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Thermomolecular Pressure in Surface Melting: Motivation for Heave Author(s): J. G. Dash Source: Science, New Series, Vol. 246, No. 4937 (Dec. 22, 1989), pp. 1591-1593 Published by: American Association for the Advancement of Science Stable URL: http://www.jstor.org/stable/1704667 Accessed: 22-11-2015 23:33 UTC

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This content downloaded from 132.174.254.159 on Sun, 22 Nov 2015 23:33:34 UTC All use subject to JSTOR Terms and Conditions increasesthe mass input, and melting has GeophysicalUnion, Washington,DC, 1985), pp. 22. Glacio-isostaticuplift ended 4000 to 5000 yearsago 59-85. (A. Weidick,in Geologyof ,A. Escherand little effect.Below the equilibriumline, in- 9. H. J. Zwally,A. C. Brenner,J. A. Major, R. A. W. S. Watt, Eds. (The GeologicalSurvey of Green- creasesln preclpltatlonreduce t le net sum- Bindschadler,J. G. Marsh, Sciet1ce 246, 1587 land, Denmark,1976), p. 450. Figure 3 in (1) mer ablationand partiallyoiset increasesin (1989). showsthat the riseis 3 mm/yearnear the coastand 9 10. Errorsare 1 SD of dHldt slope for Geosat-Geosat mm/yearin the centralarea. melting.Although the altitudeof the equi- measurcments,and SD of the meancrossover differ- 23. Accumlllationdata are summarizedin U. Radoket libriumline increaseswith increasedrem- ence plus error ill relativegeoid correctionfor al., Climaticand PhysicalCharactenstics ofthe Greenland perature,it decreaseswith increasedprecipi- Geosat-Seasatmeasuremellts. The densityof orbital Sheet:Parts I and II (Univ. of Colorado,Boulder, crossoversis largestat the maxamumlatitude of 1982). tation and with increasedcloudiness (27). 72°N and decreasessignificantly to the south, be- 24. G. de Q. Robin, Philos. Trans.R. Soc. LondonSer. B Therefore,changes in position of the equi- causeof the geometryof the groundtracks. Seasat 280, 143 (1977). data coverageis shown in H. J. Zwally, R. A. 25. D. H. Bromwich,Rev. Geophys.26, 149 (1988). libriumline might be small as temperature Bindschadler,A. C. Brenner,T. V. Martin,and R. 26. Antarcticdata in (24) suggest6% per Kelvinat the andprecipitation increase togethel-. Because H. Thomas[J. Geophys.Res. 88, 1589 (1983)] and surfaceand 11%per Kelvinabove the surfaceinver- nearly100% of the Antarcticice sheet and typical Geosat coverage in H. J. Zwally, A. C. sion layerfor the equationof M. Mellor [Polarfors- Brenner,J. A. Major,alld R. A. Billdschadler[Johns chung5, 179 (1963)]. Temperatureand accumula- 85% of the Greenlandice sheet are above HopkislsAppl. Phys. Lab. Dig. 8, 251 (1987)]. The tion records since 1965 at an Antarcticcoastal the presentequilibrium line, the dominant density of elevation differencesis also smaSlerat stationgive 18%per Kelvin[D. W. S. Limbert,in short-termeffiect is likely to be ice-sheet lower elevations,because the altimetermeasure- Environmentof West A^ntarctica:Potenttal CO2-Induced mentsare less continuousover the steeperand more Changes, M. F. Meier and C. R. Bentley, Eds. growth. An increase in precipitationand irregularsurface near the ice-sheetmargins and the (NationalAcademy of Sciences,Washington, DC, temperatureshould cause an