CHAPTER

1Introduction

CHAPTER OUTLINE

1.1 Length scales ...................................................................................................... 1

1.2 Scope and layout of the book ............................................................................... 6

1.3 Future outlook...................................................................................................... 7

References ................................................................................................................. 8

Select bibliography ..................................................................................................... 8

1.1 Length scalesMicrofluidic and nanofluidic (µ-Nafl) systems are defined as systems with functional

components with operational or critical dimensions in the 1�100 µm range for

microfluidics and 1�100 nm for nanofluidics, respectively. Therefore, we now have

the ability to study and systematically manipulate exceedingly small volumes

(approaching the order of zeptoliters or 10221 l has been discussed in literature and

listed in several bibliographic references throughout this book) of fluids and

other species. Consequently, the ability to engineer processes and phenomena that

operate at fundamental molecular lengths driving a host of applications in chemical,

biological, and particle separations, sensors, energy generation and harvesting, envi-

ronmental remediation, water purification, and at the interface of several science and

engineering disciplines is being pursued. Figure 1.1 shows a conceptual plot that

depicts how the interplay between critical length scales and subsequent device

volumes can drive several applications for µ-Nafl systems.

An identifying feature of all µ-Nafl systems is the surface-area-to-volume

(SA/V) ratio. Consider two examples: (1) a simple circular cross-section nanopipe

with a diameter of 10 nm and a length of 1 µm will have a SA/V ratio on the

order of 107 m21 and (2) a microchannel with a rectangular cross-section with a

width of 100 µm, depth of 20 µm, and a length of 1 mm will have an SA/V ratio

on the order of 105 m21. The discussion for SA/V ratios is pertinent because sev-

eral forces and related phenomena important to fluid transport at these length

scales change as SA/V ratios increase, as the governing principles dominating

these phenomena assume different relative magnitudes. For example, in the

1S. Prakash & J. Yeom: Nanofluidics and Microfluidics. DOI: http://dx.doi.org/10.1016/B978-1-4377-4469-9.00001-9

© 2014 Elsevier Inc. All rights reserved.

24 mm

40 mm

40 mm

Length

Volume(m3)

Applications

101 100 101 100 101 100

Nanofluidics(μμm)

Microfluidics(mm)

Macrofluidics(mm to m)

101

Fuel cell components

Active membrane parts

Pipelines extending toseveral meters (or longer)

Flames inmicrochannels

Electrophoreticseparation chip by Agilent

Multi layer, multifunction mass-limited sampleanalysis chip(University of

Illinois)

10−21

10−18

10−15

10−12

10−9

10–6

10−3

1

Nanofluidic sensors

Operational waterdesalination systems with

micro-nanofluidiccomponents

FIGURE 1.1

A conceptual figure which shows the common length scales spanned by microfluidics and nanofluidics along with a few examples of devices

and systems. The macroscale pipeline is used as an example to provide a reference.

nanopipe example above, if the walls of the nanopipe have an electric charge, the

surface of the channel will exert an electrostatic force. Since the charge is distrib-

uted over the channel or pipe area along the walls, the areas charge density

becomes an important consideration. Therefore, to set up a simple scaling law

comparing any surface-area term to a volume term we see that,

SA term ~ l2cand

V term ~ l3c

(1.1)

where lc denotes characteristic length.

Consequently,

SA

V~

l2cl3c

51

lc(1.2)

Equation (1.2) implies that surface-driven terms (see Chapter 3 for more

details) will dominate as volumes decrease with reducing characteristic lengths. In

Figure 1.2, we illustrate the concept of various phenomena that are influenced by

the SA/V ratio and can be important in designing and constructing µ-Nafl systems.

In turn, this gives insight to how the equations and fundamental principles can be

used for implementing the ideas to building successful devices and systems.

Following our discussion, scaling analysis can therefore provide insight to how

fluid phenomena in µ-Nafl may occur in contrast to the macroscale counterparts.

It should be noted that scaling analyses typically provide broad ideas and trends but

more detailed experimentation and analysis may be needed for specific details.

Applied electricpotential

Measurementsand

quantification

SA/V ratio

Ph

eno

men

a

1 102 104 106 108 1010

Mixing

Becomes faster → basis for rapidnanofluidic injectors and mixers

Appliedpressures

Increases rapidly

Need to measure small currents, flows, chargefluctuations, concentrations, low light environments →need for new instrumentation or creative approaches

Signal to noise is an important consideration

Electric field increases rapidly → fluid driving usingbody forces becomes viable and useful

FIGURE 1.2

A conceptual schematic showing some of the important phenomena that influence µ-Naflsystems as function of SA/V ratios.

