DROPLET FORMATION AND ENTRAINMENT IN LIQUID-GAS

MICROFLUIDIC SYSTEMS

A Thesis Presented

By

Pooyan Tirandazi

to

The Department of Mechanical and Industrial Engineering

in partial fulfillment of the requirements

for the degree of

Master of Science

in the field of

Mechanical Engineering

Northeastern University Boston, Massachusetts

August 2017

ii

TABLE OF CONTENTS

LIST OF FIGURES……………………………………………………………………………………………………………...iii

LIST OF TABLES………………………………………………………………………………………………………………. vi

ABSTRACT……………………………………………………………………………………………………………………… vii

Chapter 1. Introduction …………………………………………………………………………………………………….. 1

1.1 Microfluidics and Droplet Microfluidics ......................................................................... 1

1.2 Droplet Generation in Microfluidic Networks ................................................................. 3

1.3 A Guide Through the Thesis ............................................................................................ 7

Chapter 2. Gas-Liquid Droplet Microfluidics …………………………………………………………………….. 9

Chapter 3. Experimental ………………………………………………………………………………………………….. 12

3.1 Fabrication of Microfluidic Devices .............................................................................. 12

3.2 Control and Modification of Microchannel Surfaces..................................................... 15

3.3 Experimental Setup ........................................................................................................ 19

Chapter 4. Flow Regime Mapping …………………………………………………………………………...………. 22

Chapter 5. Dripping Regime Characterization ……………………………………………………………………27

5.1 Generation Frequency .................................................................................................... 27

5.2 Droplet Morphology ...................................................................................................... 29

5.3 Droplet Monodispersity ................................................................................................. 35

Chapter 6. Conclusions ………………………………………………………………………………………………........ 38

REFERENCES…………………………………………………………………………………………………………………... 40

iii

LIST OF FIGURES

Figure 1. A comparison of mixing reaction in a standard pressure-driven continuous-flow

microfluidic platform (a) and using a droplet-based microfluidic system (b). In a continuous-flow

scheme due to wall effects and different residence times mixing happens slower. However, by

digitizing the mixing reaction inside distinct droplets, each droplet is mixed much faster and the

total mixing time is reduced significantly as a result [13]. .............................................................. 2

Figure 2. Schematic representation of the most frequently used geometries in microfluidics for

droplet formation. (A) T-junction or cross-flow geometry, (B) co-flow geometry, and (C) flow-

focusing geometry. ........................................................................................................................... 5

Figure 3. Representation of dripping and jetting inside microfluidic capillary tubes [23]. (A)

Dripping regime; here droplet formation occurs at the tip of the inner capillary in the dripping

regime. (B) Jetting regime; in this case instabilities of an extended liquid jet creates droplets

which are commensurate to the jet diameter and are usually smaller in comparison to the dripping

regime. ............................................................................................................................................. 5

Figure 4. Axisymmetric flow-focusing architecture for controlled production of droplets using a

focusing air in a non-microfluidic format [52]. Here, the applied air pressure across the circular

orifice results in breakup of the liquid jet into individual droplets. ............................................... 10

Figure 5. Schematic representation of the fabrication procedure for production and assembly of

microfluidic devices. (1) Required channel geometry is designed and printed on transparency

sheets. (2) UV photolithography process is performed using the printed mask to define the

patterns on a negative photoresist that is coated on a silicon substrate. (3) After mold fabrication

soft lithography using PDMS prepolymer is performed to replicate the channels from the mold

into the elastic polymer. (4) After PDMS being solid, each device is cut and punched for the

inlets/outlets. (5) PDMS chips are bonded to a clean glass slide after being plasma cleaned. (6)

Final microfluidic device for water droplet formation in air. (7) Image of the flow-focusing

junction under microscope. Liquid water is injected through the middle channel and meets the

two side air streams at a flow-focusing junction. The microchannels’ depth is 40μm. ................. 14

Figure 6. Schematic of the method used treating the microchannel walls with fluorosilane

chemical. All the setup are placed inside a vacuum chamber in order to prevent the deposition of

toxic fluorosilane vapor into the environment. .............................................................................. 16

iv

Figure 7. Interaction of liquid and gas in different channel conditions. (A) After plasma

treatment; in this situation channels are hydrophilic and as a result the liquid water tends to

adhere to the side walls of the microchannel once it enters the junction. (B) After modifying the

channel walls with vaporized fluorosilane. In this case, the droplets could form in the channel.

However, due to the challenges in the coating process the generation was not reproducible. (C)

After post-baking step; here the PDMS has regained its hydrophobic nature and droplets maintain

their morphology after generation.................................................................................................. 17

Figure 8. Comparison of the surface tension forces between a glass-PDMS microchannel (left)

and a PDMS-PDMS microchannel (right). Using the provided contact angles in the table, the net

surface tension force for a glass-PDMS combination is less. Therefore, it provides less resistance

during the course of droplet generation and movement inside the channel which results in a more

reproducible formation process. ..................................................................................................... 19

Figure 9. Schematic of the flow circuit for liquid and gas control. ............................................... 20

Figure 10. Actual image of different parts of the experimental setup. (1) Air desiccator, (2)

manual coarse pressure regulator, (3) voltage-controlled valves, (4) mass flow sensors, (5) needle

valves, (6) liquid syringe pump, (7) white light source for the microscope, (8) high-speed camera

connected to the microscope, and (9) microfluidic chip placed on the microscope with all the

ports connected to their corresponding tubing. .............................................................................. 21

Figure 11. Flow regime map of water-in-air droplet formation in a planar flow-focusing

microfluidic device. Different flow regions are distinguished with different colors. The transition

between the flow regimes is also represented as a finite shaded region rather than a solid line to

account for the uncertainties associated with the experiments and calculations of the We values.

....................................................................................................................................................... 25

Figure 12. Comparison of the flow map for chips with different liquid channel sizes. The area for

the Dripping region (the green region) is reduced as the liquid channel size increases. However,

the Threading and Co-flow regions have expanded as a result of increase in the surface tensions

forces that holds the thread and prevents the detachment at lower gas flow rates. ........................ 26

Figure 13. Experimental data of droplet generation frequency as a function of air flow rate for

different liquid flow rates. We can see that there is a relatively linear correlation between the

frequency value and the air flow rate. ............................................................................................ 28

Figure 14. Experimental data of droplet generation frequency at increasing liquid flow rate for

two different gas flow rates. We can see that there is a relatively linear correlation between the

frequency value and the liquid flow rate. ....................................................................................... 28

Figure 15. Experimental data of the non-dimensioalized droplet generation frequency.

Generation frequency in this system can be scaled as ƒ∝QGQL. ................................................... 29

Figure 16. Experimental data of droplet width inside the microchannel for different liquid and

gas flows. ....................................................................................................................................... 30

v

Figure 17. Experimental data of droplet length inside the microchannel for different liquid and

gas flows. ....................................................................................................................................... 30

Figure 18. Snapshots of droplets moving inside microchannel under different gas flow rates. ... 31

Figure 19. Corrected length used in non-dimensionalizing droplet morphology data In high liquid

flows, droplet exhibit a tail-shape which deviate from their common circular morpholy. ............ 31

Figure 20. Schematic of the Flow-Focusing geometry and the nomenclature used in scaling

analysis for droplet morphology. ................................................................................................... 34

Figure 21. Droplet length normalized with the minimum width of the droplets in the Dripping

regime as a function of gas Weber number (WeG). Minimum droplet width and length are

assumed to be equal values that are obtained based on the minimum volume of the prefilled

droplet during the formation process at high gas flow rates where droplet tends to have a more

circular morphology. This minimum is dependent on the geometry of the flow-focusing

microchannel and is calculated to be about 86μm for the geometry used in out experiments. ...... 34

Figure 22. Droplet length normalized with the minimum length of the droplets in the Dripping

regime as a function of gas Weber number (WeG). Minimum droplet width and length are

assumed to be equal values that are obtained based on the minimum volume of the prefilled

droplet during the formation process at high gas flow rates where droplet tends to have a more

circular morphology. This minimum is dependent on the geometry of the flow-focusing

microchannel and is calculated to be about 86μm for the geometry used in out experiments. ...... 35

Figure 23. (Left) Experimental images of the collected droplets in the immiscible liquid solution.

