Apr 10, 2001 - Stephen J. Lane, 1Bernard A. Chouet, 2 Jeremy C. Phillips, 3 Phillip .... (gum rosin) [Cobbold and Jackson, 1992] and organic solvents as.
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106,NO. B4, PAGES 6461-6476,APRIL 10, 2001
Experimental observationsof pressure oscillations and flow regimes in an analoguevolcanic system Stephen J.Lane, 1Bernard A. Chouet, 2Jeremy C.Phillips, 3PhillipDawson, 2 Graham A. Ryan, 1andEmmaHurst 1 Abstract. Gas-liquidflows, designedto be analogousto thosein volcanicconduits,are generatedin the laboratoryusingorganicgas-gumrosinmixturesexpandingin a vertically mountedtube.The expandingfluid showsa rangeof bothflow andpressureoscillation behaviors.Weakly supersaturated sourceliquidsproducea low Reynoldsnumberflow with foam expandingfrom the top surfaceof a liquid that exhibitszero fluid velocityat the tube wall; i.e., the conventional"no-slip"boundarycondition.Pressureoscillations,oftenwith stronglong-periodcharacteristics and consistentwith longitudinaland radial resonant oscillationmodes,are detectedin thesefluids. Stronglysupersaturated sourceliquids generatemoreenergeticflows that displaya numberof flow regimes.Theseregimesinclude a staticliquid source,viscousflow, detachedflow (comprisinggas-pockets-at-wall and foamin-gasannularflow, thereforedemonstrating strongradialheterogeneity),and a fully turbulenttransonicfragmentedor mist flow. Each of theseflow regimesdisplays characteristic pressureoscillationsthat canbe relatedto resonanceof flow featuresor wall impactphenomena. The pressureoscillationsare producedby the degassing processes withoutthe needof elasticcouplingto the confiningmediumor flow restrictorsandvalvelike features.The oscillatorybehaviorof the experimentalflows is comparedto seismoacoustic datafrom a rangeof volcanoeswhereresonantoscillationof the fluid within the conduitis alsoofteninvokedas controllingthe observedoscillationfrequencies.On the basisof the experimentaldatawe postulateon the natureof seismicsignalsthat may be measuredduring large-scaleexplosiveactivity. 1. Introduction
harmonics, usuallyassociated with sourceresonance [Hurstand Sherburn,1993; Chouet, 1996a].Anotherform of seismicity, Hydrothermaland magmaticflows are frequentlytwo-phase known as eruption signal, generally accompaniesexplosive mixturesof gas and liquid, often with solid particlespresent. surfaceactivity and varies greatly in amplitudeand duration These flows generate pressure oscillations that result in [Harlow et al., 1996]. The mechanismsgeneratingeruption measurablevibrations of the ground [e.g., Chouet, 1985, 1986, signalsare unknown,but are currentlybeinginvestigated using 1988, 1996a; Chouet et al., 1994; Hurst and Sherburn, 1993;
dulian, 1994; Schlindweinet al., 1995; Kumagai and Chouet, 1999, 2000]. If the magmaticactivity intersectsthe surface,then atmosphericvibrations are also generated[e.g., Morrissey and Chouet, 1997a; Garcis et al., 1998]. The source mechanisms inferred from very long-wavelength seismic data yield informationaboutthe location,geometry,and orientationof the conduitand the space-timehistoryof the motion of the conduit wall, which is related to the pressurefield in the fluid [e.g., Ohminatoet al., 1998]. Pressuretransientsand sustainedpressure fluctuations within the conduit [e.g., Chouet, 1996a] are considered to generatelong-period(LP) seismicityand harmonic tremor,respectively.Tremor spectragenerallyfall into two broad categories:multiple peaks at unrelated frequenciesassociated with pathand/orsiteeffects;or one dominantpeak,perhapswith
computer-based models[Nishimuraand Chouet,1998]. LP events and tremor can occur during preeruption and posteruption periodsand duringexplosivevolcanicevents.These oscillations havebeenattributed,amongothermechanisms, to the resonanceof acousticallydiscretesectionsof the conduitsystem [e.g., Chouet, 1985, 1986, 1988, 1992; McNutt, 1986]. The sourceof the pressure transients triggeringthe resonance remains
elusivebutmaybe dueto nonlinearexcitationwithinanunsteady flow [Julian, 1994;Chouet,1996b]or thejerky extensionof a crack tip [Aki et at., 1977; Chouet, 1986]. The occurrenceof unstableshockwavesduringflow througha constriction hasalso beenproposedas a source[Morrisseyand Chouet, 1997a].It is also known
that individual
bubbles resonate at characteristic
frequencies.This observationmay be usedto obtainbubblesize distributions and bubblenumberdensity[Pandit et al., 1992] in bubblywaterjets. Theseoscillations are thoughtto be stimulated
•Department of Enviromnental Science, Lancaster University, byflowturbulence andaretherefore most likelytooccur in
Lancaster, England, UnitedKingdom.
inviscidflows suchas aeratedwater ratherthan in muchmore
:Volcano Hazards Team. U.S. Geological Survey, Menlo Park,viscous magmatic rhyolite foams. Clouds of bubbles arealso California. known toresonate atcharacteristic frequencies [Luetal.,1990]. 3Centre for Enviromnental andGeophysical Flows,School of
Mathematics, University ofBristol, Bristol, United Kingdom. Copyright2001 by theAmericanGeophysical Union. Papernumber2000JB900376. 0148-0227/01/2000JB900376509.00
6461
Eruptions also produce continuousacousticsignals with frequenciesranging from 0.001 to 20 Hz and above. These airbornesignalscanoftenbe correlated with pressure fluctuations and resonancewithin the volcanic conduit during eruption [Morrissey and Chouet, 1997b; Garcds and McNutt, 1997; Garcds,1997;GarcdsandHansen,1998;Garcdset al., 1998].
6462
LANE ET AL.: EXPERIMENTAL
PRESSURE OSCILLATIONS AND FLOW REGIMES
Pressureoscillationsin two-phaseflows have been observed experimentally in low-viscosity water-gas systems[e.g., Leer, 1988] and attributedto resonanceof the gas-filledcavity. WaterCO2 systemshave also demonstratedpressureoscillations(E. Brodsky, personal communication [1998], with reference to Mader et al. [1997]). Slow-decompression corn syrup experimentswith water as a volatile species[Hammer et al., 1998] showedthat pressureoscillationscan be attributedto the interactionbetweennonequilibriumdegassingand gas removal rates in higher-viscositysystems.For a given timescale,higherviscosity liquids allow a greater degree of dissolved gas supersaturation beforebubbleformationandgasescape,resulting in a pressurerise in the system. This implies that systemsfar from equilibrium may be particularly prone to oscillatory behavior due to nonlinear interactions between pressure, dissolvedgascontent,and the degreeof supersaturation required for differentmodesof gasescape[Phillipset al., 1995]. Acoustic vibrationsnaturally result from unsteadyflow and interactions with structuresimmersed in the flow [Howe, 1998]. Pressure oscillationsappearto accompanymany gas-liquidflows, and considerableefforts are made to suppresssuch oscillationsin industrialapplications[Tong and Tang, 1997]. The measurement and characterizationof pressureoscillationsare thereforevital to bridgingthe gap betweenlaboratoryfluid dynamicsimulationsof
thereforeconsiderthat our experimentsachievesomemeasureof steadystatebehavior. For horizontaltransportprocesses within the conduitthe ratio of bubble diameter to conduit diameter is the key scale. The
volcanic conduit flow, theoretical conduit flow models, and
mechanismsfor the generationof pressureoscillationsthat rely on the elasticdeformationof the conduitwalls [Julian, 1994] or changesin conduitcrosssection[Morrisseyand Chouet, 1997b] cannotbe investigated.The tubewalls are impermeable;therefore our experiments do not simulate the effects of either forced injection of groundwaterinto the conduit or loss of volatile speciesthroughthe conduit wall, both of which may occur in volcanic systems and have implications for flow behavior [Eichelberger et al., 1986; daupart, 1998]. Consequently,all experimental observationsof pressureoscillations and flow regimes in the expanding bubbly flows presented here are interpretedin termsof fundamentalprocessesof bubblegrowth andburstingor flow expansion.
seismoacoustic field measurements. In this studywe presentdata on pressureoscillations measured in expanding foam flows generated by decompressionof gum rosin-organic solvent solutions[Phillipset al., 1995].
