1 Introduction. 2 Background of the Method

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1 CAV1: sessiona7. Vlidtion of Bubble Distribution Mesurements of the ABS Acoustic Bubble Spectrometer with High Speed Video Photogrphy G. L. Chhine, K. M. Klumuck, J-Y Cheng nd G. S. Frederick DYNAFLOW, INC. 11-J Iron Bridge Rod, Jessup, MD 79 emil: Abstrct Mesurement of the bubble size distribution in liquid is very importnt for cvittion inception studies. In this pper we describe n coustics bsed device, the ABS Acoustic Bubble Spectrometer tht mesures bubble size distributions nd void frctions in liquids bsed on the mesurement of sound propgtion through the tested liquid. Short monochromtic bursts of sound t different frequencies re generted by trnsmitting hydrophone nd received by second hydrophone fter pssge through the liquid. These signls re processed nd nlyzed to obtin the frequency dependent ttenution nd phse velocities of the coustic wves. From these, the bubble size distribution (number of bubbles versus size) is obtined following solution of n inverse problem. In order to vlidte new implementtion of the instrument softwre, fundmentl experiment is conducted. Bubbles re generted in controlled fshion, nd then crefully mixed into uniform distribution in flowing system. A high-speed micro-video system is used to tke videos of the bubbles t the sme time nd within the test volume interrogted by the ABS system. Both the coustic dt nd the video frmes re then nlyzed using mny dtsets under the sme conditions, nd the results re compred. The two methods re seen to provide very close results within their limits of resolution nd within the bubble distribution vritions in the liquid. The ABS provides results very close to the time-consuming micro video photogrphy in ner rel-time in much more cost-effective fshion. 1 Introduction Determintion of the bubble popultion in smple of liquid is importnt in mny fields, the most relevnt here being cvittion. Severl techniques hve been used to-dte [1-13] nd cn be divided into opticl studies (photogrphy, hologrphy, scttering techniques,..etc.), cousticl studies (scttering, ttenution, dispersion,..etc.), nd others including electricl impednce nd cvittion susceptibility meters. Acousticl methods re inverse methods, relying on the fct tht bubbles hve strong effect on the propgtion of coustic wves. The cousticl cross-section of bubble is three to four orders of mgnitude greter thn its geometricl cross-section []. Acousticl techniques re reltively simple, nd pplicble to much lrger liquid smples. Additionlly, liquids re generlly much more trnsprent to the pssge of coustic wves thn they re to light. The predictions of existing cousticl nd opticl techniques differ widely []; for instnce, the cousticl method of Wildt [1] over-predicts the bubble popultion density by s much s two orders of mgnitude t smll rdii, nd under-predicts it significntly t lrger rdii. The error lies in the procedures used to infer the bubble popultion from the mesurements. The method used here hs been shown to be consistent method for obtining the bubble popultion from mesurements [15, 1-]. Using set of effective equtions, derived by tking the limit of the complete equtions of motion to smll bubble volume frctions [1], dispersion reltion for bubbly fluids ws developed by Commnder nd Prosperetti [17]. This reltionship ws used to obtin the ttenution nd phse velocity for given bubble popultions nd ws compred very fvorbly with mesurements. They lso found tht the computed ttenution nd phse velocity ws quite sensitive to the bubble popultion distribution. Here, we use the inverse of this procedure nd obtin two integrl equtions for the bubble density in terms of the phse velocity nd ttenution. Solution of these equtions, using mesured vlues of the ttenution nd chnge in phse velocity, llows computtion of the bubble popultion. The problem fced in the solution of these equtions is tht the equtions re ill-posed. We considered in [15,] severl pproches for solving this illposed problem, nd found tht mong the pproches tested one bsed on constrined minimiztion worked best. Bckground of the Method Consider bubbly medium consisting of liquid of sound speed c l contining sphericl bubbles of different rdii. The bubble size distribution is chrcterized by the bubble popultion density, N(), such tht N( ) d = Totl Number of bubbles per unit volume. (1) 1 1

