Nanofluidic circuitry is a nanotechnology aiming for control of fluids in nanometer scale. Due to the effect of an electrical double layer within the fluid channel, the behavior of nanofluid is observed to be significantly different compared with its microfluidic counterparts. Its typical characteristic dimensions fall within the range of 1–100 nm. At least one dimension of the structure is in nanoscopic scale. Phenomena of fluids in nano-scale structure are discovered to be of different properties in electrochemistry and fluid dynamics.

With the development of microfabrication and nanotechnology, the study of microfluidics and nanofluidics is drawing more attention.[1] Research on microfluidics found its advantages in DNA analysis, lab-on-a-chip, and micro-TAS. Devices in a microfluidic system include channels, valves, mixers, and pumps. Integration of these microfluidic devices enables sorting, transporting, and mixing of substances within fluids. However, the failure of moving parts in these systems is usually the critical issue and the main drawback. Mechanisms to control flow without using mechanical parts are always desired for reliability and lifetime.[2]

In 1997, Wei, Bard and Feldberg discovered that ion rectification occurs at the tip of a nano-sized pipe.[3] They observed that the surface charge at the wall of a nano-pipet induced a non-neutral electrical potential within the orifice. The electrical potential then modifies the concentration of ion species, resulting in an asymmetric current-voltage characteristic for the current through the pipet.

Transport of ions in the electrolyte can be adjusted by tuning the pH value in a dilute ionic solution, or by introducing an external electrical potential to change the surface charge density of the wall.[4] As an analogy to semiconductor devices, the mechanism to control charge carrier transport in electronic devices was established in the area of nanofluidics. In nanofluidics, the active control of ion transport is realized using nano-scale channels or pores.

Research efforts on micro-scaled fluidic systems started to focus on the rectifying phenomena, which can be seen only in nano-scaled systems. In 2006, Professor Majumdar and Professor Yang in University of California, Berkeley built the first "nanofluidic" transistor. The transistor can be turn on or off by an external electrical signal, allowing the control of ionic fluids in a nano-scaled channel. Their work implies a possibility to create a nanofluidic circuitry with logic functions.

The main researchers in the area of nanofluidic devices include Arun Majumdar and Peidong Yang in University of California - Berkeley, Harold Craighead and Brian Kirbyat Cornell University, Juan Santiago at Stanford University, Albert van den Berg in University of Twente, Zuzanna Siwy in University of California - Irvine, and Mark Shannon in University of Illinois - Urbana-Champaign.

For electrolyte solution in a channel with a macro- or micro-scaled radius, surface charges at the wall attract counterions and repel co-ions due to electrostatic force. Therefore, an electrical double layer exists between the wall of channel and the solution. The dimension of the electrical double layer is determined by the Debye length in this system, which is typically much smaller than the channel radius. Most of the solution in the channel is electrically neutral due to the shielding effect of the electrical double layer.

In a nanochannel, however, the solution is charged when the dimension of channel radius is smaller than the Debye length. Therefore, it is possible to manipulate the flow of ions inside the nanochannel by introducing surface charges on the wall or by applying an external electrical potential.

Ionic concentration of solution has an important effect on the ion transport. Because a higher concentration leads to a shorter Debye length for the electrical double layer at the channel wall. Its rectifying effect decreases with increasing ionic concentration. On the other hand, ion rectification can be improved by having a dilute solution.

To analyze the transport of ions in the channel, behaviors of system in electrochemistry as well as fluid mechanics need to be considered. The Poisson–Nernst–Planck (PNP) equations are utilized to describe ionic current flowing through a channel, and the Navier–Stokes (NS) equations are used to represent the fluid dynamics in the channel.

