Lab on a Chip TUTORIAL REVIEW Field effect nanofluidics Shaurya Prakash* and A. T. Conlisk* Cite this: Lab Chip,2016,16,3855 Nanoscale fluid transport through conduits in the 1–100 nm range is termed as nanofluidics. Over the past decade or so, significant scientific and technological advances have occurred in the domain of nanofluidics with a transverse external electrical signal through a dielectric layer permitting control over ionic and fluid flows in these nanoscale conduits. Consequently, this special class of nanofluidic devices is commonly re- Received 26th May 2016, ferred to as field effect devices, analogous to the solid-state field effect transistors that form the basis for Accepted 16th August 2016 modern electronics. In this mini-review, we focus on summarizing the recent developments in field effect nanofluidics as a discipline and evaluate both tutorially and critically the scientific and technological ad- DOI: 10.1039/c6lc00688d vances that have been reported, including a discussion on the future outlook and identifying broad open www.rsc.org/loc questions which suggest that there are many breakthroughs still to come in field-effect nanofluidics. Introduction The discipline most often associated with the detailed studies on transport processes is fluid mechanics. The story The ability to move ions, molecules, and water over nanoscale of the evolution of present-day nanofluidics can be related to dimensions with exquisite spatial and temporal control imply- the first experiments in 1838 by Jean Louis Marie Poiseuille ing high precision and selectivity is fundamental to all life in identifying the relations governing motion of blood.1 processes and several engineered systems. The growing em- Using pressure to drive flows, Poiseuille found that phasis and interest in the transport and behaviour of both single and small ensembles of ions and molecules in water (1:1) led to the emergence of nanofluidics as a multi-disciplinary area of study. Therefore, nanofluidics defines fluid-based where Q is the volumetric flow rate of a fluid driven by a transport processes within systems with critical dimensions Δ – pressure drop p across a tube of length L and diameter d. on the order of 1–100 nm.1 3 Consequently, as the diameter of the tube approaches nano- The domain encompassed by nanofluidics is broad with fluidic length scales, driving pressures become enormous many different types of devices, systems, and consequently (e.g. for water the pressure drop across a 100 μm long chan- applications impacted by nanofluidics. Among this variety, −18 3 nel, 1 nm in diameter for only an attoliter (10 m ) per sec- there is a class of devices, referred to as ‘field-effect’ nano- ond incompressible laminar flow would be greater than fluidic devices that borrow technological inspiration from the 2 3 GPa ). Therefore, pressure driven flows for nanofluidics solid-state electronic or semiconductor devices and form the 13,14 find niche applications. basis for this review article. Specifically, in the context of this One notable aspect of nanofluidics, and perhaps micro- article, field effect follows the analogy to solid-state electron- fluidics, is the ability for these systems to be a ‘unifier’ of ics, where an externally applied potential in a transverse di- physical principles. In particular, fluid mechanics plays the rection to the flow generates an electric field within the work- dominant role in the successful operation of these devices. ing fluid volume to affect ion and fluid transport. Notably, Moreover, because of the large surface area to volume (SA/V) the electrode being used to apply the transverse potential ratio, surfaces may be tailored electrically to achieve the de- is fluidically isolated from the nanofluidic conduit by a 15 sired objective. For many lab-on-chip applications, mass dielectric layer. transfer occurs for ions and solutes in aqueous solutions We begin by discussing many fundamental concepts that which can also be used to transport charged biomolecules govern all of nanofluidics. We also note that over the years nu- and is essential to understand. This means that the develop- merous advances have been made in many aspects of different ment of micro- and nanodevices considered here requires nanofluidics and related nanofabrication technologies with – knowledge of fluid flow and mass transfer, electrostatics, several excellent reviews and books available to the readers.1 12 electrokinetics, electrochemistry, and possibly molecular biology. All of the essential principles governing device phys- Department of Mechanical and Aerospace Engineering, The Ohio State University, ics between these disciplines occur simultaneously in a given Columbus, OH 43210, USA. E-mail: [email protected], [email protected] application. Consequently, it may be said that micro- and This journal is © The Royal Society of Chemistry 2016 Lab Chip,2016,16, 3855–3865 | 3855 Tutorial review Lab on a Chip nanofluidics bring together or unify and integrate multiple Moreover, in most channels (Fig. 1), we