immediatepos- altimetermeasurement errors are also larger. The SD 1984), pp. 116-139]. The positivelinear relation (with 3 SD editing) for Geosat-Geosatcrossovers betsveenGreenland accumulation and bl80 values itive change in the mass balance and a increasesfrom 1.06 m at 72°N to 2.93 m between (18)and, therefore, temperature give 5%per Kelvin; gradualsteepening of an , which 60°N and 63°N. Similarly,SD is 1.06 m in the modelingexperiments [M. E. Schlesingerand J. F. would continue for many years as the ice elevatiollballd between 2700 and 3300 m and4.79 B. Mitchell,Rev. Geophys. 25, 760 (1987)] show m in the bandbetween 700 and 1200 m. precipitationincreases of about 0.2 m/yearin polar flow respondedto the drivingstresses. 11. By the ExpeditionGlaciologique Internationale a regionsfor greenhousewarming associated with a In conclusion, Greenland ice-sheet Groenland(EGIG). doublingof CO2concentration, which is a changeof growth is consistent with the generally 12. H. Seckel,Medd. Groenl. 187, no. 4 (1977). about 5 to 20% per Kelvin at the latitudes of 13. A. Bauer,A. Ambach,O. Schimpp,ibid., 174, no. 1 Greenland. warmer temperatures(28) experiencedin (1968). 27. W. Ambachand M. Kuhn, pp. 255-257 in (7), this century.If climatecontinues to warm, 14. N. ReehandN. S. Gundestrup,J.Glaciol. 31,108, showequilibrium rise of 77 m perKelvin increase in 198 (1985). surfaceair temperature,a fall of 73 m per 0.1-m enhancedprecipitation in polarregions may 15. J. M. Kosteckaand I. M. Whillans,ibid. 34, 31 illcreasein snowfall,and a fall of 4 m per 10% ofEsetincreases in melting. Although the (1988). increasein cloudiness. Antarcticice sheet is a likelysource of 16. In a continuityequation, Vj equalsthe dowllward 28. J. Hansenand S. Lebedeff,Geophys. Res. Lett. 15, ice velocity plus the verticalice motion due to 323 (1988). for currentsea-level rise, its mass balanceis hori70ntaladvection. 29. J. L. Bufton,J. E. Robinson,M. D. Femiano,F. S. uncertain.Over much of Antarctica,which 17. Also, changesin Vcpare a secondaryeffiect primarily Flatow,IEEE Trans. Geosci. RemoteSensing GE-20, contains91% of the earth'sice, the annual determinedby challgesin A (t) andB(t), andchanges 544 (1982). in Vbare negligible. 30. This workis supportedby NASA'sOcean Processes mass input is only 10% of the Greenland 18. H. B. Clausen,N. S. Gundestrup,S. J. Johllsen,R. Program.I thankS. Jacobsfor his compilationof values,so that significantelevation changes Bindschadler,J. Zwally, Ann. Glaciol. 10, 10 estimatesof Antarcticmass fluxes and D. Bromwich (1988). forpointing me to literatureon polarprecipitation. I may be ten times as small. Laser altimetry 19. N. Reeh et vl., J. Glaciol. 20, 27 (1978). appreciatethe usefilldiscussions with R. Alley, R. measurements(29) are needed there, be- 20. N. Reeh, H. B. Clausen, N. Gundestrup,S. J. Bindschadler,C. Lingle, S. Stephenson,and R. causeof its betterrange precision and ability Johnsen,B. StauSer,Istt. Assoc. IXydrol.Sci. Publ. No. Thomas. 118, 177 (1977). to cover the critical ablation zones where 21. R. S. Bradleyet al., Science237, 171 (1987). 29 June1989, accepred13 October1989 radaraltimeters do not adequatelyfollow the more irregularice surfaces.

