Effect of channel geometry on alternating droplet generation

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EFFECT OF CHANNEL GEOMETRY ON

ALTERNATING DROPLET GENERATION

a thesis submitted to

the graduate school of engineering and science

of bilkent university

in partial fulfillment of the requirements for

the degree of

master of science

in

mechanical engineering

By

Muhammad Saqib

May 2018

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EFFECT OF CHANNEL GEOMETRY ON ALTERNATING DROPLET GENERATION

By Muhammad Saqib May 2018

We certify that we have read this thesis and that in our opinion it is fully adequate, in scope and in quality, as a thesis for the degree of Master of Science.

Emine Yegan Erdem(Advisor)

Barbaros C¸ etin

Zafer Dursunkaya

Approved for the Graduate School of Engineering and Science:

Ezhan Kara¸san

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ABSTRACT

EFFECT OF CHANNEL GEOMETRY ON

ALTERNATING DROPLET GENERATION

Muhammad Saqib

M.S. in Mechanical Engineering Advisor: Emine Yegan Erdem

May 2018

Droplet based microfluidics has been one of the popular topics in microfludics research for the past two decades due to several advantages which include: less amount of reagent (sample) being used, enhanced mixing in the drops due to chaotic advection, low thermal mass and large surface to volume ratio which re-sults in efficient heat transfer and encapsulation of reagents in droplets. Produc-ing droplets from two sources inside the same micro-channel has been attempted by several research groups with great success and it carries great significance due to its applications in chemical synthesis, biological analysis and targeted drug de-livery. While there are geometries available to produce synchronized alternating droplets, the mechanism of alternation in such device has not been studied. In this work a cross junction device (also known as a double T-junction device)is used; and the effect of the taper angle of the side inlet channels on the continuous generation of an alternating pattern is studied. It was found that a higher value of the taper angle results in more efficient and constantly repeating alternating pat-tern of droplets from the two sources. This study includes the statistical analysis of the experimental data to compare the performance of devices with different taper angles for side channels. Moreover the experimental data is used to mea-sure the radii of curvature at the instant of break off and used to calculate the Laplace pressure drop across the junction which enables us to compare the total pressure drop across the junction for devices with different taper angle values. Using the total pressure drop it was concluded that the hydraulic resistance of the side inlet channels is the key factor in synchronized alternating droplet pat-tern generation. In order to confirm the calculated values, a computational study is also performed which further substantiates the theory. Furthermore, using the tapered channel devices, different patterns are generated that are referred to as barcodes, by employing different flow rate combinations at the dispersed phase inlets. Finally it was showed how to generate barcodes composed of droplets with

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iv

different and same viscosity. The significance of being able to generate different patterns is related to being able to separately identify droplets from each sources while using automation in the system since the droplet size and spacing remains uniform.

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¨

OZET

T ¨

URKC

¸ E BAS

¸LIK

Muhammad Saqib

Makine M¨uhendisli˘gi, Y¨uksek Lisans Tez Danı¸smanı: Emine Yegan Erdem

Mayıs 2018

Mikro akı¸skan ara¸stırmasında, damlacık tabanlı mikro akı¸skanlar, birka¸c avan-tajından dolayı 20 yıldır gündemde olan konulardan birisidir. Bu avantajlar-dan bazıları: Daha az miktarda reaktif (numune) kullanılması, kaotik yapı¸sma, dü¸sük termal kütle ve verimli ısı transferine ek olarak damlalardaki reakti-flerin kapsüllenmesiyle sonu¸clanan büyük yüzey hacim oranıdır. Aynı mikro kanalın i¸cindeki iki kaynaktan damlacıkların üretilmesi, büyük bir ba¸sarı ile birka¸c ara¸stırma grubu tarafından denendi ve kimyasal sentez, biyolojik analiz ve hedefe yönelik ila¸c verilmesi uygulamaları nedeniyle büyük önem ta¸sıyor. Senkronize edilmi¸s alternatif damlacıklar üretmek i¸cin mevcut geometriler olsa da, bu tür ci-hazlarda geometriksel dönü¸süm mekanizması ¸calı¸sılmamı¸stır. Bu ¸calı¸smada, bir ¸capraz ba˘glantı cihazı (¸cift T-ba˘glantı cihazı olarak da bilinir) kullanırız ve bu cihazın i¸c yan kanallarının koniklik a¸cısını de˘gi¸stirerek, de˘gi¸sen modelin sürekli ¨

uretilen alternatif desenli damlacıklardaki etkisini inceleriz. Yan kanallar ve konik a¸cının daha yüksek de˘gerde olması, iki kaynaktan gelen damlacıkların daha ver-imli ve sürekli olarak tekrarlanan modelin olu¸smasını sonu¸c verir. Bu ¸calı¸sma, yan kanallar i¸cin farklı koniklik a¸cıları olan cihazların performansını kar¸sıla¸stırmak i¸cin deneysel verilerin istatistiksel analizini i¸cermektedir. Ek olarak; deney-sel veriler, kopma anında e˘grilik yarı¸caplarını öl¸cmek ve birle¸sme noktasındaki Laplace basın¸c dü¸sü¸sünü hesaplamak i¸cin de kullanılır; bu da, farklı koniklik a¸cısı de˘gerlerine sahip cihazlar i¸cin birle¸sme noktası boyunca toplam basın¸c dü¸sü¸sünü kar¸sıla¸stırmamızı sa˘glar. Toplam basın¸c dü¸sü¸sünü kullanarak, yan giri¸s kanal-larının hidrolik direncinin senkronize alternatif damlacık modeli olu¸sturmada anahtar faktör oldu˘gu sonucuna vardık. Hesaplanan de˘gerleri do˘grulamak i¸cin, teoriyi daha fazla tasdik eden bir hesapsal ¸calı¸sma da yapılır. Ayrıca, konik kanallı cihazlar ve da˘gıtılmı¸s faz giri¸slerinde farklı akı¸s hızı kombinasyonları kul-lanılarak, barkod olarak adlandırılan farklı desenler üretiyoruz. Son olarak,

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vi

farklı ve aynı viskozitedeki barkodların nasıl üretildi˘gini gösterdik. Farklı de-senler üretebilmenin önemi, damlacık boyutu ve aralıkları tekdüze kaldı˘gı i¸cin, sistemde otomasyon kullanılırken dahi, her kaynaktan gelen damlacıkların ayrı ayrı tanımlanabilmesinden gelmektedir.

Anahtar s¨ozc¨ukler : Mikro akı¸skan ara¸stırmasında, alternatif damlacıklar ¨

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Acknowledgement

In the name of Allaah, the only Creator of all that exists. All praise and thanks to Allaah for granting me the ability to complete this thesis.

First and foremost I would like to thank my research advisor Dr. Yegan Erdem. I am very grateful to her for her continuous guidance, support and cooperation throughout the period of my MSc program in the form of sharing her technical expertise, her laboratory experience and in the form of including me in the es-teemed project that I had the privilege of working on. I would like to additionally thank her for her patience, support and invaluable input and feedback into my re-search specifically her input and feedback for our conference and journal papers. I would also like to thank the jury members for their patience and invaluable feedback during thesis jury times.

I would also like to express my gratitude to Dr. Ca˘glar Elb¨uken for his invalu-able help with the SU8 mold recipe and for providing SU8 2005 so that I could use it for making my molds. The recipe that I obtained from him and discussions with him helped me to develop durable SU8 mold for my research. I would like to take this opportunity to thank the technical staff at UNAM specially Mr. Ab-dullah Kafadenk and Mr. Semih Bozkurt for their assistance with training of the equipment and for their help with the fabrication procedure for my microfluidic devices.