31.1 Length scales

Figure 1.2 discusses several critical aspects of the scaling analysis in a brief, pictorial

representation. Let us begin by considering mixing. Often in several µ-Nafl systems

(see examples in Chapters 5 and 6), there is a need to bring in distinct fluid streams

and allow these to mix. Due to confinement of the fluid in a device with large SA/V

ratios, often the viscous and surface effects will dominate the flow phenomena (see

Chapter 3 for further details), and consequently, mixing is largely driven by molecu-

lar diffusion. The time scales for molecular diffusion can be expressed as

td 5l2cDAB

(1.3)

where td is the diffusion time scale, lc is the characteristic length, and DAB is the dif-

fusion coefficient of the species of interest. Equation (1.3) shows the diffusion time

scales as the square of the characteristic length. Consequently, as we approach the

nanoscale with decreasing lc, time scales needed for diffusion decrease rapidly. For

example, if we compare two devices and, one device has half that of the other, the

smallest lc device needs four times less time to mix the same species by diffusion as

compared to the device with larger lc. This scaling has permitted development of

rapid mixers and injectors for nanoscale mixing and schemes for generating vortex-

like structures at the interface of micro- and nanochannels to enhance mixing.

As we discuss in detail in Chapter 2, µ-Nafl systems with aqueous electrolyte

solutions usually operate using principles of electrokinetics or using an applied

electric potential to generate a body force that drives the fluid flow as opposed to

pressure commonly used at the macroscale. Therefore, let us consider the scaling

of a force due to the electric field. From electrostatics, the force F on a charge

(let us say an ion or particle in the flow field; see Figure 1.3.) q in an electric

field E is given by,

F-

5 q E-

(1.4)

VappliedVwall

F = qElc

L

Axial direction of flow

FIGURE 1.3

A schematic depicting a channel with flow and the forces due to an electric field shown in

the axial direction. Note that the potential at the wall due to a finite wall surface density,

σs, will also cause a force on any particles in the fluid. A more detailed discussion of the

forces and the consequences in terms of flow phenomena and formation of electric

double layers are discussed in Chapters 2 and 3.

4 CHAPTER 1 Introduction

For a simple scaling analysis here, we will consider a 1-D field and look at the

magnitudes, so we will not consider the directionality or the vector nature of

the forces in this discussion. The electric field is usually scaled as a function of the

length, L across the potential drop; therefore, for an applied potential V the electric

field is given by,

E5V

L(1.5)

It can be noted from Eq. (1.5) that the electric field scales inversely with the

length over which the potential acts or for the forces,

F5 qV

lc(1.6)

where we have now replaced L with lc as the forces act over the characteristic

length of interest. Therefore, it is clear that the electric field force will scale

inversely with the length, that is, the smaller the characteristic length, the higher

the force due to a potential V. Contrast this with the gravitational forces that may

act in a µ-Nafl system. One useful non-dimensional parameter to consider is the

Bond number, Bo which compares gravitational forces to surface tension forces.

Equation (1.7) describes Bo as:

Bo5ðρl 2 ρFÞgl2c

σ(1.7)

where σ is the surface tension, g is the acceleration due to gravity, and ρl is the

density of the liquid or gas droplet within the surrounding fluid of density, ρF.Note that the numerator of Eq. (1.7) describes the gravitational force term

with respect to the surface tension force in the denominator. Since the numerator

scales as square of the characteristic length, the importance of gravitational forces

decreases rapidly with shrinking device length scales.

In Chapter 6, we discuss separations as one of the major application areas for

micro- and nanofluidics. It is also useful to look at some of the forces that influence

separation phenomena such as electrophoresis. Equation (1.4) describes the net electri-

cal force on a charged particle. Now, if the particle is a sphere of radius a and moves

with a velocity U in a fluid, the drag force, FD, opposing the motion is given by,

FD 5 6πηaU (1.8)

where η is the fluid viscosity, and when the electrostatic force balances the drag,

the velocity is given by,

U5qE

6πηa(1.9)

Therefore, from Eqs. (1.8) and (1.9) we once again note the scaling for forces (and

a measurable velocity) on the characteristic length, a, for the spherical particle.

The discussion here applies to charged particles. In many cases, polarizable or

dielectric particles have also been studied. In addition, there could be time-varying

51.1 Length scales

(e.g., AC potentials) electric potentials and consequently, electric fields that are also

time-varying have been used. In such cases, phenomena like dielectrophoresis can

become important. The dielectrophoretic force arises on a particle due to dielectric

polarization in the presence of a time-varying (usually non-uniform) electric field.

The dielectrophoretic force, FDEP, on a spherical particle is given by,

FDEP 5 2πa3εm Re½fCM�rðE-U E-Þ

fCM 5εp 2 εmεp 1 2εm

(1.10)

where fCM is the Clausius�Mossotti factor and εp denotes the complex dielectric

permittivity of the particle, and εm denotes the complex dielectric permittivity of

the medium. Once again, we note the scaling depends on the size of the particle,

and in contrast to the electrophoretic force, the scaling varies as the cube of the

size of the particle. Physically, fCM can be considered to provide a measure of the

frequency dependence of the polarization effects as the complex permittivities

vary with the frequency of the electric potentials causing the field and are

expressed as,

ε5 εR 2 iσω

(1.11)

where εR is the real part of the permittivity, σ denotes the electrical conductivity,

and ω is the frequency.