2 CAV1: sessiona7. When sound of frequency ϖ propgtes through the bubbly medium, the bubbles oscillte nd extrct nd re-rdite energy into the medium, thereby mking it dispersive. Ech bubble cts s n oscilltor with nturl frequency ϖ nd dmping constnt b tht depend upon the imposed frequency ϖ nd the bubble rdius,. A dispersion reltion reltes the complex sound speed, c m, in the mixture to the sound speed in the liquid, c l, s follows, with i representing the imginry unit: cl N( ) = 1+ d. c π () ϖ m 1 ( ) ϖ + ib( ) ϖ cl Replcing in () ϖ nd b with their expressions obtined in [19] we obtin with u iv c = : ( ϖ ϖ ) ( ) + k1(, ϖ ) N( ) d = u v 1; k1 =, ϖ ϖ b ϖ bϖ k(, ϖ ) N ( ) d = uv, k =. ϖ ϖ + b ϖ ( ) The quntities u nd v my be obtined by mesuring the phse velocity, c m, nd the ttenution, A, of the wve in the bubbly liquid. The ttenution A, in db per unit length, is given by ϖ v A= log 1 e. () cl 3 The Acoustic Bubble Spectrometer Technique 3.1 Experimentl Method The ABS Acoustic Bubble Spectrometer extrcts the bubble popultion from coustic mesurements of the phse velocity, c m, nd the ttenution, A, mde t severl insonifying frequencies. The device consists of set of two hydrophones connected to dt cquisition nd control bords resident on personl computer. Dt bord control signl genertion by the first hydrophone nd signl reception by the second hydrophone. Short monochromtic bursts of sound t different frequencies re generted by the trnsmitting hydrophone nd received by the second hydrophone fter pssge through the bubbly liquid. These signls re processed nd nlyzed utilizing specilized copyrighted softwre lgorithms tht we hve developed to Figure 1. Sketch of the ABS Acoustic Bubble Spectrometer Method obtin the ttenution nd phse velocities of the coustic wves, nd, from these, the bubble size distribution. The PC nd its resident signl genertion nd dt cquisition hrdwre synchronize nd control the mesurements s well s perform the dt nlysis. A sketch of the procedure is shown in Figure 1. Mesurements re conducted with the id of Grphicl User Interfce, where ll physicl, experimentl, nd nlyticl prmeters re input by the user vi series of dilog boxes. Both rw nd processed dt from experiments cn be sved to disk for future use. The results re displyed grphiclly by the interfce in rel time nd cn lso be stored or printed. 3. Inverse Problem Solution Once series of mesurements of sound speed nd ttenution in the bubbly medium is obtined t set of frequencies covering the rnge of interest, the inverse problem consists of the determintion of the bubble size distribution, corresponding to these mesurements. Such n inverse problem is difficult to ddress nd is usully ill-posed, tht is smll vritions in the mesured quntities my result in lrge vritions in the sought distribution. Since experiments re prone to mesurement errors nd numericl computtions re subject to round m (3)

3 CAV1: sessiona7. off nd other errors, this my result in the solution oscillting wildly when refining discretiztion until finlly the solution hs little reltion to the originl dt. It is thus necessry to regulrize the problem. We hve solved this issue using constrined optimiztion methods [15,1-] Experiments.1 Experimentl Setup Over the lst few yers we hve conducted mny experiments to vlidte nd improve the ccurcy of the ABS Acoustic Bubble Spectrometer [3-]. These experiments hve consisted minly of using electrolysis bubbles nd bubbles injected by vrious mens in n otherwise quiescent liquid [3-5], or bubbles generted by the impct nd penetrtion of wter jet on free surfce, or ir injection underwter [,]. The mjor difficulty in ny vlidtion test is to hve the mesurements with the technique being vlidted nd those with the vlidting techniques tken for the sme interrogted volume of the mixture nd t the sme instnt. This is in fct lmost impossible. One then tries to minimize the differences between the spce nd time constrints of both techniques. Here, the difficulty is further compounded by the vritions in time nd spce of the Test Section Pump bubble size distribution in the liquid. Since microphotogrphy is still the most ccurte nd preferred technique for vlidtion, there is mjor compromise between the desire to mesure the smllest bubble sizes possible nd to smple lrge enough volume of the liquid to ensure tht the micro-photogrphic mesurement is representtive of the much lrger volume interrogted by the reltively more globl ABS technique. The experimentl set-up used in the present study ws designed to minimize the bove-described difficulties, nd to enble vlidtion of the ABS in the cse of flowing bubbly liquid. Figure shows sketch of the set-up, while Figures 3 nd show pictures of the set-up nd the bubble injector. An mm dimeter micro-porous tube, DYNAPERM, with pore sizes 1 to 1 µm, is used for ir injection into cm 3 Plexigls mixing chmber. The tube