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# Micro and Nanofluidics: Historical Perspectives and ChallengesOPEN ACCESS

[+] Author and Article Information
A. T. Conlisk

Professor
Department of Mechanical
and Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210-1107
e-mail: conlisk.1@osu.edu

Manuscript received August 2, 2013; final manuscript received September 13, 2013; published online October 10, 2013. Assoc. Editor: Debjyoti Banerjee.

J. Nanotechnol. Eng. Med 4(2), 020908 (Oct 10, 2013) (4 pages) Paper No: NANO-13-1047; doi: 10.1115/1.4025463 History: Received August 02, 2013; Revised September 13, 2013

## Abstract

In this paper, we discuss the fundamentals of micro and nanofluidics and the interdisciplinary nature of the field. The study of fluid flows at micro and nanoscales inevitably requires expertise in and an understanding of surface chemistry, electrostatics and electrokinetics, electrochemistry, molecular biology, heat and mass transfer, and macroscale fluid mechanics simultaneously. To design devices having micro and nanoscale features requires a team approach involving chemists, biologists, medical researchers and practitioners, engineers, and systems analysts. Significant advances have been made in the last 20 years in developing the capability of designing devices with microscale and nanoscale features. However, challenges remain in each of the three pillars of micro and nanofluidics: modeling, experimentation, and fabrication. Several challenges are discussed; those falling within the areas of modeling and experiment are described in some detail. It is clear in the present research environment that understanding the micro/nanofluidic environment is crucial to achieving the efficient and cost-effective design of biomedical devices.

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## Introduction

When Richard Feynman was writing his paper titled “There's Plenty of Room at the Bottom: An Invitation to Enter a New Field of Physics” [1] presented at the American Physical Society annual meeting on December 29, 1959 there was no such thing as nanotechnology, microfluidics, or nanofluidics. In that paper, he asked the question “Why cannot we write the entire 24 volumes of the Encyclopaedia Britanica on the head of a pin?.” This would require that each of the many thousands of pages of this popular printed encyclopedia be reduced in size by 1/25,000. Feynman's vision in 1959, came at a time when there were no hand calculators, much less mainframe computers, desktops or laptops, and iPods and foreshadowed the revolution in miniaturization that has exploded during the last 20 years [2].

Feynman also suggested the explosion of interest in the science and technology at the length scale of biology, the nanoscale. Because of his vision, since 1989, The Foresight Conference on Advanced Nanotechnology has been held annually. It is to Feynman that we owe thanks for the explosion of the fields of micro and nanotechnology, a branch of which is micro and nanofluidics.

Nanotechnology and, in particular, micro and nanofluidics requires a multidisciplinary approach. The study of fluid flows at micro and nanoscales inevitably requires expertise and an understanding of surface chemistry, electrostatics and electrokinetics, electrochemistry, molecular biology, heat and mass transfer, and macroscale fluid mechanics simultaneously. To design devices having micro and nanoscale features requires a team approach involving chemists, biologists, medical researchers and practitioners, engineers, and systems analysts. As one might guess each of these disciplines speaks a different language and it is sometimes only with great effort that these technical language barriers are overcome.

In this paper, we discuss the fundamentals of micro and nanofluidics and the challenges that face the field in the future. The internet is full of the many advances that have been made in many different application areas. In the last 10 years what Feynman has foreshadowed has come true; we are talking about implantable medical devices that can prevent kidney failure [3], treat cancer, microspheres for drug delivery, devices that address tissue pathology, and a host of other topics [4], including modeling biomolecular transport at the nanoscale level [5]. See the five volume set titled “BioMEMS and Biomedical Nanotechnology” [6] for a discussion of a variety of biomedical applications of nanotechnology and micro and nanofluidics, in particular.

A specific example of a biomedical device is an electroosmotic pump, or sometimes nanopump which is used to induce transport of charged molecules. Such a device is depicted in Fig. 1. This biomedical device is useful for the delivery of various types of proteins, such as albumin and immunoglobulin both of which have many biomedical uses [7]. Eight channels are shown in the depiction but an actual device may employ 20,000–40,000 channels. In general in biomolecular transport and analysis systems, it is essential to have lots of little channels in order to distinguish the often very small molecules that are being analyzed. The device depicted on Fig. 1 is often called a synthetic nanopore membrane. In biology and chemistry, the term membrane is used to describe a thin sheet of porous material that can be either natural (the outer skin of a cell is a membrane) or synthetic.