start with the analy- scientific disciplines in a large number of applications. sis of a simpler configuration. Consider long channels where In considering the equations of motion that describe the the channel length is much larger than the width and height, interaction between forces and the subsequent motion of and the aspect ratio A = h/W ≪ 1 and the flow is fully devel- fluids, there are two main classes of forces that drive flows. oped and steady. It is also worth noting that the convective The first one is surface forces (e.g. pressure), and the second terms in the Navier–Stokes equations vanish identically due one is body forces (e.g. gravity or forces arising from electric to the fully developed and one-dimensional approximation or magnetic fields). Since mechanically applied pressure- that is commonly invoked. driven forces for nanofluidics are not practical, the use of Since the use of the electric field is the most common body forces such as electric fields is common.3 However, it is method of inducing the body force to generate transport, it is also worth noting that the use of capillary forces and osmotic commonly applied in nanofluidics (and also in microfluidics).3 gradients is also finding application for manipulation and Moreover, as described in the applications section, for field- transport of fluids in these small conduits. Next, fundamen- effect nanofluidic devices, strong electrolytes such as KCl and tal concepts underlying nanofluidics are described. NaCl form the basis for nearly all reported data. Therefore, un- der such conditions, the salt component is nearly entirely dis- Fundamental concepts, governing sociated and so the electrolyte mixture to be analyzed nomi- nally comprises three components: undissociated water and equations, and assumptions cations and anions from the salt. In the presence of the elec- tric field, the molar flux, N , for species A for a dilute solution Theoretical analysis for nanofluidic devices and components A will then be given by the Nernst–Planck equation: relies on the choice of nanoscale conduit geometry. It is im- portant to briefly review the broad-ended terminology used by (1:4) a variety of researchers. Initial investigations began in ‘ultra- 16 17 fine’ capillaries or narrow cylindrical channels. With the Here, DAB is the binary diffusion coefficient, μA is the ionic advent of advancing computing capability coupled with ad- mobility and can be related to the diffusion coefficient by vances in microfabrication and nanofabrication, a variety of nanoscale conduits were developed.3 Notably, the cylindrical with F being the Faraday constant, R being the uni- configurations were referred to as either nanocapillaries, versal gas constant, T being the absolute temperature, being nanotubes, or nanopores depending on the substrate mate- rials and aspect ratio. A different name was adopted for non- the electric field, and zA being the ionic valence. The second circular cross-sectional nanochannels referring to conduits term on the right hand side of eqn (1.4) is called electrical mi- with width and height significantly greater than the depth as gration. Now, the governing equation for the transport of spe- non-circular, slit-like nanochannels. Essentially, many nano- cies A in terms of concentration can also be written as scale conduits or nanoarchitectures exist and fall under the domain of nanofluidics. (1:5) In order to better understand the underlying physics, we begin with the governing equations for steady, incompress- ible flow in a channel. The Navier–Stokes equations in vector form are given by (1:2) where fB is the body force and u is the streamwise velocity in the x direction.1 In many cases and most commonly for the types of flows discussed in this mini-review, the flow can be as- sumed to be fully developed and the equation of motion in the streamwise direction is given in dimensionless form by (1:3) Fig. 1 Geometric layout of a nanochannel that allows analysis together with the use of approximations to eliminate the use of 2D or 3D modelling and focus on 1D modelling since aspect ratios A = h/W ≪ 1. The Note that in eqn (1.3) ,withh being the height of the schematic shows channel length L,widthW, and height h along with the x y z u v w λ , ,and components of velocity in , ,and if the modelling is done channel and D being the Debye length, as discussed below. in Cartesian coordinates. The flow is streamwise along L.Figure The first term on the right hand side corresponds to the reproduced with permission from A. T. Conlisk, Essentials of Micro- and dimensionless body force in the presence of an electric field.1 Nanofluidics, Cambridge University Press, New York, 2013. 3856 | Lab Chip,2016,16, 3855–3865 This journal is © The Royal Society of Chemistry 2016 Lab on a Chip Tutorial review Here, Ex, Ey,andEz are the scalar components of the electric expressed as mole fractions and also accounted for in calcu- field in the x, y,andz directions, and the diffusion coefficient lations for electrical potential and fluid velocity.