is plced in 1 mm Plexigls pipe where wter is injected t vrious speeds nd used to sher off the bubbles ejecting from the micropores of the DYNAPERM tube in order to generte smller size bubbles []. The bubble cloud coming out of the wter/ir injector fills out the mixing tnk, nd produces bubble distribution tht is function of the geometricl configurtion of the tnk, bubble genertor, nd free surfce. Any lrge bubbles surviving the shering ction or resulting from subsequent bubble colescence, rise to the free surfce of the tnk nd re thus eliminted from the subsequent nlysis. In one side of the mixing tnk, nd in this cse close to the tnk bottom to void ny lrge recirculting bubbles, the bubbly mixture is sucked through cm pipe into cm 3 Plexigls test section. The mixture is then guided through 3-degree ngle gentle diffuser of length 5 cm from the cm pipe into the test section. The objective is to crete smooth trnsition into lminr prllel flow in the test section, in order to minimize s much s possible unstediness of the bubble distribution in the flow. Downstrem of the test section pump tkes the liquid from the suction port through the test section nd bck into the mixing chmber through the wter injection tube surrounding the DYNAPERM tube nd used to sher the bubbles from the micropores. Two hydrophones in the form of flt trnsducers mde of piezoelectric composite mterils embedded in polyurethne for wterproofing nd shpe-forming re mounted in two sides of the test section, nd re insulted cousticlly from the structure by cork lyers. One of the trnsducers cts s the emitter side of the ABS system while the other one cts s the receiver. The size of the ctive section of ech hydrophone is 5 5 cm. 3 Trnsducers High Speed Video cmer Air/Wter Mixing Tnk Wter sher Air Injection Microporous Tube Figure. Sketch of the experimentl setup for the ABS Acoustic Bubble Spectrometer vlidtion studies ABS

4 CAV1: sessiona7. Trnsducer Trnsducer Figure. Photogrph of the test section nd the upstrem diffuser. In this cse the flow ws directed downwrd. Figure 5. Photogrph of the bubble injector: close up view of ) DYNAPERM tube (white) nd wter sher injection, nd b) injector in opertion. The other two sides of the Plexigls test section re used for opticl observtion nd mesurement in the sme mesuring volume s the ABS. Microphotogrphy is used to enble counting the bubbles opticlly. A Redlke high-speed video cmer (typiclly operted t 1, frmes per second) with mcroscopic lens is used to tke series of pictures of the bubble distribution s function of time. These imges re then nlyzed semiutomticlly using the dt nlysis system of the video-cmer. The procedure is to nlyze one frme, select in tht frme chrcteristic bubble t the upstrem side of the visulized re, skip ll following frmes in which the sme bubble is visible, (i.e. until the bubble hs left the field of view,) then select the following frme to nlyze. Usully, bout such frmes were nlyzed to provide one dt point; ll bubbles in focus re mesured nd counted to generte br chrt of the bubble size distribution. The bubbles re then grouped into bins tht corresponded to those obtined with the ABS nlysis in order to enble side-by-side comprison. The video imge is qusi-d representtion of the rel 3D bubbly flow field. However, it hs volume informtion through the depth of the opticl field considered; tht is objects will pper in focus within certin depth, ±δ, of the focus plne. δ is mesured initilly in the sme fcility using thin wire. In order to compute the number of bubbles of given size in unit volume, we use the fct tht the counted bubbles were observed in volume of size δwh, where w nd h re the width nd height of the mesurement re (usully of the order of.5cm ech). The ABS mesurements were done using the in-wll embedded hydrophones. A series of signl bursts (typiclly 5-1 periods ech) t vrious frequencies (typiclly pre-selected frequencies) within the cpbilities of the hydrophones (typiclly between 1 KHz nd 5kHz) nd the dt cquisition bord (here 1.1MHz) re used 1 to excite the first hydrophone nd re received by the second hydrophone. The ABS softwre then computes the sound phse speed nd the ttenution, nd deduces the bubble size distribution. As llowed by the softwre the experiments were conducted using either single series of frequencies, or n verge over s mny s 1 series. In this cse, the softwre considers the resulting vlues of u nd v for ech series, (see Figure 5 for 1 In the ABS, the user defines in pull down menu the number of pulses to emit for ech frequency, the number of frequencies, nd selects the frequencies to be used to drive the experiment.

