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Unformatted text preview: Electrostaticcontrol of particle deposition and HIROAKI MASUDA YAMAGUCHI KEN-ICHIRO MAKOTO TANOUE, Yoshida-Honmachi, University, Sakyo-ku, Department Engineering, of Chemical Kyoto 606-8501, Kyoto Japan 1998 Received 1998; 17 17 September July accepted inan Abstract-A two-dimensionalhas conductedelectrostatic simulation been powder-coating most flow In absent the boothcontrolling deposition. ofelectrostatic of for forces, particles particle andmage forces steamlines deposit target. electrostatic and cannot on the When (coulombic i along the near the It are inthe ofthe forces)added motion particle,rajectoriessignificantlytarget. t change From calculated isfound image hardly the that force affectsdeposited ofthe position particle. the near the region the coulombic found larger drag force to is be than force distribution aimed on target, when particle close t Particlessmall number small force the isvery tothearget. with Stokes having the regions. the width the region charge exactly specific deposit on aimed Furthermore of aimed also the of the deposition. affects ccuracyparticle a Stokes specific Electrostaticparticle 2D simulation; number; charge. Keywords: control; deposition; NOMENCLATURE coefficient (-) cc Cunningham's slip coefficient CD (-) drag deviation ofparticle Di deposited (-) position size Dp particle (gm) E electric (V/m) field electric definedequation (-) dimensionless field (7) by Eê electric defined dimensionless field (8) byequation (-) Q Eê,o dimensionless field electric definedequation (-) (9) by E* coulombic (N) force Fc force FD drag (N) force FG gravity (N) force Fj image (N) Froude number Fr (-) 120 g H Lo All i L2 Lw mp NP q/mP (q / mp)o (q / mp)* Rein Rep St Stopt u Uo U v Z W X Xp, T' Greek sj ,r A pp pG r or (D acceleration 2) (m/s gravity width nozzle of (m) ofinlet (m) length region o widthfaimed (m) region ofaimed (m) intervals region distance between and wall particle the (m) o mass fparticle (kg) (-) injected number particle specific (C/kg) charge reference ofspecific (C/kg) charge dimensionless charge specific (-) dimensionless value specific (–) charge optimum of number Reynolds (-) = HpGuo/> number Reynolds (-) particle number Stokes (-) number value (-) optimum ofStokes airvelocity (m/s) inlet velocity air (m/s) airvelocity dimensionless (-) (m/s) particle velocity dimensionless velocity (-) particle o widthftarget (m) axial coordinate (m) o aimed (m) region edge fthe most particles departed from ofdeposited (m) position Xe.; coordinate transverse (m) definedequation (m) (11) by ratio permittivity (-) of viscosityair(kg/m/s) of densityparticle (kg/m3) of densityair(kg/m3) dimensionless time (-) ofaimed (V) electric region potential electric dimensionless potential (-) 121 1.INTRODUCTION toget their Recently, ridofpollution, pollution-free areincreasing market paints share ear year.The method electrostatic [1]is force y by powder coating using remarkable andis applied thecoating automobiles, to of themost railroad one, etc. d electrostatic coating consists of articles, Because cars, omestic [1] powder ofparticles, transportcharged of to as (i)electrification (ii) particlesthetarget an ofinternalexternal field, particle or electric (iv) aerosol, formation (iii) deposition and(v)fusion particles, research each of much of has conducted process been andnumerically. has experimentally Transporting to thetarget been particles studied external work theparticles,it is forces on so [2-6]. numerically Various difficult todiscuss individual experimentally. asmost them the force Besides, of are limited only and for big simple there noreports are which concerned with targets, is selective exact and deposition ofparticlesinelectro-photographics as and coating ofimage elementsaBraun on tube. inwhicharticles ontheaimed Inthepresent fortheprocess work, p deposit ina wehave simulation tworegion tribo-charge, conducted particle by charged dimensional booth discuss accuracy particle the ofthe under coating and deposition various conditionsvelocity, size specific (air operating charge). particle and 2.CALCULATION DOMAIN 1shows calculation