ThermomolecularPressure in SurfaceMelting: REFERENCES AND NOTXS 1. W. R. Peltierand A. M. Tushingham,Science 244, Motivationfor Frost Heave 806 (1989). 2. R. Etkinsand E. Epstein,ibid. 215, 287 (1982); V. Gornitz,S. Lebedeff,}. Hansen,ibid., p. 1611. J. G. DASH 3. M. F. Meier,ibid. 226, 1420 (1984). 4. J. Hansenet al., J. Geophys.Res. 93, 9341 (1988). 5. Forexample, a detailedstudy of anAlaskan at A thermomolecularpressure is associated with surface melting, and it can drive mass 60.4°N showsthat there has been significant growth flow along an interfaceunder a lateraltemperature gradient. The pressureis a universal since 1976 as both temperatureand precipitation increased(L. R. Mayo and D. C. Trabant,in The thermodynamicfunction in the limit of thick films. It may be responsible for frost PotentialEffects of CarbonDioxide-lnduced Changes in heave in frozen ground. Alaska, J. H. McBeath,Ed. (Misc. Publ. 83-1, Univ. OfAlaska, Fairbanks, AK, 1984). 6. R. H. Thomas et al., NASA Tech. Memo. 86233 SURFACE MELTINGCONTINUES TO AT- classes of materials.The motivating (1985). tract considerableexperimental and force for the effect is the lowering of the 7. M. F. Meieret al., ,Ice Sheets, as1dSea Level: Effect of a CO2-InducedClimatic Change (National theoreticalinterest, as it involvesfun- interfacialfree-energy of a solid surfaceby a Academyof Sciences,Washington, DC, 1985). damentalquestions in surfacescience and layerof the melted material,which occurs 8. Estimatesof Antarcticaccumulation, dis- condensedmatter physics and practicalap- for all solid interfacesthat arewetted by the charge,and basal melting made since 1955 showeda positivemass balancebefore about 1974, but im- plicationsin materialsprocessing (i-5). A1- melt . Such a reduction of the free provedrecent values show that an increasein the though the phenomenonhas been explored energyallows a macroscopicallythick film of estimateof accumulation[M. B. Giovinettoand C. in a limited number of materials,it is be- the liquid to be stabilizedat a temperature R. Bentley,Antatstic J. U.S. 20, 6 (1985)] is more than offset by largerincreases in the estimatesof lievedto be a generalcharacteristic of most belowthe normalmelting point. The surface icebergdischarge [O. Orheimlp. 210 in (7):1and free energyof the film varieswith its thick- basalmelting [S. S. Jacobs,R. G. Fairbanks,Y. Horibe, in Oceanology of the AntarcticContinental Departmentof Physics,FM-15, Universityof Washing- ness and asymptoticallyapproaches the val- Shelf S. Jacobs,Ed. (Antarct.Res. Ser. 43, American ton, Seattle,WA 98195. ue for semi-infiniteliquid. This variation

22 DECEMBER I989 REPORTS I59I

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with thicknessintroduces an effectiveinter- A a quantityof solid to liquid, which would actionbetween the interfaces,equivalent to raisethe free energyof the systemabove its a negativethermomolecular pressure. In this - Melted equilibriumvalue. Conversely,the stability ------layer that this negativepressure is ...... of a liquid layerat temperaturesbelow the reportI show ///X//X////////X/X////////////X/ Solid readilyderived from the thermodynamicsof normalmelting point necessitatesa negative surfacemelting and that it has a simpleand thermomolecularpressure, that is, a suction. Mass "< universalexpression in thickfilms. Although Heat < The presenceof a thermomolecularpres- the pressureis not readilydetected in the flow flow surecan be detectedif a temperaturegradi- usual arrangementsof surfacemelting ex- B ent is imposedalong the surface.The result- periments,it can be seen under certaindy- / ing pressuregradient will causemass trans- _, - namicand steady-state conditions. The pres- _ , . port in the liquid layer,toward lower tem- Initial_ + suresthat can be generatedin ice by quite peratures(Fig. 1). Thus, masstransport and modesttemperature differences may be large heattransport are coupled in the film,analo- enough to have importantpractical conse- Fig. 1. Diagramof the thermomolecularpressure gous to the simultaneousflow of current quences.The effect may be responsiblefor and flow in surfacemelting of a simple uncon- and heat in a thermocouple.If the tempera- frostheave in frozenground. Sned interface.