Bubble removal by diffusion and porous flow

Transcription

1 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Jais Andeas Beusch Angel (s438) Suevisos: Søen Vedel and Henik Buus TU Nanoech eamen of Mico- and Nanoechnology Technical Univesiy of enmak June 9

2 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow TABLE OF CONTENTS Absac... 3 Peface... 4 Lis of symbols... 5 Inoducion... 8 Poblem saemen Flow acoss membane acy flow.... Bubble concenaion....3 iffusion....4 Mass consevaion....5 The govening equaion elimiaion Theoeical oblems Exeimenal measuemen of conac angles beween olyme maeials and wae Exeimenal sudy of bubble emoval by diffusion and oous flow Theoeical oblems Rewiing govening equaion in non-dimensional fom An exession fo he gadien of he concenaion Esimaion of an exession fo he diffusiviy... 5 Exeimenal measuemen of conac angles beween olyme maeials and wae Goal Mehod Resuls and evaluaion Exeimenal sudy of bubble emoval by diffusion and oous flow Goal Mehod Resuls and evaluaion Conclusion Recommendaion Refeence lis Aendix Aendix A Aendix B Aendix C Aendix... 59

3 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow ABSTRACT In his ojec he oblems of emoving ai bubbles fom micofluid sysems has been eaed. The oblem should be solved emoving he bubbles by diffusion and oous flow. The sysem of channels is made of PMMA and he oous membane is made of PMS. Mahemaical models have been se u in elaion o he hysical oblem. Afewads some exeimens have been made in elaion o he mahemaical models. Fo he conac angle he ess wee as execed, since i shows ha PMMA is hydohilic and PMS is hydohobic. The wo given maeials had been e-eaed in diffeen ways oo, whee he e-eamen in some cases has an affec on he esul of he conac angles. The mahemaical models fo he deceasing adius of he bubble as funcion of ime do no aoximae o he exeimens. The eason could be ha, no diffusion occus duing he exeimens, since he em fo he diffusion is dominan in he mahemaical model. When assuming hee ae no diffusion in he mahemaical model, hen he model is moe aoximae o he exeimens, bu jus on a coase level. The eason fo aoximaion on he coase level could be, because hee ae some basic hysical hemes, which in sno undesood a all. Fuhemoe i should be noed ha no many ess wee made, and i mus be ecommend o make moe ess o ge a eesenaive saisical. 3

4 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow PREFACE I is wih a gea leasue I can esen his eo, which eas Bubble emoval by diffusion and oous flow, which is a a of couse Alicaions of heoeical micofluidics. The ojec is made in a hee-week couse in June 9 on TU Nanoech. The eo is ageed fo eades wih backgound of micofluidics, caillay effecs, suface ension and diffusion. An exceional hank you fo he conibuions fo his eo o: Søen Vedel, Ph. suden, TU Nanoech, (sueviso) Henik Buus, Pofesso, TU Nanoech, (sueviso) Pede Skafe-Pedesen, Ph. suden, TU Nanoech An oveview and desciion of he symbols used in he fomulas duing he eo is given in he sa of he eo on a lis in he secion Lis of symbols. Jais Andeas Beusch Angel Øseds Plads Kongens Lyngby, June 9 4

5 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow LIST OF SYMBOLS Symbol Uni esciion m R T J K mol K Pa Pa Conac angle beween he ai-wae ineface Radius of he bubble as funcion of he ime The univesal gas consan Temeaue (in oom) The uid ove-essue The ambien essue k m acy consan Pa s Viscosiy h m bub Pa bub Pa m iffusiviy s Thickness/heigh of he membane The essue diffeence acoss he membane Absolue essue in he bubble m Radius of he bubble o he ime - Non-dimensional adius s m Chaaeisic ime defined as - Non-dimensional ime Chaaceisic scale defined as h k 5

6 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow m m v x m y m z m n bub mol 3 V bub mol c bub 3 m mol c 3 m 3 k Pa H Chaaceisic scale defined as N m Suface ension m Gadien oeao Lalace oeao m s Velociy veco Coodinae in he x-diecion Coodinae in he y-diecion Coodinae in he z-diecion Amoun of ai m Volume of bubble mol a m m s In a In w a m b m m ai bubble d m ai bubble hoizonal d m v ai bubble veical Concenaion of ai inside bubble Concenaion infiniy away fom bubble m Heny s consan - Inle fo ai Radius fo an ai molecule Chaaceisic diffusiviy defined as - Inle fo wae The heigh of he channel The widh of he channel Radius of an ai bubble m s acy flow Hoizonal diamee of an ai bubble Veical diamee of an ai bubble 6

7 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow m n bub mol V bub 3 A bub Radial coodinae Amoun of ai in bubble m Volume of a semi-sheical bubble m Suface aea of a semi-sheical bubble J J diff J inc kg m s kg m s kg m s Flux acoss he oous membane Flux fo diffusion Flux given by ime-ae of change of he amoun of ai in he bubble o is suface aea 7

