View Article Online / Journal Homepage / Table of Contents for this issue
`
`PAPER
`
`www.rsc.org/softmatter | Soft Matter
`
`Simultaneous generation of droplets with different dimensions in parallel
`integrated microfluidic droplet generators{
`
`Wei Li,a Edmond W. K. Young,be Minseok Seo,a Zhihong Nie,a Piotr Garstecki,d Craig A. Simmonsbe and
`Eugenia Kumacheva*ace
`
`Received 22nd August 2007, Accepted 8th November 2007
`First published as an Advance Article on the web 6th December 2007
`DOI: 10.1039/b712917c
`
`This paper describes geometric coupling of the dynamics of break-up of liquid threads in parallel
`flow-focusing devices (FFD), which are integrated into a multiple quadruple-microfluidic droplet
`generator (QDG). We show weak parametric coupling between parallel FFDs with an identical
`design, which leads to the slight broadening of the distribution of sizes of droplets. Using parallel
`FFDs with distinct geometries we simultaneously generated several populations of droplets with
`different volumes, yet, each of these populations was characterized by a narrow size distribution.
`Simulation of the generation of droplets in the quadruple-microfluidic droplet generator based on
`hydraulic resistances to the flow of a single-phase fluid was in good agreement with the
`experimental results.
`
`Introduction
`
`Emulsification in microfluidic devices provides the ability to
`generate droplets and plugs with a predetermined size and
`narrow size distribution.1–4 These droplets and plugs find
`important applications in microreaction synthesis,
`in high
`throughput screening of chemical reactions,5,6 in studies of
`protein crystallization,7,8 and in the continuous production of
`colloid particles with controlled size, shape and morphology.9–14
`Since the productivity of a single microfluidic droplet
`generator is relatively low, there is an increasing interest in
`the scaled-up generation of droplets with different or identical
`volumes by producing them in parallel
`integrated and/or
`modular multiple droplet generators. The challenge in the
`scaled-up production of droplets is to circumvent the broad-
`ening of their size distribution, due to the coupling between the
`devices. Significant progress has been achieved by Nisisako
`et al.15–17 in the formation of monodisperse droplets in the
`integrated multiple droplet generators with identical dimen-
`sions. Yet,
`in the study of emulsification in two parallel
`T-junction devices, Tabeling et al.18 showed that under
`particular
`conditions,
`these devices were parametrically
`coupled and produced droplets with a broadened size
`distribution.
`
`aDepartment of Chemistry, University of Toronto, 80 St. George Street,
`Toronto, Ontario, M5S 3H6, Canada
`bDepartment of Mechanical & Industrial Engineering, University of
`Toronto, 5 King’s College Road, Toronto, Ontario, M5S 3G8, Canada
`cDepartment of Chemical Engineering, University of Toronto, 200
`College Street, Toronto, Ontario, M5S 3E5, Canada
`dInstitute of Physical Chemistry, Polish Academy of Sciences,
`Kasprzaka 44/52, 01-224 Warsaw, Poland
`eInstitute of Biomaterials and Biomedical Engineering, 164 College
`Street, University of Toronto, Toronto, Ontario, M5S 3G9, Canada.
`E-mail: ekumache@chem.utoronto.ca; Fax: +1 416 978 3576;
`Tel: +1 416 978 3576
`{ Electronic supplementary information (ESI) available: Design of
`FFDs, experimental results, calculation of volumes of liquids in the
`QDG. See DOI: 10.1039/b712917c
`
`Despite a great plethora of work done on microfluidic
`emulsification in multichannel microfluidic devices,15–24 geo-
`metric coupling between integrated parallel droplet generators
`with different dimensions of the microchannels has not been
`reported. This effect is important for several reasons. First,
`variations in dimensions of microchannels that are acquired in
`the microfabrication process may lead to the broadened size
`distribution of droplets. Secondly, parallel generation of highly
`monodisperse droplets with varying dimensions has important
`applications
`in the simultaneous production of colloid
`particles with different sizes,25–27 in high throughput screening
`of the effect of droplet volume on chemical reactions, and in
`the studies of diffusion-controlled processes.28,29
`Here we report the use of the integrated quadra-droplet
`generator (QDG) comprising four parallel microfluidic flow-
`focusing devices with distinct geometries for the simultaneous
`formation of highly monodisperse droplets with different
`dimensions. Simulation of the geometric coupling between the
`flow-focusing devices in this QDG (based on hydraulic
`resistances to the flow of a single-phase fluid) provided good
`agreement with experimental results.