(A) Initial conditionsat a plane ture differenceis maintained,the massflow in equilibriumwith va- interface;(B) the proSle, as modified by flow, canbe haltedonly by appiicationof a hydro- Considera solid after an interval.Temperature and pressurein- por or a wall at temperatureT and pressure creaseto the right. static pressure,equal and opposite to the P. If the interfaceis wettedby a macroscopic thermomolecularpressure. If the interfaceis layerof the melt (m) liquid the free energy a single,low areasurface this transportmay of the layeris composedof bulk and surface At the bulktransition temperature To, Fs = be slow and difficultto detect, but it could terms FI hence bPmvanishes at To. However, the be much more readilyobserved in a porous mediumwith largeinterfacial area. Gm(T,P,d)- [plll(T,P)]d+ i\^yf(d)+ PYs chemicalpotentials differ at T < To. Ex pandingi\>-(>s - >1)to firstorder in the An importantpractical manifestation of (1) temperaturedifference the effectmay be the phenomenonof frost where d is the thickness,Pl and >1 are the heave,which occursin water-saturatedsoils densityand chemicalpotential of the bulk F(T)= ;95> (T- T ) below 0°C:.Field observations (7) and labo- liquid (1), ws is the interfacialcoefficient of ratorystudies (8) have shown the persis- the unwettedsolid (s), i\ is the difference tence of unfrozenwater in porous media between the coefficientsof the dry and when cooled to temperaturesas low as wetted interface,and f(d) is the thickness -30°C. This fluid tends to migrate along dependenceof the coefficients.In general, where qmis the latent heat of melting per temperaturegradients, toward lower tem- f(d) is a positive monotonic function tend- molecule.Combining Eqs. 2 and 5 yields a perature,where it deposits in segregated ing to unity at infinitethickness. For exam- functionalrelation for the temperaturede- bulk ice "lenses."The processcontinues as ple, in simplevan der Waalsmaterials with pendenceof d that dependson the natureof long as the temperaturedifference is main- unretardedpotentials, f(d) = (1 - cr2/d2), the intermolecularforces. For example,in tained,or until sufficientpressure is applied. where cr is a constant on the order of a the caseof van derWaals forces, with substi- Experimentsllave shown that the pressureis moleculardiameter. tution of the specific form of f(d) given proportionalto the temperaturedifference In thermodynamicequilibrium, the chem- earlier,the result is a power law in the and can amountto greaterthan 11 aun/°C ical potentialof the meltedlayer is equalto differencebenveen T and Io (8). The observedpressures are described by that of the solid. DifferentiatingEq. 1 an empiricalrelation that is identicalwith d = (-2ty2 ^7 )1/3 t-1'3 (6) Eq. 7. A descriptionof frost heave and its seriousconsequences are given in a report 1m( TvP, d) =- (-) p Ad T,P where t = (T0 - 75)/T0is the reduced by The NationalResearch Council (9) temperature.In the case of short range (TP) + (IvY) af (TP) (2) forces,where @fAda exp(-cd), where c is a Nearlyeveryone living in the northernand south- constant,the resultis a logarithmictempera- erntemperate zones has experiencedthe effectsof ice segregationand frost heaving through the The interfacialenergy term in lm intro- ture dependence,d °' 1lntl.Other types of destructionof roadsand highways,the displace- ducesan effectivepressure bPm acting on the interactions,such as dipolarforces, can pro- ment of foundations,the jammingof doors, the melted layer. This can be seen from the duce other, similarlyspecific temperature misalignmentof gates,and the crackingof mason- generalthermodynamic effect on the chemi- dependences. ry.Many people often have simply and mistakenly In contrastto the specificityof d(p, the assumedthat these effectsresult solely from the cal potentialof a system by a change in its eDcpansionof pore wateron .When con- external environment (6). If the uilper- thermomolecularpressure is a universalther- fined,water can rupturepipes, breakbottles, and turbed chemical potential of a system is modynamicfunction. From Eqs. 3 and 5 crackrocks as it freezes.However, most of the and the field energyper moleculeis destructiveeffects of frost heavingare causedby ,u(T,P) bPm= -plqmt (7) u, the chemicalpotential is changedto ","a complexprocess that results from the peculiarbehavior of water and other [1'( T,P,u)= [1(T,P) + u The negativesign indicatesthat the inter- liquidsas they freezewithin porousmaterials. In facialfree energy is loweredby surfacemelt- particular,water is drawnto the freezingsite from = A(ToP)+ bP/p (3) ing, so that l^y < 0. It may appearthat the elsewhereby the freezingprocess itself. When this Hencethe interfacialenergy term introduces interfacesare mechanicallyunstable under wateraccumulates as ice, it forcesthe apart, the influenceof a negativepressure acting producingexpansion of the externalsoil bound- an addedpressure aries,as as internalconsolidation. The dy- on the liquid and tending to pull the inter- namicprocess of ice segregationand the expan- bPm= A(df7@d)= Pi[lls(ToP)-Ai(r,P)] facesapart. However, such thickening of the sion resultingfrom freezingof the in SitU pore liquidlayer would requirethe conversionof water,together, cause frost heaving.