Gas fed the region = W) y the domain. is into inlet (Lo b Figure the with a expands (H velocity (u using nozzle = 0.06W) constant profile = uo) nd into particle booth S W 8 W. target W 0.1 )isplaced W the The ( x W 3 coating of x ofthe downstream nozzle The regionsparticle exit. aimed of are depositionsettled atintervals Each the ofL2. of aimed has width L 1. surface of The regions a potential onthe aimed is1>T theallother are walls grounded Particles are (0V). region and into booth the as flow. injected the through nozzle anaerosol 3.NUMERICAL AND PROCEDURE ONDITIONS C 3.1. flow field and electric field Air intwo-dimensional coordinates. Numerical simulation isconducted Cartesian The are to derive governing the (i) following assumptionsintroduced equations:the field and in is air,(ii) gas incompressible thevelocity istwo-dimensional steady the booth uniform state,iii)gasenters coating with ( (iv) velocity, theelectric not is to i ( potentialequal 0 Vat theboothnlet, v)gasdoes sliponthewall, surface electric is a walls (vi) regionndallother are potentialOrontheaimed (0V), flow (viii) grounded (vii) isturbulent, thespace effect negligible, charge is and both gradients ofmomentumelectric and are to (ix) the potential equal 0 at thebooth inthis outlet. thestandard model was k-s Furthermore, [7] adopted 122 1.Calculationin electrostaticbooth. domain the Figure coating 2. meshes calculation near target. domainthe FigureStaggered inthe 123 Navier-Stokes k-equation, simulation. (continuity, Governing equations equations, and and conditionsrewritten are innonequation) boundary s-equation Laplace's over mesh dimensional and discretized acontrol ona staggered forms then volume of method and solved numerically bymeans theSIMPLE [8].The typical of grid isshown Fig. ,where x 100 in 2 inthe this simulation the near target 130 meshes axial transverse and directionsused. are 3.2. Particle motion field determined, thetrajectoriescalculated are After gas and the field electric are with equation the ofparticle motion. Including force, force, drag gravity coulombic force imageorce theexternal ontheparticle, dimensionless and f as forces the ofparticleexpressed is as equation The fourth ofthe term right-hand isthe side image [1]. here, force W the concentration is The to interaction isignored because particle particleparticle low. the When distance particle the isless Dp/2, assume between and target than we 124 the is on target surface. 1shows condition Table the ofthis particledepositedthe simulation. Stokes (St) the By changing number and dimensionless charge specific we studied accuracy particle the ofthe [(q/mP)*],have deposited position. 4.RESULTS DISCUSSIONS AND 4.1. flow and Gas field electric field 3shows calculated inthe the air flow whole The velocity isequal Figure region. inlet to10 Arrows the m/s. show velocity The and ofthe scale vectors. light shade gray shows axial the equi-velocity Intheinlet profiles. region, flow develops gas fully booth. o flows around and into coating Apair flarge enters the circulating isformed 1. Table Conditions of simulation 3.Calculated inthe region = 3333). air flows whole (Rein Figure 125 that From velocity itisfound ajetstream the inthe profiles, region target booth. the exit. axial small. exists thenozzle Inother near Ux regions, velocities arevery area. in 4 value Inparticular, have negative intheblack Asshown Fig. ,a they a from center the along to edge the near target the new boundary isformed the layer itis that transverse direction. Therefore, anticipatedtheparticles not eposit may d force on the if attractive (electrostatic isabsent. 