`
`Experimental design
`
`Fig. 1a shows a schematic of the individual planar flow-
`focusing device (FFD)1 in which two immiscible liquids, a
`droplet phase, A, and a continuous phase, B, are supplied to
`the central and side channels of the device, respectively. The
`liquids are forced through a narrow orifice in which a thread of
`liquid A breaks up and releases droplets.30,31
`Fig. 1b provides a 3D illustration of the QDG with four
`parallel flow-focusing devices.19 The bottom component of the
`device is a planar, non-patterned sheet. The intermediate sheet
`is patterned with the relief features of four FFDs. The top
`sheet serves as an ‘‘adapter.’’ Liquid A is injected in inlet A
`and is split between four microchannels of identical width and
`height. Liquid B is supplied through inlet B and is split
`
`258 | SoftMatter, 2008, 4, 258–262
`
`This journal is ß The Royal Society of Chemistry 2008
`
`Published on 06 December 2007. Downloaded by Radboud Universiteit Nijmegen on 15/04/2016 15:51:21.
`
`1
`
`

`
`PAPER
`
`www.rsc.org/softmatter | Soft Matter
`
`Simultaneous generation of droplets with different dimensions in parallel
`integrated microfluidic droplet generators{
`
`Wei Li,a Edmond W. K. Young,be Minseok Seo,a Zhihong Nie,a Piotr Garstecki,d Craig A. Simmonsbe and
`Eugenia Kumacheva*ace
`
`Received 22nd August 2007, Accepted 8th November 2007
`First published as an Advance Article on the web 6th December 2007
`DOI: 10.1039/b712917c
`
`This paper describes geometric coupling of the dynamics of break-up of liquid threads in parallel
`flow-focusing devices (FFD), which are integrated into a multiple quadruple-microfluidic droplet
`generator (QDG). We show weak parametric coupling between parallel FFDs with an identical
`design, which leads to the slight broadening of the distribution of sizes of droplets. Using parallel
`FFDs with distinct geometries we simultaneously generated several populations of droplets with
`different volumes, yet, each of these populations was characterized by a narrow size distribution.
`Simulation of the generation of droplets in the quadruple-microfluidic droplet generator based on
`hydraulic resistances to the flow of a single-phase fluid was in good agreement with the
`experimental results.
`
`Introduction
`
`Emulsification in microfluidic devices provides the ability to
`generate droplets and plugs with a predetermined size and
`narrow size distribution.1–4 These droplets and plugs find
`important applications in microreaction synthesis,
`in high
`throughput screening of chemical reactions,5,6 in studies of
`protein crystallization,7,8 and in the continuous production of
`colloid particles with controlled size, shape and morphology.9–14
`Since the productivity of a single microfluidic droplet
`generator is relatively low, there is an increasing interest in
`the scaled-up generation of droplets with different or identical
`volumes by producing them in parallel
`integrated and/or
`modular multiple droplet generators. The challenge in the
`scaled-up production of droplets is to circumvent the broad-
`ening of their size distribution, due to the coupling between the
`devices. Significant progress has been achieved by Nisisako
`et al.15–17 in the formation of monodisperse droplets in the
`integrated multiple droplet generators with identical dimen-
`sions. Yet,
`in the study of emulsification in two parallel
`T-junction devices, Tabeling et al.18 showed that under
`particular
`conditions,
`these devices were parametrically
`coupled and produced droplets with a broadened size
`distribution.
`
`aDepartment of Chemistry, University of Toronto, 80 St. George Street,
`Toronto, Ontario, M5S 3H6, Canada
`bDepartment of Mechanical & Industrial Engineering, University of
`Toronto, 5 King’s College Road, Toronto, Ontario, M5S 3G8, Canada
`cDepartment of Chemical Engineering, University of Toronto, 200
`College Street, Toronto, Ontario, M5S 3E5, Canada
`dInstitute of Physical Chemistry, Polish Academy of Sciences,
`Kasprzaka 44/52, 01-224 Warsaw, Poland
`eInstitute of Biomaterials and Biomedical Engineering, 164 College
`Street, University of Toronto, Toronto, Ontario, M5S 3G9, Canada.