SCIENCE, VOL. 246 I592

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Frostheave has been suggestedas the driv- 9. Committeeon Permafrostof the Polar Research J. Haymet,ibid. 76, 6262 (1982); J. N. Israelachvili Board, Ice Segregationand Frost Heavislg (National andP. M. McGuiggan,Science 241, 795 (1988); D. ing mechanismfor the developmentof pat- AcademyPress, Washington, DC, 1984). M. Zhu and J. G. Dash, Phys. Rev. Lett. 60, 432 terned ground in permafrostterrains and 10. B. Hallet, S. P. Anderson,C. W. Stubbs, E. C. (1988); G. An aIld M. Schick, Phys. Rev. B39, alpineareas, where the seasonalmotion of Gregory,Proc. Fifth Int. Conf: (National 9722 (1989). Academyof Sciences,Washington, DC, 1988), vol. 13. I thankG. An, M. B. Baker,M. P. Den Nijs, B. pore water and ice produce sorting and l,p. 770. Hallet,and E. A. Sternfor criticismand discussions, profilingof the ground surfacein regular 11. D. H. Everett,Trans. Faraday Soc. 57, 1541 (1961); and R. Lipowskyfor pointing out an errorin a M. Vignes-Adler,J. Colloid Interf: Sci. 60, 162 earlierversion. This researchwas supportedby NSF geometricpatterns (10). (1977); R. D. Miller, Cold RegionsSci. Technol.3, grantDMR 86-11466. The physicalbasis for the persistenceof 83 (1980); R. R. Gilpin,J. Colloid Interf:Sci. 68, unfrozenwater below the normal melting 235 (1980). 12. J. Q. Broughton,A. Bonissent,F. F. Abraham,J. point has been attributedto variousmecha- Chem.Phys. 74, 4029 (1981); D. Oxtobyand A. D. 4 August 1989; accepted13 October1989 nisms,including dipolar forces, density vari- ations,and the pressuremelting of ice (11). However, the National ResearchCouncil reportsthat therehas been no consensuson the fundamentalcauses Air Ventilationby Recoil Aspirationin The limitationsof all current models may be PolypteridFishes characterizedcoltectively by simplystating that at present no model enjoys universalor general acceptance. . . It is not certainthat a determinis- ELIZABETHL. BRAINERD,KAREL F. LIEM, CRISTLANT. SAMPER tic formulationadequate for either the scientific or the engineeringneeds can be developed. High-speed x-ray cine films synchronized with intra-pleuroperitonealpressure mea- The presenttheory explainsthe ice phe- surementsshow that polypterid fishes aspirationbreathe by the deformationand recoil nomenaas consequencesof surfacemelting, of their bony-scaled integument. Paleozoic amphibians arose from ancient air- and it predicts that similar effects should breathing fishes and retained piscine bony scales in V-shaped rows along the belly. occurin othermaterials. However, although These scales resemble those of modern polypterid fishes and may have contributed to Eq. 7 is completely independent of the inhalation by elastic recoil. The discovery that polypterid fishes breathe by recoil nature of the interactions,its universality aspirationis the first evidencefor aspirationbreathing in any lower vertebrate.The use restson the assumptionthat the melt liquid of recoil aspiration by polypterids shows that elastic storage in a stiff body wall can is identicalwith the bulk.This is an approxi- contribute to inhalation in animals with limited capacityfor active aspiration. mation becausea liquid is modifiedin the proximityof its boundaries,where it is more MOSI AIR-BREATHINGFISHES, LACK- cavitydiameter decreases as lung diameter ordered (12). The range of the ordering ing the diaphragmor movable increases(Fig. 1). dependson the natureof the liquid and the ribs thought necessaryfor aspira- The use of aspirationto fill the lungs in wall. Thereforethe equationis strictlyvalid tion breathing,use a buccalpulse pump to polypterid fishes is demonstratedby the filltheir respiratory gas bladders(1). Aspira- patternof buccaland lung diameterchange As T decreases,the layer thins