[ { "id": "authors:6xgqs-qt771", "collection": "authors", "collection_id": "6xgqs-qt771", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:PROpof84", "type": "article", "title": "The stability of an evaporating liquid surface", "author": [ { "family_name": "Prosperetti", "given_name": "Andrea", "clpid": "Prosperetti-A" }, { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" } ], "abstract": "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.", "doi": "10.1063/1.864814", "issn": "0031-9171", "publisher": "Physics of Fluids", "publication": "Physics of Fluids", "publication_date": "1984-07-01", "series_number": "7", "volume": "27", "issue": "7", "pages": "1590-1602" }, { "id": "authors:15nd6-wp673", "collection": "authors", "collection_id": "15nd6-wp673", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:KOFpof84", "type": "article", "title": "Theory of evaporation and condensation", "author": [ { "family_name": "Koffman", "given_name": "L. D.", "clpid": "Koffman-L-D" }, { "family_name": "Plesset", "given_name": "M. S.", "clpid": "Plesset-M-S" }, { "family_name": "Lees", "given_name": "Lester", "clpid": "Lees-L" } ], "abstract": "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\u2013Knudsen 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.", "doi": "10.1063/1.864716", "issn": "0031-9171", "publisher": "Physics of Fluids", "publication": "Physics of Fluids", "publication_date": "1984-04-01", "series_number": "4", "volume": "27", "issue": "4", "pages": "876-880" }, { "id": "authors:z0dmc-hd783", "collection": "authors", "collection_id": "z0dmc-hd783", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:PLEpof82", "type": "article", "title": "Reply to comments on \"General analysis of the stability of superposed fluids\"", "author": [ { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" }, { "family_name": "Prosperetti", "given_name": "Andrea", "clpid": "Prosperetti-A" } ], "abstract": "Previous results by Plesset and Hsieh on the effects of compressibility for Rayleigh\u2013Taylor instability are shown to be valid, and an alternative brief deduction is given.", "doi": "10.1063/1.863824", "issn": "0031-9171", "publisher": "American Institute of Physics", "publication": "Physics of Fluids", "publication_date": "1982-05", "series_number": "5", "volume": "25", "issue": "5", "pages": "911-912" }, { "id": "authors:9rw5t-e6343", "collection": "authors", "collection_id": "9rw5t-e6343", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20201001-145812459", "type": "article", "title": "On the stability of gas bubbles in liquid-gas solutions", "author": [ { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" }, { "family_name": "Sadhal", "given_name": "Satwindar S.", "clpid": "Sadhal-S-S" } ], "abstract": "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.", "doi": "10.1007/bf00385944", "issn": "0003-6994", "publisher": "Kluwer Academic Publishers", "publication": "Applied Scientific Research", "publication_date": "1982-01", "series_number": "1", "volume": "38", "issue": "1", "pages": "133-141" }, { "id": "authors:xgyq7-szh07", "collection": "authors", "collection_id": "xgyq7-szh07", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120809-071458384", "type": "article", "title": "Bubble Dynamics and Cavitation", "author": [ { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" }, { "family_name": "Prosperetti", "given_name": "Andrea", "clpid": "Prosperetti-A" } ], "abstract": "N/A", "doi": "10.1146/annurev.fl.09.010177.001045", "issn": "0066-4189", "publisher": "Annual Reviews", "publication": "Annual Review of Fluid Mechanics", "publication_date": "1977-01", "volume": "9", "pages": "145-185" }, { "id": "authors:087px-6a914", "collection": "authors", "collection_id": "087px-6a914", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120806-144133110", "type": "article", "title": "Flow of vapour in a liquid enclosure", "author": [ { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" }, { "family_name": "Prosperetti", "given_name": "Andrea", "clpid": "Prosperetti-A" } ], "abstract": "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.", "doi": "10.1017/S002211207600253X", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "1976-12", "series_number": "3", "volume": "78", "issue": "3", "pages": "433-444" }, { "id": "authors:cqbm6-py145", "collection": "authors", "collection_id": "cqbm6-py145", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:PLEpof76", "type": "article", "title": "Comments