8 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow INTROUCTION Micofluidics means moving uids in channels on sub-millimee scale. The name mico efes o he small volumes of fluids. The echnology of micofluidics saed abou weny yeas ago. Some alicaions of he echnology of micofluidics ae injec in heads, NA chis and lab-on-a-chi sysems [7]. The behaviou of he fluidic is vey diffeen on he mico scale comaed wih he maco scale. On he mico scale, he following facos have a big effec on he behaviou of he fluid; suface ension, diffusion, lamina flow and eleco weing. In his ojec he idea is o make an inegaed micofulidic sysem on a small glass chi wih channels. This conce makes i ossible o make a comlee laboaoy on mico scale and he echnology is called lab-on-a-chi [9]. The echnology is alicable in many eseach fields. I can be used fo biological, chemisy and dug discovey. The mehod of lab-on-a-chi makes he eseach ocess fas and chea. 8

9 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow PROBLEM STATEMENT A geneal oblem of micofluidics is he aing of ai bubbles inside he micofluidic sysem. The eason is as aleady exlained he suface ension, which inceases on mico scale comaed wih maco scale. The suface ension inceases on mico scale while he fluid momenum deceases. Ongoing eseach shows ha i is ossible o emove he ai bubbles fom uid filled Micosysems by ansoing he ai acoss a oous and hydohobic membane []. This oblem is he oic of his ojec. The ai emoval model is inegaed in he micofluidic sysem as shown in Figue. In his case wae filled micofluidic channels wih hydohilic walls has a segmen of hydohobic and oous maeial []. The esence of his hydohobic wall segmen means ha he oveall enegy of he sysem is minimized if any ai bubble in he sysem is aached o he lid a he hydohobic segmen []. I is assmued ha he ai bubble has aleady aached iself, and ha he uid momenum is sufficienly small ha he bubble emains fixed (i is well documened fom exeimens) []. I is assumed ha he conac angle beween he ai-wae inefaces is θ = π/, in which case he bubble has he shae of a efec semi-shee uniquely defined by is adius () []. 9

10 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Figue : Schemaic dawing of he seu []. In he following model i will be esened how he ai of he bubble leaves his as a funcion of ime. The amoun of bubble ai is he conseved quaniy, so i is convenien o descibe he hysics in ems of mola fluxes. Moeove i is assumed ha he concenaion of ai inside he bubble is unifom, bu changes wih ime. The definiion of he concenaion is given in ems of volume and amoun of ai as volume of he bubble. n bub cbub, whee nbub is he amoun of ai and Vbub is he Vbub. Flow acoss membane acy flow acy flow also descibed as he flow acoss he membane asses ha k v (i)

11 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Whee k is he acy consan and η is he dynamic viscosiy of ai. Then, he mola flux of ai acoss he membane is found by mulilying by he concenaion c bub o find J c bub k h bub (ii) whee he gadien has been aoximaed by a linea essue do acoss he membane bub / he membane. z wih bub he essue diffeence acoss he. Bubble concenaion The bubble concenaion is defined as descibed above, o by using he ideal gas law, whee bub c bub RT, whee R is he univesal gas consan and T is he emeaue (e.g. oom emeaue). By combining he given wo exessions yields c bub RT (iii).3 iffusion Fuhemoe he ai molecules can also diffuse ino he uid, whee hey ae dissolved. This mechanism is descibed by Fick s law c J diff (iv) whee ρ is he adial coodinae of a sheical coodinae sysem wih an oigin coinciding wih he oigin of he bubble, whee he gadien of he concenaion

12 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow mus be evaluaed a he bubble bounday, e.g. a. The bounday condiions on he concenaion ae he unifom bubble concenaion and he seady sae concenaion in he uid is given by Heny s law fa away fom he bubble. This sauaed equilibium concenaion is fo each molecula secies of he ai is given by c bub a c dis (v) k H whee is he Heny s consan []. Since ai consis oughly of 78 % N, k H % O and % wae vaou, hen each of hem have hei own individual Heny s consan. A hysically coec model would exlicily models of hese consiuen secies, heefoe ai can be consideed as a single-secies gas wih a good aoximaion []..4 Mass consevaion Mass consevaion occus since he ai bubble will conac as ai is emoved fom i. In mahemaically fom i can be saed as a flux J inc, so J J J (vi) inc diff Yhe negaive sign aises since he bubble conacs, when ai is emoved. The flux J inc is given by he ime-ae of change he amoun of ai in he bubble o is suface aea n bub J inc (vii) Asuf

13 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow whee he amoun of ai in he bubble is defined as n c V, since i has bub bub bub been assumed ha c bub is he same anywhee inside he bubble. The volume and suface aea of he semi-sheical bubble ae given as V bub 3 (viii) 3 A suf (ix) whee he fis em of he suface aea accouns fo he semi-shee and he second em accouns fo he bubble-membane ineface. Afewads equaion (vii) can be ewien on he fom J c 9 inc bub (x).5 The govening equaion Fom flow acoss membane (acy flow), bubble and uid essue, bubble concenaion, diffusion and mass consevaion he following govening equaion is goen 9 RT k hrt c bub bub (xi) 3