I would like to thank my group members and colleagues Arsalan Nikdoost and Malik Abdul Wahab for their assistance in the laboratory and for the very fruitful discusions I had with them over the course of my research.

Last but not the least I would like to acknowledge the support and care from my family, specially my father, my mother, my brother Hamza and my sister Anum, throughout my stay in Bilkent University. Without their love, care and invaluable support I would not have been able to pursue and complete my higher education in Turkey.

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List of Figures

1.1 Schematic showing the design of a T-junction device . . . 3 1.2 Schematic showing the design of a Co-Flowing device . . . 6 1.3 Schematic showing the design of a Flow Focusing device . . . 7

2.1 Schematic showing the design of the microfluidic device having tapered channels at the side inlets. . . 13 2.2 Schematic showing the steps followed for the fabrication of the

microfluidic device. . . 15 2.3 Figure showing droplet generation in case of different values of α

starting from α = 0 . . . 19

3.1 (a)Graph of efficiency (ψ) vs flow rate fraction (φ) for n=1 with Qc

= 2.0µl/min. (b) Graph of efficiency (ψ) vs flow rate fraction (φ) for n=1 with Qc = 3.0µl/min. (c) Graph of number of consecutive

droplets (n) vs flow rate fraction (φ) with Qc = 2.0µl/min. (d)

Graph of number of consecutive droplets (n) vs flow rate fraction (φ) with Qc = 3.0µl/min . . . 23

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LIST OF FIGURES xiii

3.2 (a)Failed attempt in which droplet dimensions are not uniform (α = 0). (b) Alternating droplet generation with n=2 (α = 10).(c) Failed generation attempt; number of black and red droplets are unequal (α =15).(d) Alternating droplet generation with n=1 (α =25◦). . . 24 3.3 The sequence of alternation in case of tapered channels shows how

the two streams alternate in a perfectly synchronous pattern and as one stream enters the junction, the other stream is pushed back into the side channel. . . 26 3.4 The sequence of alternation in case of straight channels shows how

the two streams enter the junction at the same time without any synchronous pattern and the droplet size and spacing is also non-uniform. . . 28 3.5 Radius of curvature at the head and tail of the emerging droplet

instantaneously before break-off RHc and RT c respectively . . . . 30

3.6 Plots showing the variation of radii of curvature at the head and tail of the emerging droplet instantaneously before break-off RT c

and RHc respectively for each value of α for the flow rate

combi-nation: Qc = 2.0 µl/min and Qd = 0.2 µl/min . . . 31

3.7 Plot showing the variation of maximum pressure difference between the head and tail parts of the evolving droplets which occurs in-stantaneously before break off for each value of α for the flow rate combination: Qc = 2.0 µl/min and Qd = 0.2 µl/min . . . 32

3.8 (a) Surface plot for the evolving droplets in one complete alter-nating droplet generation cycle.(b) The pressure variation at two points in the side inlets showing pressure fluctuations for the evolv-ing droplets durevolv-ing one complete alternatevolv-ing droplet generation cycle, for α = 25 and for the flow rate combination: Qc = 2.0

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LIST OF FIGURES xiv

4.1 The droplet pattern generation in case of 2:1 and 3:1 for identical viscosity case . . . 36 4.2 The droplet pattern generation in case of 2:1 and 3:1 for different

viscosity case . . . 38 4.3 The droplet pattern generation in case of 1:1 and 2:1 for equal

vis-cosity case after mixing of reagents as the droplet is being produced 39 4.4 The droplet pattern generation in case of 1:1 and 2:1 for

differ-ent viscosity case after mixing of reagdiffer-ents as the droplet is being produced . . . 40

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List of Tables

1.1 Regimes of Droplet Generation . . . 4

2.1 Fabrication Process . . . 16 2.2 Table showing the values of taper angles and average widths of side

channels in each case . . . 17 2.3 Experiment sets . . . 18 2.4 Observations in case of different values of α for the case 2.0 µl/min

and 3.0 µl/min . . . 20

3.1 Comparison of droplet length in case of Experiments and Compu-tation . . . 31

4.1 Table showing pattern formation and corresponding flow rate com-binations . . . 37 4.2 The composition and viscosity of each sample prepared . . . 37 4.3 Table showing pattern formation and corresponding flow rate

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LIST OF TABLES xvi

4.4 Table showing pattern formation and corresponding flow rate com-binations for mixture forming droplets in case of identical viscosity 40 4.5 Table showing pattern formation and corresponding flow rate

com-binations for mixture forming droplets in case of different viscosity 40

A.1 Spin coating steps for base layer of SU8 2005 . . . 51

A.2 Soft bake steps for base layer of SU8 2005 . . . 52

A.3 Hard bake steps for base layer of SU8 2005 . . . 53

A.4 Spin coating steps for main mold layer of SU8 2050 . . . 53

A.5 Soft bake steps for main mold layer of SU8 2050 . . . 54

A.6 Hard bake steps for main mold layer of SU8 2050 . . . 55

C.1 Average droplet length and spacing data for α = 0 . . . 58

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Chapter 1 Introduction

1.1 Flow Types in Microfluidic Devices

The technology that gives us the ability to manoeuvre very small amounts of fluids (picoliters to nanoliters) inside channels having measurements from a few micrometers to a several hundred micrometers is called Microfluidics [1]. Due to its fascinating features like less reagent consumption, affordability, analysis being performed in quick time and with high resolution and sensitivity, it has been the topic of interest for several research groups for the last three decades [2]. As a result of these appealing features, microfluidics has found applications in chem-ical syntheses, synthetic and systems biology, cell biology and high-throughput screening [3].Based on the flow form of the fluid inside the microchannels, the field is divided into two types: continuous type and droplet based microfluidics [4].

1.1.1 Continuous Flow Microfluidic Devices

Continuous type microfluidics involves only one fluid flowing inside the mi-crochannel. The fluid is driven inside the microchannels by pressure driven flow

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or electro-osmotic flow. Continuous type flow has a parabolic flow profile which develops as a result of the no slip boundary condition at the wall. There is dis-persion at the walls which causes fluid at the wall to be slower than the fluid in the center of the channel. This leads to non-uniform resident times inside the microchannels which is not desirable in all the applications especially chemical syntheses and biological analyses. Furthermore the flow in microchannels is lami-nar due to the low Reynolds number which means that the mixing of the reagents is purely due to diffusion which is a slow process [5].

1.1.2 Droplet Based Microfluidic Devices

The second type of flow is droplet based flow in which the reagents are carried inside small drops or plugs flowing in an immiscible fluid. These droplets func-tion as microreactors and can then be transported, manipulated [6], manoeuvred, split, mixed [7] and heat treated [8] to utilize them in several chemical, biological, diagnostic and targeted delivery applications. There are several advantages pro-vided by droplet microfluidics over continuous flow microfluidics like enhanced mixing due to chaotic advection, efficient heat transfer due to low thermal mass and large surface to volume ratio, no dispersion of the reagent (trapped inside nanoliter droplets) with the channel walls since there is a thin film of continuous phase fluid separating droplet from walls. There are three major types of droplet generation geometries; namely flow-focusing, co-flowing and T-junction.

