Bohr and
Wheeler, and it is proposed here to describe
some of the classical theory of fission developed
by these authors.https://resolver.caltech.edu/CaltechAUTHORS:20140805-142755745Drag in Cavitating Flow
https://resolver.caltech.edu/CaltechAUTHORS:PLErmp48
Year: 1948
DOI: 10.1103/RevModPhys.20.228
The free streamline theory has been used for evaluation of the cavity drag of symmetrical wedges of arbitrary angle. The required conformal transformation is derived explicitly. This calculation is an extension of Riabouchinsky's theory of the cavity drag of a flat plate. As an approximation, the pressure distribution for a two-dimensional wedge is used to calculate the cavity drag of the corresponding cone of revolution. A comparison of the result of this approximation with experimental measurements made by Reichardt shows good agreement.https://resolver.caltech.edu/CaltechAUTHORS:PLErmp48The Dynamics of Cavitation Bubbles
https://resolver.caltech.edu/CaltechAUTHORS:20140808-114249321
Year: 1949
Three regimes of liquid flow over a body are defined,
namely: (a) noncavitating flow; (b) cavitating flow with a
relatively small number of cavitation bubbles in the field
of flow; and (c) cavitating flow with a single large cavity
about the body. The assumption is made that, for the
second regime of flow, the pressure coefficient in the flow
field is no different from that in the noncavitating flow.
On this basis, the equation of motion for the growth and
collapse of a cavitation bubble containing vapor is derived
and applied to experimental observations on such bubbles.
The limitations of this equation of motion are pointed
out, and include the effect of the finite rate of evaporation
and condensation, and compressibility of vapor and
liquid. A brief discussion of the role of "nuclei" in the
liquid in the rate of formation of cavitation bubbles is
also given.https://resolver.caltech.edu/CaltechAUTHORS:20140808-114249321The Analogy between Hydraulic Jumps in Liquids and Shock Waves in Gases
https://resolver.caltech.edu/CaltechAUTHORS:20140805-165739483
Year: 1950
DOI: 10.1063/1.1699641
The theory of the hydraulic jump is presented briefly, and the analogy between this phenomenon and the compression shock wave in gases is pointed out. The results of experimental measurements of hydraulic‐jump intersections on a water table are reported. Considerable disagreement between theory and experiment is found. Other investigators have noted a disagreement between theory and experiment for compression‐shock intersections in gases. The discrepancy in the aerodynamic case appears unlike that found in the hydraulic case. Possible reasons for the discrepancy in the hydraulic case are discussed; some sources of error are peculiar to hydraulic jumps and do not apply to compression shocks. Such factors limit the utility of the water table as an analog device.https://resolver.caltech.edu/CaltechAUTHORS:20140805-165739483Wall Effects in Cavity Flow - I
https://resolver.caltech.edu/CaltechAUTHORS:20140729-162818727
Year: 1950
[no abstract]https://resolver.caltech.edu/CaltechAUTHORS:20140729-162818727On the Stability of Gas Bubbles in Liquid-Gas Solutions
https://resolver.caltech.edu/CaltechAUTHORS:EPSjcp50
Year: 1950
DOI: 10.1063/1.1747520
With the neglect of the translational motion of the bubble, approximate solutions may be found for the rate of solution by diffusion of a gas bubble in an undersaturated liquid-gas solution; approximate solutions are also presented for the rate of growth of a bubble in an oversaturated liquid-gas solution. The effect of surface tension on the diffusion process is also considered.https://resolver.caltech.edu/CaltechAUTHORS:EPSjcp50Transmission of Gamma-Rays through Large Thicknesses of Heavy Materials
https://resolver.caltech.edu/CaltechAUTHORS:PEEpr51
Year: 1951
DOI: 10.1103/PhysRev.81.430
A study has been made of the feasibility of accurate numerical determinations of the transmission of gamma-rays through large thicknesses of materials. The first procedure investigated consists in regarding the total probability of photon transmission, Nt, as the sum of the probabilities Nn, where Nn is the probability of photon transmission with exactly n scatterings. The total expected transmitted energy, Et is similarly considered to be given by ΣEn. A numerical calculation of Nn and En has been made for n=0, 1, 2, 3 for a slab of uranium 20 cm thick, upon which photons are incident normally with energy α=10 mc2. The maximum value of Nn/N0 occurs at n=2 and of En/E0 at n=1. These calculations are also adapted to a slab of lead 35 cm thick. Consideration has been given to the behavior of Nn and En for large n, and estimates are thereby made for Nt and Et. The second procedure consists in deriving the transmission through a thick slab from a succession of transmissions through thin slabs. The transformation of an incident photon distribution into the distribution transmitted through a thin slab is conveniently expressed as a matrix, and the total transmission is then given by the iteration of the matrix on the successive transmitted distributions. Numerical results obtained by this procedure for particular incident photon distributions are presented.https://resolver.caltech.edu/CaltechAUTHORS:PEEpr51Scattering and Absorption of Gamma-Rays
