A microfluidic apparatus for the study of ice nucleation in supercooled water. drops

Transcription

1 SUPPEMENTARY INORMATION A microfluiic apparatus for the stuy of ice nucleation in supercoole water rops Clauiu A. Stan, a Grégory. Schneier, a Sergey S. Shevkoplyas, a Michinao Hashimoto, a Mihai Ibanescu, b Benjamin J. Wiley, a an George M. Whitesies a a Department of Chemistry an Chemical Biology, Harvar University, Cambrige, MA USA b OmniGuie, Inc., Cambrige, MA USA Abstract. This supplementary information file contains: i) Tabulate ata on the esigns of microfluiic channels use for ice nucleation experiments, ii) rawings of the PRTD sensor arrays use for this project, iii) a escription of the process of fabricating the PRTD sensor arrays, iv) the calibration proceure for the PRTD sensors, v) erivation of the equations use for the calculation of ice nucleation rates, vi) the generalization of these equations for the case in which the temperature of the channel fluctuates, vii) freezing temperature an cooling rate ata for ice nucleation experiments on pure water, an seee with silver ioie; an viii) six movies of freezing rops insie microfluiic channels. S1

2 The esign of microfluiic channels use for ice nucleation experiments. The critical geometrical parameters of the flow-focusing generators an of the channels are shown in igure S-1. PMD Device height: h ev nozz Water w nozz w chan low PMD igure S-1. The critical geometrical esign parameters of the microfluiic evices use for the freezing of water rops. Table ST-1 lists the geometrical parameters for the esigns that we use successfully to freeze long trains of water rops. The table also lists the typical operating parameters: the rate of flow of PMD (Q PMD ), the temperature of the nozzle (T nozz ), an the typical iameter ( rop ) an frequency (f rop ) of the rops uring stable operation. During ice nucleation measurements, the rops shoul be space from each other as far as possible to minimize thermal an hyroynamic interactions between the rops. Since the frequency of generation of rops is proportional to the rate of flow of the water that is fe into the evice, it is theoretically possible to reuce the frequency inefinitely, but practically there is a lower frequency limit below which S2

3 the generation of the rops becomes isorere. The rop frequency values liste in the table are close to, but above, this lower frequency limit. The first esign liste in Table ST-1 is the one that was use for the measurement of the rate of nucleation of ice. or this esign we also list the minimum an the maximum rop iameters that we coul achieve by changing the temperature of the nozzle. The secon esign was use to fabricate the evice shown in igure 6a, an the thir esign was use to acquire the high-resolution pictures shown in igure 6b. Table ST-1. Design parameters for microfluiic evices an typical operating conitions. # w nozz (µm) nozz (µm) w chan (µm) h ev (µm) Q PMD (m/h) T nozz (ºC) rop (µm) f rop (rop/s) Designs for PRTD arrays. igure S-2 shows rawings of the sensor arrays use for temperature measurement. The esign in figure S-2a offere the best optical access to the rops that move insie the channel, but the lack of symmetry aroun the miline of the channel mae the alignment of the sensor with the channel ifficult. The esign in igure S-2b facilitate the alignment of the array to the channel but was use only for the bottom sie of the channel since it woul mask the rops if place on top of the channel. The arrays in igure S-2c an S2- were symmetric, an ha 100-µm an 300-µm wie gaps along their centerlines to allow the optical observation of the rops. S3

4 The fabrication of the PRTD arrays. We use 50 mm x 75 mm microscope slies mae from soa-lime glass, of from fuse silica, as the substrate for the arrays. The slies were cleane first in a saturate solution of KOH in isopropyl alcohol, then in concentrate H 2 SO 4, an finally plasma-etche (Technics Plasma Stripper, moel 220; 1 Torr pressure an 100 W R power) in O 2 for 10 minutes. We spun-coate the slies at 3750 RPM for 20 s, first with a hexamethylisilazane (HMDS) primer, an then with Microposit S1813 resist; the thickness of the resist layer was ~2 µm. We printe the PRTD array esigns on chrome photolithography masks, an use these masks in a mask aligner (SUSS MicroTec MA-6) to expose the resist. After evelopment in Microposit CD-30 the slies were plasma-etche briefly (~1 minute) to remove any organic resiue from the areas which were expose an evelope. We loae the slies in an electron-beam thin-film evaporator (e-beam) an coate them first with titanium an then with platinum. The titanium ensure ahesion of the platinum to the glass, but it also ha a negative impact on the reproucibility of the PRTD sensors; we therefore use the thinnest (1-2 nm) Ti layer that still provie ahesion. The Pt layers were eposite at a rate of ~0.2 nm/s an ha a thickness of ~150 nm. The Pt-coate slies were unloae from the e-beam, soake in acetone for the lift-off of the metal from resist-coate areas, an then cleane with isopropanol. S4