1.2 Droplet Based Microfluidic Devices

1.2.1 T-Junction Devices

Owing to the simple geometry and greater ability to control the droplet size, the T-junction device is the most commonly used geometry. Thorsen et al. [9] first reported the generation of microdroplets of water in a variety of different oils in

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a network of microchannels where the continuous phase was flowing in the main channel and dispersed phase entered the main channel through a side channel that was perpendicular to the main channel as shown in Figure 1.1.

Figure 1.1: Schematic showing the design of a T-junction device

The droplet generation mechanism is governed by the capillary number Ca defined by Equation (1.1) and the ratio of the width of inlet channel of the dispersed phase to the width of the main channel, denoted by x = win/wout.

Ca = µU

γ (1.1)

In the case where x is lesser than 1, and the value of Ca is high (0.01 <Ca <0.3), the droplet generation is dominated by the shear force applied by the continuous phase on the dispersed phase in which the droplet generation occurs even before the dispersed phase stream is able to completely block the main channel thereby no pressure variation takes place. This is known as the dripping regime [10]. In this regime, droplet is generated when the shear stress applied by the continuous phase overcomes the interfacial tension that resists deformation.

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Another regime is known as the squeezing regime [11] in which the value of x is around unity and Ca values are low (10−4<Ca <0.002). In this case the thickness of the dispersed phase stream is comparable to the width of the main channel therefore the shear stress applied by the continuous phase fluid is unable to break the droplet and hence the dispersed phase stream blocks the main channel. As it blocks the main channel, the pressure across the junction begins to change as the pressure of the upstream starts to rise due to minimized fluid flow across the junction and accumulation of continuous phase fluid. This pressure rise is responsible to neck and separate the droplet from the dispersed phase stream as concluded by Xu et al. [12]. The droplet size increases linearly with flow rate ratio φ = Qd/Qc where Qd is the dispersed phase flow rate and Qc is the

continuous phase flow rate in this regime.

Xu et al. also identified a third regime in between the dripping and squeezing regimes know as the transient regime. According to their study the droplet formation in this regime is in part governed by each of the earlier defined two regimes. The capillary number ranges for each mechanism are provided in Table C.5 [12].

Table 1.1: Regimes of Droplet Generation Regime Capillary Number Squeezing regime 10−4 <Ca <0.002 Transient regime 0.002 <Ca <0.01 Dripping regime 0.01 <Ca <0.3

Another important phenomenon on the mechanism of droplet generation was described by Garstecki et al. [12]. They described the process of a single droplet formation in four steps that include the entering of dispersed phase into the main channel, the developing droplet grows and blocks the entire main channel cross-section, the growing of the droplet downstream and the thinning of the neck that connects the drop to the reservoir, and finally the neck thins to the extent that it breaks which causes the droplet to separate and move downstream while the dispersed phase stream recedes into the side channel. Glawdel et al. [13] made a further contribution to the mechanism within the transient regime by adding a further step known as the lag step. According to their experimental

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and computational study, there is clear evidence that the dispersed phase stream recoils back into the side channel slightly before the droplet generation process. They also derived scaling laws for tlag and tneck.

Wang et al. [14] showed that the effect of viscous shear stress is prevalent even if the capillary number is very low. They suggested that unlike the previous works they had used very low values (far less than 1) of flow rate ratio φ. They used the pressure drop technique using sensors before and after the junction to calculate and plot pressure drop across the junction. They concluded that the highest pressure drop (∆ PLmax) is at the point momentarily before droplet break

off and its value is given by Equation (1.2) ∆PLmax= γ 1 RT c − 1 RHc (1.2)

where RT cand RHc are the tail and head curvature radii in the axial direction

at the break off point respectively.

1.2.2 Co-Flowing Devices

The co-flowing geometry was first reported by Cramer et al. [15], where they studied the transition from jetting to dripping regimes in droplet formation. In co-flow devices the direction of flow of both continuous and dispersed phase fluids is parallel to each other as shown in Figure 1.2. The device geometry was imple-mented by inserting a capillary inside a rectangular microchannel. The dispersed phase flows through the capillary while the continuous phase flows between the capillary and rectangular channel.

The two regimes are distinguished by the location of droplet breakup. In case of jetting, the droplet breaks up at a location far downstream of the point where the two phases interact, whereas in the dripping regime the droplet breakup occurs almost at the point of initial interaction between the two phases. At high flow rates of the continuous phase the jetting regime is observed and at low flow rates the dripping regime is observed. It was also determined that the critical

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velocity at which the transition from jetting to dripping occurs is dependent on the dispersed phase flow rate. As the dispersed phase flow rate increases the critical velocity decreases due to the higher axial momentum which facilitates the jet formation downstream. The critical velocity has a similar relation with the viscosity of the dispersed phase and this is a consequence of a stable interface due to higher viscosity of discontinuous phase.

Figure 1.2: Schematic showing the design of a Co-Flowing device

Apart from that the droplet size depends on the continuous phase flow rate as well as the interfacial tension. Increasing the continuous phase flow rate decreases the droplet size since the thinning of the dispersed phase stream happens more rapidly. Increasing the interfacial tension also decreases the droplet size and increases the resistance of the interface to deformation.

1.2.3 Flow Focusing Devices

The use of flow-focusing geometry to produce monodisperse droplets was first reported by Anna et al. [16]. The geometry consists of dispersed phase flowing through the main channel while the continuous phase focuses the dispersed phase stream while entering the main channel through two opposite side channels as shown in Figure 1.3. As the two fluids come into contact they flow a small distance while passing through an orifice after which the droplet is formed either immediately or at a distance downstream depending on the factors discussed

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earlier in the co-flow case.

Figure 1.3: Schematic showing the design of a Flow Focusing device The size of droplets depends on the size of the orifice as well as the flow rates of the two phases. In some cases droplets with sizes comparable to the orifice width can be formed irrespective of the flow rates. Dreyfus et al. [17] studied the effects of complete and partial wetting on the organization of pattern formed in a flow-focusing device. They concluded that in the case of partial wetting, the droplets are unorganized and in the case of complete wetting of the channel walls, the droplets are well organized in terms of pattern of generation.

1.3 Synchronized Alternating Pattern

Genera-tion Microfluidic Devices

The generation of droplets from two sources in a regular pattern where one dis-persed phase produces one droplet and the other disdis-persed phase stream produces another droplet and this sequence continues as long as the flow rates of the contin-uous phase and the dispersed phases are maintained at a constant rate, is called alternating droplet generation.

Zheng et al. designed cross junction geometry in order to produce droplets from more than one dispersed phases in a synchronized way [18]. They observed

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multiple regimes of droplet generation and they categorized these according to capillary number, Ca.

Hung et al. reported a device to perform nanoparticle synthesis by initially producing droplets from the dispersed phase sources and then causing their coa-lescence at a later step [19]. In this work they have used, at the merging point of the dispersed channel inlets, a three sided structure called ‘wing’ to avoid return flow. They explained that the alternation is due to the push-pull mechanism among the dispersed phases.

Nisisako et al. made use of the same geometry to create continuous core-in-shell droplets of two unmixable organic fluids; both entering beside each other from two dispersed phase channels [20]. Another device based on cross junc-tion accompanied by flow-focusing to encapsulate the produced dispersed phase droplets in pairs was reported by Hirama et al. [21]. They did this by varying the hydrophobicity inside the microchannel network.