on \"Rayleigh\u2013Taylor instability of thin viscous layers\"", "author": [ { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" }, { "family_name": "Whipple", "given_name": "Christopher G.", "clpid": "Whipple-C-G" } ], "abstract": "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.", "doi": "10.1063/1.861480", "issn": "0031-9171", "publisher": "Physics of Fluids", "publication": "Physics of Fluids", "publication_date": "1976-03-01", "series_number": "3", "volume": "19", "issue": "3", "pages": "485" }, { "id": "authors:pgsxf-2n054", "collection": "authors", "collection_id": "pgsxf-2n054", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120809-152411650", "type": "article", "title": "Viscous effects in Rayleigh-Taylor instability", "author": [ { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" }, { "family_name": "Whipple", "given_name": "Christopher G.", "clpid": "Whipple-C-G" } ], "abstract": "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\u2010Taylor 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\u2010Taylor 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\u2010Taylor instability theory for a continuous medium with viscosity.", "doi": "10.1063/1.1694570", "issn": "1070-6631", "publisher": "American Institute of Physics", "publication": "Physics of Fluids", "publication_date": "1974-01", "series_number": "1", "volume": "17", "issue": "1", "pages": "1-7" }, { "id": "authors:a4e26-71435", "collection": "authors", "collection_id": "a4e26-71435", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120809-090900707", "type": "article", "title": "Collapse of an initially spherical vapour cavity in the\n neighbourhood of a solid boundary", "author": [ { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" }, { "family_name": "Chapman", "given_name": "Richard B.", "clpid": "Chapman-R-B" } ], "abstract": "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 (\u0394p/\u03c1)^\u00bd where \u03c1 is the density of the liquid and \u0394p is the constant difference between the ambient liquid pressure and the pressure in the cavity. For \u0394p/\u03c1=10^6cm^2/sec^2 \u2248 1 atm/density of water\nthe 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.", "doi": "10.1017/S0022112071001058", "issn": "0022-1120", "publisher": "Cambridge University Press", "publication": "Journal of Fluid Mechanics", "publication_date": "1971-05", "series_number": "2", "volume": "47", "issue": "2", "pages": "283-290" }, { "id": "authors:pf2z6-65187", "collection": "authors", "collection_id": "pf2z6-65187", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20151120-092553985", "type": "article", "title": "Shockwaves from Cavity Collapse", "author": [ { "family_name": "Plesset", "given_name": "M. S.", "clpid": "Plesset-M-S" } ], "abstract": "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.", "doi": "10.1098/rsta.1966.0047", "issn": "0080-4614", "publisher": "Royal Society", "publication": "Philosophical transactions of the Royal Society of London. Series A: Mathematical and physical sciences", "publication_date": "1966-07", "series_number": "1110", "volume": "260", "issue": "1110", "pages": "241-244" }, { "id": "authors:n6s7c-40r52", "collection": "authors", "collection_id": "n6s7c-40r52", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:HICpof64", "type": "article", "title": "Collapse and rebound of a spherical bubble in water", "author": [ { "family_name": "Hickling", "given_name": "Robert", "clpid": "Hickling-R" }, { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" } ], "abstract": "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.", "doi": "10.1063/1.1711058", "issn": "0031-9171", "publisher": "Physics of Fluids", "publication": "Physics of Fluids", "publication_date": "1964-01-01", "series_number": "1", "volume": "7", "issue": "1", "pages": "7-14" }, { "id": "authors:sscy3-9sz11", "collection": "authors", "collection_id": "sscy3-9sz11", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20120905-105612094", "type": "article", "title": "Reply to Comments of P. W. Smith, Jr.", "author": [ { "family_name": "Hsieh", "given_name": "Din-Yu", "clpid": "Hsieh-Din-Yu" }, { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" } ], "abstract": "In his comments on this subject, Smith has