Perpendicular-field EHD instabilities visualized in a tip-plane configuration

2002 Annual Repo Con e ence on Elec ical Insula ion and Dielec ic Phenomena Pe pendicula - ield EHD ins abili ies isualized in a ip-plane con igu a ion F. Vega, A. T. PB ez, F. J. Ga cia and A. Cas ellanos Depa amen o de Elec 6nica y Elec omagne ismo, Uni e sidad de Se illa, SPAIN Abs ac : EHD in e acial ins abili ies can be in- duced by co ona discha ge om a ip elec ode on o a liquid-ai in e ace. The co ona cu en cha ges he liquid su ace and ins abili ies may appea de- pending on he applied ol age and he liquid p op e ies. We p esen a echnique o de ec he onse o ins abili y based on image p ocessing. To es ablish he ins abili y h eshold we apply an edge-de ec ion algo i hm o images o he liquid su ace acqui ed h ough a idea came a. In oduc ion Two ypes o EHD ins abili ies may be obse ed when he su ace o a poo ly conduc ing liquid is subjec o co ona discha ge om a ip. I he liquid conduc i i y is e y low, in such a way ha he elec- ic elaxa ion ime, €/U, is g ea e han he ime he ions need o a e se he liquid hickness, &‘/(KV), a space cha ge dis ibu ion appea s. (He e E is he liquid pe mi i i y, U i s conduc i i y, d i s hick- ness, K he ion mobili y in he liquid and V he ol age ac oss he liquid laye .) The exis ence o his space cha ge gi es place o he EHD olume ins abili y induced by unipola injec ion. The ele- mn pa ame e is in his case T = eV/(Kq) (q he liquid iscosi y), and abo e T - 100 he liquid is se in o mo ion wi h a pa e n in he o m o con- ec i e hexagonal cells. The size o hese cells is o he same o de as he liquid hickness. The ins a- bili y due o unipola injec ion is a classic p oblem in Elec ohyd odynamics and has been he subjec o many s udies [l, 2, 3, 41. In a ipplane con igu a ion he ol age d op ac oss he liquid is de e mined by he co ona cu - en , and his is, in u n, de e mined by he ol - age applied o he ip, being he dependence on he ipplane dis ance a he weak [5]. The e o e, he ypical pa e n o EHD olume ins abili y due o he space cha ge is obse able applying a ew kilo- ol s o a poin o e a g ounded pla e whe e we ha e disposed silicone oil, o example. The pa e n ap pea s independen ly o he ipplane dis ance, p o- ided he cu en is o he o de o 1 PA. I he liquid conduc i i y is low, bu high enough o p e en he exis ence o space cha ge ( his occu s i €/U < &‘/(KV)), he conduc ion in he liquid is ohmic. In his case he EHD olume ins abili y is no obse able, bu ano he ype o ins abili y is possible. This is e e ed o as ose-window ins a- bili y and is due o he elec ic p essu e exe ed on he cha ged su ace [6]. Being he liquid conduc- i i y low, he elec ic cha ge on he su ace is o he same pola i y as he injec ing elec ode. The e- o e he elec ic p essu e pushes down he liquid and he ins abili y a ises as a consequence o he com- pe i ion be ween elec ic and g a i y o ces. On he con a y, i he conduc i i y o he liquid is high, he pola i y o he su ace cha ge is o opposi e sign o he applied ield. In his case he elec ic p essu e pulls up he liquid su ace [7]. In bo h cases he ele an pa ame e is U = oV,Z/pgh3, whe e V, is he po en ial applied o he ip and h he dis ance be ween he ip and he plane elec ode [8]. Cells o size la ge compa ed wi h he liquid dep h a e cha ac e is ic o he ose-window ins a- bili y, and his size dec eases as he elec ic ield on he liquid inc eases. Theo e ically, i seems ha he linea ins abili y li s appea s o an in ini e wa e- leng h [8], and his may be he eason why he pa - e n is ini ially o med by la ge cells. Since ose- window ins abili y is associa ed o he e ec o he elec ic p essu e on o he liquid su