I.臥NihonReorojiGakkaishiVo136,No.3,125-131

(JoumaloftheSocietyofR血eology,Japan)◎2008TheSocietyofR血eology,Japan

DragReductionintheFlowofAqueousSolutionsof

DetergentThroughMeshScreens

KeikoAMAKI',TomiichiHASEGAWA*8,andTakatsuneNARUMI**

'DeparimentofHomeEconomics,Faculo,ofEducation,IwateUniversiO,

3-18-33とIeda,Morioka-shi,Iwaie020-8550,Japan

HMechanicalandPyvductionEngineering,Faculo,ofEngineering,NiigatatJniversiO7

8050Ikarashi-2nocho,Niigata-shi,Niigata950-2181,Japan

(Received:September25,2007)

An experimentalstudywasconductedontheflowofaqueoussolutionsofdetergentthroughmeshscreenstomimic

clothwashing.Pressurelossesacrossthemeshscreensweremeasuredforwater,dilutepolym erandseveralaqueous

detergentsolutions.Areductionofpressuretosseswasobservedfortheflowofaqueoussolutionsoflowmolecular

weightsurfactantssuchasLaurylether(AE),Laurylbenzene-sulfonicacid-sodium salt(LAS),Benzalkonium-chloride

(BC)Sodium-dodecy1-sulfate(SDS),andHexadecyltrimety1-ammonium-bromide(CTAB),butnotforthehigh

molecularweightpolym erslikePolyethylene-oxide(PEOI8)andPolyacrylamide(PAA),throughmeshscreens･Aflow

visualizationexperimentwascarriedouttoobservetheflowpattemupstreamanddownstream ofthemeshscreen.

Photographicimagesrevealedthat,insteadofan expectedlargeconverglngflowfromtheupstreamsectionintothe

screenopenlngaSinorificeflow,thebulkoftheliquidenteringthescreenaperturetooktheform ofaliquidcolumnof

similardiameterastheinlettube.Basedonthisobservation,aflowmodel,whichledtoanewsetofdeflnitionsof

ReynoldsnumberanddragcoefrlCient,wasproposed.GoodcorrelationsofdragcoefrlCientandReynoldsnum berwere

obtainedforalltestsolutions,andthedragreductionphenomenonwasmanifestedfordetergentaqueoussolutions.

KeyWords:DragReduction/Detergent/Surfactant/MeshScreen/DragCoefFICient

1.1NTRODUCT10N

ExcessiveconsumptionOfdetergentindailylifeisamajor

environmentalconcem.Asaresult,manyindustrialresearches

areaimedonbetterproductformulationandeffectiveusageof

detergent.Tbdate,moststudieshavebeenfbcusedonthe

chemicaleffectsofdetergent,Withverylittleattentiononthe

effectofmechamicalfactorsincludingtheflowthroughfabric.

Am ongthemechanicalfactors,theforceofadhesionbetween

submicronparticlesandsubstratehasbeen血easuredby

Visserl)uslngaShearflowdeviceoranelect10SmOticflow

devicebyGotoh,etal.2)otherfactorssuchastheeffectsof

shearing3),bendingandkictiononclothes4),aswellasthe

penetratingflowofdetergentthroughclothes5,6)havealsobeen

investlgated･Amaki,eta17)measuredthedragcausedby

solutionsoflowmolecularsurfactants(detergents)flowing

overthinwiresattachedonaflatplate･Themeasureddragwas

foundtobelowerforlowmoleculardetergentsbuthigherfor

dilutepolymersolutionsthanfわrwater･Watanabe,eta18)

camiedoutanumericalanalysisforthiskindofflowusinga

viscoelasticconstitutiveequationandfoundthatfluidelasticity

decreased也e血agonlyslightlybutcausedahugereductionin

liR･However,theeffectofsurfactantsolutionsondetergency,,

isnotclari丘edfromavleWPOintoffluidmechanicsyet.

Inthepresentstudy,measurementsofpressuredropsare

conducted､ontheflowofaqueoussolutionsofdetergentthrough

meshscreens,mimickingtheflowbehaviorinclothwashing.

Pressurelossesarecomparedwiththosemeasuredwithwater

anddilutesolutionsofhigh molecularweightpolym ers.Aflow

modelisproposedtoexplainthedragreductionphenomenon

obseⅣedf♭rdetergentsolutions.Finallywementionthe

kinematiceffectofsurfactantsolutionsinclothwashing.