put\nemphasis on the special nature of the plane-wave\nsolution in acoustic problems. It is perhaps unnecessary\nto defend the importance of the plane-wave\nsolution in a linear theory.", "doi": "10.1063/1.1706607", "issn": "1070-6631", "publisher": "American Institute of Physics", "publication": "Physics of Fluids", "publication_date": "1962-02", "series_number": "2", "volume": "5", "issue": "2", "pages": "254-254" }, { "id": "authors:7dw07-13787", "collection": "authors", "collection_id": "7dw07-13787", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:HSIpof60", "type": "article", "title": "On the Propagation of Sound in a Liquid Containing Gas Bubbles", "author": [ { "family_name": "Hsieh", "given_name": "Din-Yu", "clpid": "Hsieh-Din-Yu" }, { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" } ], "abstract": "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.", "doi": "10.1063/1.1706447", "issn": "0031-9171", "publisher": "Physics of Fluids", "publication": "Physics of Fluids", "publication_date": "1961-08", "series_number": "8", "volume": "4", "issue": "8", "pages": "970-975" }, { "id": "authors:2fwdp-kes57", "collection": "authors", "collection_id": "2fwdp-kes57", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:PLEpof60", "type": "article", "title": "Theory of gas bubble dynamics in oscillating pressure fields", "author": [ { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" }, { "family_name": "Hsieh", "given_name": "Din-Yu", "clpid": "Hsieh-Din-Yu" } ], "abstract": "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.", "doi": "10.1063/1.1706152", "issn": "0031-9171", "publisher": "Physics of Fluids", "publication": "Physics of Fluids", "publication_date": "1960-11", "series_number": "6", "volume": "3", "issue": "6", "pages": "882-892" }, { "id": "authors:9y1q8-q7y42", "collection": "authors", "collection_id": "9y1q8-q7y42", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:PLEpnas60", "type": "article", "title": "Transient effects in the distribution of carbon-14 in nature", "author": [ { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" }, { "family_name": "Latter", "given_name": "Albert L.", "clpid": "Latter-A-L" } ], "abstract": "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.", "issn": "0027-8424", "publisher": "National Academy of Sciences", "publication": "Proceedings of the National Academy of Sciences of the United States of America", "publication_date": "1960-02-01", "series_number": "2", "volume": "46", "issue": "2", "pages": "232-241" }, { "id": "authors:xm4br-9r024", "collection": "authors", "collection_id": "xm4br-9r024", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:PLEjcp58", "type": "article", "title": "Ion exchange kinetics. A nonlinear diffusion problem. II. Particle diffusion controlled exchange of univalent and bivalent ions", "author": [ { "family_name": "Plesset", "given_name": "M. S.", "clpid": "Plesset-M-S" }, { "family_name": "Helfferich", "given_name": "F.", "clpid": "Helfferich-F" }, { "family_name": "Franklin", "given_name": "J. N.", "clpid": "Franklin-J-N" } ], "abstract": "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.", "doi": "10.1063/1.1744656", "issn": "0021-9606", "publisher": "American Institute of Physics", "publication": "Journal of Chemical Physics", "publication_date": "1958-11", "series_number": "5", "volume": "29", "issue": "5", "pages": "1064-1069" }, { "id": "authors:dxr4p-0hn34", "collection": "authors", "collection_id": "dxr4p-0hn34", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:HELjcp58", "type": "article", "title": "Ion Exchange Kinetics. A Nonlinear Diffusion Problem", "author": [ { "family_name": "Helfferich", "given_name": "F.", "clpid": "Helfferich-F" }, { "family_name": "Plesset", "given_name": "M.S.", "clpid": "Plesset-M-S" } ], "abstract": "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.", "doi": "10.1063/1.1744149", "issn": "0021-9606", "publisher": "Journal of Chemical Physics", "publication": "Journal of Chemical Physics", "publication_date": "1958-03-01", "series_number": "3", "volume": "28", "issue": "3", "pages": "418-424" }, { "id": "authors:8djmb-yct20", "collection": "authors", "collection_id": "8djmb-yct20", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140826-140952946", "type": "article", "title": "On the Mechanism of Cavitation Damage", "author": [ { "family_name": "Plesset", "given_name": "M. S.", "clpid": "Plesset-M-S" }, { "family_name": "Ellis", "given_name": "A. T.", "clpid": "Ellis-A-T" } ], "abstract": "A new method for producing cavitation damage in the\nlaboratory is described in which the test specimen has no\nmechanical accelerations applied to it in contrast with the\nconventional magnetostriction device. Alternating pressures\nare generated in the water over the specimen by exciting\na resonance in the \"water cavity.