(Right) detected droplets using image analysis with MATLAB. ................................................... 36

Figure 24. Actual images and size distributions of samples of 500 collected droplets within the

Dripping and Multi-Satellite Formation regimes. Liquid flow rate for both cases is 5µL/min.

Multi-Satellite Formation is obtained at higher WeG according to the flow map. In the Dripping

region by having a constant liquid and gas flow rate the generated droplets are uniform in size. In

Multi-Satellite Formation regime, however, small daughter droplets are generated beside the main

droplet which results in polydisperse distribution of the droplets. ................................................ 37

vi

LIST OF TABLES

Table 1. Measured contact angles for 10 samples of PDMS and glass substrates with the same

preparation conditions of plasma treatment followed by a prebake process. The prebake process

results in regaining the hydrophobic nature of PDMS. The glass surface also becomes less

hydrophilic after the prebake process. Smaller contact angle hysteresis of the glass substrate

results in easier droplet movement during formation. Therefore, it will help to obtain a wider

Dripping regime and higher monodispersity. ................................................................................ 17

vii

ABSTRACT

Controlled generation of droplets in microfluidic networks is a promising tool for numerous

applications in biochemistry and material sciences. Droplet-based microfluidic systems are

typically utilized for creating dispersions of a liquid or gas within a second continuous liquid

phase, such as creating uniform liquid emulsions or gas bubbles (foams). In this work, we have

studied some of the fundamental aspects of liquid droplet formation within a continuous gas flow

for creating uniform aerosols inside microfluidic channels. We have experimentally investigated

interactions of liquid water within a high-speed air flow inside confined flow-focusing

microchannels in which we identify six distinct flow regimes: Co-flowing, Threading, Plugging,

Dripping, Multi-Satellite Formation, and Jetting. These flow regimes and their transitions are

plotted and characterized based on the Weber number (We) of the two phases. Generation

frequency, morphology, and monodispersity of the droplets are characterized in more detail for

the Dripping regime and scaling laws are provided to better elucidate the mechanism of droplet

formation for this system. Results of this work establish a relationship between generation

frequency and the product of the liquid and gas flow rates. However, droplet morphology (length

and width) is exclusively dependent on the air flow rate. Finally, we demonstrate the production

of monodisperse droplets (d<100μm and σ/d<0.05) at kHz formation rates in liquid-gas

microfluidic systems. The results of this work provide practical and useful guidelines for precise

oil-free delivery of ultra-small volumes of fluid which can be integrated in Lab-on-a-Chip (LOC)

and micro-Total-Analysis Systems (μTAS) for a variety of applications in biochemical research

and material synthesis.

1

Chapter 1. Introduction

1.1 Microfluidics and Droplet Microfluidics

Microfluidics has been increasingly developed over the past two decades. A consequence of this

galloping growth is transforming the way in which many chemical and biological experimentations

are performed [1]–[4]. Thus, it has become an essential tool in a wide range of medical researches

and technical applications. Despite the wide spectrum of microfluidic devices and schemes, they

can be categorized into two major groups, continuous-flow and droplet-based systems [5].

Continuous-flow scheme is characterized by manipulation of a continuous fluid stream inside

usually-confined microchannels. In a droplet-based system, however, one fluid is broken up within

a second phase to create discrete droplets. The development of microfluidic platforms in different

science and technologies has been driven by a number of fundamental characteristics related to

system miniaturization [6]. As such, many advantages are associated with these miniaturized

platform, including the small sample volumes consumption, low-cost fabrication methods,

enhanced operational flexibility, and the ability to integrate different components within more

complex networks for different analytical schemes [7]. Droplet-based microfluidics enables even

more capabilities while overcoming some of the inherent limitations of the continuous-flow

systems. In a continuous-flow scheme, intimate contact of the continuous fluid stream with

microchannel walls is associated with parabolic velocity profile and therefore, different residence

times [8]. Moreover, near-zero velocities at the wall result in fouling and contamination of the flow

and the whole process as a consequence [9]. Creating microdroplets has emerged as a potential and

appealing approach to perform a wide range of chemical and biological processes in a peerless

fashion [10], [11]. The use of picoliter to nanoliter scale droplets further reduces sample

consumption and increases surface-are-to-volume ratio which corresponds to much faster diffusion

rates [5]. More importantly, discrete droplets are ideally suited to isolate and compartmentalize a

2

sample or reaction which obviate issues of a continuous-flow scheme (Figure 1). Therefore, unlike

continuous-flow systems, this approach allows precise definition of the components of a process

inside distinct droplets. In addition, droplet-based systems are intrinsically associated with high

throughputs and parallel processing since typical droplet-based platforms can generate hundreds to

thousands of drops per second allowing for any post process to be performed in parallel on

individual droplets [12].

Figure 1. A comparison of mixing reaction in a standard pressure-driven continuous-flow microfluidic

platform (a) and using a droplet-based microfluidic system (b). In a continuous-flow scheme due to wall

effects and different residence times mixing happens slower. However, by digitizing the mixing reaction

inside distinct droplets, each droplet is mixed much faster and the total mixing time is reduced significantly

as a result [13].

Microfluidic technologies provide tremendous advantages for precise and rapid manipulation of

fluids at sub-microliter scale inside micrometer channels. All the advantages of microfluidic

systems come at the cost of understanding physics of the flow at microscale [14], [15]. These

physics can be better understood in terms of a few dimensionless numbers. Typically, gravity

3

effects are neglected in the microfluidic domain. The importance of gravity to surface tension forces

is expressed in term of Bond number (Bo);

Bo= ∆ρgL

2

σ (1.1)

where Δρ is the density difference between the dispersed and continuous phase, g is the

gravitational acceleration, D is the characteristic length scale, and σ is the interfacial tension. Due

to micrometer dimensions of the channels in microfluidic systems the effect of interfacial tension

is more pronounced and as a result Bo<<1. The Reynolds number (Re) compares the relative

importance of inertial and viscous forces and is defined as;

Re= ρUD

μ (1.2)

where U a characteristic velocity, and μ is the fluid viscosity. Similarly, the Weber number defined

as;

We= ρU2D

σ (1.3)

compares inertia to surface tension. Capillary number (Ca) which relates the ratio of viscous to

surface tension forces is the most commonly used dimensionless parameter in droplet microfluidic

systems [15] and is defined as;

Ca= μUσ

(1.4)

Expressing the flow in terms of the above dimensionless numbers facilitates better identification of

the key parameters in droplet generation and breakup, thereby unifying the behavior of a wide

variety of microfluidic systems.