`E-mail: ekumache@chem.utoronto.ca; Fax: +1 416 978 3576;
`Tel: +1 416 978 3576
`{ Electronic supplementary information (ESI) available: Design of
`FFDs, experimental results, calculation of volumes of liquids in the
`QDG. See DOI: 10.1039/b712917c
`
`Despite a great plethora of work done on microfluidic
`emulsification in multichannel microfluidic devices,15–24 geo-
`metric coupling between integrated parallel droplet generators
`with different dimensions of the microchannels has not been
`reported. This effect is important for several reasons. First,
`variations in dimensions of microchannels that are acquired in
`the microfabrication process may lead to the broadened size
`distribution of droplets. Secondly, parallel generation of highly
`monodisperse droplets with varying dimensions has important
`applications
`in the simultaneous production of colloid
`particles with different sizes,25–27 in high throughput screening
`of the effect of droplet volume on chemical reactions, and in
`the studies of diffusion-controlled processes.28,29
`Here we report the use of the integrated quadra-droplet
`generator (QDG) comprising four parallel microfluidic flow-
`focusing devices with distinct geometries for the simultaneous
`formation of highly monodisperse droplets with different
`dimensions. Simulation of the geometric coupling between the
`flow-focusing devices in this QDG (based on hydraulic
`resistances to the flow of a single-phase fluid) provided good
`agreement with experimental results.
`
`Experimental design
`
`Fig. 1a shows a schematic of the individual planar flow-
`focusing device (FFD)1 in which two immiscible liquids, a
`droplet phase, A, and a continuous phase, B, are supplied to
`the central and side channels of the device, respectively. The
`liquids are forced through a narrow orifice in which a thread of
`liquid A breaks up and releases droplets.30,31
`Fig. 1b provides a 3D illustration of the QDG with four
`parallel flow-focusing devices.19 The bottom component of the
`device is a planar, non-patterned sheet. The intermediate sheet
`is patterned with the relief features of four FFDs. The top
`sheet serves as an ‘‘adapter.’’ Liquid A is injected in inlet A
`and is split between four microchannels of identical width and
`height. Liquid B is supplied through inlet B and is split
`
`258 | SoftMatter, 2008, 4, 258–262
`
`This journal is ß The Royal Society of Chemistry 2008
`
`Published on 06 December 2007. Downloaded by Radboud Universiteit Nijmegen on 15/04/2016 15:51:21.
`
`View Article Online
`
` / Journal Homepage
`
` / Table of Contents for this issue
`
`2
`
`

`
`least 100
`Typically, we measured the diameters of at
`droplets. Polydispersity of droplets was characterized by
`determining the coefficient of variance (CV) of the diameters
`of droplets (defined as (d/Dm) 6100%, where d is the standard
`deviation and Dm is the mean diameter of droplet).
`
`Results and discussion
`
`Emulsification in the quadra-droplet generator with identical
`flow-focusing devices
`
`Fig. 2a shows typical optical microscopy images of droplets
`generated in four identical FFDs (labeled as FFD-1 to FFD-
`4). We varied the flow rate, QA, of the droplet phase supplied
`to inlet A from 0.02 to 0.08 mL h21 and the flow rate, QB, of
`the continuous phase supplied to inlet B from 1.0 to 1.6 mL
`h21. In this range of flow rates of liquids, the droplets formed
`via the flow-focusing mechanism,30,31 and the formation of
`large discoid droplets squashed between the top and the
`bottom walls of the microchannels was avoided. Fig. 2b shows
`typical optical microscopy images of droplets just before the
`outlet of
`the QDG. No coalescence of droplets in the
`downstream and integrated channels was observed.
`The size of droplets increased with an increasing value of QA
`and a decreasing value of QB.1,19 More importantly, for each
`value of QA and QB a small but finite difference existed in the
`dimensions of droplets generated in the individual FFDs. The
`difference between the mean diameters of droplets generated in
`different FFDs did not exceed 8 mm for the size of droplets in
`
`Fig. 2 Optical microscopy images of (a) droplets formed in four
`integrated FFDs with identical geometries; (b) droplets entering the
`outlet of the QDG. The flow rate of liquids A and B are 0.02 mL h21
`and 1.0 mL h21, respectively. Scale bar = 100 mm. (c) Variation in
`polydispersity of droplets produced in four integrated FFDs and of the
`total population of droplets generated in the QDG (&). Orifice width
`in FFD-1: 50.7 ¡ 1.0 mm (n), FFD-2 50.8 ¡ 1.0 mm (%), FFD-3:
`48 ¡ 1.0 mm (e) and FFD-4 48.8 ¡ 1.0 mm (#).The height of
`channels in the FFDs was 150 ¡ 2 mm.
`
`the microfluidic quadruple-droplet generator
`Fig. 1 Design of
`(QDG).