2.EXPERIMENTAL

Figure1showsthedetailoftheexperimentalchannelsused.

Ameshscreenwasspannedinthemidstofthechannel,

normaltotheflowdirection,andthepressuredifferentialasa

functionofflOwratewasmeasuredbetweenupstreamand

down streampositionsacrossthescreenmeshusingapressure

gauge(TsukasaSokkenPZ177,Japan).Theaveragepressure

errorwasfoundtobewidlin±5%.Thetestchamelwasmadeof

125

NihonReorojiGakkaishiVol.362008

acrylicplate,andwas300rumlong,40mm x15mm rectangular

incrosssection･Meshscreensw erepastedoversectionalapertures

(15mmx15mm,10mmx10mmrectangular,and5mm

circular)drilledonaplate,andtheplatewassetinthetest

channelwithpacking.Pressuretapsweresetat82mmapart

丘omthescreen.Thepressuredifferential勾)betweenthetaps

wasmeasuredandheadlosshisde血edash-上垣/(/葛),Where

pisthedensityofliquidandgisthegravityacceleration.

Aschematicdiagram oftheexperimentalapparatusisshown

inFig.2.Thetestsolution,storedinatankof2mheight,was

madetoflowthroughthetestchannel,andtodischargeviaa

flowcontrolvalve.Theflowratewasmeasuredbyweighing

theliquiddischargedoveratimeinterval.

Thetestliquidsusedwereionexchangewater,aqueous

solutionsofPolyethylene-oxide(PEO18)andPolyacⅣlamide

(PAA),andvarioussurfactants.Thesesurfactantsinclude

Laurylether(AE(23)),Laurylbenzene-sulfomicacid-sbdium salt

(LAS),Hexadecyltrimety1-ammonium-bromide(CTAB),

Sodium-dodecy1-sulfate(SDS),andBenzalkonium-chloride

PC).Themolecularweightsandthesolutionconcentrationsof

thetestliquidsareglVeninTableI.

Viscositiesoftheliquids77Weremeasuredusingacapillary

viscometeratroomtemperature.ItcanbeseeninFig.3thatall

testedliquidsexhibitNewtonianbehaviorwi血viscositiesof

I-J ｡ 【::司 l- 荘

(Unit:mm)

Fig,1.Experimentalme血odandthechannel･

TableI.Molecularweightandconcentrationofthetestmaterials.

】Waterh] Mt)LecuhrWc]'ghtPolyesterMc血 StaidessMe血

PEO(18) 4.5×10̀ 10ppmPAL 3.4×10̀ 10ppmAEC23) 1214.5 0.01m01瓜 (I.2%) 0.5%I.AS 348.5 0.OlmolJL (0.35%) 0.5%CTAB 364.5 0.005mol札(0.18%)SⅠ)S 288.0 0.5%

126

theorderof10-3pa･S,whichisveⅣclosetothatofwater,

withintheexperimentalerrors.

Twotypesofmeshscreenswereused:polyesterandstainless

threads.AphotographofdlePOlyestermeshisshown inFig･4(a),

wherebisasideofmeshsquare.ThescreenmeshaperturesS

areeithersquareof15mmx15rrmand10xlOmm dimensions,

orcircularholesofdiameter◎5mm(Fig.4(b)).Fourkindsof

threadnumbersperinch,230(b-70/也),255(b-60Fm),270

(b-54FLm)and300(b-45FLm),Wereusedasthepolyester

mesh;while200(b-87pm)threadsperinchwasusedforthe

stainlessmeshThediameterofthemeshthreaddwas40FEm

forbothpolyesterandstainlessmeshes.

Priortotheexperimentforscreenmeshflow,Wetriedto

measurethepressuredropsthroughtheapertureswithout

screenmesh,butthosefわrthe15mmand10mmsquare

aperturesweretoosmallformeasurementanddatawere

obtainedonlyforthe◎5mmaperture.Theresultshowedthat

therewasnodiscemibledifferencebetweenwaterandthe

solutionsused.

Headtat)k

Fig.2.Schemaof血e叩params.

7.?