2. Comparing Experimental and Natural Systems
diameter of theexperimental conduit is about103timessmaller than that of a natural volcanic
conduit. Bubble sizes within the
solid gum rosin foam fragmentsrecoveredfrom the vacuum chamber range from -1 lam to 1 mm and are similar in appearance to thoseshownby Phillipset al. [1995]. Bubblesizes in naturalpumicerangefrom micrometersto centimeters.Most importantly,bubblesizeswithin the bubblyliquidsand foamsare much smallerthan the conduitdiameterin both cases,implying that the effect of bubbleson the fluid rheology [Manga et al., 1998] prior to fragmentationwill be similar. In particular,the bubblesare sufficiently small that their buoyantrise velocity is small comparedto typical flow velocities;thus the conditionof "equilibrium slip" [Tong and Tang, 1997; Melnik, 2000] is satisfied in both cases. In the experiments demonstrating fragmentation(Plate 1), individual foam slugsand gas pockets sometimesoccupythe tube diameter.Gas pocketsand magmatic foam slugscan also occupythe entire conduitwidth in smallerscalevolcaniceruptions[ Vergniolleet al., 1996]. Our experimentswere conductedin a smooth, effectively
rigid-walled(maximumstrain 10's) glass tube. Hence
The laboratoryfluid in our experiments hasbeendescribed by Phillips et al. [1995] and usessolutionsof natural pine resin (gumrosin)[CobboldandJackson,1992] andorganicsolventsas a hydrated magma analogue. Decompressionof a hydrated magma below the water exsolution pressureresults in the nucleation and growth of bubbles and the generationof an expandingfoam flow in a volcanic conduit [e.g., Massol and 2.2. Thermodynamic Similarity Jaupart, 1999;Melnik, 2000]. Similarly, decompression of the Volumeexpansionin the experimentaland naturalsystems experimental gum rosin-organic solvent solution below the depends on thenumberof molecules of volatilespecies exsolved solventexsolutionpressure(-- 20 kPa for acetoneand 60 kPa for as gasto drive the flow and on the ratio of initial to final diethyletherat 20øC) formsan expandingfoam flow in a vertical pressures (decompression ratio), both of which are related cylindricalglasstube (Plate 1). To assessthe suitabilityof this through thevolatilesolubilitylaw.Thespeciation anddiffusivity systemas an analogue to volcanic conduit processes,we must of the volatiles will determine the rates at which the exsolution considerwhetherthe systembehaviorand the balanceof forces process canproceed. Theseratesaredemonstrably highenough actingon the flowing fluid are similar at naturaland laboratory in both natural and experimentalsystemsto generateflow scales.
fragmentation. Weuseunitsof molespercubicmeterforvolatile concentration so that unit volumes of both volatile-saturated
2.1. Geometric Similarity
magmaandgumrosinwill expandby similaramounts whenthe remainssimilar.The solution In the presentcontext,geometricsimilarityis the requirement ratioof initial to final pressures usedin our experiments (15-30 wt % organic that the length scales be sufficiently large for long-range concentrations dynamical interactions to develop. These length scales are solventin gumrosin,seeTable 1) are thereforeequivalentto identifiedfrom the scalesof volcanicedificesand their products. For vertical transport the ratio of the conduit length to its diameteris the key scale.The distancefrom the volcanicvent to the volatile exsolutionlevel typically rangesfrom 500 to 5000 m, and observedconduit diametersare in the range 10 to 100 m. This yieldsa conduitlengthto diameterratio of the orderof 50. In comparison,this ratio for the experimentaltube is 40. Massol and Jaupart [1999] suggestthat steady state conditions are achievedif the eruptiondurationis longerthanthe time required for a fluid packet to ascendfrom the magma chamberto the surface. In our laboratory setup this timescale is 0.1 s or less, comparedwith an experimentalflow durationof 1 to 2 s. We
2-4 wt % waterin magmaprovidedthe decompression ratiosare similar.
The averagedpressure gradientfor explosivevolcanicflow between exsolution levelandventis =5x107/2000 = 25 kPam'• [Massol andJaupart,1999].Themeasured tubebasepressure for our experiments is --20 kPa for ether-driven flows,yieldingan
average pressure gradient of-•13 kPam'•. Giventhatthe experimental liquid density (--1000 kgm'3)ishalfthatofmagma (--2000kg m'3),the contribution of the streamwise pressure gradientto flow velocityandacceleration shouldbe similarat laboratory andvolcanicscales.The ratioof initial (exsolution level) to final (vent) pressure,which indicatesthe degreeto
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Lo[o ],• Plate 1. Schematicdiagramof experimentalsystem.Optical (0) and pressure(P) transducersare marked. The tube is isolated from the vacuumchamberwith a thin plasticrupturedisk.A still film cameraimage showsa fragmentingdiethyl ether-driven foam flow in progress,illustratingthe growthof foam from the liquidinterfaceandthe unfragmented andfragmentedregionsof the flow. Digital video frames (1/4000 s) show "typical" fragmented,gas-at-wallannular,and gas-pocket-at-wall regions of the flow.
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Plate 2. Band-passed pressure data (10-150 Hz) and spectrograms obtainedduringthe nonfragmenting acetone-driven flow. Spectrogram full-scaledeflection(FSD) is givenin the top left cornerof eachpanelandcanbe compared to theamplitudeof the band-passed pressuresignalfor eachP transducer. Vertical linesrepresentthe timesof opticaldetectionof the foam flow at theopticaltransducers adjacentto eachpressuresensor.The time of tubedecompression anddetectionof foamat O12 are beyond the limit of the plots.The noisesignalcan be seenin the first 0.6 s of each transducer data.