https://resolver.caltech.edu/CaltechAUTHORS:PLEjap51
Year: 1951
DOI: 10.1063/1.1699954
A formulation is presented of the scattering and absorption of gamma-rays in different materials. The range of gamma-ray energies considered is from 1 to 10 mc^2. Results are given for the transmission of gamma-rays through air and lead.https://resolver.caltech.edu/CaltechAUTHORS:PLEjap51A Nonsteady Heat Diffusion Problem with Spherical Symmetry
https://resolver.caltech.edu/CaltechAUTHORS:PLEjap52
Year: 1952
DOI: 10.1063/1.1701985
A solution in successive approximations is presented for the heat diffusion across a spherical boundary with radial motion. The approximation procedure converges rapidly provided the temperature variations are appreciable only in a thin layer adjacent to the spherical boundary. An explicit solution for the temperature field is given in the zero order when the temperature at infinity and the temperature gradient at the spherical boundary are specified. The first-order correction for the temperature field may also be found. It may be noted that the requirements for rapid convergence of the approximate solution are satisfied for the particular problem of the growth or collapse of a spherical vapor bubble in a liquid when the translational motion of the bubble is neglected.https://resolver.caltech.edu/CaltechAUTHORS:PLEjap52On the Stability of Fluid Flows with Spherical Symmetry
https://resolver.caltech.edu/CaltechAUTHORS:PLEjap54b
Year: 1954
DOI: 10.1063/1.1721529
The conditions for the stability or instability of the interface between two immiscible incompressible fluids in radial motion are deduced. The stability conditions derived by Taylor for the interface of two fluids in plane motion do not apply to spherical flows without significant modifications.https://resolver.caltech.edu/CaltechAUTHORS:PLEjap54bThe Growth of Vapor Bubbles in Superheated Liquids
https://resolver.caltech.edu/CaltechAUTHORS:PLEjap54a
Year: 1954
DOI: 10.1063/1.1721668
The growth of a vapor bubble in a superheated liquid is controlled by three factors: the inertia of the liquid, the surface tension, and the vapor pressure. As the bubble grows, evaporation takes place at the bubble boundary, and the temperature and vapor pressure in the bubble are thereby decreased. The heat inflow requirement of evaporation, however, depends on the rate of bubble growth, so that the dynamic problem is linked with a heat diffusion problem. Since the heat diffusion problem has been solved, a quantitative formulation of the dynamic problem can be given. A solution for the radius of the vapor bubble as a function of time is obtained which is valid for sufficiently large radius. This asymptotic solution covers the range of physical interest since the radius at which it becomes valid is near the lower limit of experimental observation. It shows the strong effect of heat diffusion on the rate of bubble growth. Comparison of the predicted radius-time behavior is made with experimental observations in superheated water, and very good agreement is found.https://resolver.caltech.edu/CaltechAUTHORS:PLEjap54aOn the Dynamics of Small Vapor Bubbles in Liquids
https://resolver.caltech.edu/CaltechAUTHORS:20140729-155852145
Year: 1955
When a vapor bubble in a liquid changes size, evaporation
or condensation of the vapor takes place at the surface of the bubble. Because of the latent heat requirement of evaporation, a change in bubble size must
therefore be accompanied by a heat transfer across the bubble wall, such as to cool the surrounding liquid when the bubble grows (or heat it when the bubble
becomes smaller). Since the vapor pressure at the bubble wall is determined by the temperature there, the result of a cooling of the liquid is a decrease of the
vapor pressure, and this causes a decrease in the rate of bubble growth. A similar effect occurs during the collapse of a bubble which tends to slow down the collapse.
In order to obtain a satisfactory theory of the behavior of a vapor bubble in a liquid, these heat transfer effects must be taken into account.