`(a) Schematic of
`the individual
`flow-focusing droplet
`generator. (b) Three-dimensional illustration of the QDG: a planar
`non-patterned bottom sheet; an intermediate sheet with an Inlet B for
`the liquid B (a continuous phase) and eight microchannels connected
`with bridge channels to form a symmetric structure comprising four
`FFDs, and an outlet; and a top sheet with an inlet A for liquid A (a
`droplet phase) which splits between four microchannels and enters the
`through holes 19–49
`FFDs
`superimposed with holes 1–4. The
`dimensions of the bottom, intermediate and top sheets in (b) were
`5 cm 6 7.5 cm, 5 cm 6 7.5 cm, and 5 cm 63 cm, respectively.
`
`between eight channels of identical width and height. When
`three slabs are sealed, the holes in positions 19–49 and 1–4 are
`superimposed, so that liquid A enters the microchannels in the
`intermediate sheet. Droplets produced in the four FFDs enter
`a common downstream channel and exit from the outlet.
`Droplets with the same diameters are produced in the QDG
`comprising FFDs with identical geometry. Droplets with
`varying dimensions are generated in FFDs with different
`widths of the orifices. The distribution of sizes of droplets is
`examined in the downstream channels of individual FFDs and
`at the exit of the QDG.
`
`Experimental
`
`Microfluidic devices were fabricated in poly(dimethylsiloxane)
`(PDMS) using soft lithography.32,33 The actual widths of the
`microchannels, especially the widths of the orifices in the individual
`FFDs, were measured prior to the emulsification experiments.
`Herein, we used two types of QDGs in which the flow-focusing
`devices had identical or different widths of the orifice.
`Filtered, deionized water was used as the droplet phase
`(introduced as liquid A, see Fig. 1a.). A 2 wt% solution of a
`non-ionic surfactant Span 80 in a light mineral oil was used as
`the continuous phase (introduced as liquid B). Liquids A and
`B were supplied to the QDG using two separate syringe pumps
`(PHD 2000, Harvard Apparatus, MA, USA). An optical
`microscope (Olympus BX41) coupled with a CCD camera
`(Evolution
`VF) was used to acquire images of droplets. The
`distribution of sizes of droplets was determined by image
`analysis of the micrographs using software Image-Pro Plus 5.0.
`
`TM
`
`This journal is ß The Royal Society of Chemistry 2008
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`
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`3
`
`

`
`the range from 80 to 135 mm. This variation did not notably
`change with the value of QB. Because of the small difference
`between the mean diameters of droplets generated in the
`individual FFDs, polydispersity of the total population of
`droplets produced in the multiple droplet generator was
`approximately 1–2% higher than the value of CV of the
`droplets generated in the individual devices (Fig. 2c). Yet,
`the value of CV for
`the total population of droplets
`produced in the QDG did not exceed 4.0%, and it did not
`significantly change with increasing flow rates of the liquids
`(see ESI{).
`We ascribed the broadening in the distribution of sizes of the
`droplets emulsified in the QDG to the weak parametric
`coupling between the individual droplet generators. Parametric
`coupling occurs when parallel microfluidic droplet generators
`are interconnected and formation of droplets in a particular
`FFD changes the frequencies of droplet formation in other
`FFDs, so that each FFD parametrically forces others.18 Close
`inspection of images of droplets moving through the down-
`stream channels in the individual integrated FFDs revealed that
`the difference in distances between the two neighbouring
`droplets did not exceed 5 mm, whereas for the droplets
`produced in the different FFDs the variation in the spacing
`was up to 20 mm. This result suggested that droplets in the
`parallel FFDs were generated at varying frequencies, and the
`emulsification process was not appreciably synchronized. In
`order to verify the effect of weak coupling between the
`individual FFDs on the broadening of the polydispersity of the
`droplets, we performed a series of control experiments in
`which we emulsified water
`in four
`independent
`(non-
`integrated) FFDs with the same geometry and dimensions
`and at the same flow rates of liquids as those used in the QDG.
`The increase in CV of the total population of droplets did not
`exceed 0.7%,
`in comparison with the value of CV of the
`droplets obtained in the individual FFDs (see ESI{). Thus,
`the small differences in the geometry of
`the individual
`FFDs that were acquired due to the finite resolution of
`the fabrication process did not explain the broadening
`of the distribution of sizes of the droplets produced in the
`QDG.