6464
LANE ET AL.' EXPERIMENTAL
PRESSURE OSCILLATIONS AND FLOW REGIMES
The Reynoldsnumber is defined as the ratio of inertial to
Table1.Solution andExperimental Conditions Used a
Psvp/Pv viscousforceswithin the expandingflow and may be expressed as Re = (U p r)/•t•, where r is the conduit radius, •e is the wt % ml Pa s Pa effective viscosityof the bubblyliquid,p is the fluid density,and 1 21.8+0.2 274+1 1.07+0.05 5000 4 U is the horizontallyaveragedvelocity. Using data from Massol acetone and Jaupart [1999], we can estimateRe at and just above the 2 22.4+0.2 315+1 0.24+0.05 2000 exsolutionlevel, where gas-volumefractionsare smalland strain acetone rates low. For a gas-volume fraction • < 0.45 and capillary 3 19.0+0.2 273+1 1.93+0.05 6000 number(see below) Ca = 0.3 (near sphericalbubbles)the fluid ether viscosityis k/•: = kGJ•t, where phase[Massoland Jaupart, 1999], the velocity increases rapidly, dv:/dz is the elongationalstrain rate, k is a constant,Goois the and the densitydecreases,resultingin a very large Re. Flow is elasticmodulusat infinite frequency,and # is the zero-frequency then implied to be turbulentin both natural [Jaupart, 1996] and viscosity.For a wide rangeof naturalcompositions, k - 0.01 and laboratoryflows upstreamof fragmentation.The Re similarity Goois in the range3-30 GPa [Dingwelland Webb,1989]. Using a duringthe early and late stagesof the natural and experimental sound speed of 2000m s-• measured ingumrosin-organic solvent flows, combinedwith the similarityin the physicalpropertiesof solutions anda density of 1000kg m-3,we estimate Goo to be the fluids, implies similar dynamic flow behavior for both --4 GPa. The value of k is not known, but we suggestabovethat systems. strain rates are similar. The viscosity of gum rosin-organic solventsolutionsis generallylower thanthat of hydratedrhyolite, but increasesmore rapidly as degassingproceeds(Figure 1). -•Gum rosin-acetone • 200C Therefore both the natural and experimental fluids may [Phi/lips et aL, 1995] 10 experience the transition from viscous fluid to brittle solid • &urnrosin-diethyl ether • 20'C behaviorasthe viscosityincreasesduringdegassing. This study Rhyolite-water • 850øC 2.3. Dynamic Similarity [HessandDing, mll, 1996]
Dynamic similarity is the requirement that natural and experimentalsystemsexhibit the sameflow regimes.This means not only matching the flow Reynolds number (Re) but also conditionsof bubbledeformationand acousticvelocity,as we are also interestedin the transmissionof pressurefluctuations.We requirethe quantificationof suitablenondimensional parameters and a demonstrationthat their values fall within the ranges defining different flow regimes. Quoting Mayinger [1981] as cited by Tong and Tang [1997, p. 355] "Scaling by use of dimensionlessnumbersonly is limited in two-phaseflow to simpleand isolatedproblems,wherethe physicalphenomenon is
a uniquefunctionof a few parameters." Similarityparameters for viscoustwo-phaseflows are not yet well-established[Tong and Tang, 1997;Kaminskiand daupart,1998],soherewe are limited to a discussionof matching appropriatelength scalesin the thermodynamic anddynamicbehaviors.
•6
&urn rosin-acetone
8
Iog•o(viscosity)[Pa$] 21690/(n[Mol/m3]+4.94)-1300
Gumrosin-diethylether Iogzo(viscosity)[PaS]= 23390/(n[Mol/m3]+6.15)-1310 0
1000
2000
3000
4000
Volatile concentration [mol/ms] Figure1.
Viscosityversusvolatileconcentration. The bold
solidline showsthe datafor hydratedrhyoliteat 850øCobtained by HessandDingwell[ 1996].Soliddotsare datafor gumrosinacetoneat 20øC obtainedby Phillipset al. [1995]. Solid squares aredatafor gumrosin-diethyl etherat 20øC.
LANE
ET AL.: EXPERIMENTAL
PRESSURE
OSCILLATIONS
AND
FLOW
REGIMES
6465
[Sparkset al., 1997; Morrissey and Chouet, 1997b]. The ratio of the measuredvelocitiesof foam fragmentsnear the tube top in the experimentalsystemto the calculatedacousticvelocities at appropriategas-volumefractionsyields Mach numbersin excess of 0.8. The nearconstantmaximumflow velocityassociatedwith a three time increasein driving pressurebetweenacetone-and ether-driven flows suggeststhat the vent Mach number is approaching unity. This impliesthat thereis a degreeof similarity in the Mach numbersof the flows in a volcanic conduitduring explosive activity and the Mach numbers of the flows in the experimentaltubeat high supersaturations. We areobservingpressureoscillationswithin the experimental fluids and comparingthese to estimatesof pressurefluctuations generatingvolcano-seismic signals;thereforewe requirea means of comparing oscillation amplitudes in systemswith greatly differingabsolutepressures.Acousticresonancein boiling water flows may have amplitudesrepresenting a significantfractionof the pressurelevel [Tongand Tang, 1997].Thereforewe adoptthe ratio of oscillation amplitude to averagepressure(AP/P)as a prerequisite for laboratorysimulationof explosivelydegassing meansof comparisonbetweendifferentsystems. magmaflowswithinvolcanicconduits. The fluid rheologyis complicatedby the presenceof bubbles 3. Methods [Mangaet al., 1998]thathavea variablenumberperunit volume A 1.5-m-long(3.8 cm internaldiameter)tubeof borosilicate andvariablesizeandcandeformduringfluid flow. The presence isvertically mounted beneath a vacuum chamber of 0.4m3 of bubblescan increaseor decreasethe apparentviscosityand glass pressure, producehighly non-Newtonianand strain-history-dependentvolume(Plate 1). The experimentaltube,at atmospheric rheoiogy at high gas-volume fractions. A dimensionless is isolatedfrom the vacuumchamberby a plasticmembranewith parameter for the behaviorof bubblesin viscousflows[Mangaet an imbeddedhot wire rupturesystem.Ruptureof the membrane al., 1998]is thecapillarynumber,Ca = (dr__/dt)# r/c•, in whichœ initiates the experiment. Pressure transducers(P) with a
Massoland daupart [1999] suggestusingthe dimensionless conduitradiusto heightratio as a scalingparameter.This is small for bothexperiments(0.013) and eruptions(-- 0.02). Massoland Jaupartalso suggestthe use of this ratio multiplied by the Reynoldsnumber (Re). These parametersrely on the relevant scalebeingthe conduitheight and thereforeassumethat radial pressuregradientsare negligible.However,becauseof the strong dependence of magmaviscosityon dissolvedwater contentsthe flow pressuresvary on much smaller length scales when fragmentation occurs[Massoland daupart, 1999;Melnik, 2000]. The strongdependence of gum rosinviscosityon organicsolvent contentsin the experimentalfluid impliesthat the conduitlength is not an appropriateexperimentallength scaleeither and that radialpressuregradientsare likely to be presentboth in volcanic and experimentalconduits.Indeed, the more rapid increaseof viscositywith degassingin the experimentalfluid (Figure 1) impliesthatthis phenomenon will be strongerin the experiments. Thereforeuseof a fluid systemwith a stronglyvolatile-dependent viscosity, as consideredhere, is likely to be an essential
is the strain,c•is the surfacetension,# is the liquid viscosity,and frequencyresponseof 10 Hz to 100 kHz are combinedwith (O) to providemeasurements of the flow r is the bubble radius. Ca representsthe ratio of the bubble opticaltransducers (Plate 1). The transducers are logged with a sampling frequency deformingto bubblerestoringforces.At low Ca (bubblesclosely boardmounted in a PC. spherical),the bubblyfluid or foamviscosityis generallygreater of 40 kHz usinga 12-bitdataacquisition Gum rosin powder is mixed with either acetone or diethyl than that of the liquid phase,while at high Ca (bubbleshighly the experimental sourceliquid [Phillipset elongated)the bubbly fluid or foam viscosityis generallyless etherto manufacture (Table 1) of the solutions are thanthat of the liquid phase[Manga et al., 1998]. The existence al., 1995].The initial viscosities measured using a falling ball viscometer. The solution volatile of tube pumice [Marti et al., 1999] suggeststhat Ca >>1 for (Table1) is measured by fully degassing samples of the explosivevolcanicflows. Microscopeobservationof fractured content experimental liquid at 80øC overnight and cooling to give solid surfaces on foam fragmentsgeneratedduringhigh decompression theresultant weightloss. ratioexperiments oftenshowselongatedbubbles,as illustratedby gumrosin,thenmeasuring The O sensordataareusedto monitorboththe presence of gas Phillips et al., [1995]. This implies that Ca >> 1 for the (low attenuation) and foam (high attenuation) in the tube at each fragmentingflows. Unfortunately,the highly friablenatureof the position andto providea visualindication of wherefoam opaquegum rosin foam makes detailed study of the bubble sensor andgaspockets arepositioned in thetubeat anyonetime. shapesand sizesdifficult. Overlap of capillarynumberand gas- slugs dataareexported to the SeismicAnalysisCode volumefraction(seebelow) impliesthat the presenceof bubbles TheP transducer will havesimilarrheologicaleffects[Manga et al., 1998] in both (SAC) program(availableat http://www-ep.es.llnl.gov/wwwep/esd/seismic/sac.html) for scaling, frequency band-passing, and the naturalandexperimentalfluids. analysis. To exploretherangeof signalamplitudes and We are specifically interested in the pressureoscillation spectral and spectrograms were behavior of the experimental system;therefore the acoustic frequencies,data were band-passed, for 10-150Hz, 50-500Hz, 500-1000Hz, and1-5kHz velocity of the experimentalfluid as a function of gas-volume generated ranges.Blankrunsandexperimental baselinedata fractionshouldbehavein a similar fashionto that in magmatic frequency wereanalyzed for transducer noise,apparatus oscillations, and systems.Calculations indicate that the acoustic velocity of hereare considered artifactfree magmaticfluids decreasesrapidly from that of the singlephase otherartifacts.Data presented and above noise unless otherwise stated.