In this paper, the equations of motion for a spherical vapor bubble will be derived and applied to the case of a bubble expanding in superheated liquid and a bubble collapsing in liquid below its boiling point. Because of the inclusion of the heat transfer effects, the equations are nonlinear, integro-differential
equations. In the case of the collapsing bubble, large temperature variations occur; therefore, tabulated vapor pressure data were used, and the equations of
motion were integrated numerically. Analytic solutions are obtainable for the case of the expanding bubble if the period of growth is subdivided into several
regimes and the simplifications possible in each regime are utilized. The growth is considered here only during the time that the bubble is small. An asymptotic
solution of the equations of motion, valid when the bubble becomes large (i.e. observable), has been presented previously, together with experimental verification.
We shall be specifically concerned in the following discussion with the dynamics of vapor bubbles in water. This restriction was made for convenience
only, since the theory is applicable without modification to many other liquids.https://resolver.caltech.edu/CaltechAUTHORS:20140729-155852145On the Mechanism of Cavitation Damage
https://resolver.caltech.edu/CaltechAUTHORS:20140826-140952946
Year: 1955
A new method for producing cavitation damage in the
laboratory is described in which the test specimen has no
mechanical accelerations applied to it in contrast with the
conventional magnetostriction device. Alternating pressures
are generated in the water over the specimen by exciting
a resonance in the "water cavity." By this means
the effects of cavitation have been studied for a variety of
materials. Photomicrographs have been taken of several
ordinary (polycrystalline) specimens and also of zinc
monocrystals. The zinc monocrystal has been exposed to
cavitation damage on its basal plane and also on its
twinning plane. X-ray analyses have been made of polycrystalline specimens with various exposures to cavitation. The results show that plastic deformation occurs in the specimens so that the damage results from cold-work of the material which leads to fatigue and failure. A variety of materials has been exposed to intense cavitation for extended periods to get a relative determination of their resistance to cavitation damage. It is found that, roughly speaking, hard materials of high tensile strengths are the most resistant to damage. While this survey is not complete, it has been found that titanium 150-A and tungsten are the most resistant to damage of the materials tested. Cavitation-damage studies, which have been carried out in liquid toluene and in a helium atmosphere, show that chemical effects can be, at most, of secondary significance.https://resolver.caltech.edu/CaltechAUTHORS:20140826-140952946Ion Exchange Kinetics: A Nonlinear Diffusion Problem
https://resolver.caltech.edu/CaltechAUTHORS:EngDivRpt85-7
Year: 1957
Ideal limiting laws are calculated for the kinetics of particle diffusion controlled ion exchange processes involving ions of different mobilities between spherical ion exchanger beads of uniform size and a well-stirred solution, The calculations are based on the nonlinear Nernst-Planck equations of ionic motion, which take into account the effect of the electric forces (diffusion potential) within the system. Numerical results for counter ions of equal valence and six different mobility ratios are presented. They were obtained by use of a digital computer. This approach contains the well-known solution to the corresponding linear problem as a limiting case. An explicit empirical formula approximating the numerical results is given.https://resolver.caltech.edu/CaltechAUTHORS:EngDivRpt85-7Ion Exchange Kinetics. A Nonlinear Diffusion Problem
https://resolver.caltech.edu/CaltechAUTHORS:HELjcp58
Year: 1958
DOI: 10.1063/1.1744149
Ideal limiting laws are calculated for the kinetics of particle diffusion controlled ion exchange processes involving ions of different mobilities between spherical ion exchanger beads of uniform size and a well-stirred solution. The calculations are based on the nonlinear Nernst-Planck equations of ionic motion, which take into account the effect of the electric forces (diffusion potential) within the system. Numerical results for counter ions of equal valence and six different mobility ratios are presented. They were obtained by use of a digital computer. This approach contains the well-known solution to the corresponding linear problem as a limiting case. An explicit empirical formula approximating the numerical results is given.https://resolver.caltech.edu/CaltechAUTHORS:HELjcp58Ion exchange kinetics. A nonlinear diffusion problem. II. Particle diffusion controlled exchange of univalent and bivalent ions
https://resolver.caltech.edu/CaltechAUTHORS:PLEjcp58
Year: 1958
DOI: 10.1063/1.1744656
The differential equation derived previously which describes the particle diffusion controlled ion exchange between spherical beads of uniform size and a well-stirred solution is solved numerically for the exchange of monovalent ions for bivalent ions, and of bivalent ions for monovalent ions. The approach is based on the Nernst-Planck equations of ionic motion. Numerical results for six different mobility ratios are presented and discussed. They were obtained by use of a digital computer. An explicit equation approximating the numerical data is given.https://resolver.caltech.edu/CaltechAUTHORS:PLEjcp58Transient effects in the distribution of carbon-14 in nature