5 CAV1: sessiona7. screen shot of these quntities) then genertes verge curves u(f) nd v(f), nd deduces from this the verge bubble popultion. Obviously, using such lrge number of repetitions is not too meningful if the bubble popultion is very unstedy. The mesured bubble sizes nd numbers re ssumed to be uniformly distributed in the volume between the two trnsducers, tht is here, in the volume cm 3. This volume is used to deduce the bubble size distribution in unit volume of the tested liquid. From the bove description, the reder should relize tht despite ll efforts there still re two inherent discrepncies between the two methods. One is the difference between the mesurement volumes, bout 19 cm 3 for the ABS nd bout 5 mm 3 for the microphotogrphy. The second difference cn be the durtion of the mesurement, which is bout second for the ABS (could be s short s 1 ms) nd few seconds for the video photogrphy. Figure. Screen shot of the ABS grphicl user interfce showing, for one of the cse studies reported here, the sound speed rtio, u, nd the ttenution rtio, v, defined bove in Eqution (3). Also shown is the resulting bubble size distribution fter solution of the inverse problem by the ABS softwre.. Experimentl Results A series of tests ws run using vrious combintions of irflow rtes into the DYNAPERM tube nd wter flow rtes through the pump. This combintion llows for vrious levels of sher nd for different void frctions. Since this pper minly ims t showing clibrtion comprisons between the ABS results nd microphotogrphy, we will not get into ll the detils of the study, but show some illustrtive exmples. Some of the figures shown below hve informtion on the flow rtes in percent of the mximum flow rtes. To mke this clerer, for most of the cses shown the configurtion of the injection tubes is such tht 1% wter flow corresponds to n verge sher velocity in the wter flow injection tube of 3 m/s. A 1% ir flow corresponds to n injection verge speed bsed on the totl surfce re of the DYNAPERM tube of.5 m/s. Figure shows typicl exmple of the dt obtined when the mesurements re done severl times under the sme conditions within few minutes prt, nd where to the nked eye the wter / bubble mixture ppernce looked quite uniform nd did not pprently chnge with time. It is quite obvious tht on the locl level, the detils of the bubble size distribution spectr (number of bubbles in unit volume of given size) despite ppernces chnge significntly between one mesurement nd the next. However, the overll trend does not chnge much. ABS % wterflow 3% Air ABS % wterflow 3% Air Test 1 Test Test 3 Test Bubble Rdius, µm Test 1 Test Test 3 Test Bubble Rdius, µm () (b) Figure. Illustrtion of the degree of vrition in the bubble size distribution in the mesurement re using ) one set of mesurement ech time with the ABS Acoustic Bubble Spectrometer, nd b) the micro video photogrphy where ech mesurement is obtined using 55 frmes. Figure 7 shows comprison between the ABS nd the photogrphy results when n verge is mde over six ABS computtions nd six video photo nlyses of imges ech. (In figure we hve only shown four of 5

6 CAV1: sessiona7. these mesurements to void more clutter in the br chrt). Here, we cn see tht the two methods give very close results, even though no ttempt ws mde to djust ny of the prmeters such s the vlue used for the depth of field or the intensity level selected to decide if n imge ws in focus or not. The decision on whether bubble ws in focus or not ws done visully by the sme opertor independently of ny knowledge of the ABS results. There definitely is room for improvement in tht re but this ws not the objective of the study here. However, the ABS ppers to cpture extremely well the chrcteristic bubble sizes. The number of bubbles of given size ppers lso to be in generl quite close to the opticl observtions. Discrepncies, however, exist but re definitely within the mrgin of vrition in the results of ech of the observtion method. These discrepncies pper to be relted to ctul vritions in the bubble popultion nd not so much due to errors in either of the mesurement methods. Figure shows the effect of doubling the mount of ir injected into the mixing chmber. As mesured directly with the video photogrphy nd indirectly with the Acoustic Bubble Spectrometer, this results in modifiction of the shpe of the bubble size distribution. Insted of simple pek in the distribution, we observe tht two peks re formed on ech side of the previous one. This is result of the complex interction between the injected ir strem from the micropores nd the shering ction of the surrounding wter flow. It is quite encourging tht both methods cpture the sme trend nd gin pper to give very close results within the vritions of the experimentl bubble/liquid distribution. Both the ABS bubble size distribution mesurements nd the micro video photogrphy mesurements were lso used to compute the void frction tht corresponds to ech mesurement. This is simply computed by summing up the volume of ll the bubbles detected or seen in unit liquid volume. Figure b shows tht s expected the computed void frction mesured by both methods pproximtely doubles s the ir injection flow rte doubles. However, one unexpected result is tht the computtion of the void frction in tht fshion is strongly prone to errors. In fct, the void frction clcultions re very sensitive to the lrgest bubbles, to which (due to their very low number) most probbly the ssumed sttistics do not pply, e.g. observing one lrge 15µm bubble in smpling volume of 1 cm 3 does not necessrily men tht we hve 1 such bubble in 1 liter. Becuse of this sensitivity the differences between the ABS nd the photogrphic method re ccentuted in the clcultion of α ABS Averge tests Photos Averge 13 frmes Bubble Rdius, µm Figure 7. Comprison between ABS mesurements nd micro video photogrphy verging six repetitions. 1 ABS 3% mx ir 1 Photo 3% mx ir ABS % mx ir Photo % mx ir Bubblr Rdius, µm Void frction, 5.E-5.E-5 3.E-5.E-5 1.E-5.E+ ABS Air 3% Air % Photos () (b) Figure. Sensitivity of ) the bubble size distribution mesurements nd b) the resulting void frction, to doubling in the flow rte of ir through the DYNAPERM microporous tube.