liquidto a minimum between 100and200m s'• ata gas-volume fraction--0.8, then rises again to the velocity of the single gas phase.Gas-volumefractionsin pumicegenerallyrangefrom 0.6 to 0.8. Gum rosin organic solvent fluids display the same behavior,but the lower liquid density,bulk modulus,and system
pressure yieldanacoustic velocity minimum of 10to 15m s'• ata gas-volume fraction of 0.5. The gas-volume fractions of preservedexperimentalfoams range from 0.75 to 0.9. We can therefore expect strong similarity between the resonance behaviorsof the naturalandexperimentalfluids. The ratio of flow velocity to acousticvelocity is known as the Mach number. Theoretical simulationssuggestthat volcanic conduit flows are often close to Mach 1, and choked, at the vent
4. Results and Interpretation Table 1 lists the conditionsfor the three experimentswe documenthere.Theseexperimentscovera rangeof sourceliquid supersaturation resultingfrom decompression. We limit ourselves to documentingthe major observationswith sufficient text to guidethereaderthroughthe figures.
4.1. Low Supersaturation Flow The experimentaloscillationfrequenciesare consistentwith longitudinaland radial resonanceof the foam column and occur
6466
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ET AL.' EXPERIMENTAL
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10 s, and (3) collapsingfoam after 10 s. We concernourselves with the firsttwo stageshere. Plate 2 showsspectrograms for each P transducerduringthe interval 0.35-2.95 s, along with the 10-150 Hz band-passed pressuredata.Vertical lines identifythe times at which the foam front was detectedby the O transducers. As the foam front passes P transducers 2, 5, and 8, thereis a rapidpressurerise(Figure2), which producesthe first significantsignalon the spectrograms (Plate2). The pressure riseis highestat P2 anddecreases through P5 and78 (Figure2). The magnitudeof the pressurerise reflects the hydrostaticpressurein the fluid column.The followingfew tenthsof seconds are characterized by low-amplitudeoscillations
O12 O10
.
•
OSCILLATIONS
07
in the 10-30 Hz range.The ratio AP/P, in whichP denotesthe solventsaturatedvapor pressure(svp = 20 kPa at 20øC for 06 acetone),is =1% for these oscillations.Following another 04 pressure stepnear 1 s at P2 andP5 andnear 1.2 s at P8 (Figure 2), higher-amplitude pressureoscillations(AP/P = 5-10%) are detected. Theseshowa 20-Hz peakwith otherdiscernable peaks 0.5 in the 80 to 100 Hz range(Plate 2). Thesetwo regionswith 03 P? differentoscillationsignatures suggestdifferentflow behaviors, andareidentifiedin Figure2 asflow "body"andflow "head." The foamdid not reachP11 or P14 duringthe courseof the analyzeddata;thereforeoscillations in theseregionsof thetube O1 occur in the gas phase. PI1 and PI4 show very similar Liquid spectrograms (Plate2) with oscillations peakedin the30 to 70 Hz source bandoccurring between1.18and 1.25s. The signalthennarrows arounda 20-Hz peak after 1.4 s, with weakercontributionsfrom •, Noise higherfrequencyoscillations. 1.0 1.5 3.0 Figure3 showsa schematic interpretation of anunfragmenting Time (s) flow in the rapid expansionphase,with the positionof flow Figure 2. Heightversustime plot of opticalandpressuresensor regionsas a functionof time as indicatedin Figure2. Initial duringthe rapidexpansion stageproduces a volatiledata for unfragmentingacetone-drivenflow. The positionsof the degassing optical (O) and pressure(P) transducersare indicated. Open poorflow headwith detectablepressureoscillations.Beneaththe hencelower-viscosity, flow symbolsrepresentthe timesat whichthe first foamfragmentsare flow headis a morevolatile-rich, higher-amplitude oscillations. Thepressure step detected (five detected on initial decompression)and solid bodysustaining thesetwo regions(Figure 2) exceedshydrostatic symbols mark the unfragmentedflow front detected by the separating optical sensors.The symbol at zero height representsthe time at valuesandmaybe associated withincreased radialstress [Massol which P14 detected pressure falling below 99 kPa on and Jaupart, 1999] in the foam as it flows. Pressureoscillations decompression.Data are shown for each P transducerat the in the flow bodydo not propagateinto the gasabovethe flow, appropriatetube height.Pressuredata are shownafter correction implyingweakcouplingbetween the gasandoscillating foam. to removetransducerdrift. The noise-freesectionof pressuredata Thissuggests thattheflowheadhasdifferentacoustic properties between0.1 and 0.3 s is syntheticdata includedto reducehigh- thanthe flow body.The flow headthusappearsto act as an pass filter end effects. The pressurerange is indicatedby the acoustic reflector or absorber. scalebar. Shadingindicatesregionsof the observedflow regimes (seetext for details).
once the resonator length is stable on a time scale of two
Transducer P0 detected continuous oscillations onlyafter0.7 s (Figure 2 and Plate 2). This impliessomeform of acoustic discontinuity betweenthe oscillatingflow bodyandthe source liquidbetween0.4 and0.7 s. Images(e.g.,Plate1) showthatthe expanding foamoriginatesfrom the surfaceof the gumrosinorganicsolventsolution.The interfacebetweenliquidandfoam
oscillationcycles.We suggest thatsimilarprocesses takeplacein presents a strongvelocitydiscontinuity of =2000m s'l on the slowlydegassing, i.e., effusiveandweaklyexplosive,magmatic basisof ourmeasured acoustic velocityof 1950m s'• in the flows in conduits.
