超声空化气泡运动方程的求解及过程模拟-许文林

许文林,何玉芳,王雅琼(,225002)　:、,,MATLAB.、,.:;;;:TQ021.9;TQ018　　　:A　　　:1007824X(2005)010055050　,.[1],、、、、.[2～5],.[1～5]、,.[4],,、、.,,、.Plesset,Rayleigh(RP)RPNNP.[6],、,[7],,、、[8～10],.,.;,,.,,MATLAB.,.1　1.1　.pasinkat:20040212;:20050118:(20176047;20476087);(03KJB530164)E-mail:[e-mail]81()Vol.8No.120052JournalofYangzhouUniversity(NaturalScienceEdition)Feb.2005,.,,,,.、,RPNNP[5～7],、,RR+(3/2)R2=d-1[(p0+2e/R0)(R0/R)3κ-2e/R-4gR/R-p0+pv+pasinkat],(1)R(m),R0(m),R(m·s-1),R(m·s-2),p0(Pa),pv(Pa,25℃3.2718kPa),pa(Pa),e(25℃7.25×10-2N·m-1),g(_/d,25℃1×10-6m2·s-1),κ,_(25℃1×10-3Pa·s),ka.t=0,R=R0,R=dR/dt=0.1.2　(),(Tmax)(pmax)[1]:Tmax=Tmin[pm(V-1)/pv],pmax=pmin[pm(V-1)/pv]V/(V-1),(2)Tmax(K),Tmin(K),pm(Pa),pminR0(Pa),pv(Pa),V.1.3　MATLAB(1),,MATLAB.[11]2　2.1　25℃,R02.6μm,pa131.7,2026.5kPa,fa19.6,24.0,48.0,76.0kHz,1.1,(a)10,,(b)1,.,,,.1,,,,.,,,.2.2　25℃,R02.6μm,fa19.6kHz,pa,2.2(a),pa,,pa,,;pa.pa,,,;,,,,.56()81　Fig.1　Radius-timecurvesforanairbubbleinwater.TimeismeasuredintheunitsoftheperiodToftheacousticfieldR0=2.6μm;(a)pa=131.7kPa;(b)pa=2026.5kPa;fa/kHz:①19.6,②24.0,③48.0,④76.02　Fig.2　Radius-timecurvesforanairbubbleinwater.TimeismeasuredintheunitsoftheperiodToftheacousticfieldp0=101.325kPa;R0=2.6μm;fa=19.6kHz;pa/p0:(a)①1.3,②1.4,③1.5,④1.6;(b)①1,②3,③5,④10,⑤15,⑥20,⑦25,⑧30,⑨40,1080,11100,12150,13200,14250,15300　　2(b),pap0,(2(a)),.pa,,,.pa20p0,12,3.:pa,,,,.,,,,.2.3　25℃,pa101.325kPa、fa19.6kHz,R03.3(a),R0,,,,R0,,.3(a)33(b)4,(R00.60μm0.61μm),571:3　Fig.3　Radius-timecurvesforanairbubbleinwater.TimeismeasuredintheunitsoftheperiodTaoftheacousticfieldfa=19.6kHz;pa=101.325kPa;R0/μm:(a)①0.2,②0.4,③0.6;(b)④0.61,⑤0.65,⑥0.7,⑦1.0;(c)⑧5.3,⑨5.4,106.0.3(b),,R0,,R0(0.7μm),,R0.,.3(c),R0(R05.3μm5.4μm),13.,R0,,(R010μm),,3(a),R0.,,,,,、R0,.2.4　(2),Tmax、pmaxpaTmin(4～7).4　Fig.4　RelationbetweenTmaxinbubbleandpa/p05　Fig.5　Relationbetweenpmaxinbubbleandpa/p0　　4～7,Tmaxpa,pmaxpa;Tmin,Tmax,pmax,Tmin,pmax,Tmin313.15K,pmax.,、.,58()86　Fig.6　RelationbetweenTmaxinbubbleandTmin7　Fig.7　RelationbetweenpmaxinbubbleandTmin,,.,.,,.3　,MATLAB.:,,;pa,,;,pa/p02～300,pa,,,.pa25p0,123;,R0,,R0,;pa,Tmax、pmax,Tmin,Tmax,pmax,Tmin313.15K,pmax;,,,.:[1]　,.[M].:,1996.[2]　,,.[J].,1995,(4):6～8.[3]　,.[J].,2001,27(1):70～73.[4]　,,　,.[J].(),2003,6(1):29～32.[5]　,,,.[J].(),2003,6(2):21～24.[6]　NEPPIRASEA.Acousticcavitation[J].PhysicsReports(ReviewSectionofPhysicsLetters),1980,61(3):159～251.