In Sec. 2, we discuss the fundamentals of micro and nanofluidics and the interdisciplinary nature of the field. Following that we discuss several challenges that may limit development of devices in the future.

## Micro and Nanofluidics

Microfluidics is generally viewed as the study of flows whose primary length scale is below about $100 μm=10-4 m$. Nanofluidics refers to flows at length scales below about 100 nm. In recent years, manufacturing techniques have been developed and used to build entire micromachines, including thermal actuators, microvalves, micro and nanopumps, gears, cantilevers, and other microdevices [8]. In many of these systems, transport is from the microscale to the nanoscale and back to the microscale. As mentioned above, these devices have been used for biomedical applications, such as drug delivery, chemical and biochemical sensors, micromixers and microseparators, rapid molecular analyzers, development of an artificial kidney, and DNA analysis and transport, to name only a few applications. Other nonbiomedical applications include water purification and desalination, defense applications of chemical and biochemical sensing, and the design of batteries and fuel cells. Applications in the biomedical field involve for the most part internal flows in micro and nanochannels and tubes. The fluids are generally electrolyte mixtures with, perhaps a biomolecular component, often a protein (e.g., albumin). Thus mass transfer occurs, and since many biomolecules (e.g., most proteins) are charged, there is an electric field as well. The determination of the identity and rates of transport of ionic and biomolecular species are one of the purposes of many micro/nanoscale devices [2].

Microfluidics, in particular, has historically been thought to comprise three interrelated activities:

1. (1)modeling: computational and theoretical
2. (2)fabrication
3. (3)experimental methods

Models of the devices described above range from continuum analytical and computational methods to molecular dynamics (MD) simulations as the length scale shrinks to the low nanometer range [2]; Bohn [9] discusses some of the experimental methods used to probe single molecules. Because of the small length scales involved, determining precisely the dimension of the fluid conduits is often difficult. Thus, fabrication of microfluidic devices requires precise control at every step of the fabrication process and even with precise control, fabrication tolerances can be greater, relatively speaking, than in macroscale manufacturing [8,10,11].

Moreover, there are inherent limitations to what can be measured at the submicron scale. Consequently, research at the microscale on down requires that the fabricator, experimentalist, and the analyst work closely and in tandem in designing micro and nanofluidic devices. In order to efficiently manufacture laboratories on a microchip, the analysis and computation of flows on a length scale approaching molecular dimensions, the nanoscale, are often required. Moreover, because the pressure drop in a channel of height h scales as $Δp~(1/h3)$, it is prohibitively large for a nanoscale channel. Thus, fluid, biomaterials, such as proteins, and other colloidal particles are most often transported electrokinetically.

In micro and nanofluidics, the surface to volume ratio is very large making the nature of the surface (e.g., its charge, roughness, and whether it is hydrophobic or hydrophilic) very important [2]. The surface to volume ratio for a channel having dimensions (L, h, W) = (1 m, 1 m, 1 m) isDisplay Formula

(1)$SV=2(1W+1h+1L)=6 m-1$

On the other hand, a channel having dimensions (L,h,W) = (3 μm, 1 μm, 40 μm) which is typical of a class of nanopore membranes (Fig. 2), the surface to volume ratio is

For a 20 nm channel, (L,h,W) = (3 μm, 20 nm, 40 μm) [12], the surface to volume ratio is even higherDisplay Formula

(3)$SV~2h~40×109 m-1$

Because of the large surface to volume ratio, a surface roughness, for example, of 5 nm in a 1 μm channel is negligible, whereas in a 10 nm channel that same roughness can have a profound effect on the flow. The same situation occurs for a cylindrical tube. In this caseDisplay Formula

(4)$SV=2R=4D$

where R is the radius of the tube.

1. (1)Surface properties of a channel or tube, such as electrical surface charge and roughness, become very important because of the large surface to volume ratio.
2. (2)Significant increases in flow rate may be attained if the surfaces of the channel are hydrophobic (water hating); that is, significant fluid slip may occur at the wall. This occurrence is termed induced slip, also called apparent slip.
3. (3)The continuum approximation may break down, especially for gas flows.
4. (4)Pressure driven flow is only viable at very low flowrates on the order of nl/min or $10-9(L/min)$, in nanoconstrained channels because of the very large pressure drops required otherwise, on the order of atmospheres.
5. (5)Molecular diffusion which is very slow at the macroscale can be fast at the micro and nanoscale, the time scale being $t~(L2/DAB)$.