https://resolver.caltech.edu/CaltechAUTHORS:PLEpnas60
Year: 1960
A prerequisite for accurate dating by means of carbon-14 is the existence of a steady state in the specific activity of the carbon in the atmosphere. The studies(1) which have been made of carbon activity supported the view that there was a state of dynamic equilibrium in the carbon exchange between natural reservoirs. A disturbance in this state is known to arise from the discharge of the combustion products from fossil fuels into the atmosphere.https://resolver.caltech.edu/CaltechAUTHORS:PLEpnas60Theory of gas bubble dynamics in oscillating pressure fields
https://resolver.caltech.edu/CaltechAUTHORS:PLEpof60
Year: 1960
DOI: 10.1063/1.1706152
The behavior of a permanent gas bubble in a liquid with an oscillating pressure field is analyzed with a linearized theory. If the assumption is made that conditions within the bubble are uniform, the thermodynamic relations found are as expected; i.e., at low frequencies the bubble behaves isothermally and at high frequencies the behavior becomes adiabatic. However, a more detailed analysis, which allows the bubble interior to vary not only in time but also in space, leads to an average isothermal behavior for the bubble even in the high-frequency limit.https://resolver.caltech.edu/CaltechAUTHORS:PLEpof60On the Propagation of Sound in a Liquid Containing Gas Bubbles
https://resolver.caltech.edu/CaltechAUTHORS:HSIpof60
Year: 1961
DOI: 10.1063/1.1706447
The theory of the propagation of sound in a homogeneous gas including the effect of heat conduction is presented for the purpose of clarifying the underlying thermodynamic process. The propagation of sound in a liquid with a homogeneous and isotropic distribution of gas bubbles is then considered. The bubbles are assumed to be sufficiently small and numerous so that the mixture can be taken to be a uniform medium. The effect of heat conduction is included. If f is the ratio of gas volume in the mixture to liquid volume, it is shown for the range of f of general interest that the acoustic condensations and rarefactions of the gaseous portion of the medium are essentially isothermal. It is also found that the attenuation of an acoustic disturbance by heat conduction is quite small.https://resolver.caltech.edu/CaltechAUTHORS:HSIpof60Theory of the acoustic absorption by a gas bubble in a liquid
https://resolver.caltech.edu/CaltechAUTHORS:HydroLabRpt85-19
Year: 1961
A complete analysis of acoustic absorption by a spherical gas bubble is developed by the application of the classical Rayleigh method. The absorption considered is that due to the viscosity and heat conduction of the gas bubble. Specific results are presented for the S-wave scatter and absorption for the case of an air bubble in water, and the absorption effects of viscosity and heat conduction alone are calculated explicitly. The results found here are of similar magnitude to those found by Pfriem and Spitzer who used an approximate procedure.https://resolver.caltech.edu/CaltechAUTHORS:HydroLabRpt85-19Reply to Comments of P. W. Smith, Jr.
https://resolver.caltech.edu/CaltechAUTHORS:20120905-105612094
Year: 1962
DOI: 10.1063/1.1706607
In his comments on this subject, Smith has put
emphasis on the special nature of the plane-wave
solution in acoustic problems. It is perhaps unnecessary
to defend the importance of the plane-wave
solution in a linear theory.https://resolver.caltech.edu/CaltechAUTHORS:20120905-105612094The collapse of a spherical cavity in a compressible liquid
https://resolver.caltech.edu/CaltechAUTHORS:DivEngAppSciRpt85-24
Year: 1963
This paper presents numerical solutions for the flow in the vicinity of a collapsing spherical bubble in water. The bubble is assumed to contain a small amount of gas and the solutions are taken beyond the point where the bubble reaches its minimum radius up to the stage where a pressure wave forms and propagates outwards into the liquid. The motion up to the point where the minimum radius is attained, is found by solving the equations of motion both in the Lagrangian and in the characteristic forms. These are in good agreement with each other and also with the approximate theory of Gilmore which is demonstrated to be accurate over a wide range of Mach number. The liquid flow after the minimum radius has been attained is determined from a solution of the Lagrangian equations. It is shown that an acoustic approximation is quite valid for fairly high pressures and this fact is used to determine the peak intensity of the pressure wave at a distance from the center of collapse. It is estimated in the case of typical cavitation bubbles that such intensities are sufficient to cause cavitation damage.https://resolver.caltech.edu/CaltechAUTHORS:DivEngAppSciRpt85-24Collapse and rebound of a spherical bubble in water
https://resolver.caltech.edu/CaltechAUTHORS:HICpof64
Year: 1964
DOI: 10.1063/1.1711058