1.2 Droplet Generation in Microfluidic Networks

Droplet formation and entrainment processes are the essential steps for using any droplet-based

system in applications which rely on discretizing a fluid sample. Many techniques for droplet

formation have been presented which can be classified in various ways [16]. Droplets in

4

microfluidic networks can be produced using either active or passive techniques. Active droplet

generation is achieved with the aid of additional energy inputs. Some of the commonly used

methods in this category utilize electrical, magnetic, mechanical, centrifugal, and thermal

mechanisms to actuate and control droplet breakup [17]. In passive methods, on the other hand,

there are no external actuation mechanisms and droplet formation solely relies on the interaction

of fluids interfaces inside special microgeometries. In comparison to active methods, passive

techniques are usually less complex and easier to implement.

Geometry of the microchannel, especially in passive formats, is of great importance for controlling

droplet generation. Various microfluidic device geometries have been demonstrated for this

purpose among which T-junction (cross-flow), co-flow, and flow-focusing configurations are the

most prevalent formats (Figure 2) [18]. In a T-junction geometry, one channel intersects a main

channel perpendicularly where one phase disperses within a continuous flow of a different phase

[19]. In a co-flow configuration, the continuous and dispersed phase flow in parallel channels

whereas the continuous phase surrounds the dispersed fluid [20]. This geometry is usually

fabricated using inserted capillary tubes and is challenging to fabricate and implement in quasi-

two-dimensional microfluidic formats. Flow-focusing geometries utilize a constriction in their

junction where both phases are hydrodynamically focused through a small orifice [21]. Since the

number of geometrical parameters in a flow-focusing geometry is higher in comparison to a T-

junction and co-flow configurations, flow-focusing systems offer a more versatile generation

scheme for controlling the droplet size and generation frequency. Several works have studied these

geometries and other variations to obtain small droplets with high degree of monodispersity.

5

Figure 2. Schematic representation of the most frequently used geometries in microfluidics for droplet

formation. (A) T-junction or cross-flow geometry, (B) co-flow geometry, and (C) flow-focusing geometry.

Despite the different configurations for droplet formation, breakup process in microfluidic systems

can be divided into a few fundamental modes. Dripping and jetting formation of droplets are usually

the two most desired modes of breakup inside microfluidic channels to produce drops [22], [23].

Dripping mode is characterized by formation and breakup of droplets very close to the dispersed

channel inlet, whereas in the Jetting regime, a liquid jet elongates in the microchannel outlet where

the breakup occurs due to growing instabilities in the liquid column (Figure 3). Dripping regime is

associated with higher monodispersity yet bigger droplets at slower frequencies comparing to the

jetting regime. By increasing either the continuous phase or the dispersed phase flow rates,

transition from dripping to jetting regime could occur. The region associated with these regimes

and their transitions to other ones is usually mapped in a plot that usually consist of capillary

numbers of the two phases in the system [24].

Figure 3. Representation of dripping and jetting inside microfluidic capillary tubes [23]. (A) Dripping

regime; here droplet formation occurs at the tip of the inner capillary in the dripping regime. (B) Jetting

regime; in this case instabilities of an extended liquid jet creates droplets which are commensurate to the jet

diameter and are usually smaller in comparison to the dripping regime.

Another major classification in microfluidic production of drops is by considering the phases

involved in the generation process (liquid or gas). In this sense, three combinations are possible i.e.

liquid-in-liquid or emulsion generation, gas-in-liquid or bubble generation, and liquid-in-gas or

aerosol generation. Creating uniform microemulsions is the most widely used class in

microfluidics. In this case, a continuous liquid phase meets the dispersed liquid in one of the

6

aforementioned geometries where individual droplets are pinched off as a result of interfacial

tension and shear forces induced by the continuous phase. Droplet sizes can be accurately

controlled in this scheme and a variety of techniques have been proposed for subsequent

manipulation of the drops in other system processes such as fusion [25]–[27], fission [28], sorting

[29], [30], and mixing [31], [32] in liquid-liquid environments [33]. Therefore, numerous

applications in microbiology, drug discovery, and particle synthesis exist that highly rely on

controlled formation on liquid droplets within a continuous liquid stream [34]–[36]. For instance,

these microdroplets are ideal for encapsulating single biological cells where specific dynamics and

metabolites can be conveniently probed within each droplet [37], [38]. Another huge area of liquid-

liquid digital microfluidic droplets is performing Polymerase Chain Reaction (PCR) in a digitized

format [39]–[42]. This process which is known as ddPCR (digital droplet PCR) has attracted

tremendous attentions during recent years as a highly-sensitive approach for DNA amplification.

In this technique, by partitioning the sample into millions of droplets, PCR can be performed on

individual drops and the number of positive compartments in which a target sequence is detected

can be counted and subsequently related to the initial number of targets in the original sample.

Research on incorporating a gaseous phase in microfluidic systems has mostly focused on

generation of uniform microbubbles and segmented gas slugs within a liquid phase. This process

has been driven by a different set of applications mainly in food industry, pharmaceutical sciences,

and medicine. For example, microfluidic formation of bubbles is proven in creation of polymer-

lipid microbubbles (PLBs) as a template for fabrication of 3D porous materials and scaffolds [43].

Moreover, using encapsulated microbubbles as ultrasound contrast agents (UCA) in medical

imaging has gained a lot of attention for their potential in early detection and characterization of

diseases [44]. Well-established microfluidic techniques have also been developed in this class for

production of highly-monodisperse bubbles in liquid environments using similar device geometries

as liquid-liquid systems [45], [46]. However, there is a paucity of studies regarding microfluidic

7

techniques for formation of liquid droplets inside a gaseous flow. Previous works related to liquid

droplet formation in a gaseous flow is provided in the next chapter. The major challenge addressed

in this thesis concerns investigation of droplet formation in gaseous microflow inside similar planar

microfluidic networks as the previous classes. The objective of this study is to gain a better

understanding of the fundamental physics behind this process with the ultimate goal of creating

uniform micron-sized droplets completely in air in microfluidic devices.

1.3 A Guide Through the Thesis

In Chapter 2, an overview of droplet formation in gaseous environments is presented. Previous

researches in this regard are mostly geared towards droplet generation using an axisymmetric

focusing air in unconfined nozzle-like geometries.

In Chapter 3, we discuss the experimental aspects of this work. The methodology for microfluidic

chip fabrication is described. We examine droplet formation in a gas flow inside a microfluidic

flow-focusing device (MFFD) with mixed hydrophobicity surface conditions. We discuss

preparation of the microchannels for obtaining monodisperse droplets in confined microchannels.

Unlike previous studies that used different surface chemical coatings to render the microchannel

fully hydrophobic, we show that incorporating a mixed hydrophobic/hydrophilic PDMS-glass

hybrid structure without chemical coatings results in the most robust droplet generation in these

systems.

In Chapter 4, we provide the experimental results of different breakup scenarios that occur in the

liquid-gas domain inside the microchannel. We identify six distinct regimes which are: Co-flowing,

Threading, Plugging, Dripping, Jetting, and Multi-Satellite Formation [47]. The effect that

microchannel size has on droplet formation is investigated towards the development of these richer

flow maps.

8

In Chapter 5, particular attention is paid to the Dripping regime for the generation of uniform

droplets. Droplet morphology, monodispersity and generation frequency are characterized as

functions of gas and liquid flow rates in this regime for the first time. Scaling laws are also provided

for the droplet morphology and generation frequency to non-dimensionalize the results.

In Chapter 6, we provide conclusions of this work and the future avenues that can be pursued for

implementation of this system in next generation Lab-on-a-Chip (LOC) technologies.