From the second comment, it is thus seen that for liquids, whether there is slip or no-slip at the wall can be a function of surface chemistry, whereas in gases, slip is entirely controlled by the magnitude of the Knudsen number, the ratio of the mean free path to the characteristic length scale. However, it should be mentioned that liquid flows remain continuum even for channels whose smallest dimension approaches 10 nm.

## Challenges

Significant advances have been made in the last 20 years in developing the capability of designing devices with microscale and nanoscale features. However, challenges remain in each of the three pillars of micro and nanofluidics. Three of these challenges are:

1. (1)In the modeling realm, current computational methods are not sufficient to resolve complex biomolecular structures. This limitation can hamper the use of computations, for example, in the biochemical sensing area where precise knowledge of protein transport requires a significant knowledge of the size, shape, and electrical properties of the biomolecule.
2. (2)Experimental techniques are insufficient to measure velocity, temperature, and concentration profiles even in a relatively simple mixture of an aqueous salt solution in channels under about $1-5 μm$ in the smallest dimension. This means that theoretical/computational techniques are the sole method for determining these profiles in channels under this dimension.
3. (3)Fabrication of nanoscale structures is still more an art than a science and reproducibility is often not possible. Thus, fabrication of nanostructures for single molecule detection is extremely expensive and time-consuming.

In Secs. 3.1 and 3.2, we discuss the first two of these challenges in more detail.

###### Computational Considerations.

The behavior of a collection of atoms and molecules is completely determined by solving the time-dependent Schröedinger equation for the wave function, Ψ for all the electrons and nuclei in the sample. The wave function contains probabilistic information about the location of each particle as the system evolves in time. For example, let us focus on a single particle (without specifying what the particle actually is) and suppose that particle is constrained to move in the x direction only. Then the wave function Ψ = Ψ (x, t), and quantum mechanics tells us that the probability that the particle will be found between x and x + dx at time t is $|Ψ(x,t)|2dx$. The unit of the wave function is $(length)-d(N/2)$ where N is the number of particles in the system and d is the dimensionality of the space [13]. A good and lucid introduction to the principles of quantum mechanics is the old and short monograph by Gillespie [14].

At the most basic level then, a molecular simulation would result in the determination of the wave function, for all of the electrons and the nuclei in the system. Of course this is a daunting task even for a few particles, and we have not gotten to the flow field! One approximation that can be made results from the observation that the mass of an electron is much smaller than that of a proton, by over 1800 times. Thus, the dynamics of the protons in a system can be decoupled from the dynamics of the electrons and this is called the Born-Oppenheimer approximation. The Born-Oppenheimer approximation requires solving for the wave function for many electrons. For example, suppose the wave function is desired for a system of 4100 water molecules, a system that contains about 1000 electrons. Then for the three dimensional system, the wave function dimension is 3000! A daunting task indeed! Not only daunting, but impossible [2].

The next level of approximation is to perform all of the calculations using some potential energy function that uses empirically determined coefficients. This method is best illustrated by the Lennard-Jones potential, called molecular dynamics simulations. It is this method that is used most often today for molecular calculations. Despite the fact that this empirical method is the most computationally efficient, it still can take several days or a week for a reasonably long computation. So the first challenge for computation of biomolecular transport is the overwhelming computational requirements of MD simulations that cannot resolve to a sufficient degree the structure of a large biomolecule.

The second computational issue stems from the fact that it is well known that particle trajectories computed from satisfying Newton's law are extremely sensitive to the initial conditions. Thus, chaos is present in any system whose particle trajectories are calculated from Newton's law as is the case with MD simulations.

So as an experienced numerical analyst, I am reading this and saying: so what good are the MD results! Well, I went searching for an explanation and found it [15]. The objective of an MD simulation is NOT to precisely predict the trajectories of every particle in the system. The aim of an MD simulation is to predict the state of a system in a mean sense, the same way that a continuum approach is used to predict the state of a system, perhaps electroosmotic flow in a channel. This fact is best stated in Frenkel and Smit [15] who point out that in a MD calculation,

“We wish to predict the average behavior of a system that was prepared in an initial state about which we know something (e.g., total energy) but by no means everything. In this respect, MD simulations differ fundamentally from numerical schemes for predicting the trajectory of satellites through space: In the latter case, we really wish to predict the true trajectory. We cannot afford to launch an ensemble of satellites and make statistical predictions about their destination. However in MD simulations, statistical predictions are good enough.”