14 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 3 ELIMITATION Fo his ojec he oblems have been limied o he following heoeical and exeimenal issues. 3. Theoeical oblems 3.. Rewiing govening equaion in non-dimensional fom Rewiing he govening equaion in non-dimensional fom by inoducing he non-dimensional adius and ime scales and., (xii) whee is he adius of he bubble, is he ime, is chaaceisic ime and he adius of he bubble a he ime. is Fuhemoe use following chaaceisic scales of he sysem k, h,, (xiii) whee and ae chaaceisic lenghs and is he chaaceisic diffusiviy. Moeove k is acy consan, h is heigh/hickness of membane, is suface ension, is uid ove-essue, is ambien essue and is viscosiy. 4

15 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 3.. An exession fo he gadien of he concenaion To solve he govening equaion i is necessay wih an exession fo he gadien of he concenaion. Afewads he govening equaion can be made fully dimensionless Esimaion of an exession fo he diffusiviy An exession fo he diffusiviy should be found fo ai molecules ino wae. I can be esimaed using he Einsein elaion (equaion 6.49 [3]). In his case i is also necessay o esimae he adius of an aveage ai molecule. 3. Exeimenal measuemen of conac angles beween olyme maeials and wae Make a es of he conac angle beween e-eaed olyme maeials and wae dos. Fuhemoe i is necessay o invesigae he imoance of e ea hydohilic and hydohobic maeials 3.3 Exeimenal sudy of bubble emoval by diffusion and oous flow Make ess of gaseous bubbles in an ohewise uid in filled micofluidic sysems. The idea of his es is o comae he execed esuls fom he mahemaical model wih he eal esuls fo he coelaion beween he deceasing adius of he gaseous bubble and he ime. In ode o solve govening equaion (xi) is dimensionless fom has been imlemened in MATLAB and solved fo aoiae values of he hysical aamees using numeical mehods. Fuhemoe i will be eviden o efom a deeminaion of he efficiency of bubble emoval by adjusing he given aamees as descibed in secion 6.. 5

16 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 4 THEORETICAL PROBLEMS 4. Rewiing govening equaion in non-dimensional fom The govening equaion is given as equaion (xiv). 9 RT k hrt c bub bub (xiv) The govening equaion (xiv) is ewien in non-dimensional fom by inoducing he non-dimensional adius and ime scales and along wih he chaaceisic scales of he sysem. k (xv) h whee is a chaaceisic lengh, k is acy consan and h is heigh/hickness of membane. (xvi) whee is a chaaceisic lengh, is suface ension, is uid oveessue and is ambien essue. (xvii) 6

17 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow whee is uid ove-essue, is ambien essue, is viscosiy and is he chaaceisic ime. (xviii) whee is a chaaceisic diffusiviy. bub (xix) whee bub is essue diffeence acoss he membane and bubble as funcion of ime. is adius of he (xx) whee is he adius of he bubble, is non-dimensional and he bubble a he ime. is he adius of (xxi) whee is he ime, is non-dimensional and is chaaceisic ime. I should be noed ha and ae consans. The dimensionless equaion is [fo inemediae esuls, see Aendix A] 7

18 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 8 c RT 9 (xxii) The las em c RT will be made dimensionless in secion 4..

19 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 4. An exession fo he gadien of he concenaion In ode o solve he govening equaion (xiv), an exession fo he gadien of he concenaion is needed. The diffusion equaion is solved fo a efec sheical ai bubble in an infinie volume of wae. The esul is used as a cude aoximaion o he case a hand. The equaion of diffusion is given as c x y, z,, v c x, y, z, cx, y, z, (xxiii) whee he fis em efes o he change of he concenaion ove ime, he second em efes o he concenaion conveced by he velociy field and he hid em efes o diffusion and Fick s law. Assuming ha he velociy v is negligible, he second em on he lef hand side may be negleced. v (xxiv) Using a sheical ola coodinae sysem o eesen he hysics, he concenaion mus be indeenden of and by symmey, so he igh hand side of equaion (xxiii) becomes c, c, (xxv) whee bubble. is he Lalace oeao, c is he concenaion and is he adius of he 9

20 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow So based on equaion (xxiv) he equaion of diffusion (xxiii) can be ewien as c, c, (xxvi) The soluion o equaion (xxvii) is given by Esein and Plesse in [4], whee he gadien of concenaion c also is given. c cbub c (xxvii) k whee c bub is he b ubble concenaion and c is he concenaion infiniy away fom he bubble. The wo concenaions ae c bub bub RT RT whee bub is he absolue essue in he bubble, R is he univesal gas consan, T is he emeaue, is he uid ove-essu e, is he ambien essue, is he sufa ce ension, is dimensionless and is he adius of he bubble a he im e.