9

Chapter 2. Gas-Liquid Droplet Microfluidics

Spontaneous generation of liquid droplets within a gaseous flow in microfluidic networks is a

newer approach to the conventional liquid-in-liquid systems. One of the main advantages of this

approach for droplet formation is the possibility of creating uniform particles purely in air

(monodisperse aerosols) and without the presence of a second liquid carrier. Therefore, the final

product can be readily attained obviating extra washing steps to remove the carrier oil [35].

Moreover, generation of droplets in a liquid medium is usually facilitated by adding surfactants to

the continuous liquid carrier. However, it is believed that using certain surfactants may impose

usage limitations mainly due to cross-contamination of the droplet contents [48], [49]. Surfactants

are clearly not required for droplet generation in a gaseous phase, ensuring preservation of the

droplets’ contents.

Some early works have investigated the breakup of a liquid jet into droplets using a focusing air in

unconfined nozzle-like geometries as in Figure 4 [50]–[54]. Here, a flowing liquid through a

capillary tube is forced through a coaxial round orifice located downstream of the tube. The liquid

stream is drawn by a focusing gas stream discharging through the nozzle into an infinitely large

chamber. In this scheme, drop breakup occurs as a result of the instability of a capillary jet and it

has been demonstrated that under certain conditions [54]–[56], monodisperse droplets can be

achieved from an unstable liquid jet.

10

Figure 4. Axisymmetric flow-focusing architecture for controlled production of droplets using a focusing air

in a non-microfluidic format [52]. Here, the applied air pressure across the circular orifice results in breakup

of the liquid jet into individual droplets.

Generation of monodisperse drops within a microfluidic system is an entirely different process due

to confinement induced effects [57]. Interaction of liquid and gas inside confined microchannel

geometries has also been widely studied in the operation of Proton Exchange Membrane Fuel Cells

(PEMFC) [58]–[67]. However, droplet generation in gaseous microfluidic systems that employ

similar architectures as those used in conventional oil-based systems has been the subject of a very

few studies during recent years. The gas flow velocities required for droplet generation are at least

an order-of-magnitude higher than those employed when using a highly viscous oil phase. As such,

inertial effects become more prominent and relevant in the fluid-fluid interactions of these systems.

Droplet detachment has been numerically and experimentally investigated in a T-shaped junction

under the introduction of a high-speed gaseous flow [68], [69]. It was demonstrated that the

mechanism responsible for the breakup of the drops transitions from hydrodynamic pressure

difference (arising from the microchannel confinement) at lower Re to inertial drag at higher Re as

the gaseous flow increases. Confined generation of aqueous droplets has also been shown in a

11

circular capillary co-flow system using gas as the continuous phase. Under relatively low liquid

flow rates (less than 1 μl/min) and gas velocities (below 3 m/s) uniform droplets between 250μm

and 320μm were obtained within concentric hydrophobic glass capillaries [70]. More recently,

confluence of liquid in a gaseous stream in various planar confined flow-focusing microgeometries

was studied. It was shown that over a wide range of liquid and gas flow rates three main regions

(i.e. Dripping, Jetting, and Stratified Flow) are observed within confined PDMS microchannels

[71]. While this study provided useful insights regarding the dynamics of gas-liquid interactions in

planar flow-focusing geometries, it did not address several key aspects of this system. For example,

the monodispersity and characteristics of the droplets generated within the Dripping region was not

presented. This is very relevant information towards the design of these systems since the Dripping

regime is one of the two desirable modes of operation for droplet generation. Furthermore, neither

study looked at the effect that flow conditions has on the droplet morphology or generation

frequency in this flow regime.

12

Chapter 3. Experimental

3.1 Fabrication of Microfluidic Devices

We fabricated the microfluidic devices using standard photolithography process with SU-8 and soft

lithography with polydimethylsiloxane (PDMS) [72]. First, the flow-focusing configuration was

designed in a CAD software (SolidWorks 2014) and then printed out on high-resolution

transparencies (CAD/Art services). A 4-inch single side polished silicon (Si) substrate is used as

the master mold. The mold is prepared using standard photolithography process with a negative

near-UV photoresist (SU-8 2050 Microchem Corp.). Initially, the substrate is cleaned with acetone

and isopropyl alcohol, and dried with a nitrogen gun. The clean wafer is spin-coated (Laurell

Technologies) with the photoresist. The spinning speed is initially set to 500rpm for complete

spreading of the photoresist followed by a final speed of 3000 rpm for 1 min to obtain 40μm

thickness. Residues of the photoresist also known as edge beads were removed from the sides of

the substrate using a razor blade to ensure a flat coated surface for better mask attachment and

exposure process. The coated wafer is then baked for solvent removal on a hot plate at 65°C and

95°C respectively. The prebaked mold is left at room temperature for about 5 min to reduce thermal

stresses in the photoresist layer. The transparency mask sheet which contains the chip geometries

is attached to a borosilicate glass sheet to provide a rigid support for the mask when covering the

wafer. The mask and the wafer are loaded in the mask alignment equipment (Quintel 4000 Mask

Aligner) and exposed to UV light through the printed mask for about 45s. The exposed wafer is

then post-baked with similar temperatures as the prebake step for 5 min and 10 min respectively.

Once the mold reached the room temperature after the post-bake, it was soaked in a solution of SU-

8 developer for defining the micropatterns on the photoresist. A hard-bake process at 120°C is

performed for improving the adhesion of the photoresist to the wafer as well as balancing the

thermal stresses in the photoresist film. Once the mold fabrication is complete, microfluidic chips

13

were casted out of the SU-8 master molds by performing standard soft lithography method.

Polydimethylsiloxane (PDMS) prepolymer mixture (Sylgard 184, Dow Corning) is prepared from

the elastomer base and curing agent at a 10:1 weight ratio. The solution is then placed onto the

Silicon mold and is degassed in a vacuum chamber. The assembly is cured at 80°C for

approximately 2 hours on a leveled hotplate. Hardened PDMS is carefully peeled from the mold.

The available area on a 4-inch silicon mold allows a number of devices to be replicated in a single

lithography process. Each microfluidic chip is cut out of the PDMS layer. After punching the

required flow inlets/outlets, each chip is cleaned with DI water and dried with a nitrogen gun. Each

piece is then bonded to a pre-cleaned standard microscope glass slide (Thermo Scientific) using an

oxygen plasma cleaner (Harrick Plasma). Finally, the chips are post-baked for 4 hours at 200°C

and can be used for experiments after being cooled down to room temperature. The fabrication

process and final device and the microchannel configuration is depicted in Figure 5.

14

Figure 5. Schematic representation of the fabrication procedure for production and assembly of microfluidic

devices. (1) Required channel geometry is designed and printed on transparency sheets. (2) UV

photolithography process is performed using the printed mask to define the patterns on a negative photoresist

that is coated on a silicon substrate. (3) After mold fabrication soft lithography using PDMS prepolymer is

performed to replicate the channels from the mold into the elastic polymer. (4) After PDMS being solid, each

device is cut and punched for the inlets/outlets. (5) PDMS chips are bonded to a clean glass slide after being

plasma cleaned. (6) Final microfluidic device for water droplet formation in air. (7) Image of the flow-

focusing junction under microscope. Liquid water is injected through the middle channel and meets the two

side air streams at a flow-focusing junction. The microchannels’ depth is 40μm.