Decompression to low volatile supersaturations produces essentiallyunfragmenting foam flows and displaysvery minor fragmentation uponinitial decompression. Figure2 showsthe positionsof the fragmentedand unfragmented flow fronts,the oscillatory pressure data,andtheevolutionof differentregionsof the flow as a function of time for an acetone-driven flow into a
chamberpressureof 5 kPa air. Five fragmentswere detected aheadof the unfragmented flow front. This wastypicalof the initialbehaviorof all the 1ow-supersaturation experiments carried out.Thereis a time delayof 0.35 s betweendecompression and thedetection of flow expansion. Thistimeis presumably required for the generation of criticalbubblenuclei.Followingbubble nucleation,the flow behaviorcan be dividedinto threestages basedon the expansion rate.Theseare (1) rapidflow expansion between0.4 and 1.2 s, (2) static foam columnbetween1.2 and
source liquidandcalculated foamvelocity of 10m s".Benoit and McNutt[1997]propose thatsucha velocity-controlled boundary formsthebaseof theresonating conduit atArenalVolcano. They alsoinvokea velocity-controlled boundary at the top of the conduit,formedhere by the flow head. This demonstrates the experimentalgenerationof acousticstructuressimilar to those proposed to explainfield datafromvolcanicconduits.
Thestablenatureof theoscillation frequencies issuggestive of a resonant oscillation.
The establishment of a near-stable
resonator lengthovera periodof at leasttwo oscillation cycles (0.1 s at 20 Hz) maybe a factorcontributing to the increase in oscillation amplitude asthe flow wanesat =1 s (Figure2). The lengthof thisresonator (the flow body)is estimated to be 0.5 m at I s, assuming thatthe flow headboundaryis locatedbetween P2 andP5 andthatsomesourceliquidremains. Thissuggests an
acoustic velocity of 20m s-' atthefundamental frequency of 20
LANE ET AL.' EXPERIMENTAL
PRESSURE OSCILLATIONS
AND FLOW REGIMES
6467
fraction. This may imply that 20 Hz is not the fundamental
frequencybut the first harmonic.As the frequencyresponse of boththe P transducers and the spectralanalysismethodis poor below--10 Hz we may be observingthe fundamentaloscillation frequencybut be unableto resolveit from the first harmonic.The need for resonatorstability may explain the suddenonset of seismicand acousticresonantoscillationfrom broadbandsignals observed at Arenal Volcano. This may also provide an explanation for the intervalsof seismicandacousticquiescences that appearto follow increasingrates of acousticand seismic frequencychanges[Garcdset al., 1998]. Accordingto our
Gas flo
Oscillations(10-30 Hz) detected in gasafter ~ 1.• s when flow head consumed.
observations, suchquiescences maybeindicative of anincreasing rate of changeof acousticvelocity and/or cavity dimension leadingto resonator instability. With the removalof the flow headby redissolution of acetone vapordegassing from the flow body,asevidencedby the onsetof acousticoscillationat 1.2 s, we may expecta frequencyreduction as the lengthof the oscillatingfoam columnincreases.At 1.2 s thetotal foam columnis only --5 cm longerthanat 1 s; however, the oscillatingflow body lengthhas increasedfrom =0.5 to 1.03 m (Figure2). This yieldsa fundamentalresonantfrequencynear 6 Hz anda firstharmonicnear 12 Hz. This shiftis not apparentin the Plate2 spectrogram, probablybecausethesefrequencies are at the limit of the sensordetectioncapabilitiesas statedabove. Visualanalyses of thepressure traces(Figure2) from P0 between 1.2 and 1.6 s and after 1.8 s provide evidenceof two to three cyclesof oscillationswith peak-to-peakamplitudesof 1 kPa at frequencies 1 s timescaleof the experiment.
Thisexperiment shows thatacoustic pressure oscillations area
fundamental consequence of foamexpansion andcollapse and probably resultfromdynamic instability [TongandTang,1997]. Theoscillations do notrequirechanges in tubecrosssection, speeds, or otherspecialconditions to occur.It is known Figure 3. Schematicrepresentation of flow regimesandpressure transonic noiseemissions in bubblyliquids originate in the oscillationsduring the rapid expansionphase of the acetone- thatenergetic collective oscillation of thosebubbles [Luet al., 1990],butthe drivenunfragmentingfoamflow.
fundamental causes of pressure fluctuations stimulating the resonanceare not clear. However, the nonlinear behavior of
Hz. Assumingthat mostof the degassed acetoneis lockedwithin the bubbles,we obtainan averagegas-volumefractionof 0.750.80. The calculated value of acoustic velocity under
viscosity, andhencediffusivity,as a functionof volatilecontent
in a nonequilibrium compressible system mayplaya role.We suggest thata possible oscillation generation mechanism during
nonequilibrium conditions [Kieffkr, 1977]is--12ms'• forthisgas foam stasisand collapseis due to bubblecoalescence and
6468
LANE
15,'x ! X, o /
'
.
•
ET AL.'
• RIo .
EXPERIMENTAL
• ,
j
f•nt•
flow
!.
PRESSURE
,
,
/, . /
OSCILLATIONS
AND
FLOW
REGIMES
more positionallystable (Plate 4). The fragmentationlevel was observedto oscillatearoundP8 for --1.4 s. Fragmentationactivity then rapidly decreasedwith occasionalfragmentsspalling from the flow front. The unfragmented foam flow then slowly ascendedthe tube, emerginginto the vacuumchambersometime after loggingceased.The correlationbetweenpressureoscillation behaviorand flow regimeis apparentto the eye in Plates3 and4, and we now consider further the data from transducers P2 and P8 for acetone- and ether-driven
flows.
Single cycle oscillationsare detectedby transducerP2 (Plate 5) between 0.45 and 0.75 s during the acetone-driven flow. Multicycle oscillationswith strongLP characterreoccurbetween 1.05 and 1.35 s. These oscillations
.•
R2 R3•
• 0.SN •
of.,%. unfmg•nted •eq flow [•
o
..•r,,, R3
I •
Zero •!1
f
veloci•
.
i,
R4
i
Liquidsource
0.1
0.3 •ise
occur in a narrow band of 10-
30 Hz and have peak-to-peakamplitudesof 1 kPa (AP/P -- 5%).
R42•9io n
There
•., ]-03
is also some indication
range.Tla..... ß
11•..,
•JllO•..•[
t ,,c ,•,...... •JI
[11•..•o•..•
of oscillations
in the 80-100
Hz
;•o*;"-* corresponds to th,. decline
uo•,,,lll•&Ll•JllO
'
•U• rosin-acetone o
fragmenting flow 0.5 Time (s)
0.7 ? •
0.9
mpact 'spikes'
1.5 P14
--•
Plate3. Heightversustimeplotof opticalandpressure sensor
013
dataforthefragmenting acetone-driven flow.Thepositions of theoptical (O) andpressure (P)transducers areindicated. Open symbols represent thetimesat whichthe firstof 150foam
fragments aredetected, and solid symbols mark theonset of Pll
o10
unfragmented flow.Thesymbol atzeroheight represents thetime ,,--, at which P14 detectedpressurefalling below 99 kPa on
decompression. Pressure dataare shownaftercorrection to
IE
'--'
•
frogm½.ntcd • flow
1.0
removetransducer drift. The noise-freesectionof pressure data _o P8
•n vo
between 0.1 and0.3 s is synthetic dataincluded to reduce high- +-
passfilterendeffects. Thepressure rangeis indicated bythe ._r: scale bar.Shading indicates regions oftheobserved flowregimes+(seetextfordetails).
._mP5
Rga
,
' R2b •
•
, O4
a2,R3o• R4- a•ion [ bursting,a mechanismproposedfor the generationof volcanic tremorby Ripepeand Gordeev[ 1999].