5 igure S-2. a) 200 µm Drop flow + Source - Source b) + Sense - Sense + Sense - Sense c) ) igure S-2. Drawings, to scale, of the sensors from ifferent PRTD array esigns. The scale bar in rawing a) applies to all rawings. Drawing a) also shows the outline of a 400-µm wie channel aligne with the array. S5

6 Annealing the PRTD arrays at ~500 ºC for 12 hours lowere the resistance of the sensors an improve significantly their reproucibility. The last fabrication step was to coat the slies (except the leas use for electrical connections) with a 200-nm protective layer of SiO 2 in an e- beam. The SiO 2 layer also provie a surface that coul bon to plasma-oxiize PDMS; since PDMS oes not bon to platinum layers, boning a PDMS slab irectly to the unprotecte arrays coul cause leaks of flui from the evice. The calibration of the PRTD arrays. The calibration proceure was essential for achieving goo accuracy in temperature measurements. The main challenge for the accurate calibration of the sensors was the creation of the uniform an stable thermal environment for the sensor arrays. We use a ry calibration scheme using multiple insulation stages to filter out temperature variations an to reuce the rift rate of the temperature. The complete microfluiic evice an a calibrate PRTD thermometer (Hart Scientific , calibration accuracy ±0.04 º C) were place in contact with an aluminum plate (100 mm wie, 150 mm long, an 6 mm thick) using thermal grease. The aluminum plate sat insie an aluminum box with 12-mm thick walls (inner space 115 mm wie, 125 mm long, an 140 mm high). To minimize the thermal conuction between the box an the plate, the plate was place slante insie the box an polyurethane foam pas (5 mm thick) were use at the contact points between the plate an the box. A liqui heat exchanger was place in contact with the thickwalle aluminum box, an the box was place insie a thermally insulating box with 30-mm thick walls mae of expane polystyrene foam. To achieve a given calibration temperature, we ran ethanol from a temperature-stabilize bath (aua RP 890) through the heat exchanger. Although the temperature of the ethanol in the S6

7 bath fluctuate in some cases by as much as 0.1 ºC aroun the set temperature of the bath, the temperature of the evice was practically constant because of the weak thermal coupling between the aluminum box an the plate. The same weak coupling cause a very slow response of the temperature of the evice after a change in the set temperature of the bath: the stabilization of temperature of the evice took approximately 5 hours. The sensitivity of the measurement of temperature was goo enough to measure rifts smaller than ºC/min. In a typical calibration run we measure these rifts, an recore calibration ata only if the temperature rift was equal or less than ºC/min. A calibration run consiste of electrical resistance measurements at five or six temperatures between -50 ºC an 50 ºC. or each sensor an calibration temperature we measure the resistance 20 times to reuce the effect of electrical noise. We fitte the resistance ata from the sensors to a parabolic function of temperature; using higher-orer polynomial functions of temperature i not improve significantly the quality of the fit. Since the number of calibration temperatures was larger than the number of fit parameters, the fits were over-etermine, an we coul use the resiuals of the fit to evaluate that the precision of the calibration, for a single calibration run, was better than 0.01 ºC. Between ifferent calibrations, the changes in the calibration curves were larger, but these changes are likely to be cause primarily by the hanling of the evice between calibrations. The calibration coefficients of very thin (~150 nm) PRTDs sometimes change after the evices were installe on the col plate. To juge the reproucibility of the calibration, we compare the pairs of calibration that exhibite, over several ays, the least rifts. Since in these cases the largest changes were approximately 0.03 ºC, we evaluate that the reproucibility of calibration proceure is equal to or better than 0.03 ºC. S7