15

3.2 Control and Modification of Microchannel Surfaces

The wetting behavior of the microchannel walls plays a critical role in the performance of droplet-

based microfluidic systems that use a planar architecture. In conventional liquid-in-liquid systems

the surface of the microchannels is modified to reduce droplet interactions with the walls. In other

words, stable water-in-oil emulsions can be formed in hydrophobic microchannels and on reverse

emulsions (oil-in-water) the microchannels should be hydrophilic (oleophobic). Although PDMS

is intrinsically hydrophobic, the use of oxygen plasma for bonding renders them hydrophilic which

makes liquid handling difficult within microchannels. Moreover, compatibility issues of PDMS

surfaces with organic solvents [73], including a variety of the oils used in droplet-based systems,

pose additional challenges for droplet generation in liquid-liquid systems. Obtaining the conditions

that suit the generation process is usually achieved by manipulating the microchannel surfaces

through chemical coatings. A variety of techniques and chemicals are employed to achieve the

desired hydrophobicity as well as solvent compatibility [74]. However, the chemicals used for this

purpose are typically hazardous to work with. Moreover, applying a reproducible and uniform

coating especially in confined microchannels is a challenge from the preparation perspective.

Having a gaseous phase as the carrier fluid entirely eliminates the compatibility issue of PDMS in

our system. Figure 7A represents the behavior of droplet formation after plasma treatment in this

liquid-gas system. Droplets in this case show an affinity to ride on the side walls due to their

hydrophilic condition after exposure to plasma. As a result, droplets are not capable of keeping

their morphology during formation and tend to spread and form a liquid film on the side walls. To

overcome this issue, we implemented two methods for modify the properties of the microchannel

walls. In the first approach, we used a fluorosilane to coat the microchannels. Because of the silanol

groups existing on the surface of the PDMS, a wide spectrum of silanes can be used for surface

modification[74], [75]. We tested Trichloro(1H,1H,2H,2H-perfluorooctyl)silane (FDTS 97%,

Sigma-Aldrich) to modify the surface of the PDMS using vapor deposition [76]. Since coating

16

process prior to bonding caused some issues and prevented strong adhesion of the PDMS chips to

the glass substrate, we performed the deposition after the bonding step. The process for treating the

microchannels inner surfaces involves passing the vaporized FDTS into the bonded PDMS

microchannel as shown in Figure 6 [77]. For this purpose, a microdroplet of FDTS is placed on a

slide next to the previously-bonded chip, while the outlet of the chip is connected to the vacuum

port of a micro diaphragm pump (Parker Corp.) All the parts, including pump, chip, and slide are

placed inside a vacuum chamber. By turning on the pump the vaporized silane is directed towards

the inlets of the chip and is forced to pass through the microchannels and being deposited on the

channel walls. After 1 hour of coating process, the chip was disconnected from the vacuum pump,

and used for the droplet generation experiments. Results of droplet formation after applying silane

on the walls is shown in Figure 7B. Although, droplet generation after silane coating showed

improvements, the results were not consistent due to the challenges associated with the

experimental procedure of applying the chemical on the confined structure. Therefore, we tried a

different and more robust approach to tackle this issue.

Figure 6. Schematic of the method used treating the microchannel walls with fluorosilane chemical. All the

setup are placed inside a vacuum chamber in order to prevent the deposition of toxic fluorosilane vapor into

the environment.

In the second approach, a high-temperature post-baking step was used instead of chemical

treatment to achieve the surface conditions suitable for droplet generation in our system. Table 1

shows the measured contact angles for PDMS and glass substrates after the post-bake process. This

17

technique ensures that all the PDMS walls regain their hydrophobic nature in a fast and uniform

manner, minimizing the tendency of the droplets to adhere to the walls as shown in Figure 7C. This

process is very reproducible and does not involve the challenges of the previous technique.

Figure 7. Interaction of liquid and gas in different channel conditions. (A) After plasma treatment; in this

situation channels are hydrophilic and as a result the liquid water tends to adhere to the side walls of the

microchannel once it enters the junction. (B) After modifying the channel walls with vaporized fluorosilane.

In this case, the droplets could form in the channel. However, due to the challenges in the coating process the

generation was not reproducible. (C) After post-baking step; here the PDMS has regained its hydrophobic

nature and droplets maintain their morphology after generation.

Table 1. Measured contact angles for 10 samples of PDMS and glass substrates with the same preparation

conditions of plasma treatment followed by a prebake process. The prebake process results in regaining the

hydrophobic nature of PDMS. The glass surface also becomes less hydrophilic after the prebake process.

Smaller contact angle hysteresis of the glass substrate results in easier droplet movement during formation.

Therefore, it will help to obtain a wider Dripping regime and higher monodispersity.

Static Angle

(θS)

Advancing Angle

(θA)

Receding Angle

(θR)

Glass 60±4 69±5 52±5

PDMS 102±4 116±4 75±5

In confined microfluidic channels droplet morphology is bounded by the microchannel dimensions.

Thus, if the diameter of the generated droplet exceeds the height of the microchannel the droplet

will be in contact with the top and bottom walls which result in additional interactions that influence

18

the formation process. This condition occurred throughout the Dripping regime of our system. It

has been observed that using a non-hydrophobic glass substrate as the bottom wall enables a more

robust and reproducible dripping over a wider range of the flow map with higher monodispersity.

We believe this behavior can be related to the smaller contact angle hysteresis of a glass slide in

comparison to a PDMS surface. Based on the measurements of the static, advancing, and receding

contact angles for the glass and PDMS (see Table 1) surfaces we can schematically represent the

droplet inside the microchannel from a side view as shown in Figure 8 for each case. From these

measurement two things become apparent. First, post-bake treatment of the glass substrate

substantially reduces its hydrophilicity, rendering it partially hydrophilic. Secondly, the droplet

holding or restraining force from surface tension effects is smaller for the hybrid (glass substrate-

PDMS) structure than for the PDMS-PDMS one, due to the smaller overall contact angle hysteresis

effect. This can be quantified by comparing the added top and bottom hysteresis of the hybrid

structure ((γcosθRP - γcosθA

P) + (γcosθRG - γcosθA

G)) to the hysteresis from the PDMS-PDMS

structure (2(γcosθRP-γcosθA

P)). This results in a surface tension force for the hybrid structure that

is less than half that of the PDMS-PDMS structure. As a result, especially in lower flow rates of

the gaseous phase, we speculate that the higher surface tension force from the PDMS-PDMS

structure creates an added hindrance to the motion of the droplet while being formed and generated.

Therefore, obtaining a reproducible formation process within the flow conditions of the Dripping

regime in these structures becomes a challenging task, with the delineation of the boundary between

the Dripping regime and its neighboring regimes becoming more blurred.

19

Figure 8. Comparison of the surface tension forces between a glass-PDMS microchannel (left) and a PDMS-

PDMS microchannel (right). Using the provided contact angles in the table, the net surface tension force for

a glass-PDMS combination is less. Therefore, it provides less resistance during the course of droplet

generation and movement inside the channel which results in a more reproducible formation process.

3.3 Experimental Setup

A custom microfluidic test setup has been developed for the experimental investigation of the gas-

liquid droplet generation. The gas used as the continuous phase in all the experiments is air at room

temperature which is supplied from the facility compressed air source. The air is first dried by

passing through a desiccator and cleaned using 0.2μm filters (Wilkerson Corp.). Air is regulated in

multiple steps before being routed into the microfluidic chip inlets. A manual coarse pressure

regulator (SMC corp, up to 50 psi) reduces the pressure of the supply line. A voltage-controlled

pressure regulator (Proportion-Air, up to 18±0.04 psi) is used to deliver a precise air pressure into

the system. For real-time monitoring of the air flow rate, an in-line mass flow meter (Sierra Smart-

Trak2) is placed in the setup. All pressure regulators and flow sensors are powered using dedicated

24V DC power supplies. A data logger/switch unit (Agilent 34970A) is also used for data

acquisition which is controlled by a customized LabVIEW interface for controlling the valve and

collecting data from the flow meter. A needle valve (Swagelok) is also placed upstream of the chip

for a finer flow regulation prior to injection. The air stream bifurcates after passing through the

needle valve and is connected to the corresponding inlets of the chip through 1/16-inch PEEK tubes.