7 CAV1: sessiona Bubble Rdius, µm H.S.VIDEO ABS Figure 9. Bubble size distribution in condition where lrge bubbles were injected into the test section. Comprison between ABS results nd video photogrphy nlysis. In order to test the system when there re two very different peks in the bubble size distribution, the position of the ir genertor ws on purpose misplced in order to force some lrge bubbles to be directly injected in the suction end upstrem of the test section. In this cse, the configurtion shown in Figures nd 3 resulted in bubbles ccumulting in nd bove the test section due to grvittionl forces on the lrger bubbles, which opposed the downwrd motion of these bubbles. In order to still be ble to conduct the mesurement with uniform flow, the test section ws turned upside down to hve the feed section to the diffuser come from below nd the test section on the top. In this cse, grvity force ws in the sme direction s the direction of the flow nd the problem of bubble ccumultion ws eliminted. Figure 9, shows the resulting ABS determined bubble sizes nd the direct opticl mesurements. Agin we cn see very good correspondence between the two methods in the detected bubble sizes, with discrepncies in the bubble number in the sme rnge s the repetition error in the experimentl reliztion of the sme bubble / liquid configurtion. 5 Conclusions Since bubble size distribution cn ply n importnt fctor in cvittion studies especilly in cvittion inception. It is very useful to be ble to chrcterize the studied liquid for its properties in terms of not only overll ir content or dissolved oxygen, but lso in terms of the ctul detil of the bubble size distribution. The instrument tested in this study, the ABS Acoustic Bubble Spectrometer, ppers to hve importnt dvntges tht mke it useful. It llows ner rel time on line mesurement of the bubble size distribution. It cn be designed to be non-intrusive, such s here, where the trnsducers were locted in the wlls of the test section. It hs the dvntge of exmining lrge volume of the liquid if necessry. More importnt, the study presented here shows tht the system, previously tested successfully using synthetic dt nd in complex configurtions, provides very stisfctory results under controlled experiments when compred with direct simple but time consuming method such s microphotogrphy. Both wys of mesuring the bubble size distribution give very close results in terms of bubble sizes, nd differences, which re in the rnge of the sctter errors in the experiment itself, for the bubble numbers. One dditionl dvntge of the method is its flexibility nd dptbility to improvements in the hrdwre. Limittions now re due to the limittions in the frequency responses of the hydrophones nd in the dt cquisition rtes of the PC Crds. Improvement in the existing cpbilities of the industry cn be rpidly implemented in the modulr system. Acknowledgments The ABS Acoustic Bubble Spectrometer ws initilly developed under SBIR Phse I nd Phse II grnts from the Ntionl Science Foundtion. We re most grteful to tht support. Mny people t DYNAFLOW contributed in severl wys to further developments. 7 References 1. H. Medwin, In situ coustic mesurements of bubble popultions in costl ocen wters, J. Geophys. Res. 75, , H. Medwin, Counting bubbles cousticlly: review, Ultrsonics, 15, 7-13, H. Medwin, Acousticl Determintion of Bubble-Size Spectr, J. Acoust. Soc. Am.,, 11-1, N. Breitz nd H. Medwin, Instrumenttion for in situ cousticl mesurements of bubble spectr under breking wves, J. Acoust. Soc. Am.,, ,