Thus, in order to compute properties from the stored particle trajectories, such as density, concentration, and velocity profiles a method for averaging the noisy data is required. The many-body problem is chaotic in the sense that each particle trajectory is strongly dependent on its initial condition. Thus, the trajectories can only be calculated statistically, or as averages of the trajectories of many particles. This averaging process may lead to deletion of some important physics.

The third challenge in the modeling area is the process of developing a continuum model for a nanopore membrane. As mentioned above, an actual device rendered in Fig. 1 may employ 20,000–40,000 channels. These channels can be on the order of h = 10–20 nm in the smallest dimension to distinguish the often very small molecules that are analyzed. A typical channel geometry used in hemofiltration membranes is depicted on Fig. 2. Several computational questions come to mind. Can we solve for the flow in each of the 40,000 channels that make up the membrane? If not, how do we distinguish a typical channel or group of channels in a membrane? Is a statistical analysis required as in MD? I know of no model of a membrane of the type depicted on Fig. 1 that can account deterministically for the flow in the individual channels. Typically, each channel is treated as a separate and distinct entity. Of course, such a model cannot be expected to predict the location of membrane fouling and concentration polarization, two major problems in membranes used today.

###### Experimental Methods at the Micro and Nanoscale.

Most, if not all, experimental methods appropriate for microfluidic applications use tracer particles. Many of the experimental methods used today in the microfluidics area originated in high Reynolds number flows; examples include laser Doppler velocimetry (LDV), molecular tagging velocimetry (MTV) [16], and particle image velocimetry (PIV) [17,18]. These experimental techniques can be distinguished by the type of tracer used and the spatiotemporal characteristics of the measurement: LDV, for example, yields a point measurement of velocity with excellent temporal resolution (up to MHz), while PIV, the most commonly used velocimetry method, gives a two or three velocity components in a 2D plane (2D-2C or 3D-3C), while volumetric (3D-3C) PIV is being extended from the macroscale to the microscale [19]. MTV, on the other hand, typically gives a measurement of up to two of the three velocity components over a one-dimensional line or a two-dimensional plane. An excellent reference book that describes these methods in more detail is the monograph edited by Breuer [20].

The above mentioned experimental visualization techniques have a minimum spatial resolution of about 50 μm for LDV and 500 μm for PIV in macroscale applications [19]. Spatial resolutions as fine as ∼2.5 μm have been achieved with LDV and PIV for applications at the microscale [21]. However, even these “best case” limits exceed the typical pore dimensions in a nanopore membrane by about four orders of magnitude! Thus, it is impossible with these techniques to measure velocity, concentration, and temperature profiles in a channel smaller than these resolution limits, smaller than a few microns. The conclusion must be that these two velocimetry methods should be interpreted as bulk flow measurement techniques at the nanoscale. The level of resolution of these methods at the micro and nanoscale means that developing analytical and computational models for micro and nanoscale flows is not only necessary but essential.

## Conclusions

Understanding the micro/nanofluidic environment is crucial in the efficient and cost-effective design of biomedical devices. The good news is micro/nanofluidic devices are being built and becoming commercial products. The bad news is micro/nanofluidic devices are expensive and often require multiple trials before they work or what is more important, are economical. Moreover, because experiments cannot be made at nanoscale, modeling at the nanoscale is essential since in the nanoscale environment, only flow rate and other global quantities, such as ζ-potential, can be validated. Because of the computational resources required, it is difficult to design devices based on molecular dynamics simulations alone. Nevertheless, this situation does not obviate the fact that there is a crucial need to integrate high fidelity and possibly complex component models with system level design models.

There are other challenges to component/system design strategies that have not been mentioned in the discussion here: there are many unknowns in surface chemistry; there are finite-size ion effects; and unknowns in the properties and structure of complex biomolecules. Regarding this last observation, biomolecular characterization data are lacking and there are little data on how and why proteins and other biomolecules deform and change shape, although this situation is improving with the continued development of the protein data bank (PDB). In the past 10 years, the three dimensional structure of many proteins has been determined experimentally, usually by protein crystallography and the data have been stored in the PDB by Brookhaven National Laboratory. The web site is located at www.rcsb.org and the PDB was originally created in 1971. The Worldwide protein data bank was created in 2004 to coordinate the worldwide dissemination of protein structures. Ribbon diagrams of protein structure, also known as Richardson Diagrams [22], which are an interpolation of the smooth curve through the polypeptide chain of the protein, can be downloaded in a variety of formats. It should be mentioned that all of these structures are for equilibrium conditions; the development of high fidelity models using data from the PDB for biomolecular transport in a possibly complex flow environment is in its infancy.