21 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow c k bub H k H whee he concenaion a infiniy is aken o be he equilibium concenaion siulaed by Heny s law and k H is he Heny s consan. When using he dimensionless equaion fom secion 4. and inseing he soluion fo c he finally dimensionless equaion can be wien as he fom given in equaion (xxxviii) [fo inemediae esuls, see Aendix B] 9 (xxviii) whee is a chaaceisic lengh, is uid ove-essue, is ambien essue, is non-dimensional, is non-dimensional, is he diffusiviy, is he chaaceisic diffusiviy and is he adius of he bubble a he ime. The las em fo he diffusiviy is he dominaing faco. Inseing values can ove i. An examle of inseing he values is shown in Aendix C

22 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 4.3 Esimaion of an exession fo he diffusiviy The diffusion consan deemines how fas a concenaion diffuses a ceain disance. The Einsein elaion (equaion 6.49 [3]) may be used fo esimaing. This elaion is k BT (xxix) 6a whee k B is he Bolzmann consan and a oom emeaue (T = 3 K). Fuhemoe is a he adius if an ai molecule and is he viscosiy. T k B.385 J/K 3K J I is necessay o esimae he aveage adius fo an ai molecule o find. A simle agumen is given in [8]. The incile of he agumen is o make a simlifying geomey fo mean fee ah [8]. Fom he given homeage he adius a of an ai molecule is a m (xxx) Since he viscosiy of wae is. 3 Pa s So is k T 6a 6π J/K 3K 9 m. 3 s m. Pa s B (xxxi)

23 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow The calculaed value fo is aoximaely he same as he value fo small ions in wae, which is (equaion 5.8a [3]) 9 (xxxii) m s Theefoe i is execed ha ai mus diffuse a lile slowe in wae comaed wih small ions in wae. The imoan facos, which have an influence on he gade of diffusion is esecially he emeaue, he adius of he molecule and he viscosiy. Whee following saemens ae valid fo diffusion: A highe emeaues he diffusion mus becomes highe and evese. When using bigge molecules, hen he diffusion mus be slowe and evese. The diffusion should be highe, when using a fluid wih a low viscosiy and evese. 3

24 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 5 EXPERIMENTAL MEASUREMENT OF CONTACT ANGLES BETWEEN POLYMER MATERIALS AN WATER 5. Goal The goal is o invesigae he imoance of e eaed hydohilic and hydohobic maeials. By definiion, if he conac angle is below 9 º he maeial said o be hydohilic ohewise i is called hydohobic as shown in Table. Table : Conac angle fo hydohilic and hydohobic maeials. Conac angle esciion < 9 º Hydohilic > 9 º Hydohobic The invesigaed maeials and hei e-eamen ae given in Table. Table : Maeials, which should be invesigae. Numbe Thickness [mm] Maeial Pe-eamen.5 PMMA Cleaned wih soa wae and Milli-Q, UV 5 s and heaed 5 min a 85 C befoe soage. PMMA Cleaned wih soa wae and Milli-Q, UV 5 s and heaed 5 min a 85 C befoe soage 3.5 PMMA Cleaned wih soa wae, Milli-Q, 96% ehanol and Milli-Q, UV 5 s and heaed 5 min a 85 C befoe soage 4. PMMA Cleaned wih soa wae, Milli-Q, 96% ehanol and Milli-Q, UV 5 s and heaed 5 min a 85 C befoe soage 4

25 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 5.5 PMMA Taken diecly afe emoval of oecive film 6.5 PMMA min UV iadiaed diecly afe emoval of oecive film and aken o conac angle mee igh afe (cooled o oom emeaue) 7. PMMA Taken diecly afe emoval of oecive film 8. PMMA min UV iadiaed diecly afe emoval of oecive film and aken o conac angle mee igh afe (cooled o oom emeaue) 9 - PMS PMS cued a 65 C fo h 5 min on PMMA cleaned wih soa wae and Milli-Q - PMS PMS cued a 65 C fo h 5 min on PMMA cleaned wih soa wae and Milli-Q (eused PMMA shee wied wih clean oom issue) - PMS PMS cued a 65 C fo h 5 min on PMMA cleaned wih soa wae and Milli-Q (3d ime eused PMMA shee wied wih clean oom issue) Fo he e-eamen following can be execed: Alcohols decease he suface ension ogessively []. Sufacans as soa decease he suface ension and, once a minimum is eached, no moe effec []. PMMA ofen is efeed as maeial, because of is modeae oeies, easy handling and ocessing, and low cos, bu behaves in a bile manne when loaded, esecially unde an imac foce [6]. Fuhemoe PMMA is oical clea and hydohilic, heefoe i is an advanage o use fo sysems fo micofluids, because i makes i ossible o see he fluid in he channels. 5