4.2. High SupersaturationFlow
Theseexperimentalflows includea numberof flow regions with characteristic pressure oscillationbehaviors.We suggest that suchbehaviors may be observed in stronglyexplosivemagmatic
0.5 P?
unfr•mented flow
R3 Zero well
veioc• flow
'
>
Gum rosin-die, hyl ether
fragmentingflow
1
flows in conduits.
The generalbehaviors of acetone-andether-driven flowsare illustratedin Plates3 and4, andthe flow parameters are listedin Table 1. The transitionbetweenfragmentedand unfragmented acetone-driven flow movedup the tubewith an averagevelocity
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Time
of 1 m s'•, thusdefining thefieldintimeandspace withinwhich Plate 4. Height versustime plot of optical and pressuresensor
the flow wasfragmented(Plate3). The flow rapidlywanedasthe source solution became depleted in =1 s. Fragmentation effectivelyceasedat this point,andthe unfragmenting foam flow slowlyexpandedup the tubewith occasionalemissionof slowly movingfoam slugsfrom its top surface.The fragmentedether-
data for fragmentingether-driven flow. The positionsof the optical (O) and pressure(P) transducersare indicated. Open symbols represent the times at which the first of 270 foam fragmentsare detected,and solid symbolsmark the onset of unfragmented flow. The symbolat zeroheightrepresents the time drivenflowfront(Plate4) reached a peakvelocity of 34 m s'l, at which P14 detected pressurefalling below 99 kPa on similarto thatof the acetone-driven flow (32 m s'l, Plate3) decompression. Pressuredataare shownafter beingcorrectedto despite having potentially 3 times the driving pressure.This removetransducerdrift. The noise-freesectionof pressuredata impliesthat theseflows were overpressured in a mannersimilar between0.1 and0.3 s is syntheticdataincludedto reducehighto someexplosivevolcanic conduitflows [Sparkset al., 1997]. passfilter end effects.The pressurerange is indicatedby the The ether-driven flows behaved differently from the acetone- scalebar.Shadingindicatesregionsof the observed flow regimes driven flows, in that the detectedfragmentationlevel was much (seetext for details)
LANE ET AL ßEXPERIMENTAL
PRESSURE
OSCILLATIONS
REGIMES
6469
signalis a factor of 3 lessthan, and the averagesignalamplitude is similarto that in the acetone-drivenflow (Fig. 8), that is, AP/P -- 3-10 times less for the ether-driven flow comparedwith the acetone-driven flow in this region. These observationsare consistentwith the more stable fragmentationlevel and indicate
140
that the ether-driven
20
140
AND FLOW
zooo
100
•
1 I
I
P2 Gumrosin- diethylether
•, ,
60
\
t , c•.
flow
is steadier
than the acetone-driven
flow. This suggeststhat seismic activity may be strongerand more variable during changesin flow behavior in a volcanic conduitthanduringa moreestablishedflow pattern. Plate 6 showsoptical, pressure,and bandpassed pressuredata for transducerP8 during the acetone-drivenflow. Regionswith different optical and pressure oscillation signatures can be delineated. Region I (R l) spans 0.25 to 0.72 s (Plate 3) and correspondsto fragmented flow as detected by the optical transducers07 and 09 (Plate 6). R I can be subdividedinto R la and R lb basedon the characteristicpressureoscillationbehavior as summarizedin Table 2. Region 2 (R2) covers0.72-0.87 s, and can again be subdividedaccordingto the pressureoscillation behavior(see Table 2). Region 3 (R3) movesby P8 after 0.87 s. Table
2 summarizes
the oscillation
behavior
observed
in this
region.The pressuregradientis higher in R2, especiallyin R2a, 20 comparedto R I or R3, as indicated by the raw pressuretrace (Plate 6), but we are not able to accuratelyquantify the pressure 0.• 0.4 0.6 0.8 z.o •.• z.4 gradientwith the datapresentedhere. o ' FSr) Time (s) Plate 7 showsoptical, pressure,and bandpassed pressuredata Plate 5. Spectrograms of 10-150Hz andband-passed pressure for transducerP8 duringthe ether-drivenflow. Plate4 showsthat P8 was close to the fragmentationlevel for most of the flow data from transducerP2 for acetone- and ether-driven flows. P2 measures datafromthezero-velocity-at-wall region(R3) of these duration. On the basis of the optical and pressureoscillation flows, which is dominatedby oscillationspeakingat 20 Hz or signatures (Table 2) the boundarybetweenregionsR2a and Rlb less. We indicate where these oscillations are similar to longis seento passback and forth pastP8 (Plate 7) as the level of periodseismicevents. fragmentationalsooscillates.
Plate8 givesa schematic representation of theflowregionsin the two fragmentingflows describedabove,and Table 2 of the flow and establishmentof a stable, slow moving foam column. This is similar to the situation observed in the
summarizes theoscillatorybehaviorof bothflows.
Region4 containsthe sourceliquid. As in the weakly supersaturated flows,thisregionremainsacoustically isolated unfragmenting flow. Narrowband oscillations continueafter fromthe liquiduppersurfaceso that 1.35s butat reduced amplitudes. Theether-driven flow produces fromthe foamexpanding oscillations arenotsignificant in R4 (Figure2, Plates3 a morecontinuous signalin the 10-30Hz range,alsoincluding pressure oscillations arenot some80-100Hz peaks(Plate5). The peakamplitudeof the and4, andTable2). This impliesthatpressure
Table2. FlowRegime Distinction Based onOptical, Pressure andImageData' Flow Region 1a
OpticalTransducer tube diameter scale
Fragmented 1b
gaspockets tube diameter scale
Fragmented 2a
gaspockets bubbles smaller than
Detached,
PressureTransducer low levels of oscillation
tube diameter
significantcontinuous 0.5-5 kHz signals;wave packetsof few kilopascalamplitudes
flow of foam
as lb with largeamplitude(few kilopascals) broadbandoscillationsin 10-500Hz rangecentered
annular foam-in-
foamin gas
at 80-100 Hz; 10-30 Hz oscillationsin ether-driven
annular
flow
2b
bubbles smaller than
Detached,gas pocket
tube diameter
Image Data foam fragments and gas
slugsandgas
gas flow
narrowband signalcenteredat 80-100 Hz; 10-30 Hz oscillationsin ether-drivenflow; low amplitude 0.5-5 kHz signalswith no wavepackets
gas-pocket-at-
10-30 Hz signalof a few kilopascalsamplitude;low amplitude80-100 Hz signaloccasionallydetected
foam flow wets
no oscillations detected
foam growsfrom liquid surface
wall flow
at wall
3
bubbles smaller than
Zero wall velocity 4
Staticliquid aSee also Plate 8.
tube diameter
tube wall
6470
LANE ET AL.: EXPERIMENTAL
PRESSURE OSCILLATIONS
'-' Rlb
60
'
'1"' ' ....... I '•
'1
ß' ]
'
AND FLOW REGIMES
•
• '
ß
7.5
62 Fragmented I' Fragmented flow
R3
'
I
In-gc•
I flow
• bubble-
I
':"
I
'"'
I
ß
I
'
annular • at-wall flow •
iii
5.0
Zero-velocity-at-wall flow 4.0
flow
ii
I
'07
3.0
•
I-5 kHz(xIO)
•
I 2.0
1.0
'I
' I ' ! I' I
900
i
0.9 I
I
!t-ß •I ",
i
30
ß
,-,
I
litIt',
20
0.8 >' 0.7
,
-
II
,1. , . , ,
' • '••'' ' 1' Ill' • , • , 0.5
O.4 0.3
0.2
I
2800
0
•
0.4 -'"0.5
'
ß
4250
0.6 ._-----0.7 '--'-'
,,'-..', ....