\" By this means\nthe effects of cavitation have been studied for a variety of\nmaterials. Photomicrographs have been taken of several\nordinary (polycrystalline) specimens and also of zinc\nmonocrystals. The zinc monocrystal has been exposed to\ncavitation damage on its basal plane and also on its\ntwinning 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.", "publisher": "ASME", "publication": "Transactions of the ASME", "publication_date": "1955-10", "volume": "77", "pages": "1055-1064" }, { "id": "authors:zg2gz-87p65", "collection": "authors", "collection_id": "zg2gz-87p65", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140729-155852145", "type": "article", "title": "On the Dynamics of Small Vapor Bubbles in Liquids", "author": [ { "family_name": "Zwick", "given_name": "S. A.", "clpid": "Zwick-S-A" }, { "family_name": "Plesset", "given_name": "M. S.", "clpid": "Plesset-M-S" } ], "abstract": "When a vapor bubble in a liquid changes size, evaporation\nor 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\ntherefore 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\nbecomes 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\nvapor 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.\nIn 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.\n\nIn 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\nequations. In the case of the collapsing bubble, large temperature variations occur; therefore, tabulated vapor pressure data were used, and the equations of\nmotion were integrated numerically. Analytic solutions are obtainable for the case of the expanding bubble if the period of growth is subdivided into several\nregimes 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\nsolution of the equations of motion, valid when the bubble becomes large (i.e. observable), has been presented previously, together with experimental verification.\n\nWe shall be specifically concerned in the following discussion with the dynamics of vapor bubbles in water. This restriction was made for convenience\nonly, since the theory is applicable without modification to many other liquids.", "publisher": "Massachusetts Institute of Technology", "publication": "Journal of Mathematics and Physics", "publication_date": "1955-01", "series_number": "4", "volume": "33", "issue": "4", "pages": "308-330" }, { "id": "authors:dhgp6-86k43", "collection": "authors", "collection_id": "dhgp6-86k43", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:PLEjap54a", "type": "article", "title": "The Growth of Vapor Bubbles in Superheated Liquids", "author": [ { "family_name": "Plesset", "given_name": "M. S.", "clpid": "Plesset-M-S" }, { "family_name": "Zwick", "given_name": "S. A.", "clpid": "Zwick-S-A" } ], "abstract": "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.", "doi": "10.1063/1.1721668", "issn": "0021-8979", "publisher": "Journal of Applied Physics", "publication": "Journal of Applied Physics", "publication_date": "1954-04-01", "series_number": "4", "volume": "25", "issue": "4", "pages": "493-450" }, { "id": "authors:qdw7p-13j05", "collection": "authors", "collection_id": "qdw7p-13j05", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:PLEjap54b", "type": "article", "title": "On the Stability of Fluid Flows with Spherical Symmetry", "author": [ { "family_name": "Plesset", "given_name": "M. S.", "clpid": "Plesset-M-S" } ], "abstract": "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.", "doi": "10.1063/1.1721529", "issn": "0021-8979", "publisher": "Journal of Applied Physics", "publication": "Journal of Applied Physics", "publication_date": "1954-01-01", "series_number": "1", "volume": "25", "issue": "1", "pages": "96-98" }, { "id": "authors:z9t32-e6894", "collection": "authors", "collection_id": "z9t32-e6894", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:PLEjap52", "type": "article", "title": "A Nonsteady Heat Diffusion Problem with Spherical