Liquid flow control is provided by a glass syringe using a high precision syringe pump (PHD2000

20

Harvard Apparatus). The accuracy of the injected flow rates are within 0.35% of the specified value

for the flow. Imaging and visualization of the formation process is facilitated using a high-speed

CMOS camera (Photron SA5) which is capable of providing a 7500 frames per second (fps) at the

resolution of 1024×1024. The camera is mounted to an inverted microscope (Nikon Ti-U) and

illumination is provided by a metal halide white light (Prior Scientific). Schematic and actual

images of the experimental setup are shown in Figure 9 and Figure 10 respectively.

Figure 9. Schematic of the flow circuit for liquid and gas control.

21

Figure 10. Actual image of different parts of the experimental setup. (1) Air desiccator, (2) manual coarse

pressure regulator, (3) voltage-controlled valves, (4) mass flow sensors, (5) needle valves, (6) liquid syringe

pump, (7) white light source for the microscope, (8) high-speed camera connected to the microscope, and (9)

microfluidic chip placed on the microscope with all the ports connected to their corresponding tubing.

In order to analyze the population of the generated drops, they are collected off the chip after

generation in air, inside a different liquid phase. For this purpose, n-Hexadecane (Sigma-Aldrich

Corp.) which is almost insoluble in water, is used as the collection medium. In order to prevent

droplets from merging inside the solution 2% of the nonionic surfactant span 80 (Sigma-Aldrich

Corp.) is mixed with the oil. The outlet of the microfluidic chip is cut and submerged in the oil bath

[78]. As a result, the generated droplets are collected downstream of the device outlet once they

transition into the oil medium.

22

Chapter 4. Flow Regime Mapping

Unlike liquid-liquid droplet microfluidic systems that are usually characterized by the Capillary

number (Ca) of the two fluids [24], [79], Ca in our experiments always remained below 0.02. In

contrast, the Reynolds number (Re) for the continuous gaseous phase was in the range between 10

and 600 indicating the relevance of inertia in this system. However, such high Re and low Ca for

all the flow conditions of the system do not clearly illuminate the fundamental mechanisms behind

the different flow regimes. Therefore, we employed the Weber number (We) to parametrize the

droplet breakup processes as it changed in a moderate range in our experiments (We ≡ Re.Ca).

Utilizing We led to a better characterization of the flow regimes presented in this system. The We

number for both phases is defined as:

We =ρU2

DH

σ

(4.1)

where ρ and σ are the fluid density and interfacial tension respectively. Air is used as the gaseous

phase whose density throughout the experiments were calculated considering its compressible

behavior inside the microchannels. Distilled water serves as the liquid phase. U is the average fluid

velocity inside the channel which is calculated by dividing the flow rate by the cross section area,

and DH represents the hydraulic diameter of the rectangular cross section of the microchannel. The

We for the gaseous phase (WeG) is defined based on the throat cross section at the flow-focusing

junction, and for the liquid phase WeL is defined based on the liquid channel dimensions. Using the

aforementioned definitions, WeL is in the range 0.0001-0.3 and WeG in the range 0.008-25. These

wide range of flow conditions result in various breakup modes which are explained in the following

section.

Experiments on each chip were performed by initiating a gaseous flow inside the device to prevent

the liquid from flooding the microchannels. Liquid water is subsequently injected into the flow-

23

focusing junction. Mapping experiments were conducted by setting a specified flow rate and

increasing the gas flow rate. As such, the maps consist of multiple horizontal lines of a fixed flow

rate (WeL), with transitions occurring as the flow rate (WeG) is changed (increased). We conducted

several experiments using multiple chips to account for wettability changes associated with the

chips being exposed to large amount of water for a long period of time. Over a wide range of flow

conditions we observed six distinct regimes which are defined as: Co-Flowing (■), Threading (♦),

Plugging (▲), Dripping (●), Jetting (►), and Multi-Satellite Formation (▼). A typical flow regime

map depicting these different breakup modes is shown in Figure 11 based on WeG and WeL. In this

map the region associated with each flow regime is distinguished with a different color. The gray

areas in the plot represent the transition regions across which the transition between two regimes

takes places. We used these finite transition regions rather than infinitesimally thin solid lines to

depict the change in the flow regime more realistically. This is more consistent with the

observations from experiments since flow regime transition could occur anywhere within the

shaded regions from a statistical point of view, which is determined by the microfluidic chips and

flow rate measurements in the experiments. However, dashed lines are also included in the flow

map as a reference and guideline to distinguish between the actual flow regimes and intermediate

transition regions. Furthermore, these lines can be considered as approximate boundaries between

each two flow regime regions.

At low values of WeG, the flow is characterized by the formation of liquid threads that extend along

the microchannel outlet. We observed that at low values of liquid flow (for WeL<10-2), the formed

thread does not remain stable along the outlet. In this region which is referred to as the Threading

regime, an unstable thread extends downstream of the junction where it breaks up intermittently at

different locations and results in multiple plugs and droplets. In the Co-flowing regime, which

occurs at higher values of WeL, the liquid thread is stable and extends throughout the microchannel

outlet. As the value of WeL increases, the thickness of this continuous liquid thread increases until

24

it obstructs the microchannel outlet. A periodic breakup takes place at higher WeG where each

formed thread is broken up into a single plug whose length is bigger than its width

(LDroplet>2WDroplet). This corresponds to the Plugging region, with threads that break up very close

to the flow-focusing junction at a distance Lbreakup<10Woutlet measured from the junction. The

Dripping regime is observed beyond the Plugging regime when the inertia forces start balancing

the surface tension forces at the junction (around WeG≈0.3). In this regime, circular drops are

formed at the junction which are highly-reproducible and uniform over a wide range of frequencies

and sizes. Increasing WeG, however, creates a chaotic condition that involves unsteady and random

droplet breakup dynamics. It can be seen from the flow map that a transition from the Dripping to

the Multi-Satellite Formation regime occurs around WeG≈6. Beyond this point a polydisperse spray

of the liquid is generated inside the microchannel. The Multi-Satellite Formation regime has not

been previously reported in liquid-liquid systems since its appearance is mostly due to the highly

inertial nature of the continuous phase which is usually negligible in oil-water systems. We

observed that at higher liquid flows a long liquid jet is formed after the junction which breaks into

individual droplets due to Rayleigh capillary instability [80]. In this Jetting regime, characterized

by droplet tip streaming of an extended liquid jet, droplet generation is less controlled. However,

generated droplets are in the order of the liquid jet diameter and much smaller than the droplets

from the Dripping regime.

25

Co-Flowing

Dripping

Threading Multi-Satellite

Formation

Plugging Jetting

Figure 11. Flow regime map of water-in-air droplet formation in a planar flow-focusing microfluidic device.

Different flow regions are distinguished with different colors. The transition between the flow regimes is also

represented as a finite shaded region rather than a solid line to account for the uncertainties associated with

the experiments and calculations of the We values.