## Acknowledgements

The work appreciates the support of the Army Research Office under Grant No. 55734EG, Professor Frederick Ferguson, contract monitor and the NSF NSEC Center for the Affordable Nanoenginering of Polymeric Biomedical Devices, EEC-0914790. A more detailed discussion of all of these issues appears in Ref. [2] from which portions of this manuscript have been excerpted.

## References

Feynman, R. P., 1961, There's Plenty of Room at the Bottom, Reinhold Publishing, New York, pp. 282–296.
Conlisk, A. T., 2013, Essentials of Micro- and Nanofluidics With Applications to the Biological and Chemical Sciences, Cambridge University Press, New York.
Humes, H., Fissell, W., and Tiranathanagul, K., 2006, “The Future of Hemodialysis Membranes,” Kidney Int., 69, pp. 1115–1119. [PubMed]
Lee, A. P., and Lee, L. J., eds., 2006, BioMEMS and Biomedical Nanotechnology Volume I Biological and Biomedical Nanotechnology, Springer, New York.
Conlisk, A. T., 2006, “Modeling Biomolecular Transport at the Nanoscale,” BioMEMS and Biomedical Nanotechnology: Biological and Biomedical Nanotechnology, A. P.Lee, L. J.Lee, and M.Ferrari, eds., Springer-Verlag, New York, pp. 399–434.
Ferrari, M., ed., 2006, BioMEMS and Biomedical Nanotechnology, Springer, New York.
Peters, T., 1996, All About Albumin: Biochemistry, Genetics and Medical Applications, 3rd ed., Academic Press, San Diego, CA.
Gad-el Hak, M., 2001, The MEMS Handbook, CRC Press, Boca Raton, FL.
Bohn, P., 2009, “Nanoscale Control and Manipulation of Molecular Transport in Chemical Analysis,” Annual Review of Analytical Chemistry, Vol. 2, E.Yeung and R.Zare, eds., Annual Reviews, Palo Alto, CA, pp. 279–296.
Nguyen, N. T., and Wereley, S. T., 2002, Fundamentals and Applications of Microfluidics, Artech House, Norwood, MA.
Lee, L. J., 2006, “Nanoscale Polymer Fabrication for Biomedical Applications,” BioMEMS and Biomedical Nanotechnology, Volume I Biological and Biomedical Nanotechnology, A. P.Lee and L. J.Lee, eds., Springer, New York, pp. 51–96.
Conlisk, A. T., Datta, S., Fissell, W. H., and Roy, S., 2009, “Biomolecular Transport Through Hemofiltration Membranes,” Ann. Biomed. Eng., 37(4), pp. 732–746.
Styer, D. F., 1996, “Common Misconceptions Regarding Quantum Mechanics,” Am. J. Phys., 64, pp. 31–34.
Gillespie, D. T., 1970, A Quantum Mechanics Primer, International Textbook Company, Scranton, PA.
Frenkel, D., and Smit, B., 2002, Understanding Molecular Simulations From Algorithms to Applications, 2nd ed., Academic Press, San Diego, CA.
Lempert, W. R., Magee, K., Ronney, P., Gee, K. R., and Haugland, R. P., 1995, “Flow Tagging Velocimetry in Incompressible Flow Using Photo-Activated Nonintrusive Tracking of Molecular Motion,” Exp. Fluids, 18, pp. 249–257.
Adrian, R. J., and Yao, C. S., 1985, “Pulsed Laser Technique Application to Liquid and Gaseous Flows and the Scattering Power of Seed Materials,” Appl. Opt., 24, pp. 44–52. [PubMed]
Adrian, R. J., 1991, “Particle-Imaging Techniques for Experimental Fluid Mechanics,” Ann. Rev. Fluid Mech., 23, pp. 261–304.
Yoda, M., 2006, “Nano-Particle Image Velocimetry,” Biomolecular Sensing, Processing and Analysis, R.Bashir and S.Wereley, eds., Springer, New York, pp. 331–348.
Breuer, K., ed., 2005, Microscale Diagnostic Techniques, Springer-Verlag, Berlin.
Czarske, J., Buttner, L., Razik, T., and Muller, H., 2002, “Boundary Layer Velocity Measurements by a Laser Doppler Profile Sensor With Micrometre Spatial Resolution,” Meas. Sci. Technol., 13(12), pp. 1979–1989.
Richardson, J. S., 1985, “Schematic Drawings of Protein Structures,” Meth. Enzymol., 115, pp. 359–380. Available at http://www.ncbi.nlm.nih.gov/pubmed/3853075 [PubMed]
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## References