26 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Figue : PMMA sucue [6]. PMS is oically clea. Afe olymeizaion and coss-linking, solid PMS samles will esen an exenal hydohobic suface. This suface chemisy makes i difficul fo ola solvens (such as wae) o we he PMS suface, and may lead o adsoion of hydohobic conaminans. Plasma oxidaion can be used o ale he suface chemisy, adding silanol (SiOH) gous o he suface. This eamen endes he PMS suface hydohilic, allowing wae o we (his is fequenly equied fo, e.g. wae-based micofluidics). [5]. Figue 3: PMS sucue [5]. 5. Mehod The mehod of measuing he conac angles ae done by using an insumen called a o shae analyse sysem SA Mk as shown on Figue 4. 6

27 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Figue 4: The seu of he insumens fo he es of he conac angle. The ocess was done in following ses as shown in Table 3. The desciion of he given ses is valid fo all yes of esed olyme samles. Table 3: esciion of he ses fo he measuemens of he conac angles. Se esciion The used insumens wee make eady fo use A olyme samle was laced on he adjusable lafom 3 The adjusable lafom was adjused, so he camea can ge a icue of he wae do on he olyme samle 4 The comue was used fo make a do on he suface of he olyme samle 5 The camea egiseed a lo of measuemens of he conac angle beween he given olyme samle and he wae wih small inevals 6 The wae do was emoved and maked wih a en on he olyme samle o avoid o use he same aea fo fuhe ess 7 Se o 6 could afewads be done again fo anohe olyme samle 7

28 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Afewads Excel is used fo calculae aveage values and sandad deviaions fo he measuemens of he conac angles. 5.3 Resuls and evaluaion Picues of he wae do on some of he given maeials ae shown in Table 4. The size foma of he dos is no elevan in his case, because he conac angle is he same indeendenly on he size of he dos. Table 4: Picues of he wae do on some of he maeials, whee he numbes ae wih efeence o Table. Numbe Picue 3 4 8

29 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Figue 5 shows he aveage- and sandad deviaion values fom he measuemens. The measuemens have been done on wo diffeen days fo some of he maeials. The measuing of he maeials efes o Table. Figue 5: Resuls fo he angles wih aveage and ST. Fom he gah on Figue 5 i can be seen ha he angles fo PMS and PMMA ae as execed, since he daa fo he PMS and PMMA ae hydohobic and hydohilic esecively. Fuhemoe i can easily be ead off fom he gah on Figue 5 ha he conac angle is highe fo PMMA wih a hickness of.5 mm (maeial no, 3, 5 and 6) comaed wih PMMA wih a hickness of. mm (maeial no, 4, 7 and 8). The eason is because hee is lasicize in he PMMA, whee he hickness is.5 mm. I affecs on he suface ension and he conac angle, in which he conac angle becomes highe comae wih he one fo PMMA wih a hickness of. mm. 9

30 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Fuhemoe he emeaue affecs on he suface ension, when aising he emeaue hen he suface ension becomes lowe (see Figue 6) and he conac angle mus be lowe oo []. Theefoe he vaiaion of he emeaue mus be aken in consideaion, when analyzing he saisical gah fo he conac angles. Figue 6: eendence of suface ension of ue wae on emeaue (a he sauaion essue coesonding o ha emeaue) []. Fo he PMMA cleaned wih soa wae, Milli-Q, 96% ehanol and Milli-Q, UV 5 s and heaed fo 5 min a 85 C befoe soage (maeial no 3 and 4) has a gea affec on he conac angle, when he hickness is. mm (maeial no 4), since he conac angle becomes vey smalle in his case comaed wih he one, whee he hickness is.5 mm (maeial no 3) wih a diffeence on abou º. The eason fo he smalle conac angle is he ehanol, bu since he samle had been heaed o 85 ºC, i should be execed ha all he ehanol evaoae, since ehanol has a boiling oin a 78.4 ºC. Bu since he PMMA wih a hickness of. mm has a lowe conac angle, i indicaes a diffusion of he ehanol in he PMMA. I enail ha he.5 mm PMMA will easie becoming hooughly wam comaed wih he PMMA wih a hickness of. mm. 3

31 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow When PMMA is eaed wih min UV iadiaed diecly afe emoval of oecive film and aken o conac angle mee igh afe (cooled o oom emeaue) (maeial no 6 and 8), a hicke hickness gives a smalle conac angle (abou º) oo. The eason fo he smalle conac angle is maybe he oecive film, which obably consiss of small amouns of ehanol. And he coclusion hee mus be he same given fo he PMMA cleaned wih soa wae, Milli-Q, 96% ehanol and Milli-Q, UV 5 s and heaed fo 5 min a 85 C befoe soage. Anohe eaon could be ha afe emoving he oecive film, and hen he suface of he PMMA has been changed, because of he combinaion of dislodgmen and adheence. In eal i mus be ecommend making moe ess o ge a eesenaive numbe of daa befoe making a saisical analysis. 3