Some numerical solutions are presented which describe the flow in the vicinity of a collapsing spherical bubble in water. The bubble is assumed to contain a small amount of gas and the solutions are taken beyond the point where the bubble reaches its minimum radius up to the stage where a pressure wave forms which propagates outwards into the liquid. The motion during collapse, up to the point where the minimum radius is attained, is determined by solving the equations of motion both in the Lagrangian and in the characteristic form. These are found to be in good agreement with each other and also with the approximate theory of Gilmore which is shown to be accurate over a wide range of Mach number. The liquid flow during the rebound, which occurs after the minimum radius has been attained, is determined from a solution of the Lagrangian equations. It is shown that an acoustic approximation is valid even for fairly high pressures, and this fact is used to determine the peak intensity of the pressure wave as it moves outwards at a distance from the center of collapse. It is estimated in the case of typical cavitation bubbles that such intensities are sufficient to cause cavitation damage.https://resolver.caltech.edu/CaltechAUTHORS:HICpof64Shockwaves from Cavity Collapse
https://resolver.caltech.edu/CaltechAUTHORS:20151120-092553985
Year: 1966
DOI: 10.1098/rsta.1966.0047
The determination of the stresses produced by cavity collapse has been of interest since Rayleigh's discussion of the problem. One theoretical calculation relating to this problem is the magnitude of the pressure pulse which is radiated when a spherical bubble collapses and rebounds in a liquid. A calculation of this kind has been made although it was necessary to idealize the physical situation. The peak pressures predicted by this treatment were of the order of some thousands of atmospheres and could, therefore, furnish a mechanism for the damage of solid surfaces. Since these peak pressures decrease rapidly with distance from the centre of the bubble, the solid boundary must be in the immediate neighbourhood of the bubble in order that damage may be produced by this mechanism. In this situation spherical collapse or rebound cannot be expected to take place. An additional disturbance from spherical symmetry arises because the spherical shape is unstable. There is now both theoretical and experimental evidence that jet formation may develop from this unstability, and could under suitable conditions give rise to cavitation damage. This evidence is briefly discussed.https://resolver.caltech.edu/CaltechAUTHORS:20151120-092553985Collapse of an initially spherical vapor cavity in the neighborhood of a solid boundary
https://resolver.caltech.edu/CaltechAUTHORS:rptno85-49
Year: 1970
Vapor bubble collapse problems lacking spherical symmetry are solved here using a numerical method designed especially for these problems. Viscosity and compressibility in the liquid are neglected. The method uses finite time steps and features an iterative technique for applying the boundary conditions at infinity directly to the liquid at a finite distance from the free surface. Two specific cases of initially spherical bubbles collapsing near a plane solid wall were simulated: a bubble initially in contact with the wall, and a bubble initially half its radius from the wall at the closest point. It is shown that the bubble develops a jet directed towards the wall rather early in the collapse history. Free surface shapes and velocities are presented at various stages in the collapse. Velocities are scaled like (Δp/ρ)^1/2 where ρ is the density of the liquid and Δp is the constant difference between the ambient liquid pressure and the pressure in the cavity. For Δp/ρ = 10^6 (cm/sec)^2 ~ 1 atm./density of water the jet had a speed of about 130 m/sec in the first case and 170 m/sec in the second when it struck the opposite side of the bubble. Such jet velocities are of a magnitude which can explain cavitation damage. The jet develops so early in the bubble collapse history that compressibility effects in the liquid and the vapor are not important.https://resolver.caltech.edu/CaltechAUTHORS:rptno85-49Collapse of an initially spherical vapour cavity in the
neighbourhood of a solid boundary
https://resolver.caltech.edu/CaltechAUTHORS:20120809-090900707
Year: 1971
DOI: 10.1017/S0022112071001058
Vapour bubble collapse problems lacking spherical symmetry are solved here using a numerical method designed especially for these problems. Viscosity and compressibility in the liquid are neglected. Two specific cases of initially spherical bubbles collapsing near a plane solid wall were simulated: a bubble initially in contact with the wall, and a bubble initially half its radius from the wall at the closest point. It is shown that the bubble develops a jet directed towards the wall rather early in the collapse history. Free surface shapes and velocities are presented at various stages in the collapse. Velocities are scaled like (Δp/ρ)^½ where ρ is the density of the liquid and Δp is the constant difference between the ambient liquid pressure and the pressure in the cavity. For Δp/ρ=10^6cm^2/sec^2 ≈ 1 atm/density of water