Surya et al. conducted both experimental and numerical studies to identify regimes of droplet generation which were; merged, stable, transitional and laminar [22] and used a cross junction geometry composed of straight channels to generate alternating droplets. Another numerical study focusing on the same features of droplet generation but by varying the angle at which side channels merge to the main channel and viscosity ratio of the dispersed and continuous phases was performed by Ngo et al. [23]. Jin et al. studied the regularity of alternating mode to conclude that regularly alternating mode of droplet generation is always accompanied by regular merging of droplets [24].

1.4 Thesis Overview

In this work the effect of dispersed phase channel geometry on the repetitive synchronized alternating droplet generation was studied. The effect of varying the taper angle of dispersed phase channels on the alternating droplet generation

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stability has been studied. The synchronization is significant in applications such as chemical synthesis because of its capacity to maintain the accurate proportion of reactants in the microreactor (droplet). Moreover, for such applications the device needs to be consistent with regards to the size of droplets and the spacing so that it may be made compatible with automation. Due to this the influence of the angle of taper on the uniformity of droplet size and spacing was also studied. It is safe to say that the physics behind most mechanisms is well known to-day due to the contributions of several researchers over the last two decades, and it will enable the droplet based systems to be reliably used in commercial applications such as point of care diagnostics and chemical synthesis. The other requirements, however, for a successful transition to commercial applications are droplet manipulation and post processing. These aspects of microfluidics require creativity and precision and many researchers have already displayed successful results in terms of droplet transportation [25], mixing [7], thermal processing [26], encapsulation [27],[28],[29].

Chapter 2 introduces the basic concept of cross junction devices and discusses the designs of previous devices that were used to generate droplets from two sources inside a single microchannel and then presents the novelty in the device suggested in this work. Furthermore, the chapter discusses the importance of this improvement and its significance in the field of microfluidics. The criteria for stable synchronized alternating droplet generation are described. Moreover, it describes the design of the microfluidic device and the fabrication procedure required to fabricate the device. Finally the observations made during experi-ments with the suggested design after identifying the necessary components of the experimental setup are discussed.

Chapter 3 presents the three step pathway to study the physics behind the alternating droplet generation and why an increase in taper angle α results in a stable and synchronized pattern formation. The first step includes studying the statistical data to infer which device displays best performance. The second step involves studying the Laplace pressure data obtained from experiments and using this data in the equation which govern the physics behind droplet formation in a

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T-junction device. The third step consists of developing a computational model for the cross-junction device to apply the experimental conditions in order to confirm the conclusions drawn from the second step.

Chapter 4 presents the generation of different barcodes using the geometry with the best performance in terms of alternating droplet generation, in order to distinguish between the droplets from the two sources and to show how it could be used in automation of a process involving alternating droplet genera-tion. Moreover this barcode generation is also shown for droplets with different viscosities in addition to the identical viscosity case. Furthermore, experimental results of barcode generation performed with a device that is able to form droplets of mixtures of two fluids altenatively from the side channels is discussed. This is done for the cases where viscosities of the two droplet phases are identical and also different.

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Chapter 2 Design of Microfluidic Device

As previously discussed, there are some well-established techniques to produce droplets from a single source in a microfluidic device by using passive components. Now the focus will be on the production of droplets from more than one source inside the same microchannel network again using passive components. The reason for the significance of this particular topic is the ability to control droplet production from more than one source inside a single microchannel which would be useful in applications such as chemical synthesis and multiplexed analysis.

2.1 Previous Designs from Literature

In an effort to produce synchronized alternating droplets from two sources inside a single microchannel, there has been a lot of work by different research groups. First of all Barbier et al. [30] reported producing droplets from two sources using two separate T-junctions and then combining the main channels of these separate T-junctions to collect the droplets inside one microchannel. In this way they were able to collect the two droplet types in the same microchannel. But this design lacked compactness and reliability since there is the chance of coalescence at the intersection of the two main channels. Secondly Tan et al. [31] reported forming

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droplets from two sources inside the same channel by having two T-junctions at a small distance from each other; which means that the same stream of continuous phase was shearing the droplets from the two dispersed phase streams inside the main channel. In this case the synchronization of droplet to form a droplet train would become a challenging task since the droplets from each stream form independently from each other.

Another design in this regard has been reported by Frenz et al. [32] in which an oil stream that flows through a central channel forms droplets by shearing the dispersed phase streams flowing in the two side channels, after which the droplets from the two sources are led to a common channel parallel to but narrower than the main oil channel. Again in this design there is a possibility that the droplets from the two sources might merge once they enter the common channel. Hong et al. [33] reported the production of alternating droplet generation in a similar way but their design had additional components like the furcated junction, pressure oscillator, a converging junction and a y-junction. All these designs are limited to either pattern formation or applications that involve merging of the two phases like chemical reactions. In contrast to these designs, Zheng et al. [18] used a cross junction device to form synchronized alternating droplets from two sources in the same microchannel, and this particular design can be used for the purpose of forming a droplet train as well as for merging applications.

Byung-Ju et al. [34] used inclined channels at the sides having an inclination of 45◦ with the main channel for more efficient alternating droplet production. Later in the main channel they also studied mixing of the droplets from two sources. On the other hand Ngo et al. [23] used a range of angle of inclination of the side channel with the main channel and they deduced that an angle of 60◦ was optimum for an alternating digitized pattern formation. It must be noted here that these studies were not focused on studying alternating pattern rather they were focused on studying mixing of droplets once they are generated in the former case and studying different regimes of droplet formation in the latter case. Wang et al. [35] reported a device capable of accommodating gas/liquid/liquid three phase flow inside the same microfluidic channel. In their design, they used

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two T-junctions at a specific distance from each other. At the first T-junction, gas bubbles were formed by the continuous phase which in this case was water and was flowing into the main channel from the side channel. The gas which was air in this case was flowing in the main channel from the start and hence when the gas bubbles reach the second T-junction, they shear the organic oil flowing in from the side channel hence forming a droplet of the oil. Therefore water is acting as the carrier fluid and the gas and oil are the dispersed phases flowing in the main channel.

Figure 2.1: Schematic showing the design of the microfluidic device having tapered channels at the side inlets.

2.2 Finalized Design

In this work the typical cross-junction device geometry is modified to study the effect of taper angle of the dispersed phase channel on the pattern formation and repetition. It is proposed that since the alternation of droplets from the two sources is dependent on the push-pull mechanism [19], therefore the hydrody-namic resistance of the side channels would play a vital role in pattern repetition. So considering the facts that the hydrodynamic resistance depends on the width and height of a rectangular channel and that the width of the side channel should

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be smaller than the width of the main channel at the junction, it was decided that the side channels of the cross-junction device should be tapered as shown in Figure 2.1.

The width of the main channel is 150 µm and the width of the side channels is 60 µm. The reason for having the ratio of side channel width to main channel width less than 1 is that in this way the droplets will be formed near the junction and in this way the two droplet streams will have minimum time to interact with each other and thus cross-contamination will be prevented. The height of the entire microchannel device is designed to be 90 µm. The devices are fabricated using the standard soft lithography technique [36],[37] which will be discussed later in the document.The working fluids used in this study are olive oil (viscous continuous phase) and deionized water (dispersed phase). In cases where the viscosity of the dispersed phase needs to be varied, glycerol is used as a means of varying the viscosity. No surfactant [38] is used so that the performance of the device could be monitored purely based on geometry.

The fluids were injected by means of syringe pumps and the plungers were connected to the device through capillary tubing. After the fabrication procedure, the microchannels were primed with the continuous phase so as to render the channel surface hydrophobic.