5 force) Figure effectively targetthe of target Arrows electric in vicinitythe surface. show shows calculated field the the force The a shade thegray shows of scale equi-potential electric vectors. light nd on and If particles charged are negativelyapositive isapplied voltage profiles.the and repulsive force on theaimed the regions the region, attractive works theaimed w at between force orks intervals them. 4.2. rajectories T I near 6a b the ofparticles thetarget = 102).n (Fr Figure and shows trajectories flow and force drag are 6 Fig. a,only gravity and force considered theparticles The which from center the of booth, the along steamlines. particle, isinjected the In 6 coulombic and force image on surface. Fig. b,including deposits thetarget the and the force, trajectories dramatically particles near aimed deposit the change region, cannot deposit region. Although 2and are tothe particles 3 close aimed they o On force at onit because repulsive works theedge fthem. theother the hand, of nozzle ishardly affected is from wall, 4, particlewhich injected thevicinitythe vectors. C of 4. air flows the (Rein (a) FigureCalculated near target = 3333).Velocity (b) ontours axial (lJx). velocity 126 5.Calculated potential near target = 0.00133, +L2) = electric profilesthe Figure LI/(LI electric (b) of electric (<1». 0.2]. Lines force.Contours potential (a) of 6. near the (a) + (b) = + + + FigureTrajectoriestarget.YF= FD FG. Y F FD FG FC FI. 127 = I, 7. curves the [Rein St (q/mp)* ' = 0.00133, FigureForce near target = 3333,= 0.25, Table 2. The influenceimage on particle position = of the forcethe deposition (Rein St= (q/mp)* = 3333, 0.25, = I,Eê.o 0.00133, +L2) 0.2) L)/(Li = the force it flows s Therefore,particle bycoulombic and almost alongteamlines. on inject under conditions stronglythe positions. trajectories these depend surface. we how forces the on particle near target Next investigate the change the the between particle ofthe 7 the LW distance Figureshows distribution forces. isthe from the distance the axes respectively, wall. horizontal vertical show, and and The force. particles surface theaxial normalized gravity The and force bythe target and decelerated at the inthenozzleLw> 3W) immediately areaccelerated ( than the force When nozzle Therefore,drag isnegative. Lwisless 0.02W, exit. value the and coulombic affects trajectorieshasmaximum atLw =0.01 W force atthe o aimed For avery coulombic isinduced edge fthe force because large region. If is than force constant.LW less O.OOO1Lw< O.O1 coulombic isalmost < W W, ofthe The O.OO1 W, force position image increases gradually. deviation deposited W in 2. due image isabout to force 0.00001asshownTable Therefore, force image isnegligible applications. inactual 4.3. Evaluationparticle deposition of Stokes of atvarious numbers 8 the (St). Figureshows ranges particle deposition axis The horizontal isthe axis positionparticle of and vertical isthe depositionthe The of The gray show Stokes number. three areas theaimed regions. deviation 128 8. ofparticle inconnection number = with Stokes [Rein 3333, Figure Ranges deposition (D;) particle deposition isevaluated (10) (11). byequations and where e,; theedge ftheaimed and is themost o X is region XP.; departed position ofdeposited from Ifall inthe particles Xe, ;. particles deposited aimed region, wedefined < 0, and other D; > 0. For the case, ifSt D; example, = 0.5and then = W Xe, Therefore 1.5. L= 0.02W, Xp, j O.15 and l = 0.12 W . D= 4.3.1. number. 9 the between Influence ofStokes Figureshows relationship St andD ;.The dimensionless charge / mp)* to 1.0.This is equal specific (q figure means thesmaller inother that thesmaller size St, words, particle orthesmaller airvelocity the ofthe IfSt small, yields higher accuracy deposition. istoo particles cannot onthe So optimum condition inthe exists particle or size deposit target. the airvelocity. the coulombic (Fc,,) hanges inallofthe force little Although axial c aimed the than regions, transverse force atthe ofthe islarger drag (Fp,y) edge target that thecenter it. Asaresult, particle beyond aimed and at of the flows the region on the value the deposits theinterval Then shows largest among three region. D3 aimed regions. 