ace, an his is o o de eoQ2/h2, only i he ipplane dis ance is low he ins abili y is obse able. Fo example, o a 1 mm dep h laye o co n oil, he ins abili y appea s when he ol age applied o he ip is close o 4 kV and he dis ance is o he o de o 3 cm. Al hough he ose-window ins abili y seems o be caused by he ac ion o su ace elec ic o ces i appea s only i he e is injec ion o cha ge in o he su ace, and he mechanism o ins abili y is essen ially di e en om ha in classic s udies 191. The ose-window ins abili y appea s also in liq- uids whe e he EHD olume ins abili y is p esen . Usually i appea s a ol ages abo e he olume in- s abili y h eshold, when he su ace has al eady been de o med. In hese si ua ions bo h pa e ns, ha o small and ha o la ge cells, a e supe im- posed [lo]. Al hough he ose-window ins abili y can be de- ec ed by looking a he su ace wi h unaided eye, a mo e eliable de ec ion p ocedu e is desi able. We ha e de eloped a de ec ing echnique based on dig- i al image p ocessing. The same echnique can be use ul o de ec ing o he luid ins abili ies. 0-7803-7502-5/02/$17.00 8 2002 IEEE 216 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on July 14,2023 a 10:50:21 UTC om IEEE Xplo e. Res ic ions apply. U Figu e 1: Poin o pla e con igu a ion o he obse e ion o EHD ins abili ies. Table 1: Physical p ope ies o he liquids used in he expe imen s. Silicone oil Cas o oil E 2.73 4.69 &7/m3) 960 958 .(m"4 50. 600. uC(W1m-') 6. 7. lo-" K(m2/Vs) 5 ' 10-10 4 ' 10-11 Se up The expe imen al se up is shown in igu e 1 and de- sc ibed in de ail elsewhe e [6, lo]. A high- ol age sou ce is connec ed o a poin elec ode. Below he poin , he e is a plane ci cula elec ode which is g ounded. A ew millili e s o poo conduc ing liq- uid a e disposed on o he elec ode. The elec ode is moun ed on a ame made o plexiglass ha p e- en s he liquid om lowing ou o he elec ode. The su ace o he unpe u bed liquid is a ci cle o diame e 4.5 cm. An elec ome e connec ed be- ween he plane elec ode and he g ound allows o moni o he elec ic cu en . In o de o ha e a good isualiza ion, he pla e is a piece o glass ea ed wi h Ti02 o make a ans- pa en elec ode. A ideo came a is placed below he elec ode and connec ed o a compu e , whe e he images a e s o ed o u he p ocessing. A piece o pape glued a ound he poin ac s as ligh di use and p o ides a good backg ound o he images. Al hough se e al liquids ha e been es ed (sil- icone oil, w n oil, cas o oil, oli e oil), he esul s ha we p esen he e co espond o cas o oil and sil- icone oil, whose p ope ies a e enume a ed in able 1. ~ 217 Image p ocessing The human-eyebased de e mina ion o he ol age a which he ins abili y begins has some sho com- ings. Fi s , he measu e is based on a human de- cision on a unique measu e ( he minimum ol age o which he ins abili y is appa en ). This is some- wha subjec i e, i.e., dependen on he expe imen e ap i udes o aining. Second, i canno be im- plemen ed au oma ically. An al e na i e, machine- based me hod is desi able o au oma ic implemen- a ion and alida ion o he is me hod. We ha e implemen ed an image-p ocessing me hod ha allows o de e mine accu a ely he min- imum ol age o which he ins abili y appea s. We acqui e a se o images o he liquid su ace o di - e en alues o he applied ol age, om well below he ins abili y h eshold up o a ol age a which he ins abili y is clea ly de eloped. Fo each image, a nume ical algo i hm compu es a numbe ela ed o he o al leng h o op ical edges, hese being cha ac- e ized by ha ing a local maximum o ligh in ensi y g adien . This numbe is expec ed o be a cons an while he applied ol age is unde i s c i ical alue; abo e his ol age, new edges, associa