`We conclude that in the range of flow rates of liquids studied
`in the present work, weak coupling between parallel FFDs
`integrated in the QDG broadened the polydispersity of
`droplets. The broadening was not significant and the droplets
`generated in the multiple droplet generator could be defined as
`‘‘monodispersed’’.34
`
`Fig. 3 Optical microscopy images of droplets generated in the QDG
`comprising four FFDs with different widths of the orifices. The mean
`orifice widths of FFD-1 to FFD-4 were 41 ¡1 mm, 50 ¡ 1 mm, 61 ¡
`1 mm, and 75 ¡ 1 mm. In (a) QA = 0.2 mL h21, QB = 1.0 mL h21 and in
`(b) QA = 0.2 mL h21, QB = 2.0 mL h21. The height of QDG is 150 ¡
`2 mm. Scale bar = 100 mm.
`
`Emulsification in the quadra-droplet generator integrating flow-
`focusing devices with different geometries
`
`In the second series of experiments, emulsification was carried
`out in the QDG combining four parallel FFDs with non-
`identical design. The widths of the orifices in the individual
`FFDs were set to 41 ¡ 1, 50 ¡ 1, 61 ¡ 1, and 75 ¡ 1 mm (all
`other dimensions of
`the microchannels were maintained
`identical to previous experiments).
`In the emulsification process, we used the values and the
`ratios of flow rates of liquids A and B that produced droplets
`in the flow-focusing regime. The results of these experiments
`are presented in Fig. 3 and in Table 1.
`In the entire range of flow-rate ratios QB/QA, emulsification
`in the FFDs with wide orifices (FFD-3 and FFD-4) generated
`a single population of large monodispersed droplets.
`In the FFDs with narrower orifices (FFD-1 and FFD-2) at
`low flow-rate ratios of liquids A and B (QB/QA , 6) two
`populations of droplets with different sizes, each with narrow
`polydispersity, were obtained. The ratio between the number
`of droplets of each population varied with the flow-rate ratio
`
`Table 1 Mean diameter (Dm) of droplets formed in individual droplet generators and of the total population of droplets generated in QDG
`QB/mL h21
`
`FFD-3
`
`FFD-4
`
`V1/V2/V3/V4
`
`b
`
`a
`QB/QA
`
`FFD-1
`
`FFD-2
`
`Orifice width/mm
`Mean droplet diameter, Dm/mm
`
`1/1.22/1.49/1.83
`75
`61
`50
`41
`1/1.30/1.34/1.68
`188
`170
`166 + 83
`144 + 63
`5
`1
`1/1.42/1.57/1.83
`180
`159
`152
`136 + 41
`6
`1.2
`1/1.56/1.73/2.79
`174
`147
`142
`130 + 29
`7
`1.4
`1/1.87/2.03/2.92
`166
`143
`139
`120
`8
`1.6
`1/2.27/2.45/3.82
`161
`137
`132
`115
`9
`1.8
`1/2.40/2.71/3.87
`152
`130
`122
`108
`10
`2.0
`a QA= 0.2 mL h21. b V1/V2/V3/V4 is the mean volume ratio of droplets formed in four FFDs, normalized by V1. Calculation of the volume of
`droplets with different sizes is given in ESI.35
`
`260 | SoftMatter, 2008, 4, 258–262
`
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`
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`4
`
`

`
`QB/QA. For QB/QA = 6, FFD-2 produced a single population
`of droplets, and for 8 ¡ QB/QA ¡ 10 all FFDs produced a
`single population of droplets with CV of 2–3%. The mean
`diameter of droplets decreased with a decreasing width of the
`orifice. The size of droplets produced in FFD-1 decreased
`abruptly for QB/QA . 10, and for QB/QA . 25 the thread of
`liquid A did not break up in droplets. For QB/QA ¢ 40, the
`stream of the droplet phase did not enter the orifice of FFD-1.
`Fig. 4a shows the effect of flow-rate ratio QB/QA on the
`volume fractions of droplets produced in parallel FFDs. The
`volume fraction of droplets formed in an individual FFD was
`defined as Ri = (Vi/Vtot) where Vi is the total volume of droplets
`produced per unit time in individual FFDs, and Vtot is the total
`volume of droplets obtained in the quadra-droplet generator.
`Dashed lines in Fig. 4 show the ratio of volume of an orifice in an
`individual FFD to the total volume of orifices in the quadra-
`droplet generator. For QB/QA . 6, the value of Ri for FFD-4
`increased, the value of Ri for FFD-1 decreased, and the values of
`Ri for FFD-2 and FFD-3 remained almost constant. These
`effects implied that with an increasing ratio of flow rates of
`liquids, the FFDs with the widest orifice consumed an increasing
`volume of the droplet phase, at the expense of the liquid entering
`the FFD with the narrowest orifice.