2.3 Fabrication of the device

The fabrication of each microfluidic device was done using the conventional soft lithography technique. The SU8 master mold was prepared on a polished 4” Si wafer in the clean room by using the Mask Aligner and Nanoimprint Lithography equipment as shown in Figure 2.2. After making the SU8 master, the PDMS mold was prepared in the microfluidics laboratory and then it was bonded to a glass slide using the Plasma Cleaner in the lab. The steps for this are also shown in Figure 2.2. The entire process, the description of each step and the locations where each step was performed are tabulated in Table 2.1.

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Figure 2.2: Schematic showing the steps followed for the fabrication of the microfluidic device.

2.4 Characterization of the Devices

While observing the droplet generation from each of the devices, the emphasis is on carefully observing three things in particular: droplet generation pattern, droplet size and droplet spacing.

2.4.1 Droplet generation pattern

The pattern of droplet formation is important for several reasons. Firstly the pattern can be used as a barcode; therefore it is important that the pattern is

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Table 2.1: Fabrication Process StepNo. Name of

process Description Locale 1 Cleaning A 4 inch Si wafer is cleaned using

acetone, IPA, water and then dried

UNAM cleanroom 2 Spin-coating The wafer is then coated with

SU 8 2050

UNAM cleanroom 3 Pre-bake The sample is baked at

65 C & 95 C

UNAM cleanroom 4 Exposure The sample is then exposed

to UV light

UNAM cleanroom 5 Post-bake The sample is again baked at

65 C & 95 C

UNAM cleanroom 6 Development Sample is developed in the

developer solution UNAM cleanroom 7 PDMS mould making

PDMS is mixed with curing agent, poured ontothe sample, baked and then peeled off to form mould

Microfluidics lab

8 PDMS bonding

PDMS mould is then bonded to glass using Plasma cleaner after making holes for inlets and outlets

Microfluidics lab

9 Tube fixing

Plastic capillary tubing is fixed in the holes and sealed with epoxy

Microfluidics lab

accurately and repeatedly produced. Secondly for the droplets to be mixed later and be used for a chemical reaction then it is again essential that the pattern is repeated otherwise the concentration of reactants in the mixture will be imprecise.

2.4.2 Droplet size

The droplet size determines what volume of fluid is trapped inside the interface between the continuous and dispersed phase inside the microchannel. It is very significant because it determines what concentration of that reagent is involved in a chemical reaction. Moreover if the device is to be used with automation, then the droplet size needs to be extremely precise because it is going to influence

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Table 2.2: Table showing the values of taper angles and average widths of side channels in each case

Device Number Taper Angle (α) Average width (µm) 1 0 60 2 5 760 3 10 1480 4 15 2205 5 20 2980 6 25 3750

how the sensors respond to the movement of the droplets inside the microchannel network. The droplet size values within ±10% of the average droplet size for that flow rate combination is regarded as an acceptable droplet otherwise it is excluded from the efficiency. The average droplet size values for different values of α and different flow rate combinations are given in the Appendix C.

2.4.3 Droplet spacing

Similar to the case of droplet size, the droplet spacing is also an important pa-rameter to control if the device needs to be used with automation and droplet merging. The droplet spacing values within ±10% of the average droplet spacing for that flow rate combination is regarded as acceptable otherwise it is excluded from the efficiency. The average droplet spacing values for different values of α and different flow rate combinations are given in the Appendix C.

2.5 Performance parameters

In order to be able to compare the performance of devices, a couple of parameters are introduced that are indicative of the device performance; efficiency ψ and number of droplets per stream n. Efficiency is defined as the number of droplet pairs that were successfully generated out of a hundred consecutive droplet pairs.

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All droplet pairs that did not fulfill the criteria of pattern, size and spacing were excluded from the efficiency. Number of droplets per stream is the average number of droplets generated by each stream successively.

2.6 Methods

Two major sets of experiments were performed on each of the devices. In the first experiment set the continuous phase flow rate was fixed at 2.0 µl/min and in the second set it was set at 3.0 µl/min. In each of the experiment sets, the dispersed phase flow rate was varied, hence the flow rate fraction φ was varied. This is shown in Table 2.3.

Table 2.3: Experiment sets Case # Qc Qd1 Qd2 (φ) Case # Qc Qd1 Qd2 (φ) (µl/min) (µl/min) 1 2.0 0.15 0.15 0.13 7 3.0 0.2 0.2 0.12 2 0.2 0.2 0.17 8 0.3 0.3 0.17 3 0.3 0.3 0.23 9 0.5 0.5 0.25 4 0.4 0.4 0.29 10 0.6 0.6 0.29 5 0.5 0.5 0.33 11 0.8 0.8 0.35 6 0.6 0.6 0.38 12 0.9 0.9 0.38

In this section, the observations made during the experiments that were listed in Chapter2 will be discussed. After the process of priming each microfluidic device with the continuous phase, the dispersed phase is injected into the side channels. Later, the flow rates for each phase are set and the device is allowed to reach steady state. Once the steady state is reached, the observations are made through the camera attached to the microscope.

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2.7 Results

The first among the set of values used for taper angle α was zero. This means that the side channels in this case were straight. Therefore the average width of the channel was almost equal to the width at the junction. In the case of this device, the droplet generation pattern was not repetitive for most of the observations and droplets were generated randomly from each dispersed phase inlet and in many instances there was unusual droplet merging at the junction as well. The droplet size was also varying considerably during the droplet generation. Additionally, due to the random sequence of droplet generation and deviation of individual droplet size from mean droplet size, the droplet spacing was non-uniform.

Figure 2.3: Figure showing droplet generation in case of different values of α starting from α = 0

The next value of α that was used was 5◦. The side channels of the device were inclined at 5◦ to the vertical axis. As a result of this taper, the average width of the channels was different to the width of the side channels at the junction. In this case it was observed that the non-uniformity in the droplet size and droplet spacing, which was observed in case of straight channels, had been eliminated. But the pattern of droplet generation was disrupted occasionally. The most important observation in this case was that more than one consecutive

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Table 2.4: Observations in case of different values of α for the case 2.0 µl/min and 3.0 µl/min Alpha α Number of droplets per stream n Highest Efficiency Flow rate fraction φ 2.0 µl/min 10 4 51 0.12 15 1 74 0.23 20 1 78 0.29 25 1 97 0.38 3.0 µl/min 10 4 58 0.12 15 1 69 0.29 20 1 86 0.12 25 1 92 0.12

droplet was generated from each dispersed phase stream in this device. This is the parameter that is defined as n in the previous chapter. The value of n for this device was 6.

Further the value of α is increased to 10◦. Since the angle of taper is increased, the average width also increases as compared to the average width in case of lower angles. A similar trend was seen in the case of this device, except that the value of n in this case was lower as compared to the case of 5◦. In other words each stream of dispersed phase produced n number of consecutive droplets in succession but the value of n is 4.

Moving further to the next value of α which is 15◦, it was observed that the number of sequenced droplets (n) further decreased in this case and it is with this device that alternating droplet generation was observed but with very low efficiency. It is worth mentioning that the droplet size and spacing was observed to be uniform in the case of this device. This is the device which was reported to show alternating droplet generation with lowest efficiency. The pattern of alternation was regularly disrupted, but the disruption was far less than that in case of α = 0.