ed o cells, de elop suddenly. Since he ypical size o cells de- c emes m he ol age inc eases, he o al leng h o edges in he image should inc ease mono onically. The e o e, he in e sec ion o a linea o pa abolic i o he compu ed leng h o edges o high enough ol ages wi h i s alue o ze o ol age is expec ed o be a good measu e o he c i ical ol age. We ha e adop ed he numbe o de ec ed edge- pixels as a measu e o he o al edge leng h. We apply i s ly an edge-de ec ion il e called SUSAN ( om Smalles Uni alued Segmen Assimila ing Nu- cleus, see [ll] o de ails), whose esponse o each pixel o he o iginal image is in ense only in he icini y o an edge, in he he same way ha g adien maps. Howe e , since he me hod is in eg al, i be- ha es e y well in he p esence o noise, unlike he mo e adi ional de i a i e-based me hods. These de i a i e-based me hods could also be used, bu p e ious noise il e ing o images would be manda- o y. Compa a i ely, he SUSAN edge il e is as e and mo e eliable. The numbe o non-black pix- els o his esponse canno be used o ou pu pose because he wid h o he edges is la ge o lowe ol ages, gi ing mo e edge pixels han expec ed. I is necessa y o hin he edges, i.e., selec he pix- els which locally ha e maximum g adien . To his end, we selec only he pixels ha ha e maximum SUSAN in ensi y in he di ec ion pe pendicula o Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on July 14,2023 a 10:50:21 UTC om IEEE Xplo e. Res ic ions apply. Figu e 2 Image o he liquid su ace as seen om below by he came a. The ol age applied o he poin is 8 kV (nega i e pola i y), he elec ic cu en h ough he liquid is 1.74~ A. The liquid is cas o oil. he edge, using as neighbo hood a 3 x 3 mask. A simple linking me hod o pixels, based on icini y and app oxima e di ec ion o edges, allows disca d- ing spu ious edge poin s, as isola ed pixels, usually o igina ed by noise. Figu e 3 Bi map o he edge poin s co esponding o he p e ious pic u e. Table 2: A e age size- D o he mwindow cells in silicone oil as a unc ion o he applied ol age V,, o se e al liquid laye hicknesses. p = 2.5 cm. 1 Vp(kV) I 6.5 I 7.0 I 8.0 I 9.0 I 10.0 d = 0.6 m n I D(m) I 0.34 I 0.34 I 0.30 I 0.25 I 0.20 d = 1.3 mm I D(m) I 0.61 I 0.52 I 0.41 I 0.27 I 0.24 .. Resul s Figu e 2 shows a pic u e o he osewindow ins a- bili y o a ol age a which he ins abili y is well de eloped (V, = 8 kV, nega i e pola i y). The liq- uid is cas o oil and we use 2 ml, co esponding o a dep h o d = 1.3 mm. The ipplane dis ance is 3.5 cm. The diame e o he liquid su ace is 4.5 cm. In ables 2 and 3 we p esen he a ia ion wi h he ol age applied o he ip o he a e age size o he cells, in ose-window ins abili y. Table 2 co e- sponds o silicone oil, whe e a space cha ge densi y is expec ed and he conduc ion in he liquid is no ohmic. Table 3 co esponds o cas o oil, whe e no space cha ge is p esen and he conduc ion is ohmic. In bo h ypes o liquid he size o he cells has he same beha io : i dec eases i he elec ic ield in- c eases and inc eases i he liquid laye hickness in- c eases. The ypical size o he cells is la ge com- pa ed wi h he liquid dep h and ends o be g ea e o he ohmic liquid han o he non-ohmic one. The dependence o he cells size on he elec ic ield in ensi y is esponsible o he a ia ion o his size om he cen e , whe e he ield is mo e in ense, o he pe iphe y. This a ia ion is e y isible in igu e 2. Al hough he cells end o be hexagonal, he a ia ion o hei size induces he p esence o many de ec s, mo e o hem pen agons. Figu e 3 shows he bi map wi h de ec ed edge poin s co esponding o his image. The edges co e- sponding o he hame ea u es a e also p esen when he ins abili y is no , and con ibu e o he e