The above discussion shows that length scales can play a critical role in how

different phenomena occur at the micro- and nanoscale. Scaling analysis can help

provide a quick comparative analysis of the dominance of one aspect or force

over another. For example, scaling analysis has been shown to be useful in study-

ing effects of velocity, as the velocity field in electroosmotic flow (see Chapter 2

for definitions) of a solution with ionic strength of 1 M through a 45 nm channel

is similar to that of a 0.2 mM solution through a 1 µm channel. Much more detail

is available on dimensional and scaling analysis in Conlisk’s book as listed in the

bibiliography. One caveat we would like to point out is that the scaling analysis

or use of non-dimensional parameters is inherently based on the continuum

assumption, and so care must be taken in predicting or extrapolating trends when

such an assumption might not be valid at nanoscale.

1.2 Scope and layout of the bookThe main theme for this book is structured around the idea of “systems.”

Therefore, a “system” is defined as the main functional unit of interest.

Consequently, the system can be a small particle or a region in space where flu-

idic phenomena occur, or a device component, or a complete operational unit that

6 CHAPTER 1 Introduction

can perform multiple functions. The context for each type of system is discussed

throughout the book.

In Chapter 2, we present a brief theoretical background needed for µ-Naflsystems. All essentials are covered here; however, for an in-depth discussion the

interested reader is directed to the vast bibliography throughout the book.

Chapter 3 discusses the role of interfaces and presents an overview of how inter-

nal interfaces (e.g., surfaces) and external interfaces (e.g., connections to the out-

side world) can influence fluidic phenomena. At the same time, the challenges

and opportunities that arise due to interfacial phenomena and the theory behind

these phenomena are also discussed. Chapter 4 presents a detailed discussion on

the micro- and nanofabrication aspects needed to design and construct these

devices. Chapters 5 and 6 present an overview for fluid manipulation, lab-on-

chip, and energy- and environment-related applications using a large variety of

examples from the scientific literature to demonstrate the versatility of µ-Naflsystems. In Chapter 5, we present two case studies that discuss details about an

integrated gas-sensing and chromatography system and a microscale nanofluidic

flow regime sensor. The case studies capture the multi-component fabrication. In

addition, the case studies also highlight the complexity of µ-Nafl systems that can

perform several unit operations on a single platform.

1.3 Future outlookNascent scientific fields like micro- and nanofluidics (really started as a field in

1990s) can evolve rapidly and grow in directions unforeseen by the best scientists

and engineers. Therefore, our attempts to gaze into the future are fraught with

grave risks. However, a few trends are clearly emerging. With continued and

rapid advances in micro- and nanofabrication, scaling of devices or device arrays

to meet requirements for high-throughput applications are now a reality. µ-Nafldevices continue to grow in areas of sensors, medical and bio-related applications,

and energy and environment applications. This growth is built on several years of

work on micropumps, microvalves, and thermal-fluid phenomena at the micro-

and nanoscale.

On the theoretical and computational side, techniques like molecular dynamics

elucidate the fundamentals at length scales where the continuum assumptions

do not work. Continuum methods provide insight to experimentally observed

phenomena, and large-scale system modeling along with multiscale models can be

one way to bridge all the various theories, length scales, and experimental efforts.

Finally, while several microscale systems have been built, nanoscale systems

still operate for the most part, at the individual component level. Therefore, truly

integrated nanosystems or hybrid micro-nanosystems present an opportunity for

further growth. We believe that the potential is vast and is challenged only by the

ingenuity and imagination of fellow scientists and engineers.

71.3 Future outlook

References[1] Conlisk AT. Essentials of micro- and nanofluidics: with applications to the biological

and chemical sciences. Cambridge, UK: Cambridge University Press; 2012.

[2] Prakash S, Pinti M, Bellman K. Variable cross-section nanopores fabricated in silicon

nitride membranes using a transmission electron microscope. J Micromech Microeng

2012; 22.

[3] Prakash S, Yeom J, Shannon M.A, editors. A microfabricated impedance sensor for

ionic transport in nanopores. 11th solid-state sensors, actuators, and microsystems

workshop. Hilton Head Island, SC;2006.

Select BibiliographyAbgrall P, Nguyen N-T. Nanofluidics. Artech House; 2012.

Israelachvili J. Intermolecular and surface forces. London: Academic Press; 1991.

Madou M. Fundamentals of microfabrication. Boca Raton, Florida: CRC Press; 1997.

Madou MJ. Fundamentals of microfabrication and nanotechnology. Boca Raton, FL: CRC

Press; 2012.

Nguyen N-T, Wereley ST. Fundamentals and applications of Microfluidics. Artech House;

2010.

Piruska A, et al. Nanofluidics in chemical analysis. Chem Soc Rev 2010;39:1060�72.

Prakash S, Piruska A, Gatimu EN, Bohn PW, Sweedler JW, Shannon MA. Nanofluidics:

systems and applications. IEEE Sensors J 2008;8(5):441�50.

8 CHAPTER 1 Introduction