8 Derivation of the formula for the calculation of ice nucleation rates. The basic formula for the calculation of the freezing rate R can be efine by eq. (SE1), R 1 N δt N = (SE1) where δt the observation time in secons, N is the number of rops that freeze within δt, an N is the number of liqui supercoole rops at the beginning of investigation; the unit of rate is 1/s. We rewrote eq. (SE1) using the particular conitions of our experiment, in which the temperature ecreases uring the measurement, an in which we calculate the freezing rate using freezing events from a finite range of freezing temperatures. This range of freezing temperatures correspons to a range of freezing positions along the channel. Equation (SE1) becomes: R 1 N ( x0 ) N ( x) = (SE2) t( x) t( x ) N ( ) 0 x0 R T ( x0 ) T ( x) N ( x0 ) N ( x) 1 = (SE3) t( x ) t( x) T ( x ) T ( x) N ( x ) where x 0 is the position in millimeters where the observation starts an x the position in millimeters where it ens. The temperature of the rops at these positions are T(x 0 ) an T(x), respectively. or the first rop investigate, t(x 0 ) the time when the rop is at position x 0 an t(x) the time when it is at position x. (Since all the rops are assume to have ientical spees, the choice of the rop oes not influence the calculation of R.) N (x 0 ) is the number of liqui rops entering the observation region at x 0, an N (x) the number of remaining liqui rops that exit the observation region at x. S8

9 Equations (SE2) an (SE3) can be use to calculate the ice nucleation rates if ata specific to our experiment (the position-epenencies of the rop spee, rop temperature, an freezing probability) is available. We nevertheless expresse the ata using a ifferent set of variables: the iniviual temperatures at which freezing initiates in a rop, T (in ºC), an the rate of change of the temperature at freezing, (T/t) (in ºC/s). These variables, along with the volume of the sample of water, can be use to compare ice nucleation ata prouce by ifferent ice nucleation apparatuses because they are not experiment-specific. To express the freezing rate as a function of temperature, the epenent variable in eq. (SE3) has to be change from position, x, to temperature, T. This change of variable is possible if the temperature epens monotonously on the position (i.e. the temperature is always coler at further positions in the channel). or the ice nucleation experiment in pure water that we reporte here, this is not the case: the temperature reache a minimum, an then increase before all rops froze. To apply the temperature-epenent formulas that we list here, we iscare from analysis freezing events that occurre while the temperature of the rops increase. We also iscare events occurring at cooling rates between -2 ºC/s an 0 ºC/s because the errors in etermining the cooling rate were large in that case. After the change of variable from x to T, eq. (SE3) becomes: R T0 T N ( T0 ) N ( T ) 1 = (SE4) t T ) t( T ) T T N ( T ) ( R T 1 ( T ) = ( T ) ( N ( T )) (SE5) t N ( T ) T Here the rops are investigate in a temperature interval spanning from T 0 (the upper temperature) to T (the lower temperature). N (T) is the number of rops that froze at temperatures lower than T, an (T/t)(T) the rate of cooling (ºC/s) of the rops as a function of S9

10 their own temperature; these two functions can be evaluate numerically from the experimental ata on freezing temperatures an on cooling rates. The generalization of the calculation of freezing rates for the case in which the temperature of the channel fluctuates. The erivation of eq. (SE5) assumes that all rops cool in exactly the same fashion (i.e. when rops reach a given position in the channel, they have the same temperature). This is not always the case for out apparatus, because the temperatures along the channel can fluctuate uring the recoring of a ata set. The generalization of eq. (SE5) must allow the calculation of freezing rates for arbitrary pairs of freezing temperatures an cooling rates. Once the temperatures (an also the cooling rates) start to fluctuate, the set of freezing events is no longer a statistical ensemble of ientical systems, an the problem of measuring the freezing rates becomes one of averaging the results of ifferent experiments. To generalize eq. (SE5) we average the freezing rate given by eq. (SE1). We use the following averaging formula, (SE6), R ( T, ) = Total number of rops = 1 Total number of rops l = 1 1 δt f (SE6) where R (T,) is the rate of freezing at temperature T calculate across a finite temperature bin of with (spanning from T-/2 to T+/2), is the rop inexing number, δt is the passage time of roplet through the temperature bin, an the functions f an l are efine as follows: 1, if freezes between T + f = 2 0, otherwise an T 2 (SE7) S10