e ence numbe o edge pixels. Looking ca e ully a his pic- u e i is no ed ha some o he cen al cells look o ha e a double bounda y. This is a consequence o he shadow ha he suppo o he poin p ojec s in o he liquid su ace. This e ec wa ns us agains he consequence o a bad backg ound o a de ec i e illumina ion. Un o una ely, we canno emo e he poin om ou se -up, and i s shadow canno be a oided. Figu e 4 is a plo o he numbe o pixels in- ol ed in edges as a unc ion o he ol age applied o he ip. The esul s co espond o 1 ml olume o silicone oil (laye dep h 0.6 mm) and he ipplane dis ance is 2.5 cm. The wo lines i ing he da a in e sec a a poin ha de e mine he c i ical ol - age, 5.8 kV. The co esponding alue o he pa am- e e U is 5.5x10W3, which is somewha g ea e han he alue expec ed in a pu ely plane geome y [SI. Acknowledgmen s This wo k has been ca ied ou wi h inancial sup po om MCYT unde esea ch p ojec BFM2000- 1056. The au ho s acknowledge echnical suppo 218 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on July 14,2023 a 10:50:21 UTC om IEEE Xplo e. Res ic ions apply. Table 3 A e age size D o he osewindow cells in cas o oil as a unc ion o he applied ol age V,, o se e al liquid laye hicknesses. p = 3.5 n. 6 1 - - - - - - e e ence le el om “Talle de la Facul ad de Fisica”. Re e ences [l] J. M. Schneide and P. K. Wa son, “Elec o- hyd odynamic s abili y o space-cha gelimi ed cu en s in dielec ic liquids. I Theo e ical s udy”, Phys. Fluids, ol. 13, pp. 1948-1954, 1970. [2] P. K. Wa son, J. M. Schneide and H. R. Till, “Elec ohyd odynamic s abili y o space- cha ge-limi ed cu en s in dielec ic liquids. I1 Expe imen al s udy”, Phys. Fluids, ol. 13, pp. 1955-1961, 1970. [3] P. A en and R. Mo eau, “S abili B elec ohy- d odynamique des liquides isolan s soumis ?I une injec ion unipolai e”, J. Mlcanique, ol. 11, pp. 471-520, 1972. [4] P. A en and J. C. Lac oix, “Nonlinea hyd o- dynamic s abili y o liquids subjec ed o unipo- la injec ion”, J. MLcnnigue, ol. 18, pp. 469- 510, 1979. [5] R. Coelho and J. Delbeau, “P ope ies o he ipplane con igu a ion”, J. Phys D: Applied Physics, ol. 4, pp. 12661280, 1971. [SI A.T. PB ez. ”Rose-window ins abili y in low conduc ing liquidsn, J. Elec os a ., ols. 40,41, pp. 141-146, 1997. [7] D. Koulo a-Neno a, B. Mal aison and P. A - en, “In e acial EHD ins abili y o wo supe - imposed liquids”, Pm. 12 h ICDL, pp. 472- 475, Rome (I aly), 1996. [SI F. Vega and A. T. Pha. “Ins abili y in a non- ohmic/ohmic luid in e ace unde a pe pendic- ula elec ic ield and unipola injec ion”, Phys. Phi&, ol. 14, no. 8, 2002. 191 G. I. Taylo and A. D. McEwan, “The s abil- i y o a ho izon al luid in e ace in a e ical I 0 2 4 6 8 10 V@(W Figu e 4 Numbe o pixels (in housands) in ol ed in edges as a unc ion o he applied ol age. The e e - ence line co esponds o he pixels p esen in he liquid con aine edges. The c i ical ol age is unambiguously de e mined by he in e sec ion o he wo lines d awn. The liquid is silicone oil. Nega i e pola i y. elec ic ield”, J. Fluid Mech., ol. 22, pp. 1-15, 1965. [lo] F. Vega and A. T. PB ez. “Co ona-induced elec- ohyd odynamic ins abili ies in low conduc - ing liquids” (submi ed o publica ion in Ez- pe imen s in Fluids). [ll] S. M. Smi h and J. M. B ady. ‘SUSAN - a new app oach o low le el image p ocessing” In . Jou nal o Compu e Vision, ol. 23 no. 1, pp. 45-78. 1997. Au ho add ess: An onio Cas ellanos, Depa - men o de Elec 6nica y Elec omsgne ismo, Facul ad de Fisica, A da. Reina Me cedes s/n. 41012 Se illa. SPAIN Email: [email p o ec ed] 219 Au ho ized licensed use limi ed o: Uni e sidad de Se illa. Downloaded on July 14,2023 a 10:50:21 UTC om IEEE Xplo e. Res ic ions apply.