Symmetry", "author": [ { "family_name": "Plesset", "given_name": "M. S.", "clpid": "Plesset-M-S" }, { "family_name": "Zwick", "given_name": "S. A.", "clpid": "Zwick-S-A" } ], "abstract": "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.", "doi": "10.1063/1.1701985", "issn": "0021-8979", "publisher": "Journal of Applied Physics", "publication": "Journal of Applied Physics", "publication_date": "1952-01-01", "series_number": "1", "volume": "23", "issue": "1", "pages": "95-98" }, { "id": "authors:d6dn1-30y81", "collection": "authors", "collection_id": "d6dn1-30y81", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:PLEjap51", "type": "article", "title": "Scattering and Absorption of Gamma-Rays", "author": [ { "family_name": "Plesset", "given_name": "M. S.", "clpid": "Plesset-M-S" }, { "family_name": "Cohen", "given_name": "S. T.", "clpid": "Cohen-S-T" } ], "abstract": "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.", "doi": "10.1063/1.1699954", "issn": "0021-8979", "publisher": "Journal of Applied Physics", "publication": "Journal of Applied Physics", "publication_date": "1951-03-01", "series_number": "3", "volume": "22", "issue": "3", "pages": "350-357" }, { "id": "authors:9y2y9-2e565", "collection": "authors", "collection_id": "9y2y9-2e565", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:PEEpr51", "type": "article", "title": "Transmission of Gamma-Rays through Large Thicknesses of Heavy Materials", "author": [ { "family_name": "Peebles", "given_name": "Glenn H.", "clpid": "Peebles-G-H" }, { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" } ], "abstract": "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 \u03a3En. 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 \u03b1=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.", "doi": "10.1103/PhysRev.81.430", "issn": "0031-899X", "publisher": "Physical Review", "publication": "Physical Review", "publication_date": "1951-02-01", "series_number": "3", "volume": "81", "issue": "3", "pages": "430-439" }, { "id": "authors:gma52-sej66", "collection": "authors", "collection_id": "gma52-sej66", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:EPSjcp50", "type": "article", "title": "On the Stability of Gas Bubbles in Liquid-Gas Solutions", "author": [ { "family_name": "Epstein", "given_name": "P. S.", "clpid": "Epstein-P-S" }, { "family_name": "Plesset", "given_name": "M. S.", "clpid": "Plesset-M-S" } ], "abstract": "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.", "doi": "10.1063/1.1747520", "issn": "0021-9606", "publisher": "Journal of Chemical Physics", "publication": "Journal of Chemical Physics", "publication_date": "1950-11-01", "series_number": "11", "volume": "18", "issue": "11", "pages": "1505-1509" }, { "id": "authors:hsnwm-scv05", "collection": "authors", "collection_id": "hsnwm-scv05", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140729-162818727", "type": "article", "title": "Wall Effects in Cavity Flow - I", "author": [ { "family_name": "Birkhoff", "given_name": "G.", "clpid": "Birkhoff-G" }, { "family_name": "Plesset", "given_name": "M.", "clpid": "Plesset-M-S" }, { "family_name": "Simmons", "given_name": "N.", "clpid": "Simmons-N" } ], "abstract": "[no abstract]", "issn": "0033-569X", "publisher": "Brown University", "publication": "Quarterly of Applied Mathematics", "publication_date": "1950-07", "series_number": "2", "volume": "8", "issue": "2", "pages": "151-168" }, { "id": "authors:9zwsf-cm683", "collection": "authors", "collection_id": "9zwsf-cm683", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140805-165739483", "type": "article", "title": "The Analogy between Hydraulic Jumps in Liquids and Shock Waves in Gases", "author": [ { "family_name": "Gilmore", "given_name": "F. R.", "clpid": "Gilmore-F-R" }, { "family_name": "Plesset", "given_name": "M. S.", "clpid": "Plesset-M-S" }, { "family_name": "Crossley", "given_name": "H. E., Jr.", "clpid": "Crossley-H-E-Jr" } ], "abstract": "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\u2010jump 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\u2010shock 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.", "doi": "10.1063/1.1699641", "issn": "0021-8979", "publisher": "American Institute of Physics", "publication": "Journal of Applied