Feynman, R. P., 1961, There's Plenty of Room at the Bottom, Reinhold Publishing, New York, pp. 282–296.
Conlisk, A. T., 2013, Essentials of Micro- and Nanofluidics With Applications to the Biological and Chemical Sciences, Cambridge University Press, New York.
Humes, H., Fissell, W., and Tiranathanagul, K., 2006, “The Future of Hemodialysis Membranes,” Kidney Int., 69, pp. 1115–1119. [PubMed]
Lee, A. P., and Lee, L. J., eds., 2006, BioMEMS and Biomedical Nanotechnology Volume I Biological and Biomedical Nanotechnology, Springer, New York.
Conlisk, A. T., 2006, “Modeling Biomolecular Transport at the Nanoscale,” BioMEMS and Biomedical Nanotechnology: Biological and Biomedical Nanotechnology, A. P.Lee, L. J.Lee, and M.Ferrari, eds., Springer-Verlag, New York, pp. 399–434.
Ferrari, M., ed., 2006, BioMEMS and Biomedical Nanotechnology, Springer, New York.
Peters, T., 1996, All About Albumin: Biochemistry, Genetics and Medical Applications, 3rd ed., Academic Press, San Diego, CA.
Gad-el Hak, M., 2001, The MEMS Handbook, CRC Press, Boca Raton, FL.
Bohn, P., 2009, “Nanoscale Control and Manipulation of Molecular Transport in Chemical Analysis,” Annual Review of Analytical Chemistry, Vol. 2, E.Yeung and R.Zare, eds., Annual Reviews, Palo Alto, CA, pp. 279–296.
Nguyen, N. T., and Wereley, S. T., 2002, Fundamentals and Applications of Microfluidics, Artech House, Norwood, MA.
Lee, L. J., 2006, “Nanoscale Polymer Fabrication for Biomedical Applications,” BioMEMS and Biomedical Nanotechnology, Volume I Biological and Biomedical Nanotechnology, A. P.Lee and L. J.Lee, eds., Springer, New York, pp. 51–96.
Conlisk, A. T., Datta, S., Fissell, W. H., and Roy, S., 2009, “Biomolecular Transport Through Hemofiltration Membranes,” Ann. Biomed. Eng., 37(4), pp. 732–746.
Styer, D. F., 1996, “Common Misconceptions Regarding Quantum Mechanics,” Am. J. Phys., 64, pp. 31–34.
Gillespie, D. T., 1970, A Quantum Mechanics Primer, International Textbook Company, Scranton, PA.
Frenkel, D., and Smit, B., 2002, Understanding Molecular Simulations From Algorithms to Applications, 2nd ed., Academic Press, San Diego, CA.
Lempert, W. R., Magee, K., Ronney, P., Gee, K. R., and Haugland, R. P., 1995, “Flow Tagging Velocimetry in Incompressible Flow Using Photo-Activated Nonintrusive Tracking of Molecular Motion,” Exp. Fluids, 18, pp. 249–257.
Adrian, R. J., and Yao, C. S., 1985, “Pulsed Laser Technique Application to Liquid and Gaseous Flows and the Scattering Power of Seed Materials,” Appl. Opt., 24, pp. 44–52. [PubMed]
Adrian, R. J., 1991, “Particle-Imaging Techniques for Experimental Fluid Mechanics,” Ann. Rev. Fluid Mech., 23, pp. 261–304.
Yoda, M., 2006, “Nano-Particle Image Velocimetry,” Biomolecular Sensing, Processing and Analysis, R.Bashir and S.Wereley, eds., Springer, New York, pp. 331–348.
Breuer, K., ed., 2005, Microscale Diagnostic Techniques, Springer-Verlag, Berlin.
Czarske, J., Buttner, L., Razik, T., and Muller, H., 2002, “Boundary Layer Velocity Measurements by a Laser Doppler Profile Sensor With Micrometre Spatial Resolution,” Meas. Sci. Technol., 13(12), pp. 1979–1989.
Richardson, J. S., 1985, “Schematic Drawings of Protein Structures,” Meth. Enzymol., 115, pp. 359–380. Available at http://www.ncbi.nlm.nih.gov/pubmed/3853075 [PubMed]

## Figures

Fig. 1

Drawing of a nanopump containing a nanopore membrane. In many of these systems, transport is from the microscale to the nanoscale and back to the microscale.

Fig. 2

Typical geometry for a channel in a nanopore membrane [12]

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