8 CAV1: sessiona7. 5. H. Medwin nd N.D. Breitz, Ambient nd trnsient bubble spectrl densities in quiescent ses nd under spilling brekers, J. Geophys. Res., 9, , F. McIntyre, On reconciling opticl nd cousticl bubble spectr in the mixed lyer, in Ocenic Whitecps, edited by E.C. Monhn nd G. Mcniocill, Reidell, New York, 75-9, D.M. Oldenziel, A new instrument in cvittion reserch: the cvittion susceptibility meter, J. Fluids Engg., 1, 13-1, 19.. S. Vgle nd D.M. Frmer, The mesurement of Bubble-Size Distributions by Acousticl Bcksctter, J. Atmos. Ocen. Tech., 9, 3-, T. Ohern, J. Torczynski, S. Tssin, S.Ceccio, G. Chhine, R. Duriswmi, nd K. Srkr, Development of n Electricl Impednce Tomogrphy System for n Air-Wter Verticl Bubble Column, Proceedings, Forum on Mesurement Techniques in Multiphse Flows, ASME IMEC&E, C.-T. Hsio, G. Chhine & N. Gumerov, An efficient electricl impednce tomogrphy softwre combining boundry element method nd genetic lgorithm, OptiCON'99 Optimiztion Softwre, Methods, nd Applictions Conference Proceedings, Newport Bech, Cliforni, USA, October 1th -15th, N.A. Gumerov, G.L. Chhine & A.G. Goumilevski, Dipole pproximtion method nd its coupling with the regulr boundry element method for efficient electricl impednce tomogrphy, Boundry Element Technology XIII, C.S. Chen, C.A. Brebbi, nd D.W. Pepper (eds.), pp. 17-, WIT Press, Southmpton, UK, G.L. Chhine nd Y. Shen, Bubble Dynmics nd Cvittion Inception in Cvittion Susceptibility Meters, Journl of Fluids Engineering, Vol. 1, No, pp. -53, December L. d Agostino, nd A.J. Acost, On the design of cvittion susceptibility meters, th Americn Towing Tnk Conference, R. Wildt, editor, Physics of Sound in the Se, Prt IV, Ntionl Reserch Council, R. Duriswmi, S. Prbhukumr & G.L. Chhine, Bubble counting using n inverse coustic scttering method, J. Acoust. Soc. Am., 1, , R.E. Cflisch, M.J. Miksis, G.C. Ppnicolu, nd L. Ting, Effective Equtions for wve propgtion in bubbly liquids, J. Fluid Mech, 153, 59-73, K.W. Commnder nd A. Prosperetti, Liner pressure wves in bubbly liquids: Comprison between theory nd experiments, J. Acoust. Soc. Am., 5, R. Duriswmi nd G.L. Chhine, Bubble density mesurement using n inverse coustic scttering technique, NSF SBIR Phse I project report, lso Dynflow Technicl Report 9-1, S. Prbhukumr, R. Duriswmi, & G.L. Chhine, Bubble size mesurement using inverse coustic scttering: Theory & Experiments, ASME Cvittion & Multiphse Flow Forum, R. Duriswmi, S. Pbhukumr & G.L. Chhine, Development of n Acoustic Bubble Spectrometer (ABS) Using n Acoustic Scttering Technique, DYNAFLOW, INC. Technicl Report 91-1, July A. Prosperetti, Physics of Acoustic Cvittion, in Frontiers in Physicl Acoustics, XCIII Corso, Soc. Itlin di Fisic, Bologn, Itly, 15-1, 19.. S.W. Provencher nd R.H. Vogel, Regulriztion techniques for inverse problems in moleculr biology, in Numericl tretment of inverse problems in differentil nd integrl equtions, edited by P. Deuflhrd nd E. Hirer, Birkhuser, Boston, C. Ait Hocine nd M. Ourem, Bubble Size Mesurement Study, DYNAFLOW, INC. Internl Technicl Report.-31, Oct Frncois nd Mxime, Study for Bubble Size Mesurement Techniques, DYNAFLOW, INC. Internl Technicl Report.-, Feb G. L. Chhine, R. Duriswmi, nd G. Frederick, Detection of Air Bubbles in HP Ink Crtridges Using Dynflow's Acoustic Bubble Spectrometer Technology, DYNAFLOW, INC. Technicl Report 971-1, O. Poulin nd L.-X. Renux, Acousticl nd Opticl Study of Air Entertinment Due to Jet Impct on Free Surfce, DYNAFLOW, INC. Internl Technicl Report.-5, Sept G.L. Chhine, K.M. Klumuck, Fesibility of Mesuring Aphron Microbubbles in Drilling Fluids with Dynflow's ABS, DYNAFLOW, INC. Technicl Report 991-1, T. Jürgensen nd Leonrd Gbrielle, Study of the prmeters influencing the genertion of microscopic bubbles, DYNAFLOW, INC. Internl Technicl Report.-5, Oct..