Physics", "publication_date": "1950-03", "series_number": "3", "volume": "21", "issue": "3", "pages": "243-249" }, { "id": "authors:d1ygw-wmq60", "collection": "authors", "collection_id": "d1ygw-wmq60", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140808-114249321", "type": "article", "title": "The Dynamics of Cavitation Bubbles", "author": [ { "family_name": "Plesset", "given_name": "M. S.", "clpid": "Plesset-M-S" } ], "abstract": "Three regimes of liquid flow over a body are defined,\nnamely: (a) noncavitating flow; (b) cavitating flow with a\nrelatively small number of cavitation bubbles in the field\nof flow; and (c) cavitating flow with a single large cavity\nabout the body. The assumption is made that, for the\nsecond regime of flow, the pressure coefficient in the flow\nfield is no different from that in the noncavitating flow.\nOn this basis, the equation of motion for the growth and\ncollapse of a cavitation bubble containing vapor is derived\nand applied to experimental observations on such bubbles.\nThe limitations of this equation of motion are pointed\nout, and include the effect of the finite rate of evaporation\nand condensation, and compressibility of vapor and\nliquid. A brief discussion of the role of \"nuclei\" in the\nliquid in the rate of formation of cavitation bubbles is\nalso given.", "issn": "0021-8936", "publisher": "American Society of Mechanical Engineers", "publication": "Journal of Applied Mechanics", "publication_date": "1949-09", "volume": "16", "pages": "277-282" }, { "id": "authors:p09rn-2ka81", "collection": "authors", "collection_id": "p09rn-2ka81", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:PLErmp48", "type": "article", "title": "Drag in Cavitating Flow", "author": [ { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" }, { "family_name": "Shaffer", "given_name": "Philip A., Jr.", "clpid": "Shaffer-P-A-Jr" } ], "abstract": "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.", "doi": "10.1103/RevModPhys.20.228", "issn": "0034-6861", "publisher": "Reviews of Modern Physics", "publication": "Reviews of Modern Physics", "publication_date": "1948-01-01", "series_number": "1", "volume": "20", "issue": "1", "pages": "228-231" }, { "id": "authors:vhvw0-46n05", "collection": "authors", "collection_id": "vhvw0-46n05", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:20140805-142755745", "type": "article", "title": "On the Classical Model of Nuclear Fission", "author": [ { "family_name": "Plesset", "given_name": "M. S.", "clpid": "Plesset-M-S" } ], "abstract": "The first experiments on neutron bombardment\nof various elements carried out by\nFermi and his collaborators included the study\nof the group of activities observed in uranium\nwhich were at that time ascribed to transuranic\nelements. The great number of studies following\nthis first work led finally to the results of Hahn\nand Strassmann which showed clearly that many\nof the activities ascribed to transuranic elements\ncame, instead, from nuclei of approximately\nhalf the mass of uranium. The startling conclusion\nthat these activities must arise from the\nsplitting of the uranium nucleus under neutron\nbombardment into two fragment nuclei was\npointed out by Meitner and Frisch, and was\nquickly confirmed by subsequent experiments. In\nthe first theoretical discussion of this new type of\nnuclear reaction, Meitner and Frisch proposed\nthe name fission for the process, and compared it\nwith the splitting that may take place in a liquid\ndrop in oscillation. This model was supported by\nBohr who correlated it with other nuclear\nproperties and, at the same time, emphasized\nhow far the phenomenon of nuclear fission may\nbe described classically. A very complete theoretical\ndiscussion of both the classical and\nquantum aspects of fission was given by Bohr and\nWheeler, and it is proposed here to describe\nsome of the classical theory of fission developed\nby these authors.", "doi": "10.1119/1.1991623", "issn": "0002-9505", "publisher": "American Association of Physics Teachers", "publication": "American Journal of Physics", "publication_date": "1941-02", "series_number": "1", "volume": "9", "issue": "1", "pages": "1-10" }, { "id": "authors:xz8df-qa035", "collection": "authors", "collection_id": "xz8df-qa035", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:BROpr39", "type": "article", "title": "On the Equality of the Proton-Proton and Proton-Neutron Interactions", "author": [ { "family_name": "Brown", "given_name": "Frederick