`We attribute the re-distribution of droplet phase volumes
`between the FFDs to the difference in hydrodynamic path
`resistances to the flow of liquids in the devices with different
`geometry. This effect occurs in addition to the non-synchro-
`nized break-up of the liquid threads.17 The flow rates in
`corresponding sections of separate paths were not equal
`because the differences in orifice widths were coupled through
`the interconnected channels.
`Determining the flow rates of the fluid streams just prior to
`entrance into their respective orifices can elucidate the effect of
`varying orifice widths on the size of droplets. To demonstrate
`this effect, we analyzed a significantly simpler problem of flow of
`a single phase (with the properties of water, see ESI{) in all
`sections of the microchannel network. All other effects related to
`the multiphase flow, the properties of liquids, or other non-
`geometric
`considerations
`required more
`sophisticated
`approaches that were beyond the scope of the present analysis.
`For convenience, we used subscripts A and B to distinguish
`between the streams of the same liquid entering the orifice from
`top sheet (stream A) and intermediate sheet (stream B) (Fig. 1a).
`The purpose of this distinction was to track the volume fraction
`of stream A passing through the different orifices and obtain
`theoretical predictions of flow-rate ratios that can be readily
`compared to our experimental results (see ESI{).
`Fig. 4b shows the variation in the calculated volume
`fraction, Ri, of stream A in each FFD, plotted as a function
`of the ratio QB/QA. With increasing ratio QB/QA the value of
`Ri decreased for FFD-1 (comprising the narrowest orifice),
`and increased for FFD-4 (comprising the widest orifice),
`similarly to the trend shown in Fig. 4a. Furthermore, Fig. 4c
`shows
`that
`the experimental
`results and the results of
`modelling are in good agreement ( similar good agreement
`between the experimental and simulation results was obtained
`with the assumption that the streams A and B have the
`properties of the light mineral oil, see ESI{). Thus although we
`have only analyzed the simplified case of one-phase flow, the
`
`Fig. 4 (a) Variation in experimental volume fraction Ri of droplets
`generated in FFD with different geometry plotted as a function of the
`ratio of flow rates of continuous to droplet phases for FFD-1 (&),
`FFD-2 (D), FFD-3 (e), and FFD-4 (%). (b) Variation in calculated
`volume fraction Ri, of stream A, in FFDs with varying orifice widths,
`plotted as a function of the ratio of flow rates of continuous to droplet
`phases. The horizontal dashed lines represent the volume fraction of an
`orifice in an individual FFD to the total volume of orifices in the QDG
`(bottom to top lines correspond to FFD-1 to FFD-4, respectively). (c)
`Comparison of calculated and experimental values of Ri.
`
`uneven distribution of the volume of stream A between the
`coupled FFDs explains the trends in the variation of the size of
`droplets obtained in the QDG.
`Close examination of Fig. 4c reveals that the experimental
`values of Ri for FFD-1 were higher than the calculated Ri
`values. This discrepancy suggests that for narrow orifices, the
`multiphase flow, the rate-of-flow controlled break-up, and the
`
`This journal is ß The Royal Society of Chemistry 2008
`
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`5
`
`

`
`Laplace pressure played a crucial role in determining droplet
`size and frequency of droplet formation.31,36
`
`Conclusions
`
`Using a multiple droplet generator integrating four flow-
`focusing devices with different geometries, we studied geo-
`metric coupling between the devices in the emulsification
`process. In the control experiments we verified the existence of
`weak coupling between the devices with identical geometries,
`which led to the moderate broadening in polydispersity of the
`total population of droplets, in comparison with that of single
`FFDs. Emulsification in the droplet generator combining
`parallel FFDs with distinct geometries occurred with strong
`coupling and produced droplets with varying size and size
`distributions. Experimental results were in good agreement
`with the results of modelling. The results of this work can be
`used in the simultaneous production of highly monodisperse
`droplets with a pre-designed difference in dimensions.
`
`Acknowledgements
`
`support of NSERC
`The authors acknowledge financial
`Canada. PG acknowledges the support of the Foundation
`for Polish Science.
`
`References
`
`1 S. L. Anna, N. Bontoux and H. A. Stone, Appl. Phys. Lett., 2003,
`82, 364.
`2 T. Thorsen, R. W. Reberts, F. H. Arnold and S. R. Quake, Phys.
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`262 | SoftMatter, 2008, 4, 258–262
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