.?J

O0

00

l1

11

【S･d巴

LL

■▲

Il

▼

γwl1/S]

Fig.3.Viscosityofthetestedliqllids77measuredbyacapillaryviscometer.71isdeBnedastheratioofthewallshearstresstothewallshearrate7tv･Thetemperatureis17-20oC･

AMAKl･HASEGAWA･NARUMl:DragReductlOnintheFlowofAqueousSolutlOnSOfDetergentThroughMeshScreens

ThevelocityoftheliquidflOwingthroughthescreenwas

calculatedbydividingthemeasuredf一owratebyaneffective

nowarea.Forsquareopenings,thevelocitythroughthemesh

㍗"isgivenaS

v",=91 (1)(7S

wherea-# istheporosity,whichrepresentstheratioofthe

effectivepassarea∑b2inthemeshtotheareaofaperturesS.

3.RESUu~SANDDISCUSSl0N

Experimentalresultsarepresentedintermsofheadlosshas

afunctionofstrainrateVm/bforalltest.liquidsinFigs15(a-f),

wherecasesA,BandCrepresentsthesize5'of15mmx15- ,

10rrmxlOmm ,and◎5mmrespectively.Itisevidentthathis

notaunlquefunctionofV/b,butdependsslightlyonthetread/I.I

densityandmorestronglyontheopeninggeometryand-size.

ConsiderthecaseforthenowthroughthelOmm screen,as

shownbyCaseBinFigs.5(a)-(f),valuesofhcorrelatewell

withV/bonlyinthestrainraterangeoflessthan2×103sec~t1)1

forwaterandthe10ppmPEOsolution(Figs.5(a),(b)),butis

extendedtohlgherrangesofstrainratef♭rothersolutions.For

instance,thecorrelationisextendedtoV/bupto4×103sec-I1l.I

forLASandAE(23)(Figs.5(C)(d)),and104see-】forPAA

andCTAB(Figs.5(e)(f)).Furthermore,hexhibitsasteep

riseatacertaincriticalvalueofV/b,beyondwhichnofurtherりJ

I

OtLOSt

l

Apertures(The且reZLIsS･)

(b)

(Unit;nm)

Flg4.(a)Photoofthescreenmeshandthedefinitionorbandd.(b)MeshscreensandtheareaoftheaperturesS.

increaseinV/blSObserved.Thisphenomenonisevidentin/〟

CasesAandちfbrLAS(Fig.5(C))andAE(Fig.5(d))

solutions,andisalsoobseⅣedf♭rwater(Fig.5(a)),although

itseFectissmall.

Figure6givestheresultsofheadlossasafunctionofstrain

ratef♭rallthetestsolutionsflowmgthroughthescreenmesh

of300threadsperinch.Itisseenthat,exceptfわrthePAA

solution,aunlqueCO汀elationisobtainedf♭rallothersolutions

includingwateruptoastrainrateof2×103see-1･Beyondthis

rate,theheadlossesfわrwaterandPEOsolutionbecomelarger

thanthoseofAE,LASandCTABsolutionsatthesamestrain

rate.ThePAAsolutionexhibitsthelargestheadlossoverthe

samestl･ainraterange.Inotherwords,lowmolecularweight

surfactantssuchasAE,LASandCTABshowdragreduction

effectscomparedwithwater,buthighmolecularweight

LOB

102

呈101

100

Vm佃〔1/sec]A(15mm) B(10…) C(め5m)TlヽTtadsJTYh lllTead血 h llTeadsrlLEh0230△255ロ 270◇300

○▲80

050

0

232527

30如

●▲■

◆

230

255270

30 0

LOB

LO2

良

旦101｣=

100

Vm/b[1/㌍cJ

Figl5 LossheadhagalnStthestrainrateV",/bforpolyestermesh･(a)Ionexchangewater,(b)PEO1810ppm,(C)LASO･OlmoUL,(d)AE(23)

0.01moVL,(e)PAA10ppmforthecaseB,(f)CTABO･005moVLfor血ecaseB

127

NihonReorojiGakkaishiVol.362008

polym erslikePEOandPAA,whichareknowntobegood

drag-reducingagentsinturbulentflows,donotgiveanydrag

reducingeffectinflowthroughwiremesh*,asseeninthis

flgure.Thiseffectisshown moreclearlyinFig.7fortheflOw

ofthesamesurfactantsolutionsthroughastainlesssteel200/

inchmesh.

(*)

OnthePEO(18)solution,onsetofdragreductionin

turbulentpipeflowisatthewallshearstressI*光0･4Pa9),W

whichcorrespondsto也eshearrateof4001/S.Thisvalueof

shearrateiswellbelowthoseofthepresents山dyexcept

severalpointsofverylowshearrate(seeFig.5(b)).Therefore

itisthoughtthatthemoleculeofPEO18isunderthecondition

ofdragreducingiftheflowisaturbulentshearflow.