W.", "clpid": "Brown-F-W" }, { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" } ], "abstract": "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).", "doi": "10.1103/PhysRev.56.841.2", "issn": "0031-899X", "publisher": "Physical Review", "publication": "Physical Review", "publication_date": "1939-10-15", "series_number": "8", "volume": "568", "issue": "8", "pages": "841-842" }, { "id": "authors:48m2d-f3k68", "collection": "authors", "collection_id": "48m2d-f3k68", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:PLEpr36", "type": "article", "title": "Note on Neutron-Proton Exchange Interaction", "author": [ { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" } ], "abstract": "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 ....", "doi": "10.1103/PhysRev.49.551", "issn": "0031-899X", "publisher": "Physical Review", "publication": "Physical Review", "publication_date": "1936-04-01", "series_number": "7", "volume": "49", "issue": "7", "pages": "551" }, { "id": "authors:6n4tj-51167", "collection": "authors", "collection_id": "6n4tj-51167", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:PLEpr35", "type": "article", "title": "Inelastic Scattering of Quanta with Production of Pairs", "author": [ { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" }, { "family_name": "Wheeler", "given_name": "John A.", "clpid": "Wheeler-J-A" } ], "abstract": "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.\n\nWhile 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.", "doi": "10.1103/PhysRev.48.302", "issn": "0031-899X", "publisher": "Physical Review", "publication": "Physical Review", "publication_date": "1935-08-15", "series_number": "4", "volume": "48", "issue": "4", "pages": "302-306" }, { "id": "authors:pk2sr-v9h41", "collection": "authors", "collection_id": "pk2sr-v9h41", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:MOLpr34", "type": "article", "title": "Note on an Approximation Treatment for Many-Electron Systems", "author": [ { "family_name": "M\u00f8ller", "given_name": "Chr.", "clpid": "M\u00f8ller-C" }, { "family_name": "Plesset", "given_name": "M. S.", "clpid": "Plesset-M-S" } ], "abstract": "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.", "doi": "10.1103/PhysRev.46.618", "issn": "0031-899X", "publisher": "Physical Review", "publication": "Physical Review", "publication_date": "1934-10-01", "series_number": "7", "volume": "46", "issue": "7", "pages": "618-622" }, { "id": "authors:qkab2-48b19", "collection": "authors", "collection_id": "qkab2-48b19", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:OPPpr33", "type": "article", "title": "On the Production of the Positive Electron", "author": [ { "family_name": "Oppenheimer", "given_name": "J. R.", "clpid": "Oppenheimer-J-Robert" }, { "family_name": "Plesset", "given_name": "M. S.", "clpid": "Plesset-M-S" } ], "abstract": "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.", "doi": "10.1103/PhysRev.44.53.2", "issn": "0031-899X", "publisher": "Physical Review", "publication": "Physical Review", "publication_date": "1933-07-01", "series_number": "1", "volume": "44", "issue": "1", "pages": "53-55" }, { "id": "authors:jfzk9-7k168", "collection": "authors", "collection_id": "jfzk9-7k168", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:PLEpr32", "type": "article", "title": "The Dirac Electron in Simple Fields", "author": [ { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" } ], "abstract": "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.", "doi": "10.1103/PhysRev.41.278", "issn": "0031-899X", "publisher": "Physical Review", "publication": "Physical Review", "publication_date": "1932-08-01", "series_number": "3", "volume": "41", "issue": "3", "pages": "278-290" }, { "id": "authors:j3tk5-42415", "collection": "authors", "collection_id": "j3tk5-42415", "cite_using_url": "https://resolver.caltech.edu/CaltechAUTHORS:PLEpr30", "type": "article", "title": "Relativistic Wave Mechanics of Electrons Deflected by a Magnetic Field", "author": [ { "family_name": "Plesset", "given_name": "Milton S.", "clpid": "Plesset-M-S" } ], "abstract": "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.", "issn": "0031-899X", "publisher": "Physical Review", "publication": "Physical Review", "publication_date": "1930-12-15", "series_number": "12", "volume": "36", "issue": "12", "pages": "1728-1731" } ]