32 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 6 EXPERIMENTAL STUY OF BUBBLE REMOVAL BY IFFUSION AN POROUS FLOW 6. Goal The goal is o make ess of gaseous bubbles in an ohewise uid-filled in (in his case MQ wae has been used) filled micofluidic sysems. In his case he idea is o comae he execed esuls fom he mahemaical model (equaion (xxxvi)) wih he exeimenal esuls fo he coelaion beween he deceasing adius of he gaseous bubble in he uid and he ime. Fuhemoe i will be eviden o efom a deeminaion of he efficiency by adjusing he given aamees as descibed in secion 6.. Fuhemoe i should be noed ha no and no fom Table have been used in his es fo PMMA and PMS esecively. 6. Mehod I is mos clea o divide he exeimenal seu in wo as; he inenal aamees and he exenal aamees. The inenal aamees efe o he layou of he micofluidic sysem, which consis of a micofluidic sysem of PMMA wih an inegaed membane of PMS. In his case he gas (ai) will be emoved by he mechanisms descibed in secion. A se u of he layou of he micofluidic sysem is shown in Figue 7. 3

33 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Figue 7: Layou of micofluidic sysem. In a feeds he chi wih ai fo oducion of bubbles. In w is inle fo wae and conneced o a syinge um o move he inoduced ai bubble o he membane. The oule is conneced o a comue conolled essue souce []. Figue 8: A icue of he PMMA chi wih channels. The given inenal aamee is a changeable PMS membane wih a diamee on mm and vaying heigh as seen in Table 5. Fuhemoe he used micofluidic sysem has channels wih a coss secion wih a heigh (a) of µm and a widh (b) of 5 µm as illusaed on Figue 9. 33

34 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Table 5: Inenal aamees, which can be adjused fo he heigh of he PMS membane. Symbol esciion Sizes h Heigh vaiaion osiioned ove a mm dee chambe, o 3 mm Figue 9: An illusaion of he channels wih a coss secion wih a heigh (a) of µm and a widh (b) of 5 µm. Pincile dawing and no o scale. When assembled he sysem looks as shown in Figue. Figue : Layou of seu. The chi is filled wih wae hough um and um is used o inoduce ai. When an ai bubble is osiioned unde he membane using um, he essue is adjused by he essue souce. The chi is monioed hough a micoscoe []. 34

35 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow A lis of each of he used exenal aamees is given in Table 6. Table 6: Lis of he used exenal aamees. Exenal aamee Numbes Tye Pum CMA/Micodialysis CMA 4 Chemyx N3 Valve Uchuch Scienific P-73 shu-off valve Micoscoe Leica MZ6 seeo micoscoe equied wih a Pixelink PL-A74-E digial monochome camea Pessue egulao Fluigen MFCS-8C 35 mba Teflon ubes - Bohlende S 8- PMS ineconnecion blocks - Poduced in-house Table 7: Exenal aamees, which can be adjused. Symbol esciion Sizes Vaying fluid essue by using he essue egulao 5 o 3 mba wih a se of 5 mba, bu should in fac in his ojec only be done fo, and 3 mba Fom he exenal and inenal vaiables i can be seen ha hee ae ( 3 3 ) nine combinaions in all. The used aamees wee a essue on and 3 mba and membane hickness on and mm. Afewads he PMMA chi and he PMS should be igh. Using scews can do i and nus as illusaed on Figue and Figue. 35

36 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Figue : Side view of he membane being comessed beween he chi and PMMA comession iece mouned wih scews and nus. awing no o scale []. Figue : A icue of he membane being comessed beween he chi and PMMA comession iece mouned wih scews and nus. The ocess of ses duing he eaaion was as follows in Table 8 and he ocess of ses duing he exeimen was as follows in Table 9. The ocess of ses duing he exeimen means he mehod of how an ai bubble was moved ino he membane aea and he size of he bubble was ecoded. 36

37 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Table 8: Pocess of ses duing he eaaion. Se esciion The Fluigen MFCS-8C was uned on, eheaed and he essue was calibaed The syinge B lasic ml was filled wih MQ wae and mouned in Chemyx N3 3 The essue esevoi was filled wih MQ wae 4 The Hamilon Gasigh ml syinge was mouned in CMA 4 5 The syinge ums fo uming wee eaed 6 The chi has been aligned and mouned in seu 7 The chi and seu has been flushed wih wae, unil all ubings fom inle o oule wee filled wih wae 8 Ai was umed ino he chi, unil he inle channel was ai filled 9 The ime lased micoscoe was eaed deending on execed ime ange Table 9: Pocess of ses duing he exeimen. Se esciion A given amoun of ai was umed ino he chi using um Valve was closed 3 The essue was alied 4 The ime lase ecoding was saed 5 The ai bubble was moved o he membane aea using um (he wae um) 6 Valve was closed 7 Measuing ocess was acivaed 8 The heigh diffeence beween he essue esevoi and he chi is accouned fo he hydosaic essue 37

38 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Figue 3: A icue of he seu of he insumens fo he exeimen. Figue 4: A icue of he seu fom Figue 7. 38

39 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Figue 5: A icue fom he Leica micoscoe fo an ai bubble owads o he caviy wih wae, whee he essue was 3 mba and he hickness of he membane was mm. Fuhemoe is he diamee of he caviy wih wae mm. Figue 6: A icue fom he Leica micoscoe fo an ai bubble, whee he essue was 3 mba and he hickness of he membane was mm. Fuhemoe is he diamee of he caviy wih wae mm. The adius of he bubble is found by using hoo-ediing ogam called Coel PHOTO-PAINT. In he fis case he hoo-ediing ogam was used o find he 39