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A further increment of 5◦, (α = 20◦) showed the continuation of the same pat-tern observed throughout. The number of consecutive droplets per each stream reduced and remained at one. The efficiency of the pattern was around 80% as compared to 70% in case of 15◦. The droplet size and spacing were uniform in this case as well. Since the efficiency seems to increase with an increase in taper angle of the side channels, it was decided to further increase the value of α to see if the efficiency of droplet generation pattern increases further. This trend is demonstrated in Table 2.4

In the case when the value of α was increased to 25◦, the pattern of alternating droplet was repeated with the highest efficiency as compared to all other values of α. The device was generating droplets from the two sources in a synchronized pattern one after the other. The size of the droplets was uniform and the spacing between adjacent droplets was constant. Another important observation was that as one of the droplet sources was forming a droplet, the other source was pushed back into its side channel. The highest value of efficiency achieved was 98%.

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Chapter 3 Mechanism of droplet generation

In the previous chapter the observations made when the taper angle of the side channels is increased in a cross-junction device were discussed . These observa-tions lead to the conclusion that having a higher taper angle has a positive effect on pattern repetition, droplet size and droplet spacing for alternating droplet generation.

In this chapter I will discuss the physics behind this phenomenon and how the increment in the taper angle leads to a more stable and uniform alternating droplet generation. This will be done in three steps. In the first step the quanti-tative analyses of the droplet generation efficiency and its statistical analysis by calculating the efficiency of the droplet generation devices, that relation to taper angle is discussed. Next the head and tail radius of curvature of the droplet in-stantaneously before break off will be measured and plotted which will be used to calculate the Laplace pressure at the time of breakup. Comparison of Laplace pressure values at droplet breakup point, will reveal the governing mechanism behind the alternation of droplets. Finally, as the third step, a computational model will be discussed to confirm our hypothesis and therefore reach a conclusion about the role of taper angle in the stable alternating droplet generation.

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3.1 Efficiency of Droplet Generation

In Chapter2 the performance measures as efficiency ψ and n were introduced and defined. To ensure that the efficiency is a fair indicator of the device performance, 100 consecutive droplets generated by the device are observed . The number of droplets generated in the correct sequence with uniform droplet size and spacing is recorded as the efficiency of the device at that flow rate.

Figure 3.1: (a)Graph of efficiency (ψ) vs flow rate fraction (φ) for n=1 with Qc= 2.0µl/min. (b) Graph of efficiency (ψ) vs flow rate fraction (φ) for n=1

with Qc= 3.0µl/min. (c) Graph of number of consecutive droplets (n) vs flow

rate fraction (φ) with Qc = 2.0µl/min. (d) Graph of number of consecutive

droplets (n) vs flow rate fraction (φ) with Qc = 3.0µl/min

Figures 3.1a & 3.1b show the efficiency of droplet generation ψ at 2.0 and 3.0 µl/min respectively plotted for different values of α over a range of flow rate fraction values. It can be seen from these figures that the efficiency is the lowest

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for the lowest value of α which is zero, and it gradually increases to a maximum as the value of α is increased to 25◦.

Figure 3.2: (a)Failed attempt in which droplet dimensions are not uniform (α = 0). (b) Alternating droplet generation with n=2 (α = 10).(c) Failed generation attempt; number of black and red droplets are unequal (α =15).(d) Alternating droplet generation with n=1 (α =25◦).

This trend can be related to the trend seen in Figures 3.1c & 3.1d in which number of consecutive droplets per stream n is plotted at Qc= 2.0 µl/min and Qc

= 3.0 µl/min for different values of α over a range of flow rate fraction values. In these figures it can be seen that when α is zero, the efficiency of alternating droplet generation is the lowest because of the absence of any pattern and because of repeated variation is droplet size and spacing as shown in Figure 3.2a. For higher values of α (5 − 10◦), the value of n is greater than 1 as shown in Figure 3.2b and it denotes the presence of some instability in the droplet generation process even though it is less than that in case of α = 0. As the value of α increases further, the value of n decreases steadily until it reaches 1 but still at α 15 and 20 the efficiency is low as shown in Figure 3.2c which points to the fact that the instability in droplet generation is gradually decreasing but is still not eliminated. As the value of α is further increased to 25◦, the number of droplets is reduced to one and the efficiency reaches the highest value which is around 98% as shown in Figure 3.2d. Therefore the highest angle shows the most stable and repetitive pattern in alternating droplet generation.

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3.2 Governing Physics Behind Alternating Droplet

Generation

3.2.1 Evaluating the Capillary Number

The droplet formation inside a T-junction device is governed by three forces; the interfacial tension, force due to the increased resistance of continuous phase flow provided by the dispersed phase stream entering the junction and blocking the channel, and the shear force applied by the continuous phase on the dispersed phase stream [39] [40]. The Bond number was evaluated for this system and since the value of the Bond Number comes out to be far less than 1, therefore it can be safely concluded that the effect of gravitational forces is negligible. The Capillary number is the criterion for determining which force is dominant in the droplet formation process as has been already discussed in Chapter1. Here the values relevant to our study to evaluate the Capillary number are used.

For evaluating the Capillary number Ca the values used are: Viscosity (µ) = 0.0562N s_m2 [41], Speed (U ) = 2.32 × 10

−3_{m/s, Cross-sectional area (A) = 1.49 ×}

10−8m2_{, and Surface Tension (γ) = 1.642 × 10}−2 N m[42].

Ca = µU_γ = 7.94 × 10−3

It can be concluded from the Ca number range that droplet generation is in the regime known as squeezing in which the interfacial forces are dominant over shear forces. Another conclusion that can be inferred from this is that the decisive factor in droplet generation is the pressure field over the droplet surface. A droplet will form only when the resultant pressure applied by the continuous phase stream on the dispersed phase is greater than the resultant pressure applied by the dispersed phase stream. This resultant pressure applied by the dispersed phase stream can be calculated by finding the difference between the pressure inside the dispersed phase inlet channel and the Laplace pressure change over the surface of the evolving droplet. For that reason it is essential that the radii

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of curvature are experimentally measured and from that the Laplace pressure change over the surface of the evolving droplet is calculated.

3.2.2 Total Pressure Drop Across the Junction

In order to fully understand the mechanism of droplet generation in the cross-junction device, it is important to consider the total pressure drop across the junction in case of the tapered channels which is given by Equation (3.1)

PT T 1= PS+ ∆PT S1 (3.1)

Figure 3.3: The sequence of alternation in case of tapered channels shows how the two streams alternate in a perfectly synchronous pattern and as one stream enters the junction, the other stream is pushed back into the side channel. ∆PT S1= γ 1 RT + 1 rT − 1 RH − 1 rH (3.2)

Where, PT T 1is the resultant pressure drop across the junction due to T S1, PS

is the steady pressure drop across the junction, ∆PT S1 is the Laplace pressure

difference of the head and tail parts of the evolving droplet of T S1, rH and rT

are the head and tail radii respectively in the radial direction, RH and RT are

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As the tapered stream 1 T S1 starts filling the junction as shown in Figure 3.3a, there is a pressure accumulation upstream of the junction. Equation (3.1) defines the total pressure drop at the junction due to T S1.