In addition to the flow conditions, the geometry of the microchannel flow-focusing section plays

an important role in the flow map characteristics of this system. We were interested on the influence

that liquid microchannel size has on the Dripping regime in particular. Three different chips with

liquid channel widths of 25μm, 50μm, and 100μm were considered for this part. Flow mapping

experiments were conducted for the wider liquid channels (50μm and 100μm) and the results are

compared against the original flow map with the narrower liquid channel (25μm) as shown in

26

Figure 12. For these maps we have only included the approximate dashed lines to better compare

the flow regimes layout together. It can be seen that increasing the liquid channel size results in a

smaller Dripping region, which is highlighted with the green color in the flow map. Increasing the

size of the liquid channel results in larger surface tension forces that hold the droplet during

formation. Therefore, higher detaching forces are required to pinch-off the thread at the junction to

create discrete droplets. This will shift the transition from the Threading and Plugging regimes to

the Dripping regime to higher values of WeG. Transition to the Satellite Formation regime is less

dependent on the liquid channel size since it is mostly due to the inertial effects of the gaseous

phase. According to the flow maps, the Satellite Formation transition typically occurs around

WeG≈6-7 for all the chips. Consequently, increasing the size of the liquid channel would shrink the

Dripping region by expanding the Threading and Co-flow region.

Figure 12. Comparison of the flow map for chips with different liquid channel sizes. The area for the

Dripping region (the green region) is reduced as the liquid channel size increases. However, the Threading

and Co-flow regions have expanded as a result of increase in the surface tensions forces that holds the thread

and prevents the detachment at lower gas flow rates.

0.001

0.01

0.1

0.1 1 10

0.001

0.01

0.1

0.1 1 10

0.001

0.01

0.1

0.1 1 10

25μm 50μm

100μm

WeG

We L

27

Chapter 5. Dripping Regime Characterization

5.1 Generation Frequency

In this chapter, three important aspects of the Dripping regime are investigated by characterizing

the generation frequency, morphology of the droplets inside the microchannel, and monodispersity

of the generated droplets within this region. The frequency of droplet formation (ƒGeneration) is

obtained by manually counting the number of droplets generated over a given time interval from

the high-speed videos. To do this, the sequential images taken from the high speed camera were

analyzed in a lower speed to count the generated droplets with naked eye. Figure 13 and Figure 14

show the frequency data for the Dripping regime at different liquid and gas flow rates. It can be

seen that the frequency varies between less than 30 up to 1000 Hz (drops per second) over the entire

Dripping regime. Results show that frequency of the generation increases as either the liquid or gas

flows increase. Moreover, experimental plots show that frequency values are proportionate with

both flow rates. Therefore, we scaled the frequency in this system as the product of the two flow

rates (i.e. ƒ∝QGQL). In order to non-dimensionalize the frequency results, flow rates are non-

dimensionalized by characteristic inertial velocities (U*=(σ/ρDH)1/2) obtained from a Weber number

of unity for both phases, and a characteristic timescale (τ*=DH/U*). Therefore, generation frequency

can be non-dimensionalized as ƒ(τ*Gτ*

L)1/2. The results of this scaling are shown in Figure 15.

28

Figure 13. Experimental data of droplet generation frequency as a function of air flow rate for different liquid

flow rates. We can see that there is a relatively linear correlation between the frequency value and the air

flow rate.

Figure 14. Experimental data of droplet generation frequency at increasing liquid flow rate for two different

gas flow rates. We can see that there is a relatively linear correlation between the frequency value and the

liquid flow rate.

0

400

800

1200

0 10 20

ƒG

ener

ati

on

(Hz)

QG (mL/min)

A

0

400

800

1200

0 20 40

ƒG

ener

ati

on

(Hz)

QL (μL/min)

B

29

Figure 15. Experimental data of the non-dimensioalized droplet generation frequency. Generation frequency

in this system can be scaled as ƒ∝QGQL.

5.2 Droplet Morphology

Images of the droplets moving inside the microchannel are captured and analyzed to determine

their corresponding length and width. Experiments are conducted multiple times for each flow

condition to verify the reproducibility of the measured values. In the presence of a continuous gas

flow we always find a finite gap between the droplets and the walls within the Dripping regime.

Therefore, both the width and length of the droplets change as a function of flow rate. Figure 5

shows the droplet length and width as a function of gas flow rate (QG), for different liquid flow

rates (QL). Snapshots of the droplets inside the microchannel for different flow conditions shown

in Figure 18 clearly demonstrate these changes in length and width. It can be seen that a higher air

flow rate results in decreasing both length and width. However, liquid flow rate does not have an

apparent effect on the droplet width. Moreover, at high liquid flow rates, droplets exhibit a long tail

0.0001

0.001

0.01

0.01 0.1 1

ƒ(τ

* Gτ* L

)1/2

QG/(U*GD2

H,G) QL/(U*LD

2H,L)

30

which deviated from their common circular morphology. In order to take into account this length

for later scaling analysis, we used a correct length for this purpose as shown in Figure 19.

Figure 16. Experimental data of droplet width inside the microchannel for different liquid and gas flows.

Figure 17. Experimental data of droplet length inside the microchannel for different liquid and gas flows.

80

130

180

5 10 15 20

WD

rop

let(μ

m)

QG(mL/min)

80

100

120

140

160

180

200

5 10 15 20

LD

rop

let(μ

m)

QG (mL/min)

QL=1 μL/min

QL=5 μL/min

QL=10 μL/min

QL=20 μL/min

QL=30 μL/min

QL= 40 μL/min

31

QL=5μL/min

QG=8 mL/min

QG=10 mL/min

QG=12 mL/min

QG=14 mL/min

QG=16 mL/min

Figure 18. Snapshots of droplets moving inside microchannel under different gas flow rates.

Figure 19. Corrected length used in non-dimensionalizing droplet morphology data In high liquid flows,

droplet exhibit a tail-shape which deviate from their common circular morpholy.

100μm

1.

32

During the course of the generation process, a droplet starts forming from the liquid microchannel

in the flow-focusing junction. As the liquid is injected into the droplet volume, the droplet grows

in the plane at the junction. The droplet is attached to the liquid microchannel by a surface tension

force that can be scaled as,

Fσ ~ σDH,L (5.1)

where DH,L is the hydraulic diameter of the liquid microchannel. As the droplet protrudes into the

junction, it experiences inertial forces of the high speed gaseous medium that co-flows with the

liquid droplet. The inertial force of the gaseous phase can be scaled as;

FI ~ρQ

G2

DH,G4 h(W*-WL) cos θ (5.2)

where DH,G is the hydraulic diameter of the gas microchannel, h is the droplet height which is equal

to the channel height, θ is the angle at which the air enters the junction, WL is the liquid

microchannel width, and W* is the droplet width during the formation stage (see Figure 20). When

the aforementioned forces balance, the droplet width can be approximated as

W*~σDH,G4 /ρQ

G2 hcosθ+WL. However, the morphology of the droplets was assessed from the images

of the droplets moving inside the microchannel outlet after the droplets are detached. As such, a

similar scaling dependence can be used for the measured width with respect to the inertial force but

with a different proportionality factor and minimum width. To calculate this minimum width (W),

we consider the limiting case of W*≈WL which occurs experimentally at high gas flow rates and

also from the scaling equation. In this case, the prefilled droplet volume in the junction forms a

rectangular liquid ligament whose width is in the order of the liquid microchannel width and the

length is stretched to the throat of the junction (∆Z). This volume results in minimum droplet width

of 86μm after detachment, assuming a circular morphology for these droplets at high gas flow rates,

which is a reasonable assumption based on the experimental data. Since the complete generation

process always starts with the prefilling process, this obtained droplet size can be considered the

33

minimum width and length that can be achieved within the Dripping regime. Therefore, droplet

width can be calculated as W=C1 σ ρQG2⁄ +C2, where C1 takes into account the geometrical

parameters and a fitting factor, and C2 is the minimum droplet width that can be achieved in the

Dripping regime of this system.