40 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow diamee of he caviy wih wae, since he diamee is given and can be used as efeence. The mehod is given in Aendix. When he coodinaes is found, hen he adius of he ai bubble can be calculaed as he half of he aveage diamee of he ai bubble as given in (xxxii). aibubble d aibubblehoizonal d aibubbleveical (xxxiii) 4 The ai bubbles ae assumed o have a comleely cicula coss secion in he model, alhough his is clealy no he case, as shown in Figue 6. The aoximaion of equaion (xxxxii) hus gives an aveage adius, o be used as inu fo he model. In ode o make he gahs fo he adius of he ai bubble as a funcion of he ime, five o six oins have been aken. 6.3 Resuls and evaluaion The exeimenal esuls fo he adius of he ai bubble as funcion of he ime has been comaed wih he esuls of he model. The ess have been done fo following inenal and exenal aamees given in Table. The esuls have only been eaed fo he measuemen seies, whee i was ossible o see he ai bubble, since he adius of he ai bubble should be calculaed. In elaion o Table fou ess esuls ae acceed and can be analyzed. 4

41 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Table : Oveview of he ess, whee he chosen aamees ae given. ae of Pessue Thickness of Seies Commens measuing [mba] he membane [mm] 7 h June 9 3 Failed no ossible o see he ai bubble, because of he hin membane o oical oblems wih he micoscoe 7 h June 9 3 Possible o see he ai bubble 7 h June 9 3 Possible o see he ai bubble 7 h June 9 Possible o see he ai bubble 8 h June 9 93 Possible o see he ai bubble The fou ess esuls, which ae acceed, ae fuhe named in following way as given in Sho name on Table. 4

42 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Table : Sho name infomaion fo he acceed ess esuls. ae of Pessue Thickness of he Seies Sho name measuing [mba] membane [mm] 7 h June 3 Ex 9 7 h June 3 Ex 9 7 h June Ex3 9 8 h June 9 93 Ex Comaison beween Ex, Ex, Ex3 and Ex4 The elaion beween he adius of he ai bubble and he ime is given on Figue 7 fo he exeimens. Fo he case Ex3 a essue a mba was used, when he essue was abou 3 mba fo he ohe hee cases (Ex, Ex and Ex4). Fom he gah on Figue 7, i can be seen ha he size of he ai bubble deceases fase, when he essue is highe, when comae Ex and Ex3. Fuhemoe have all hee gahs, whee he essue was abou 3 mba aoximaely he same fom (Ex, Ex and Ex4), jus deending on he sa adius of he ai bubble. Theefoe i mus be efficien o use a highe essue if he ai bubble should be emoved a a shoe ime. 4

43 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Figue 7: Comaison beween Ex, Ex, Ex3 and Ex Comaison beween Exs and Models I is imossible o make comaisons beween he mahemaically models and he exeimenal gahs as seen on Figue 8. The eason is because of he dominaing em in he finally dimensionless equaion (xxxviii). Fom his i can be seen ha i mus be ineesing o y o se he dominaing em o zeo, i means se he diffusiviy =. This analysis will be examined in secion

44 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Figue 8: Comaison beween Ex, Ex, Ex3 and Ex4 and hei mahemaical models Comaison beween Exs and Models fo = Since i is imossible o make comaisons beween he mahemaically models and he exeimenal gahs as descibed in secion 6.3., hen i is assumed o negligible he dominaing las em fom he finally dimensionless equaion (xxxviii). And he equaion will afewads seem ou like shown in equaion (xxxiv). 9 (xxxiv) 44

45 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Whee and ae chaaceisic lenghs, is uid ove-essue, is ambien essue, is non-dimensional, is non-dimensional and is he adius of he bubble a he ime. Afe neglecing he em of diffusiviy, he models ae aoximae o he exeimenal gahs on a coase level as shown on Figue 9. The eason o he coase aoximaion could be, because no diffusion occus in he exeimen. Fuhemoe is he mahemaically gahs linea, when he exeimenal gahs ae non-linea. Thee mus be any basic hysical hemes, which we have no cub a, which lay a ole. Figue 9: Comaison beween Ex, Ex, Ex3 and Ex4 and hei Mahemaical models, whee =. 45