0.1
0.9
,..
1.0
140
•1,'-11
-
Spectrogram Scale o
I
FSD
e.g. 14000
o
i
!
20
2
0.2
0.4
o,6
0.•
•.0
•.2
•.4
Time (s) Plate 6. Data from P8 duringfragmentinggum rosin-acetone foam flow. Diagonaltrace indicatesraw data from P8. Tracesoffsetto 15, 35, and45 kPa are 50-500Hz, 0.5-1.0 kHz, and 1-5 kHz bandpasseddatadisplayedat 10X actual amplitude.Two top linesrepresent the presence of foamat 07 and09. Background spectragrams showfrequencies in the range50-5000 Hz with eachof the six panels(demarkcdby scaledaxes)havingthe full-scaledeflection(FSD) as shownat thetop left, or bottomleft, corners. Flow regionsandtheirsubregions areidentifiedat thetop The band-passed dataand spectragramin the 10-150 Hz bandare shownin bottomwith a differenttimescale.
LANE
ET AL.'
EXPERIMENTAL
PRESSURE
OSCILLATIONS
AND
FLOW
REGIMES
6471
5.0
t
4.0
3.0
kHz (x5) 30
J
i
t
,
2.0
1.0
0.5
0.5-1.0kHz (xS)
50-500
Hz
t
0.4
-
0.3
0.1
o
140
60 " 0.2
0
•
0.4
37 000
0.6
0.8
-: FSD
Time(s)
1.0
1.2
20
1.4
Plate 7. Data from P8 duringfragmentingether-drivenfoam flow. Diagonaltraceindicatesraw datafrom P8. Traces offsetto 10, 20, and 30 kPa are 50-500 Hz, 0.5-1.0 kHz, and 1-5 kHz band-passed data displayedat 1X, 5X and 5X actualamplitude,respectively. Two top linesrepresentthe presence of foam at 07 and09. Background spectrograms showfrequencies in therange25-5000Hz witheachof thetwopanelshavingthefull-scaledeflection (FSD) asshownat bottomrightcorners.Sqrtindicates a squarerootscale.Flow regionsandtheirsubregions are identifiedat thetop.The band-passed dataandspectrogram in the 10-150Hz bandareshownin bottompanelwith a differenttimescale.
6472
LANE ET AL.' EXPERIMENTAL
PRESSURE OSCILLATIONS
AND FLOW REGIMES
fraction betweenthe liquid and foam, which causesan acoustic velocitychangeof 2 ordersof magnitudeacrossthe barrier. Region3 represents a sectionof the flow wherethe expanding foam is in contactwith the tube wall. In this region the foam flowssubjectto the usualno-slipconditionat a solidboundary. Pressureoscillationsin region R3 display dominantfrequencies in the range 10-30 Hz and may possibly contain lower frequenciesbasedon visual observationof the pressuredata (Plate 3-5). The interpretationof theseoscillationsis the sameas our previousinterpretationof unfragmentingflows, i.e., resonant longitudinaloscillationof the foam.The nonequilibriumacoustic velocity [Kieffer, 1977] calculatedfor gum rosin-organicsolvent
Vacuum(• 10 Po)
Low levels of oscillation.
Higheroscillation
amplitudes thanRio.
foamisbetween 10and15m s'l atgas-volume fractions ranging
Lowamplitude
from 0.2 to 0.8. A 20+5 Hz fundamentalresonantfrequencyand resonatorlength of one half wavelengthyields a foam column lengthof 0.2-0.5 m. Thesedimensions are lessthanthe lengthof the unfragmented foam column(Plate 3 and 4), thusallowingfor otherflow regionsto exist.Oscillationsin the 80-100 Hz range are also observed(Plates 5-8), and we interprettheseas weak radialoscillationmodesin fashionsimilarto the unfragmenting
continuous 0.5-5 kHz
signalwith wove
pockets of several kPo.
flows.
Region R2 is subdividedinto regionsR2a and R2b. Image data (Plate 1) showthat visible (0.5 cm and larger)gaspockets developbetweenthe tube wall and the flowing foam in region R2b. These pocketsthen merge, giving rise to a foam-in-gas
Broadband.
80-100 Hz with
0.5-5 kHz signal andwovepockets. 10-30 Hz present
annular flow, that is the flow detaches from the tube wall, in
regionR2a.Thesetwo subregions aredetectable by theirpressure o
•-
LL.
0
in ether flow. Narrowbond.
80-100 littl•
Hz with
0.5-5
kHz
[P5 signal. 10-30Hz • present inetherflow. n,
AP/P:
7-17%
10-30
Hz
longitudinal m P2
oscillation.
Low•mplitud½ 80-100
Hz radial
oscillation.
AP/P:
2-10%
oscillation signatures(Plate 6 and Table 2) and are visible in
imagesof the flows(Plate 1). As the foampasses fromregionR3 into R2b, there is a rapid changein the pressureoscillation behavior.In the acetone-drivenflow the dominantfrequency changesfrom 20 Hz in R3 to 80-100 Hz in R2b (Plate6). In the ether-driven flow the passage of the fluid acrossthis boundaryis markedby the onsetof more prominent80-100 Hz peaks.The oscillation amplitude also increases by---50% across this boundary. The foam then flows from R2b into R2a, and the
•
o
pressure oscillationspectrumchangesagain,with an upfrequency broadening andthe generation of somewavepackets.This canbe seen from the raw and band-passedpressuretraces and the spectrogramsin Plate 6. The 3-5 kPa oscillationamplitudes observedin R2a are the highestamplitudesobservedin the flow field. We interpretthe 80-100 Hz oscillationsas radial modesthat are nowableto increasein amplitudebecause of the presence of gas at the interface between the foam and tube wall. The 20-Hz
oscillationsare consideredto have the same origin as those detected in R3, i.e., a longitudinal resonant mode. The upfrequency broadening in R2a may be associated with a reduction in the diameter of the foam core or onset of different
oscillationmodesas separationfrom the wall becomescomplete. The pressuregradientis greatestin regionR2 (Plate 6), which is consistentwith numerical simulations of volcanic conduit flows,
½ '¾
Noise. AP/P - 0 o
indicating that the greatest pressuredrop occurs across the fragmentationlevel or zone [Massoland.]aupart, 1999;Melnik, 20001. RegionRI is definedby the presenceof opticallydetectedgas pockets(Plate 6), and the flow in this region consistsof foam
fragmentsdispersedin gas (Plate 1). A changein pressure oscillationbehaviorcoincideswith the optically detectedgas
Plate 8. Schematicrepresentation of flow regimesand pressure pockets.The oscillations are complexand dependon the oscillationsin a fragmentingfoam flow. The positionsof the prevailingexperimental conditions.It is also possibleto pressuretransducersare indicated,and the flow regionsare subdivideregionRI on the basisof the .pressure oscillation positionedas in the acetone-driven flow at---0.7 s, and ether-
behavior(Plate6 and Table 2). RegionRla showsvery little spectral signalcharacterized by low or undetectable oscillations at all frequencies andrarewavepackets. Therearetwotypesof associated withthesewavepackets. Somearebroadband, generatedwithin the sourceliquid. The acousticimpedance spectra across thefoamgrowthsurfaceis sufficientto preventsignificant while othersshowevidenceof a discreterangeof frequenciesin transmission of pressure oscillations from the foamabove.This the0.6-5 kHz band(e.g., at 0.52 s in Plate6). Wavepacketsare common in regions Rib andR2a,rarelypresent in impedance barrieris createdby the rapidchangein gas-volume particularly driven flow at---0.3s.