the jet had a speed of about 130m/sec in the first case and 170m/sec in the second when it struck the opposite side of the bubble. Such jet velocities are of a magnitude which can explain cavitation damage. The jet develops so early in the bubble collapse history that compressibility effects in the liquid and the vapour are not important.https://resolver.caltech.edu/CaltechAUTHORS:20120809-090900707Viscous effects in Rayleigh-Taylor instability
https://resolver.caltech.edu/CaltechAUTHORS:20120809-152411650
Year: 1974
DOI: 10.1063/1.1694570
A simple, physical approximation is developed for the effect of viscosity for stable interfacial waves and for the unstable interfacial waves which correspond to Rayleigh‐Taylor instability. The approximate picture is rigorously justified for the interface between a heavy fluid (e.g., water) and a light fluid (e.g., air) with negligible dynamic effect. The approximate picture may also be rigorously justified for the case of two fluids for which the differences in density and viscosity are small. The treatment of the interfacial waves may easily be extended to the case where one of the fluids has a small thickness; that is, the case in which one of the fluids is bounded by a free surface or by a rigid wall. The theory is used to give an explanation of the bioconvective patterns which have been observed with cultures of microorganisms which have negative geotaxis. Since such organisms tend to collect at the surface of a culture and since they are heavier than water, the conditions for Rayleigh‐Taylor instability are met. It is shown that the observed patterns are quite accurately explained by the theory. Similar observations with a viscous liquid loaded with small glass spheres are described. A behavior similar to the bioconvective patterns with microorganisms is found and the results are also explained quantitatively by Rayleigh‐Taylor instability theory for a continuous medium with viscosity.https://resolver.caltech.edu/CaltechAUTHORS:20120809-152411650Comments on "Rayleigh–Taylor instability of thin viscous layers"
https://resolver.caltech.edu/CaltechAUTHORS:PLEpof76
Year: 1976
DOI: 10.1063/1.861480
In a paper by Craik, (1) frequent references are made to our paper (2) which we believe are incorrect. It may also be pointed out that quite unusual circumstances would be required to provide a physical basis for Craik's analysis; the experiments described in his paper are not appropriately explained by his analysis.https://resolver.caltech.edu/CaltechAUTHORS:PLEpof76Flow of vapour in a liquid enclosure
https://resolver.caltech.edu/CaltechAUTHORS:20120806-144133110
Year: 1976
DOI: 10.1017/S002211207600253X
A solution is developed for the flow of a vapour in a liquid enclosure in which different portions of the liquid wall have different temperatures. It is shown that the vapour pressure is very nearly uniform in the enclosure, and an expression for the net vapour flux is deduced. This pressure and the net vapour flux are readily expressed in terms of the temperatures on the liquid boundary. Explicit results are given for simple liquid boundaries: two plane parallel walls at different temperatures and concentric spheres and cylinders at different temperatures. Some comments are also made regarding the effects of unsteady liquid temperatures and of motions of the boundaries. The hemispherical vapour cavity is also discussed because of its applicability to the nucleate boiling problem.https://resolver.caltech.edu/CaltechAUTHORS:20120806-144133110Bubble Dynamics and Cavitation
https://resolver.caltech.edu/CaltechAUTHORS:20120809-071458384
Year: 1977
DOI: 10.1146/annurev.fl.09.010177.001045
N/Ahttps://resolver.caltech.edu/CaltechAUTHORS:20120809-071458384On the stability of gas bubbles in liquid-gas solutions
https://resolver.caltech.edu/CaltechAUTHORS:20201001-145812343
Year: 1982
DOI: 10.1007/978-94-009-7532-3_12
It was shown some time ago by use of diffusion theory that a gas bubble in a liquid-gas solution was unstable. This problem has been reconsidered recently in two papers both of which propose to develop a stability analysis solely from thermodynamic considerations. The first of these studies purports to find stability for a gas bubble in a liquid-gas solution. Some possible sources of error in this analysis are mentioned here. The second study considers a particular system of a bubble in a liquid drop immersed in a second liquid in which the gas is insoluble. A condition of stability is then found. This system is reconsidered here simply in terms of the ideas of diffusion theory. The stability conditions may then be stated in simple physical terms.https://resolver.caltech.edu/CaltechAUTHORS:20201001-145812343On the stability of gas bubbles in liquid-gas solutions
https://resolver.caltech.edu/CaltechAUTHORS:20201001-145812459
Year: 1982
DOI: 10.1007/bf00385944
It was shown some time ago by use of diffusion theory that a gas bubble in a liquid-gas solution was unstable. This problem has been reconsidered recently in two papers both of which propose to develop a stability analysis solely from thermodynamic considerations. The first of these studies purports to find stability for a gas bubble in a liquid-gas solution. Some possible sources of error in this analysis are mentioned here. The second study considers a particular system of a bubble in a liquid drop immersed in a second liquid in which the gas is insoluble. A condition of stability is then found. This system is reconsidered here simply in terms of the ideas of diffusion theory. The stability conditions may then be stated in simple physical terms.https://resolver.caltech.edu/CaltechAUTHORS:20201001-145812459Reply to comments on "General analysis of the stability of superposed fluids"