46 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 7 CONCLUSION Imoan conclusions fom he wok ae oulined in he following bulle oins: The Govening equaion has been ewiing in a non-dimensional fom by inoducing he non-dimensional adius and ime scales and. An exession fo he gadien of he concenaion has been found and he govening equaion has afewads been made fully dimensionless. An esimaion of an exession fo he diffusiviy has been made using he Einsein elaion. Tes fo he conac angles show ha he esuls fo PMS and PMMA ae as execed, since he daa fo he PMS and PMMA ae hydohobic and hydohilic esecively. Tes fo he conac angles show ha he esuls fo he e-eamen have an affec on he esuls fo PMMA in some cases. Tes fo he bubble emoval by diffusion and oous flow show ha he mahemaical and numeical soluions diffe exemely fom he esuls fom he exeimen. Bu if he diffusion coefficien is assumed o be zeo, hen he mahemaical and numeical soluions ae moe aoximae o he esuls of he exeimen on a coase level. Fuhemoe Tes fo he bubble emoval by diffusion and oous flow shows ha a highe essue esuls in a shoe ime, befoe he ai bubble is emoved fom he micofluidic sysem. 46

47 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 8 RECOMMENATION A ecommendaion fo fuhe wok in elaion o he ojec is exlained hee on bulle oin fom: I will be eviden o make moe daa esuls, as moe daa mean bee saisical analyses. Tess fo Tes should be made finish fo he ohe e-eaed maeials oo. I should be consideed o use ohe maeials. Moe basic hysical undesanding is necessay. I could be he eason fo he mahemaically model deviae exemely o he exeimens fo Tes. 47

48 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 9 REFERENCE LIST [] P. Skafe-Pedesen, Laboaoy execise fo couse Alicaions of heoeical micofluidics, TU Nanoech, 9 [] S. Vedel and H. Buus, Bubble emoval by diffusion and oous flow, TU Nanoech, 9 [3] H. Buus, Theoeical Micofluidics, Oxfod Univesiy Pess, 8 [4] P. S. Esein and M. S. Plesse, On he Sabiliy of Gas Bubbles in Liquid-Gas Soluions, Califonia Insiue of Technology, 95 [5] Wikiedia PMS h://en.wikiedia.og/wiki/polydimehylsiloxane /6/9 [6] Wikiedia PMMA h://en.wikiedia.og/wiki/acylic_glass /6/9 [7] Wikiedia Micofluidic h://en.wikiedia.og/wiki/micofluidic /6/9 [8] Esimae of molecula size: a moe fomal mehod h:// ance_id= /6/9 [9] Miconi Micofluidics h:// /6/9 [] Heny s law h:// 3/6/9 [] Wikiedia Suface ension h://en.wikiedia.og/wiki/suface_ension 3/6/9 48

49 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow APPENIX Aendix A Rewiing equaion (xiv) in elaion o k and h gives k c bub bub 9RT h RT Equaion (xv) has been used c bub bub 9RT RT Mulily wih RT 9 c RT bub bub Equaion (xx) and (xxi) have been used c bub bub 9 RT Equaion (xviii) has been used 9 c RT bub bub Equaion (xix) has been used 49

50 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 5 c RT 9 Equaion (xx) and (xxi) have been used c RT 9 Mulily wih c RT 9 c RT 4 9 c RT 4 9 ivide wih

51 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow c RT Equaion (xvi) has been used 9 c RT Place he same aamees on he numeao and he denominao and divide wih c RT 9 Equaion (xvii) has been used

52 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 5 c RT 9 The las em c RT will be made dimensionless in secion 4..

53 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 53 Aendix B c RT 9 9 k R RT 9 k c c RT bub

54 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 54 9 k k RT H Since k H RT is a vey small value, since Heny s consan is dominaed o RT, he em can heefoe be negleced. The equaion hen becomes 9 k Use equaion and yields he final dimensionless equaion.

55 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 55 9 Se ino he squae oo 9 Use 9

56 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 56 Aendix C Inseing values in imensionless equaion is given 9 Call following nd em : em : 3 d Assume ha he sae is, hen he mos facions in he nd and 3 d em can be negleced. And he ems can be assumed o be of he following e-wien fom. nd em : d em : 3

57 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow The values fo he consans ae given below: k 8 5 m Chaaceisic lengh h k m acy s consan 3 h m Heigh of he membane 3.5 m Radius a = 3 Pa 3 mba 35 Pa amosheic m 3.8 s Chaaceisic diffusiviy s Chaaceisic ime 3 Pa s Viscosiy fo wae. iffusiviy fo ai in wae 9 m s imensionless lengh. 6 m Chaaceisic lengh 7.9 Suface ension fo wae 3 N m Afe inseing he values i gives nd em = 3 d em =

58 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow 58 I can be seen ha he em is vey smalle comaed wih he em and heefoe mus he em be he dominaed em in he equaion.

59 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Aendix In fis case he coodinaes of he edges of he caviy of wae should be found. I was done as shown on Figue, Figue and Figue. Afewads he coodinaes of he edges fo he ai bubble can be found as shown on Figue 3 and he mehod is he same as fo he caviy of wae o find he hoizonal and veical coodinaes. Figue : Making he edges of he caviy wih wae, which is used as a efeence wih a diamee of mm. 59

60 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Figue : Finding he hoizonal coodinaes. Figue : Finding he veical coodinaes. 6

61 33443 Alicaions of heoeical micofluidics Bubble emoval by diffusion and oous flow Figue 3: Making he edges of he ai bubble. 6