LANE
ET AL.: EXPERIMENTAL
PRESSURE
regionsR la and R2b, and neverpresentin regionsR3 and R4, that is, they are dominantly presentwhen the flow is fully detachedfrom the tube wall but still interactingwith the wall on occasion.This implies that the wave packetscould be due to direct impacts,or a stick-slipmechanism,betweena foam slug andthe noseof a pressuretransducer. This processis more likely to cause broadband wave packets than a series of discrete frequencies. Another possibility is that the wave packets represent resonantoscillationof the gasbetweenfoamslugs.This processwouldlikely manifestin a spectrummadeof a seriesof
OSCILLATIONS
AND
FLOW
REGIMES
6473
shear near the conduit wall. The gas-at-wall annular flow observedin region R2a in our experiment(Plate 8) has features similar to those observed in core-annular
flows in that the flow is
again organizedwith its lowest-viscositycomponent(the gas) at the wall so as to minimize viscousenergy dissipation.However, the mechanismleading to this "lubricated"flow organizationis obviouslyquitedifferentin the foam-in-gasannularflow. The physicalmechanismfor the developmentof gaspocketsat the tube wall in our experiments underlies the eventual fragmentationof the foam and the generationof the mist, or narrowband peaks. Assuming a gasacoustic velocity of240m s-• fragmentedflow. Insightsinto possiblemechanismsare provided by the theoreticalanalysisof Massol and Jaupart [1999], who and a typicalmeasuredgaspocketlengthof 0.1 m, one obtainsa fundamental frequencyof 1.2 kHz, nearthe low end of the range suggestthat if the lengthscaleover which a significantpressure of discretefrequencies observed(Plate6). The seriesof observed change occurs is much smaller than the conduit length, then resonantfrequencies are complexanddo not appearto be simple radial pressuregradientsdevelop.Thesepressuregradientsarise harmonic series. becauseunderthe assumption of Poiseuilleflow in R3, the foam nearthe conduitwalls is movingat a slowerspeedthanthat in the flow
5. Discussionof Experimental Observations Our experimentalobservationssuggestthat noneruptingor effusive magmatic foam flows will generate low-frequency narrowbandseismicsignalswhosefrequenciesare controlledby the conduit dimension and acousticvelocity of the fluid. Our observations also suggestthat explosiveeruptionsgeneratelowfrequencyand relatively high-amplitudenarrowbandsignalsonto whichhigher-frequency broadbandsignalsare superimposed. The flow behaviors exhibited by vertical flows of boiling water and liquid metal rangefrom bubblythroughslug flow, to churnflow, to liquid-at-wallannularflow, to mist flow [Tongand Tang, 1997]. Gum rosin-organic solvent, hydrothermal, and magma-watersystemsare also examplesof boiling flows. The gum rosin-organicsolventflow regimesrangefrom bubbly/foam (zero velocityat wall) flow throughdetached(gas-pocket-at-wall and gas-at-wallannular)flow to coarsemist (fragmented)flow. Normal annularflow developsas gas bubblesconcentrateat the central, high-velocity region of the flow in responseto the Bernoulli effect [Tong and Tang, 1997]. A major fluid mechanical
difference
between
these industrial
and volcanic
or
core.
The
foam
close
to the wall
is therefore
nearer
equilibriumandmoredegassed with a higherliquidviscosityand gas-volumefraction. With less dissolvedvolatile, lower bubble pressuresare maintainedby the "old" foam near the tube walls than by the "fresh"foam in the flow core. The foam at the tube wall is thereforemore non-Newtonianand permeableand will fail in a brittle fashion at lower strain rates than the foam in the
flow core. This is especially so when viscosity is a strong functionof volatile content,as in rhyolitesand gum rosin(Figure 1). The Poiseuilleflow breaksdown upon enteringR2, and the radial heterogeneities(gas-at-wall with foam core) and steep pressuregradient(Plate 6) in the R2 region of our experimental flows support the theoretical observation of radial pressure gradients having developed in R3. We suggest that the developmentof horizontalpressuregradientsin R3 as viscosity increasesbecauseof degassing,especiallyat the tube wall, leads to a changein flow regime in R2 and ultimatelyto fragmentation in R1. Oncean annularflow hasdevelopedand flow wall friction becomeseffectivelynegligible,the foam coremay be fragmented eitherby the high-velocitygasstreamin the annulusas in rapidly heatedboiling flow [Tong and Tang, 1997], or by vibrational, viscous,or viscoelasticinstabilityof the foam core independent of the aerodynamic instability due to gas flow. If the experimentalflows are consideredto be similar to explosive volcanicflows, then a rapid sequenceof flow regime changes from Poiseuillethrough bubble-at-walland invertedannularto mist flow may be expectedto underlie magma fragmentation also.In this case,the sequenceof regimechangesis considered to be generatedby the developmentof radial pressuregradientsas a consequenceof rapid liquid viscosity increase [Massol and Jaupart, 1999]. If similarity is not consideredclose, then our experimentsstill demonstrate that a rangeof flow behaviorricher than previously considered[e.g., Massol and Jaupart, 1999; Papale, 1999; Melnik, 2000] is likely to exist in explosive
analogue-volcanicsystemsis the viscosityof the liquid phase, which is much higher (and increasing)for both gum rosin and magmacomparedto water or liquid metals.This meansthat the relative motion of the bubblesand liquid is very small on the timescale of an explosive event, thereby preventing the developmentof a normal annularflow. As discussedin the next paragraph,the developmentof radial pressuregradients[Massol and Jaupart, 1999] with high pressurein the coreof the flow is alsolikely to suppressthe developmentof liquid-at-wallannular flow as this gradientfavors higher gas-volumefractionsat the tubewall andthusleadslogicallyto the gas-at-wallannularflows observedhere. Tongand Tang [1997] documentone instanceof formationof gas-at-wall,or invertedannular flow. This occurs volcanic flows. when a subcooledliquid entersa hot sectionof tube that has a The pressure oscillation signatures documentedhere are highheatflux. Gasis generated rapidlyat the wall leadingto an invertedannularflow. The liquid core is then brokenup by the distinctiveenoughto be usedin the identificationof flow regimes rapidly escapinggas in the annulus to form a mist flow. (Table 2). This suggeststhat different flow regimes identified Illustrations of this type of flow bearstrikingphenomenological within a fragmenting volcanic conduit flow may likewise similaritiesto fragmentinggum rosin-organicsolvent flows generatedifferentpressureoscillationsignatures.Flow similarity (Plate 1). Physicalprocesses generatinginvertedannularflow in betweenexperimentaland volcanic conduit flows suggeststhat a low-viscosity boilingfluid are unlikelyto be similarto thosein the oscillatory behaviors should be similar. Pressure changes eithergumrosin-organicsolventor magma-waterflows but may within a fluid-filled cavity will deform the solid boundingthe showsimilaritywith hydrothermal systems.Two-liquidsystems cavity, and pressureoscillationswithin the cavity will radiate are knownto segregate to producecore-annular flows [Carrigan elasticwaveswithin the confiningmedium [e.g., Aki et al., 1977; and Eichelberger,1990;Josephand Renardy, 1992] with the Ferrick and St. Lawrence, 1984; Chouet, 1985, 1986, 1992, and strain low-viscosityliquid (e.g., mafic magma,water) migratingto the 1996a].Thesesignalscan be detectedby seismometers wall and enclosinga core of high-viscosityliquid (e.g., silicic gauges.In experimentalflows the pressureoscillationsproduce verysmallstrains (