https://resolver.caltech.edu/CaltechAUTHORS:PLEpof82
Year: 1982
DOI: 10.1063/1.863824
Previous results by Plesset and Hsieh on the effects of compressibility for Rayleigh–Taylor instability are shown to be valid, and an alternative brief deduction is given.https://resolver.caltech.edu/CaltechAUTHORS:PLEpof82Theory of evaporation and condensation
https://resolver.caltech.edu/CaltechAUTHORS:KOFpof84
Year: 1984
DOI: 10.1063/1.864716
The theory of evaporation and condensation is considered from a kinetic theory approach with a particular interest in the continuum limit. The moment method of Lees is used to solve the problem of the steady flow of vapor between a hot liquid surface and a cold liquid surface. By incorporating the singular nature of the problem, the forms of the continuum flow profiles found by Plesset are recovered. The expression for mass flux has the form of the Hertz–Knudsen formula but is larger by a factor of 1.665. A result of the theory is that the temperature profile in the vapor for the continuum problem is inverted from what would seem physically reasonable. This paradox is significant in that it casts a shadow of doubt on the fundamental theory.https://resolver.caltech.edu/CaltechAUTHORS:KOFpof84The stability of an evaporating liquid surface
https://resolver.caltech.edu/CaltechAUTHORS:PROpof84
Year: 1984
DOI: 10.1063/1.864814
A linearized stability analysis is carried out for an evaporating liquid surface with a view of understanding some observations with highly superheated liquids. The analytical results of this study depend on the unperturbed temperature near the liquid surface. The absence of this data renders a comparison with experiment impossible. However, on the basis of several different assumptions for this temperature distribution, instabilities of the interface of a rapidly evaporating liquid are found for a range of wavenumbers of the surface wave perturbation. At large evaporating mass flow rates the instability is very strong with growth times of a millisecond or less. A discussion of the physical mechanism leading to the instability is given.https://resolver.caltech.edu/CaltechAUTHORS:PROpof84Tensile Strength of Liquids
https://resolver.caltech.edu/CaltechAUTHORS:20140603-150555330
Year: 2014
The theory of the tensile strength of a pure liquid is developed and it is shown that it predicts much larger tensile strengths than are observed. This theory is modified and extended under the supposition
that liquids usually contain nuclei which are here taken to be solid particles. It is shown that the theory leads to more moderate predictions of tensile strength provided the solid particles are not wetted by the liquid. It is also shown that Brownian motion will serve as
the mechanism whereby solid particles can remain in suspension in liquids.https://resolver.caltech.edu/CaltechAUTHORS:20140603-150555330The analogy between surface waves in a liquid and shocks in compressible gases: experimental study of wave forms
https://resolver.caltech.edu/CaltechAUTHORS:20140603-151624030
Year: 2014
The subject matter covered in this report concerns the characteristics of the surface waves produced in the ripple tank by the wave generators and the effect on the wave form of adding detergents to the working fluid. The results will be presented under the following headings:
1. Experimental procedure.
2. The wave generators.
3. Variables affecting wave strength.
4. Effect of adding detergents to working fluid.
5. Summary and conclusions.https://resolver.caltech.edu/CaltechAUTHORS:20140603-151624030Cavitating Flows
https://resolver.caltech.edu/CaltechAUTHORS:20140603-144623046
Year: 2014
There are very few differences between the fluid dynamics of
liquids and gases. The viscosity of water, for example, is 10^-2 poise at 20° C while the viscosity of air at this temperature is about 2 X 10^-4 poise. The kinematic viscosity of water is 10^-2 cm^2/sec compared with 0.15 cm^2/sec for air. As one would expect from simple kinetic theory, the viscosity of gases increases with increasing temperature; the viscosity of liquids on the other hand decreases rather rapidly as the temperature rises. While
the speed of sound in water is about four times that in air, there is a more interesting consequence of the equation of state. A pressure pulse with
an intensity of several hundred psi, which propagates as a strong shock in air, will propagate acoustically in water with a negligible production of entropy.https://resolver.caltech.edu/CaltechAUTHORS:20140603-144623046Scaling Laws for Incipient Cavitation Noise
https://resolver.caltech.edu/CaltechAUTHORS:20140626-153701552
Year: 2014
The noise produced by the motion or a body through a liquid differs from that produced by the motion of a body through a gas because of the possibility or cavitation in the liquid case. An adequate theory or cavitation and cavitation noise is not yet available, but the application
or dimensional analysis together with the theoretical information so far obtained can yield scaling laws for this flow situation.