Furthermore,theconcentration10ppmishighepoughto

generatedragreductioninturbulentpipeflows･9･10,ll)onthe

PAA10ppmsolution,thelargepressurelossshowninFig.6

isthoughttobecausedbytheelasticstressorsomevortices

generatedupstreamofthemeshscreen･12,13)

3.1 CorrelationBetweenReynoldsNumberandDrag

CoefFicient

Sofar,flowthroughmeshscreenshasbeenregardedasan

extemalflowaroundthethreadsofthemeshandthefollowlng

103

102

号10lJ=

100

loll

VJbl1/sec]

Fig.6.hforal1thesolutionsusedforthescreenmeshof300threadsperinch(polyestermesh).

V,nn)[1/sec]

Fig.7.hagainstV/bforthestainlessmesh200/inch.a

128

definitionsofReymoldsnumberanddragcoeWICienthavebeen

adopted14):

Reynoldsnumber: (Re)a-壁 , (2)l′

whereUisthemeanvelocityoftheflowapproachingthe

screen,disthediameterofthethreadweavlngthescreenof

thesquaremeshandvisthekinematicviscosityoftheliquid.

Dragcoefficient:K-%h･ (3,

Thefollowingexperimentalcorrelationforairbetween(Re)d

andKwasproposed14,15):

K-Kの.義 - (4･1)

K--(諾 )2 (412)

An attemptwagmadetocoITelatethepresentexperimental

resultsusingEq.(4.1),asshown inFigs.8(a)and(b)forwater

flowingthroughthe15×15rrmsquaremesh,andforAE(23)

solutionflowingthroughthecircularholeof◎5mm,

respectivelyJtisevidentthatneithertheexperimentaldata

collapseintoamastercurve,northeyfltWiththeempirical

correlationforair.Thepresentresultssuggestthattheextemal

flowmodelmaynotbeasuitablemodelfortheliquidmesh

flow;perhapsanintemAlflowmodelmaybemoreappropnate.

Forintemalflowthroughmeshscreens,Reynoldsnum ber

ReanddragcoencientCDmaredefinedasfollows:Jn

Fig.8.A汀angementOfthepolyestermeshdatabytherelationshipf♭rair(lines).(Re)aistheReynoldsnumbergivenby(Re)d=%whereUisthemeanvelocityoftheflowapproachingthescreen,disthediameterofthethreadweavingthescreenofthesquaremeshandvisthekinematicviscosityoftheliquid.Kisthedrag

coefrlCientgivenbyK-欝･(a)waterfor15mmx15mmand(b)AE(23)0.01mol/Lfわr¢5〝〝〝.

AMAKl･HASEGAWA･NARUMl.DragReduct10nlntheFlowofAquec･usSolutlonsc･fDetergentThroughMeshScreens

Figures9(a)and(b)presentallexperimentalresultsfわrwater

andAE(23)Solutionsobtainedimallthreecases,A,BandCin

termsofRemagalnStCD",,reSPeCtively･Theexperimental

resultsareseentobewellco汀elatedfわreachcase,irrespective

ofthenumberortheopenlngOfthethreads･However,amaster

curvecannotbeobtalnedforalldatabecauseofthedifferences

intheapertureopenlng∫.Hence,thef一owmodelmustbe

refinedbyadoptlnganewSetOfdefinitionsforReynolds

numberanddragcoeFICient.

AcloseexaminationofFigs.5(C)and(d)revealsthatthe

steepriseinhoccursalmostatthesameflowrateevenfor

differentdimensionsofS.ThiscriticalflOwrateyieldsa

conventionalReynoldsnumberof3600,Calculatedusingthe

lTleanVelocityintheinlettubeandthediallleterOftheinlet

山beconnectlngtOthechannel.ThiscriticalReynoldsnumber

suggeststhatthetransitionfromlaminartoturbulentflowsin

theinlettubemayinfluencetheexperimentalresult,ormore

generally,thattheflowcomlngfromtheinlettubemayaffect

thenowupstreamofthemeshscreen.ThisconjectureWas

verifiedwithavisualizationexperimentbyinJeCtlngacolor

liquidupstreamofthemeshscreen,asshowninFig･10(a)･It

canbeobservedfromthefigurethatacylindricalcolumnof

liquidappearstobecomlngfromtheinlettubeandhittingthe

meshscreen.Amodeloftheflowinthevicinityofthescreen

isgraphicallyrepresentedinFig.10(b)･

Intheflowmodel,itisassumedthatthef一uidnowlngfrom

theinlettubeintothechanneldoesnotdivergeslgnificantly,if

any,andapproachesthemeshscreenasaliquidcolumnof

Flg･9･DragcoefrlClentCDmaganStReynoldsnumberReforpolyestermesh.Subscl-1ptJ77illdicatestheqtlal-tltleSbasedonthemeSllvelocItymtheopenlngS･(a))Onexchangewater,(b)AE(23)0.0111101/L