From Figure 3.3b it can be seen that radius of curvature of T S1 becomes higher due to which ∆PT S1 is reduced which in turn means that the value of

PT T 1 becomes less according to Equation (3.1). Moreover it is observed that T S2

is squeezed back into the side channel (Figure 3.3c) due to the pressure increase upstream of the junction. In the meantime due to this squeezing back of T S2, ∆PT S2 (Laplace pressure difference of the head and tail parts of the evolving

droplet of T S2) is reduced according to Equation (3.2), and the reason for this is that the value of curvature is reduced. However there are a couple of reasons due to which the T S2 is squeezed back into the side channel instead of entering the junction. It can be seen that while the T S1 evolves in the junction, as shown in Figure 3.3c, the passage of the oil phase is hindered and it can only pass through the small side gaps between the stream and the channel walls. This results in pressure accumulation at the junction and leads to an auxiliary hindrance for the T S2 apart from the hindrance from T S1. Moreover, the change in radius is insignificant for T S2 in comparison to the change in case of T S1 as shown in Figure 3.3c.

As shown in Figure 3.3c, RH and RT attain highest values and then return back

to their original lowest values right after the droplet detaches (Figure 3.3d), and the cycle continues (Figure 3.3e). During this time the values of the curvatures (radial and axial) fluctuate from infinity then to its initial value. So, as per Equation (3.2), the ∆PLmax maximum pressure difference between the head and

tail parts of the evolving droplets which occurs instantaneously before break off can be simplified as per Equation (3.3) if the insignificant difference between the head and tail radii respectively in the radial direction is neglected. In this equation the radii of curvature of the head and the tail part of the evolving droplet instantaneously before break off in the axial direction are denoted by RHc and

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∆PLmax= γ 1 RT c − 1 RHc (3.3)

Figure 3.4: The sequence of alternation in case of straight channels shows how the two streams enter the junction at the same time without any syn-chronous pattern and the droplet size and spacing is also non-uniform.

Furthermore after the droplet is formed from T S1, (Figure 3.3d) the junction is immediately unclogged and pressure accumulation at the junction is released because continuous phase fluid has an unhindered path to flow. In the meantime T S2 is unable to enter the junction until 160 ms as shown in Figure 3.3 because of the high pressure at the junction. But as soon as the droplet of T S1 detaches from its stream, T S2 enters the junction since now it is opposed by very low pressure resistance from T S1 and the continuous phase fluid (Figure 3.3d). Moreover as it can be seen in Figure 3.3e, T S1 is pushed back into its side channel and the pattern repeats itself over and over.

Figure 3.4a shows the initiation of the sequence of a droplet pair generation for the case of straight channels at the dispersed phase inlets. For this case the total pressure drop across the junction is defined as shown in Equation (3.4)

PST 1= PS+ ∆PSS1 (3.4)

Where, PST 1 is the total pressure drop across the junction due to SS1, PS

is the steady pressure drop across the junction, ∆PSS1 is the Laplace pressure

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At this point it would be appropriate to compare the droplet pair generation in case of both devices by looking at the surface evolution of each stream during one pair generation cycle. By observing the entire sequence of pair generation in case of both devices, the difference in pattern generation is pointed out . From Figure 3.3c it can be inferred that T S2 is squeezed into the side channel but because of the tapered shape of the side channel, the radius of curvature of T S2 starts to increase due to which ∆PT S2 decreases according to Equation (3.4) and

T S2 has the tendency to enter the junction after a droplet is detached from T S1. However, in case of straight side channels (see Figures 3.4b & 3.4c), there is no change in radius of curvature of the stream as the cross section of the channel is uniform throughout. Therefore in this case ∆PSS1 and PST 1will remain constant;

and hence SS2 is unable to enter the junction unhindered after SS1 has formed a droplet.

3.2.3 Radius of Curvature Measurements and Laplace

Pressure

As it has already been pointed out in our earlier discussion: the synchronized alternation of droplets is dependent on the ability of the latter stream to enter the junction (see Figures 3.4d & 3.4e), hence the axial head and tail radii of curvature instantaneously before break off ( RHc and RT c), shown in Figure 3.5,

are significant in the study of the occurrence of alternation of droplet pairs. Using the data from our experiments, RT c and RHc are measured (see Figure

3.5) for ten consecutive droplets and the average of these ten values is used as the radius of curvature value. This process is conducted for the flow rate combination: Qc = 2.0 µl/min and Qd = Qc µl/min for each value of α and the results are

plotted and shown in Figures 3.6a & 3.6b. It is most appropriate to use either range or standard deviation error bars since the data belongs to a single group. In order to include all the values that may occur, I have used the standard deviation error bars in these two plots [43]. As shown in Figures 3.6a & 3.6b, the values of RT c and RHc are lower for high values of α than they are for low values of α.

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Figure 3.5: Radius of curvature at the head and tail of the emerging droplet instantaneously before break-off RHc and RT c respectively

By using the Equation (3.3), the values of ∆PLmax were evaluated from the

average of the ten successive radii of curvatre values for each value of α and the results were graphed in Figure 3.7. The trend of the plot suggests that the value of ∆PLmax is high in case of high values of α than they are for low values of α.

If this trend is applied to Equation (3.2) and Equation (3.4), it can be clearly seen that the pressure drop at the junction instantaneously after break off of one droplet will be higher in case of high values of α which means that the other stream will be able to enter the junction with less resistance and will be able to push back the other stream into the side channel. This will result in synchronized alternating droplet generation.

3.3 Numerical Study

1

In order to understand the difference in alternating droplet generation mechanism in case of straight and tapered channels, it must be pointed out that in case of straight channels at side inlets, SS1 still enters the junction even after generating a droplet, and while SS2 is still generating a droplet (Figure 3.4e). Contrary to that, observing the experiments with the device with tapered channels, as can

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Figure 3.6: Plots showing the variation of radii of curvature at the head and tail of the emerging droplet instantaneously before break-off RT c and

RHc respectively for each value of α for the flow rate combination: Qc = 2.0

µl/min and Qd = 0.2 µl/min

be seen in Figure 3.3e, T S1 retreats into its side channel during the time T S2 is forming a droplet. This difference in the observation in case of the two devices suggests that there is a specific pressure gradient between the two streams in case of higher values of α, therefore while one stream is producing a droplet the other stream retreats into its inlet channel. In contrast to that the straight channels case does not have a pressure gradient between the dispersed phases and due to which random behavior is observed continuously since the two of them enter the junction at the same time.

Table 3.1: Comparison of droplet length in case of Experiments and Com-putation Type of Value Average Droplet Length (µm) Experimental 217.8 Computational 210.7

In order to confirm our theory, a computational study is performed using COM SOLM ultiphysics®using 2D geometry, and since the radial curvatures are approximately the same for the droplet instantaneously before break off therefore using 2D simulation for that instant is a fair approximation. The droplet lengths

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Figure 3.7: Plot showing the variation of maximum pressure difference between the head and tail parts of the evolving droplets which occurs instan-taneously before break off for each value of α for the flow rate combination: Qc = 2.0 µl/min and Qd = 0.2 µl/min

for the experiments and the simulation are compared in Table 3.1. The develop-ment of the oil-water interface for a single droplet pair can be seen in Figure 3.8a. The points A and B are the points of highest pressure variation throughout the droplet pair generation which is why they have been selected to show the pres-sure variation, and the plotted results are shown in Figure 3.8b. Initially at time t = 0.46s, the pair of streams rival to enter the junction but because the pressure at A is higher than the pressure at B at that point in time, T S1 slides into the junction. While T S1 grows into the junction, T S2 retreats (Figure 3.4a) because in this duration the pressure at B is greater than the pressure at A. Moreover, just before break off, the pressure at A is 983 Pa at t = 0.82s, and using this value can be found PT T 1 (Equation (3.1))which is evaluated as 284 Pa. Using Figure

3.7, the ∆PLmax for α = 25◦ comes out as 259 Pa. Therefore rest of the pressure

drop according to Equation (3.1) is in the form of steady pressure drop PS which

may be approximated to be equal in all cases of α. All in all, it can be clearly observed that PT T 1 is higher in case of higher value of α. All these observations

conclusively show that there is greater pressure build-up at the junction in case of lower values of α. I will use the expression for the hydraulic resistance of a fluidic channel which is shown in Equation (3.5) to explain this difference in pressure build-up:

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RHyd=

12µL wh3_{(1 − 0.63}h

w)

(3.5)

where L is the length of the channel, w is the width of the channel and h is the height of the channel.