11 1, if is liqui when reaching T + l = 2 0, otherwise (SE8) Equation (SE6) can be easily aapte to use experimental ata as its input variables: R Total number of rops T ( T freeze ) f 1 = 1 t ( T, ) = (SE9) Total number of rops l = 1 where (T/t) (T freeze ) is the rate of cooling of rop when it freezes at the temperature T freeeze. The evaluation of functions f an l requires only the comparison of the freezing temperature of rop with the upper an lower bin temperatures. Equation (SE9) reuces to eq. (SE5) for rops cooling in the same fashion, an is accurate if the ratio of the number of rops frozen insie the bin to the starting number of liqui rops is small (<~0.1). If this ratio is large (>~0.1), eq. (SE9) unerestimates the freezing rate when freezing is a stochastic process. or our experimental ice nucleation ata, the ratio of frozen to liqui rops was small for most of the temperature bins, because of the large number of freezing events that we recore. Nevertheless, this ratio became large at the lowest temperatures. or the calculation of homogenous nucleation rates we correcte the nucleation rate accoring to the formula: J corr ln 1 All rops f All rops l ( T, ) = J ( T, ) (SE10) All rops All rops f l S11

12 where J corr (T,) an J(T,) are the correcte, an the uncorrecte rates of nucleation calculate at temperature T in a bin of with T. This correction factor is approximate, an we evaluate that it has the effect of overestimating the nucleation rates if the ratio of frozen rops to liqui rops is larger than approximately 0.5. Other electronic files inclue in the supplementary information. The other files inclue with the supplementary information are the freezing temperature an cooling rate ata for ice nucleation experiments on pure water, an seee with silver ioie; an six movies of freezing rops insie microfluiic channels. Raw ata from ice nucleation experiments. These two text files are name Stan_Whitesies_2008-Jun-04_reezing_Temperatures_37211_Pure_Water_Drops.rtf, an Stan_Whitesies_2008-Dec-23_reezing_Temperatures_8900_AgI-seee_Water_Drops.rtf. They contain the freezing temperatures, an cooling rates at the moment of freezing, for all the ata we reporte in this paper. The ata is liste in a tab-elimite format, an the file contains a text heaer containing the escriptions of the experiment an of the ata liste in the file. The ata can be importe into most spreasheet computer programs if the text heaer is elete. Movies of freezing rops in a microfluiic channel. The first four out of six movies are uncompresse. Except for image cropping an for selection of a frame range for the purpose of reucing the size of the files, these four movies were not processe after they have been ownloae from the camera. The file names list the recoring frame rate of the movie, an the size of the image area. S12

13 The last two movies are vieo presentations of the freezing processes. They use the uncroppe raw footage from the first two movies, an were eite by aing ynamic text escriptions. i) Stan_Whitesies_2007-Aug-02_CompleteImagereezing_AgIseee_Water_1000fps_15000x563micron.avi : This movie shows the full sequence of rop hanling: generation, cooling, an freezing. A full frame from this movie is sown in figure 6a. ii) Stan_Whitesies_2006-Dec- 21_HighResolutionreezing_Pure_Water_16000fps_1791x223micron.avi : This movie shows with high temporal an spatial resolution the two-step process of freezing in supercoole water: first the rapi formation of ice enrites, an then the more graual freezing of the rest of the water insie the rop. The sequence of images in figure 6b was extracte from this movie. iii) Stan_Whitesies_2008-Jun- 04_reezingMovieSection_Pure_Water_1000fps_11682x308micron.avi : This movie is part of the actual movie recore for the measurement of homogenous nucleation rates; the image in this movie was not croppe. iv) Stan_Whitesies_2008-Dec-23_reezingMovieSection_AgIseee_Water_1400fps_5462x202micron.avi : This movie is part of the actual movie recore for the measurement of heterogeneous nucleation rates; the image in this movie was not croppe. v) Stan_MicrofluiicIceNucleation_YouTube-Part1_ mov S13

14 Movie presentation base on the movie (i) showing the full sequence of rop hanling. The footage use in this presentation shows only homogenous freezing events. vi) Stan_MicrofluiicIceNucleation_YouTube-Part2_ mov Movie presentation base on the movie (ii) showing the freezing process image with high spatial an temporal resolution. S14