In section II, a brief dissussion will be given or the scaling laws
for hydrodynamic noise in some cases of non-cavitating flow; this discussion is included tor oompleteness. In section III, a summary or the
present information on the scaling law. for incipient cavitation noise will be presented.https://resolver.caltech.edu/CaltechAUTHORS:20140626-153701552On the Propagation of Sound in a Liquid Containing Gas Bubbles
https://resolver.caltech.edu/CaltechAUTHORS:20150713-152651809
Year: 2015
In the first portion of this paper a review is given of the theory of the propagation of sound in a homogeneous gas taking into account the effect of heat conduction. This consideration is preliminary to the treatment in the second portion of the paper of the propagation of sound
in a liquid with a homogeneous and isotropic distribution of gas bubbles. Again the effect of heat conduction is included. If f is the ratio of gas volume in the mixture to liquid volume, it is shown for the range of
values of f of general interest that the acoustic condensations and rarefactions of the gaseous portion of the medium are essentially isothermal. It is also found that the attenuation of an acoustic disturbance
by heat conduction is quite small.https://resolver.caltech.edu/CaltechAUTHORS:20150713-152651809The Theory of Rectified Diffusion of Mass into Gas Bubbles
https://resolver.caltech.edu/CaltechAUTHORS:20150713-141317248
Year: 2015
The problem considered is the behavior of a gas bubble in a liquid saturated with dissolved gas when oscillating pressures are imposed on the system. This situation is encountered in experiments on cavitation and in the propagation of sonic and ultrasonic waves in liquids. Since gas diffuses into the bubble during the expansion half-cycle in which the pressure drops below its mean value, and diffuses out of the bubble during the
compression half-cycle in which the pressure rises above its mean value, there is no net transfer of mass into or out of the bubble in first order. There is, however, in second order a net inflow of gas into the bubble
which is called rectified diffusion. The equations which determine the system include the equation of state of the gas in the bubble, the equation of motion for the bubble boundary in the liquid, and the equation for the
diffusion of dissolved gas in the liquid. In the solution presented here, the acoustic approximation is made; that is, the amplitude of the pressure oscillation is taken to be small. It is also assumed that the gas in the
bubble remains isothermal throughout the oscillations; this assumption is valid provided the oscillation frequency is not too high. Under these conditions one finds for the mean rate of gas flow into the bubble the expression
(dm/dt) = (8π/3)D C_∞ R_0 (ΔP/P_0)^2 where D is the diffusivity of the dissolved gas in the liquid, C_∞
is the equilibrium dissolved gas concentration for the mean ambient pressure P_0, R_0 is the mean radius of the bubble, and ΔP is the amplitude of the acoustic pressure oscillations. It may be remarked that the most important
contribution to the rectification effect comes from the convection contribution to the diffusion process.https://resolver.caltech.edu/CaltechAUTHORS:20150713-141317248Cavitation Erosion in Non-Aqueous Liquids
https://resolver.caltech.edu/CaltechAUTHORS:20151123-165919186
Year: 2015
Cavitation erosion rates in the organic liquids formamide, ethanol,acetone and glycerol are compared with the rate in distilled water. As is to be expected,these non-ionizing liquids, which are chemically less reactive with metals than water, show lower damage rates. The cavitation
damage rates have also been measured for solutions of these organic liquids in water and all these solutions show a monotonic decrease in going from pure water to the pure organic liquid except glycerol. The water-glycerol solutions go through a minimum damage rate for a solution with molecular ratio of glycerol to water of approximately 1 to 1. Solutions of ethanol in glycerol show a maximum in damage rate for a solution with molecular ratio, glycerol/ ethanol, of about 2 to 1. Qualitative differences in the cavitation bubble cloud in the various liquids studied are
indicated by short exposure photographs.https://resolver.caltech.edu/CaltechAUTHORS:20151123-165919186