almostthesamedialneter(6mm)oftheinlettube.Thehquid

columndoesnotchangethediahleterinpasslngthroughthe

llleShscreenof10x10mmand15×15mmapertures,but

changethediameter&om6mmto5mminpasslngthrough

themeshscreenof㊥5mmcircularaperture.Basedonthis

model,twoadditionalvelocitiesare丘lrtherintroduced.These

arethevelocityoftheinlettubeVandthevelocitythroughthe.I

meshscreenbasedontheliquidcolumnoftheinlettubeV･/,仰Thesetwovelocitiesaredeflnedrespectivelybythefollowlng

relationships:

V,-& (7,

Y ,川-% (8)

whereD-6mmforthe10x10mmand15×15rrm apertures,

andD-5mmforthe(∋5mmaperture.Thus,amodified

Reynoldsnumberandamodifleddragcoed:lCientareredefined

asfわllows,

Re,,"=坦 (9)V

h

cD'7m =% '10'

TheexperimentalresultsshowninFig.9arere-plottedin

Fig.lluslngthemodifiedReynoldsnumberanddrag

coefflCientgivenbyEqs.(9)and(10)respectively.Itisseen

fromFigs.ll(a-C)thatalldatacollapseintoasinglemaster

curvebelowacertaincriticalReynoldsnumberandare

inverselyproportionaltotheReynoldsnumberapproximately･

Thiskindofinvel~SeprOpOrtlOnalitytoReynoldsnumberhas

∵ 二 ‥ ㌦(a)

///////////

一 一千 ~雌 -:--:…一声 -L毒L-

p+A p p

(b)

m esh

Flg.10.(a)PhotooftheIlquidcomulgfromtheinlettubeandhlttingthescreenmesh.(b)Themodelrepresentation･

129

NihonReorojiGakkaishiVol.362008

beenreportedbyseveralpapers･16･17,18)weseealsointhe

flgureSthathincreasessuddenlybeyondthecriticalReynolds

number,independentofthenum berofthreadsandthescreen

areaS,althoughthecriticalReynoldsnum berisstillslightly

dependentonS.Itappearsthattheproposedflowmodelis

adequatefortheflowofdilutesolutionsthrough meshscreens.

Itisalsointerestingtonote,bycomparingFigs.1I(b)and(C)

withFig.ll(a)thatthedragcoefrlCientsobtainedforthe

detergentsolutions,AE(23)andLAS,aremuchlowerthanthat

obtainedforwateratthesameReynoldsnum ber.Thsindicates

adragreductionphenomenon,andsurfactantssuchasthose

usedinthepresentstudyareeFectivedrag-reducersforflow

throughmeshscreens.Bycontrast,PEOandPAAsohtions,

whicharewell-known drag-reducersforturbulentflowinpIPeS,

didnotmanifestanydragreductionphenomenoninScreennow,

asalreadyshowninFig.6.Consequently,itissuggestedthat

surfactantsusedasdetergentspromotethepenetrationof

washingliquidsintoclothesbydecreasingtheresistanceofthe

liquidandbringaboutahighere氏ciencyondetergency.