and the tion has never been demonstratedin air- shownin Fig. 1. UnlikeAmia lung diameter, proximityeffect becomes more important; breathingfishes or amphibians,although its Polypteruslung diameter increasesrapidly as a result, the pressure falls below the use has been suggested (2) and refuted (3) while the mouth is still open, andthe buccal asymptoticrelation in a nonuniversalman- for the Amazonianfish Arapaima,and esti- and lung diametersincrease simultaneously. ner vating lungfishmay ventilatetiny amounts This patternindicates that air is suckedinto (<0.3 ml) of air by aspiration(4). We show the lungs through the open mouth, rather thatpolypterid fishes ventilate their lungs by than being forced in by a buccalpump. A REFERENCES AND NOTES aspirationand that this is accomplishedby mouthfulof air is usuallypumped onto the 1. D. Nenow and A. Trayanov,J. Cryst. Growth 79, 801 (1986). the deformationand recoil of their bony- lungs at the end of inhalation, but this 2. A. A. Chernov,Z. Phys. Chem. Liepzig 269, 941 scaledintegument. We call this novel venti- buccalair contributesless to the total venti- (1988). latory mechanism"recoil aspiration."The latedvolume than does the aspiratedair (6) 3. J. F. van der Veen, B. Pluis, D. van der Gon, in Chemistryand Physics of Solid Surfaces (Springer- discoverythat polypteridfishes breatheby (Fig. 1, Polypterus,lung diameterincrease Verlag,New York,1988), vol. VII. recoilaspiration may affectour understand- aftermouth is closed).Sometimes, however, 4. J. G. Dash,Proceedings ofthe Solvay Congresson Surface ing both of early tetrapod breathingme- the buccal air is simply expelled from the Science,F. W. De Wette,Ed. (Springer-Verlag,New York,1988). chanicsand of the role of elasticstorage in opercularopenings at the end of the air- . . 5. , Contemp.Phys. 30, 89 (1989). ventl. .atlon. breath.X-ray cine films also show that po- 6. See, for example,L. D. I,andauand E. M. Lifshitz, Statistical Physics (Pergamon, New York ed. 3, The fundamentaldifference between pulse lypteridfishes exhale through the opercular 1980), vol. 5, part 1, p. 73. pump and aspirationventilation is that in openings and inhale through the mouth: 7. D. M. Andersonand N. R. Morgenstern,Proc. pulse pump systems air forces the lung to they do not, as others have suggested, Second Int. Conf Permaflost(National Academy of Sciences,Washington, DC, 1973), pp. 257-288. expand,whereas in aspirationsystems air is breathethrough the spiracles(7). 8. Representativearticles describing laboratory studies suckedinto the alreadyexpanding lung (5). Aspirationbreathing requires the genera- of frost heaveare R. W. R. Koopmansand R. D. In fishesusing a buccalpulse pump, such as tion of negativepressure in the body cavity Miller,Proc. Soil Sci. Soc. Am. 30, 680 (1966); F. J. Radd and D. H. Oertle, Proc. Second Int. Conf: the bowfin, Amia calva, the mouth cavity surroundingthe lungs. We have measured Permafrost(National Academy of Sciences,Washing- expandsto fill with air and compressesto considerablenegative pressures in the pleur- ton, DC, 1973), p. 377. M. Vignes and K. M. Dijkema,J. Colloid Interf Sci. 49, 165 (1974); M. pump air into the lung. The lung begins to operitonealcavities of two polypteridspe- B. G. M. Biermans,K. M. Dijkema,D. A. De Vries, fillonly afterthe mouth is closed,and buccal cies, Polypterussenegalus and Erpetoichthysca- Nature264, 166 ( 1976); S. W. Hopke,Cold Regions labaricus.X-ray cine filmssynchronized with Sci. Technol.3, 111 (1980); M. Buil, J. Aiguirre- Puente,A. Soisson,C. R. Acad. Sci. Paris 293, 653 Museumof ComparativeZoology, HarvardUniversity, pressuremeasurements show that the most (1981). Cambridge,MA 01238. negativepleuroperitoneal pressure occurs at

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