The volume of the droplet in the dripping regime can be related to the generation frequency and

the liquid flow rate via conservation of mass of the liquid flow,

Vdroplet = Q

L

ƒ (5.3)

If the droplet is assumed to have a relatively uniform width over its entire length, the volume of the

droplet is proportional to the product of its dimensions. Therefore, the volume can be approximated

as Vdroplet ∝ LWh, where L, W, and h are the droplet length, width, and height, respectively. In order

to be consistent with the assumed (and mostly observed) droplet volume, experimental data for the

measured length were corrected in some cases where the droplet contained a morphology with non-

uniform width. By substituting the aforementioned scaling for the frequency (ƒ∝QGQL), droplet

length can be scaled as L~1/hWQG. Figure 24 shows the normalized droplet morphology using the

minimum values obtained in the Dripping regime as a function of the WeG. It can been seen that

both droplet length and width decrease with increasing gas flow. However, the effect of liquid flow

rate is less discernable in the morphology and more pronounced in the formation frequency.

34

Figure 20. Schematic of the Flow-Focusing geometry and the nomenclature used in scaling analysis for

droplet morphology.

Figure 21. Droplet length normalized with the minimum width of the droplets in the Dripping regime as a

function of gas Weber number (WeG). Minimum droplet width and length are assumed to be equal values that

are obtained based on the minimum volume of the prefilled droplet during the formation process at high gas

flow rates where droplet tends to have a more circular morphology. This minimum is dependent on the

geometry of the flow-focusing microchannel and is calculated to be about 86μm for the geometry used in out

experiments.

0

1

2

3

0 5 10

W/W

min

WeG

Scaling

QL=1

QL=5

QL=10

QL=20

QL=30

QL=40

35

Figure 22. Droplet length normalized with the minimum length of the droplets in the Dripping regime as a

function of gas Weber number (WeG). Minimum droplet width and length are assumed to be equal values that

are obtained based on the minimum volume of the prefilled droplet during the formation process at high gas

flow rates where droplet tends to have a more circular morphology. This minimum is dependent on the

geometry of the flow-focusing microchannel and is calculated to be about 86μm for the geometry used in out

experiments.

5.3 Droplet Monodispersity

Generated droplets are collected off the chip in a glass vial filled with a different liquid which is

immiscible with the water droplets. Captured images from the collected droplets were processed

using a customized MATLAB program to analyze the size of the drops and their distribution as

shown in Figure 23. Since the droplets are spherical after transitioning into the liquid medium, we

use the droplets’ diameter as the characteristic length scale in this part. Comparison between

droplets in the Dripping and Multi-Satellite Formation regions is shown in Figure 24. Size

uniformity of the collected droplets within the Dripping regime demonstrates the controlled

generation of the droplets within this region. The generated droplets have a polydispersity index

0

1

2

3

0 5 10

L/L

min

WeG

Scaling

QL=1

QL=5

QL=10

QL=20

QL=30

QL=40

36

(PDI) defined as σ/d (where σ represents the standard deviation of the droplet diameters and d is

the average diameter of the generated drops), of less than 5%. Droplets generated in the Dripping

regime can form a uniform closely-packed structure inside the liquid medium as shown in the

figure. Satellite Formation regime, however, results in polydisperse droplets which are distributed

over a wide range of diameters even for a fixed flow condition.

Figure 23. (Left) Experimental images of the collected droplets in the immiscible liquid solution. (Right)

detected droplets using image analysis with MATLAB.

37

Figure 24. Actual images and size distributions of samples of 500 collected droplets within the Dripping

and Multi-Satellite Formation regimes. Liquid flow rate for both cases is 5µL/min. Multi-Satellite Formation

is obtained at higher WeG according to the flow map. In the Dripping region by having a constant liquid and

gas flow rate the generated droplets are uniform in size. In Multi-Satellite Formation regime, however, small

daughter droplets are generated beside the main droplet which results in polydisperse distribution of the

droplets.

Dripping regime

Multi- Satellite Formation regime

38

Chapter 6. Conclusions

Combination of fluid behavior at microscale and advances in microengineering methods have

provided unique capabilities for controlling fluid-fluid interfaces. Controlled generation of liquid

droplets in microfluidic networks is an area of huge promise for a variety of applications in

biochemistry and material science. Droplet-based microfluidic devices typically employ

dispersions of one liquid within a continuous immiscible liquid phase, such as the creation of

uniform water-in-oil emulsions. Thanks to recent technological advancements in microfabrication

techniques, droplets can be produced in a planar chip format. In addition to the ease of fabrication,

planarization provides considerable benefits in terms of size and cost of the droplet system and,

more importantly, it enables the integration of the device in more complex LOC platforms.

Generation of aqueous liquid droplets using a continuous gaseous phase has been recently

demonstrated within microfluidic devices. This approach provides great potentials in modern Lab-

on-a-Chip (LOC) systems for high-throughput production of oil-free particles and airborne

microreactors. In this work we investigated different aspects of controlled formation of uniform

micrometer-sized water droplets in air using a microfluidic flow-focusing device (MFFD). The

droplet generation module is fabricated following standard soft lithography techniques with PDMS.

A standard microscope glass slide acts as the bottom surface on which each device is bonded using

a lab-scale plasma cleaner. Microfluidic devices are finally post baked at high temperatures for

several hours. The hydrophilic bottom wall (glass) creates a mixed surface condition inside the

microchannel since the post bake step renders the PDMS walls highly hydrophobic. By using a

PDMS-glass hybrid structure, we found six different flow regimes in this system: Co-flowing,

Threading, Plugging, Dripping, Jetting, and Multi-Satellite Formation. We further investigated the

Dripping regime which corresponds to controlled generation of monodisperse droplets at the flow-

focusing junction inside the microchannel. It was shown that increasing the liquid channel size

39

results in a smaller Dripping regime. Generation rate, droplet morphology, and monodispersity of

the droplets were investigated for different liquid and air flows within the Dripping regime. Results

of this work demonstrate smaller droplets (less than 100μm) at higher generation rates (up to 1

kHz) that are highly uniform in size (PDI<%5) which shows a significant improvement for liquid-

in-gas microfluidic systems. The contributions presented in this article provide practical guidelines

towards creating oil-free uniform droplets that can be used as templates for microparticle and

microfiber synthesis with control on the size and frequency. Moreover, many biochemically

relevant applications can also benefit from uniform digitization of sample within a gaseous

medium, namely for aerosol drug delivery and high-throughput screening of targets from gaseous

media. It is worth mentioning that in addition to the principal advantages of using droplet-based

systems for enhancing reaction rates and detection precision, the high-speed droplets generated in

this method, in contrast to conventional liquid-in-liquid generation, represent the basis for a new

approach based on droplet pair collisions for fast efficient micromixing [81], [82]. This

incomparable feature would indeed provide a significant development towards manufacturing fast

and efficient LOC platforms in which airborne microreactors can be constructed and different

reagents can be rapidly mixed afterwards for detection purposes.

40

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