3.2 DragReductionMechanisms

Therehavebeenmanystudies,boththeoreticaland

experimental,ondragreductioninturbulentpipeflOwuslng

polym eradditives.Acomprehensivereviewonthissubject

canbefわundinarecentpaperbyMin,etal.19)However,血e

dragreductionphenomenonobseⅣedinthepresentstudy

doesnotcorrespondtoanyofthepreviousstudies,becausethe

phenomenonoccursoveraReynoldsnumberrangewell

belowtothoseencounteredinturbulentpipeflow,asseenin

Figs.Sand9.Thisindicatesthatthedragreductionobserved

inthepresentstudymaybecausedbyamechanismtotally

difFerent&omthatobservedfordilutepolymersolutionsin

turbulentpipe,flow.AsseenBomFig.5,water,PEOandall

130

othersurfactantsolutionshavealmostthesamelossheadh

untilthestrainrateV/breachesaround2x103see-I.Above/〟

thisvalueofstrainrate,theheadlossesmeasuredforwaterand

PEObecomeshigherthanthoseforthesurfactantsolutions.In

otherwords,a血agreductionphenomenonwasobseⅣedfb∫

thesurfactantsolutionsascomparedtowaterflow.Onepossible

causeof也eobseⅣed血agreductionis血edestaもilizationof

disturbancesoreddiesintheflowupstreamofthemeshscreen

causedbythesurfactantmolecules.Contrarytothis,ithas

beenreportedthatintubularflow,dilutePEOandHEC

solutionstendtogeneratefluctuationsprlOrtOreachingthe

conventionaltransitionfrom laminartoturbulentflow

observedinwaterflow,resultinginhigherpressurelossesin

lam inarflowofdilutepolym ersolutions･20,21)An otherpossible

causefb∫dragreductionistheboundaryslipbetweenthe

surfactantsolutionandthesolidsurfacessuchasthepolyester

andstainlesssteelsurfacesusedinthepresentstudy.Boundary

slipbetweenNewtonianliquidsandsubstrateshavebeen

recentlyreportedbynum erousresearchers･2223･24)However,the

slipeB:ect,althoughcannotbecompletelyruledout,isdeemed

nottobeamaincausesincetheeffectoftheconventionalslip

phenomenonismuchlessthanthepresentdragreduction

effect.Although thedragreductionphenomenonobservedfor

theflOwofsurfactantsolutionsthroughmeshscreensinthe

presentstudyisreal,noneoftheconventionalmechanisms

proposedinliteraturetoexplainturbulentdragreductionin

pipeflowapplieshere.Itiscurrentlybelievedthatthedrag

reductionphenomenonobseⅣedherecouldbeduetocomplexニノ

interactionsintheinterfaceregionbetweenthehydrophilic

andlipophilicgroupsofthesurfactant,andthesubstratewall.

However,furtherworkisrequiredtoclarifythecauseofdrag

reductioninmeshflowandtoproposeaplausiblemechanism.

Fig111ICDtp,againstRe,,桝forpolyestermesh,wheresubscriptst,mmeanthatquantitiesarebasedonthemeshvelocityCalculatedaomthevelocityoftheliquidcomingBomtheinlettube.(a)ionexchangewater,(b)LAS0.Olmol/L,(C)AE(23)0.01mol/L.

AMAKI･HASEGAWA･NARUMI:DragReductionintheFlowofAqueousSolutionsofDetergentThroughMeshScreens

4.CONCLUDINGREMARKS

PressurelossesacrossmeshscreensfortheflOwofwater

anddiluteaqueoussolutionsofdetergentsandpolym erswere

measured･Itwasfoundthatsolutionsoflowmolecularweight

surfactantssuchasAE,LAS,BC,SDSandCTABshow

sigmiflCantdragreductioneffectscomparedwithwater,butnot

thehighmolecularweightpolym erslikePEOandPAA,which

arewellknOwntobegooddragreducingagentsinturbulent

pipeflows.

TheheadlossoverthemeshscreenlSgreatlyinfluencedby

theconditionsoftheliquidupstream oftheinlet.Flow

visualizationshowedthatverylittledivergenceoftheflow

丘omtheinlettothemeshscreenoccursinthechamelandthe

liquidentersthemeshscreenmainlyasaliquidcolumnof

diametersimilartotheinlettube.Aflowmodelbasedonthis

observationwasproposedwhichyieldedagoodcorrelationof

dragcoefncientwithReypoldsnumber.

SurfactantssuchasLAS,AE,BCandSDSareusedinvast

quantitiesindetergents.Thepresentexperimentalresults

suggestedthatdetergentsareeffectiveforremovalofdirt

stainSinwashingnotonlyduetotheirchemicaleffects,but

alsoduetotheincreasedmobilityofdetergentliquidsbetween

clothingthreads,asaresulttoitsdrag-reducingcharacteristic.

Acknowledgements

ITheauthorswishtoexpressmanythankstoProf.CarlosTiu

forcomm entsandsuggestionsoncontentsandEnglish.They

gratefullyacknowledgealsomanyhelpsbyMr.Ryuichi

Kayaba,Mr.MasahiroKamsawaandMr.YoshihikoIino.

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