Figure 3.8: (a) Surface plot for the evolving droplets in one complete alter-nating droplet generation cycle.(b) The pressure variation at two points in the side inlets showing pressure fluctuations for the evolving droplets during one complete alternating droplet generation cycle, for α = 25 and for the flow rate combination: Qc = 2.0 µl/min and Qd = 0.2 µl/min

In all of our microfluidic devices, the parameters are identical except the width of the side channels that are shown for different values of α in Table 2.2.In case of the tapered channels the width of the side channels is taken as the average of the two end widths of the side channel. The lower values of α have a lower width w due to which the RHyd (hydraulic resistance) is very high as per Equation (3.5),

while the value of w is considerably high for higher values of α, and hence in that case the RHydis far lower. This in turn means that the tapered channels allow the

stream producing a droplet to freely generate a droplet without any interruption from the other stream because the low value of RHyd allows the other stream to

retreat easily onto its channel. Whereas in case of lower values of α, the high resistance causes both streams to enter the junction at the same time and hence disrupt the synchronized alternating pattern.

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By analyzing the data from the experiments designed in Chapter2, it is con-cluded that the alternating pattern of droplets from two sources is highly influ-enced by the angle of taper α. At low values of α, the resistance of the side inlet channels is higher due to the lower cross-sectional area and specifically due to the smaller width of the channels due to which both streams display haphazard behavior and enter the junction at the same time without any pattern or synchro-nization2_{. Whereas at higher values of α, the average width of the side channels}

is higher which leads to lower RHyd (hydraulic resistance) and hence one stream

is pushed back into its side channel as the other is producing a droplet which results in synchronized alternating droplet generation.

2_{This work was published as a Research Article in the Journal Scientific Reports on January}

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Chapter 4 Barcode Generation in case of

Identical and Different Viscosities

In the previous chapter the effect in case of increasing the taper angle of the side channels on the synchronization of alternating droplet pattern formation in a cross junction device was described . In this chapter it will be discussed how the taper angle influences the formation of droplet barcodes such as m:1 (where m is an integer greater than 1) in case of identical and different viscosities of the dispersed phases. I will also discuss the formation of droplet barcodes in case of two fluids mixing in the side channel and forming a droplet from the side channels in case of identical and different viscosities.

It has already been stated that the repetition of pattern in alternating droplet generation is crucial to the device’s usefulness in automation. Likewise, to be able to continuously distinguish between the two droplet sources it is extremely important to be able to maintain a repeating barcode. Moreover using viscous and non-viscous reagents inside the same plug enhances mixing inside the plug [44]. For this purpose experiments were performed to determine how different barcodes could be generated having droplet ratio as m:1. These experiments can be broadly categorized into two types; case one is when the viscosity of the two dispersed phase streams is equal and case two is when the viscosities of the two

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dispersed phase streams are different from each other. For further investigation a single channel and two channels combining into a single channel at each of the sides of the cross junction device have been used. For being able to relate the flow rates of the dispersed phases to the pattern of droplet generation, the ratio of the flow rate of dispersed phase streams Ω expressed by Equation 4.1 is introduced.

Ω = Qd1 Qd2

(4.1)

4.1 Single Channel at Dispersed Phase Inlets

4.1.1 Equal Viscosity case

Since better results for synchronized alternating droplet generation were obtained from the device with tapered side channels, the same device was tested for gen-erating different barcodes. In this case, the dispersed phase was deionized water without any additives expect soluble dyes in order to distinguish between the droplets, the flow rate of the continuous phase was kept constant at 2.0 µl/min and the dispersed phase flow rates were started from 0.2 µl/min and gradually the flow rate of the red dispersed phase was increased until a stable pattern of droplets was observed.

Figure 4.1: The droplet pattern generation in case of 2:1 and 3:1 for identical viscosity case

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The Table 4.1 shows that as the flow rate ratio becomes 2:1, the droplet gen-eration ratio also becomes 2:1 as shown in the Figure 4.1. Furthermore, as the flow rate of the red dispersed phase is further increased and the ratio reaches a value of approximately 3, the pattern of droplet generation is observed to assume the same value as shown in the Figure 4.1.

Table 4.1: Table showing pattern formation and corresponding flow rate combinations Case # Qc (µl/min) Qd1 (µl/min) Qd2 (µl/min) Flow rate ratio (Ω) Observations 1 2.0 0.40 0.2 2 Pattern Observed 2:1 2 0.7 0.2 3.5 Pattern Observed 3:1

4.1.2 Different Viscosity case

To test the effectiveness of the device with dispersed phases of different viscosity flowing in each side channel, mixture of deionized water and glycerol is used. Since glycerol is more viscous than water and also soluble in water, it can be used to vary the viscosity in this case [45]. The Table 4.2 shows the samples prepared and the composition and viscosity of each sample.

Table 4.2: The composition and viscosity of each sample prepared

Sample # Mass fraction glycerol (xg) Viscosity of Solution (mPa.s) 1 0.318 2.49 2 0.390 3.71 3 0.620 10.0

In the case of different viscosity, there were patterns observed for synchronized droplet generation. In this case the device with taper angle 25 is used and the less viscous mixture of water and glycerol (sample 1) as one dispersed phase with flow rate 0.15 µl/min and deionized water as the other dispersed phase with flow

Effect of channel geometry on alternating droplet generation

EFFECT OF CHANNEL GEOMETRY ON

ALTERNATING DROPLET GENERATION

a thesis submitted to

the graduate school of engineering and science

of bilkent university

in partial fulfillment of the requirements for

the degree of

master of science

in

mechanical engineering

By

Muhammad Saqib

May 2018

ABSTRACT

EFFECT OF CHANNEL GEOMETRY ON

ALTERNATING DROPLET GENERATION

¨

OZET

T ¨

URKC

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Acknowledgement

Contents

List of Figures

List of Tables

Chapter 1

Introduction

1.1

Flow Types in Microfluidic Devices

1.1.1

Continuous Flow Microfluidic Devices

1.1.2

Droplet Based Microfluidic Devices

1.2

Droplet Based Microfluidic Devices

1.2.1

T-Junction Devices

1.2.2

Co-Flowing Devices

1.2.3

Flow Focusing Devices

1.3

Synchronized Alternating Pattern

Genera-tion Microfluidic Devices

1.4

Thesis Overview

Chapter 2

Design of Microfluidic Device

2.1

Previous Designs from Literature

2.2

Finalized Design

2.3

Fabrication of the device

2.4

Characterization of the Devices

2.4.1

Droplet generation pattern

2.4.2

Droplet size

2.4.3

Droplet spacing

2.5

Performance parameters

2.6

Methods

2.7

Results

Chapter 3

Mechanism of droplet generation

3.1

Efficiency of Droplet Generation

3.2

Governing Physics Behind Alternating Droplet

Generation

3.2.1

Evaluating the Capillary Number

3.2.2