129 in with Stokes [Rein = 9. ofthe deposition FigureDeviationparticle = connection number 3333, = 1, Lj /(L j (q/mp)* =0.00133, + L2) 0.2]. with charge = ofthe 10. s Figure Deviationparticle inconnectionpecific [Rein3333, deposition = = (q/mp)p C St 0.25, = 10-3 /kg, + L2) 0.2]. between 10 the 4.3.2. charge. Figure shows relationship Influencespecific of = In figure, larger the a St and (q/mp)* (q/mp)* D;atRein 3333nd = 0.245. this are causes greater The the DL. reasons asfollows; force is of particleaffectedthe area the by coulombic is (1)The where motionthe wider that small / m p) * . than for (q from at region (2)Transverse velocitythedeparted position theaimed is particle for (q/mp)*, particle the than for Therefore,large higher that small (q/mp)*. the onthe flows region. region deposits interval beyond aimed and cannot on Then ¡enlarges. specific istoo Ifthe small, D particles deposit the charge that than gravity Itisfound force. the force because coulombic issmaller the target the the conditions incontrolling exist particle deposition. optimum operation the W have 4.3.3. region. e discussedaccuracy Influence width the ofthe of aimed under width aimed (LI) itsinterval ofparticle region and deposition constant ofthe 130 11. ofthe with Stokes [Rein Figure Deviationparticle inconnection number = 3333, deposition = 1, + = (q/mp)* LII(LIL2) 0.333]. 12. ofthe with charge = Figure Deviationparticle inconnectionpecific [Rein3333, deposition s = St=0.25, + L2) 0.333]. 13. between normalized the regionoptimumof width aimed and of value Figure Relationshipthe St, atthe region (q/mp)* aimed 1. 131 i previous sections.fact,tisnecessary In i tochangeaccordingthe to L, (L2)nthe inelectro-photographics, For the objects. example, are size a character they the of size image of elementsaBraun etc. on we studied accuracy the tube, Thereforehave ofparticle for widths 11 depositionvarious oftheaimed region. Figuresand 12 = show calculated forthecase L I I(L LZ) 0.333. tendency the results of The + t accuracy isenhanced orspecific becomes isthe as asSt smaller same thathe charge in previous shownthe sections. However, isless 0.5 any Dihere than in conditions; < at0.025 St < 0.075, hasa negative The shows value. fact that D3 especially inthe We the particles perfectly internal ofthe deposit region aimed region. define which inimize and variationthem shown a and m of is as D;, the Stopt function of i 1 the of b + LZ)nFig. 3.For case L,/(L¡+ L2)> 0.2, oth = 0.08], and have constant [Stopt 0.022, a value = Stopt (q/mp.opt)* This the respectively.iswhy particles perfectly onthe deposit aimed under region the condition L I / i +Lz). oflarge (L in order the of inan Consequently, tocontrol position thedeposited particles electrostatic process, necessary (i)thewidth the itis toset of aimed coating region, and t optimum t optimum size optimumvelocity (iii)he air (ii) he particle or specific charge. 5.CONCLUSION For ontrolling the we have aerosol ina c particle deposition, conducted simulations two-dimensional electrostatic booth. absenceelectrostatic of forces, coating Inthe almost along and the theparticles flow thesteamlinesonly particles from injected thecentral ofthenozzle on surface. thecoulombic If region deposit thetarget and forces included, trajectories dramaticallythe the near aimed image are change Force near target calculated. shown thedrag are Itis that region. distributionsthe force coulombic play and force important inthe roles trajectoriesimage but force israrelyffective. theparticlevery totheaimed e When is close coulombic region, than drag The force greater the force. accuracy deposit is ofthe isa position function ofairvelocity, size specific and we optimum particle and charge, therefore have conditions. When consider we the itis touse particle deposition,necessary asmall controlling Ifwe inthe Sthavingsmall a one specific charge. useonly nozzle electrostatic the flow the coating, deposited isaffectedthe position by circulating around target. ofthe we t Then, guesshattheaccuracy deposited position beimproved may ifmany are which the to considerably nozzles used, spray particles perpendicular whole ofthe under condition <0.6. ofSt the region target the Acknowledgement Ltd. a This was supported work partly Co., bySamsung DisplayDeviccs, and Grantof in-Aid Scientific for Research 10555265) theMinistry Education, from (No. of Science, and Culture, Sports Japan. 132 REFERENCES Powder Research Press 1.J.F. ElectrostaticCoating. Studies ( 1984). Hughes, in electrostatic L. and J. ofcharged trajectories 2.M. Ang P. Lloyd, Investigation particle powder J. Flow 823-836 1 (1987). coating Int. Multiphase3, system, metal in and K. 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