[7]　SERVANTG,CALTAGIRONEJP,GEVARDA,etal.Numericalsimulationofcavitationbubbledynamicsin-ducedbyultrasoundwavesinahighfrequencyreactor[J].UltrasonSonochem,2000,7:217～227.[8]　RAEJ,ASHOKKUMARM,EULAERTSO,etal.Estimationofultrasoundinducedcavitationbubbletempera-turesinaqueoussolutions[J].UltrasonSonochem,2005,12:325～329.(下转第68面)591:TheeffectofmembranetreatmentprocessesonbiologicalstabilityofdrinkingwaterJIRong-ping1,2,LUXi-wu2(1.CollofEnvironSci&Engin,YangzhouUniv,Yangzhou225009,China;2.DeptofEnvironEngin,SoutheastUniv,Nanjing210096,China)Abstract:Theeffectofmicrofiltration,ultrafiltration,nanofiltrationandreverseosmosisonremovalorganicpollutantsindrinkingwaterwasdiscussedinthispaper.Theinfluenceofmembranetreatmentprocessesonbiologicalstabilityofdrinkingwaterwasanalyzed.Theprocessofmicrofiltrationandul-trafiltrationisnotbiologicalstable.Theeffluentofnanofiltrationandreverseosmosishasbetterbio-stability.Keywords:membranetreatmentprocess;biologicalstability;drinkingwatertreatment(责任编辑　晓　文)(上接第59面)[9]　MEIDANIAR,HASANM.Mathematicalandphysicalmodellingofbubblegrowthduetoultrasound[J].ApplMathModelling,2004,28:333～351.[10]　BALASUBRAMANIAMR.Briefcommunicationthermocapillaryandbuoyantbubblemotion[J].IntJMulti-phaseFlow,1998,24(4):679～683.[11]　,,,.MATLAB[J].(),2004,7(1):49～54.ModelingandsimulationofbubblemotioncausedbyultrasoundXUWen-lin,HEYu-fang,WANGYa-qiong(CollofChem&ChemEngin,YangzhouUniv,Yangzhou225002,China)Abstract:Themodeltodescribebubbledynamicmotioncausedbyultrasoundwaspresented,whichincludedtheeffectsoffluidviscosity,surfacetensionandvaporpressureofthesolvent.ThegeneralmodelequationwassolvedandthecavitationprocesswassimulatedusingMATLAB.Theeffectsofthefactors,suchasultrasonicfrequency,ultrasonicintensityandinitialradiusofthebubble,onthebubblemotionandcavitationprocess,andthemaximumtemperatureandpressureaffectedbybulksolutiontemperatureandtheultrasonicintensityincollapsingbubblewerediscussedinaqueoussolu-tion.Thesimulationresultsshowthatthefrequency,theultrasonicintensityandtheinitialradiusofthebubblehavegreateffectsonthebubbledynamicsandcavitationprocessandbothofthemaximumtemperatureandpressureareverysensitivetothebulksolutiontemperatureandtheultrasonicinten-sity.Thisworkprovidesaveryimportantbasisfortheapplicationofultrasoundtoavarietyofchemi-calsystems.Keywords:ultrasound;cavitation;dynamicmodel;simulation(责任编辑　时　光)68()8