The PNP equations consist of the Poisson equation:[5][6]

∇

2

ϕ

−

1

ε

0

ε

∑

a

z

a

e

n

a

{\displaystyle \nabla ^{2}\phi =-{\frac {1}{\varepsilon {0}\varepsilon }}\displaystyle \sum {a}z{a}en{a}}

and the Nernst–Planck equations, which gives the particle flux of ion species

a

{\displaystyle a}

due to a concentration gradient and electric potential gradient:

J

a

= −

D

a

( ∇

n

a

z

a

e

n

a

k T

∇ ϕ )

{\displaystyle {\boldsymbol {J}}{a}=-D{a}(\nabla n_{a}+{\frac {z_{a}en_{a}}{kT}}\nabla \phi )}

where

ϕ

{\displaystyle \phi }

is the electrostatic potential,

e

{\displaystyle e}

is the unit charge of electron,

ε

0

{\displaystyle \varepsilon _{0}}

is the permittivity in vacuum, and

ε

{\displaystyle \varepsilon }

is the dielectric constant of solution;

D

a

{\displaystyle D_{a}}

,

n

a

{\displaystyle n_{a}}

and

z

a

{\displaystyle z_{a}}

are the diffusivity, the number density of ions, and the valence of ion species

a

{\displaystyle a}

.

The solution in steady-state satisfies the continuity equation. To describe fluid velocity field in the channel, using Navier–Stokes equations:

∇ ⋅ (

n

a

u

J

a

)

0

{\displaystyle \nabla \cdot (n_{a}{\boldsymbol {u}}+{\boldsymbol {J}}_{a})=0}

∇ ⋅

u

= 0

{\displaystyle \nabla \cdot {\boldsymbol {u}}=0}

u

⋅ ∇

u

=

1 ρ

[ − ∇ p + μ

∇

2

u

− (

∑

a

z

a

e

n

a

) ∇ ϕ ]

{\displaystyle {\boldsymbol {u}}\cdot \nabla {\boldsymbol {u}}={\frac {1}{\rho }}[-\nabla p+\mu \nabla ^{2}{\boldsymbol {u}}-(\displaystyle \sum {a}z{a}en_{a})\nabla \phi ]}

where

p

{\displaystyle p}

,

u

{\displaystyle {\boldsymbol {u}}}

,

μ

{\displaystyle \mu }

, and

ρ

{\displaystyle \rho }

are pressure, velocity vector, viscosity, and density of fluid, respectively. The equations above are usually solved with numerical algorithm to determine the velocity, pressure, electric potential, and ionic concentration in the fluid, as well as the electric current flow through the channel.

Ionic selectivity is defined to evaluate the performance of a nano-channel for ionic flow control.[7] Ionic selectivity is the ratio of the difference in currents of majority and minority carriers to the total current carried by both positive and negative ions,

I

{\displaystyle I}

. For a nanochannel with perfect control over cation and anion, the selectivity is unity. For a nanochannel without ionic flow control, the selectivity is zero.

S

I

−

I

−

I

I

−

{\displaystyle S={\frac {I^{+}-I^{-}}{I^{+}+I^{-}}}}

A nanofluidic diode is a device that rectifies ionic current through an electrolyte-filled nanopore or nanochannel. Rectification occurs when applied voltages of equal magnitude but opposite polarity produce currents of different magnitudes. The device therefore conducts more readily under one voltage polarity, although current can still flow under the opposite polarity.[8]

Rectifying behaviour can arise from asymmetry in pore geometry, surface-charge distribution, or the conditions near a pore opening. Examples include charged conical nanopores and channels with different surface charges along their length.[9]

In charged conical pores, the applied voltage can produce different ion distributions depending on its polarity. Ion accumulation near the narrow opening increases local conductivity, whereas ion depletion reduces it. These changes produce the higher-current and lower-current states associated with rectification. Which voltage polarity produces each state depends on the pore orientation and surface charge.[8]

By applying an additional electrode on a nanochannel as the gate electrode, it is possible to adjust the electrical potential inside the channel.[10][11] A nanofluidic field-effect transistor can be made of silica nanotubes with an oxide as the dielectric material between the metal gate electrode and the channel.[12] The tuning of the ionic current, therefore, can be achieved by changing the voltage applied on the gate. The gate bias and the source-drain bias are applied to adjust the cation and anion concentration within the nanochannel, therefore tuning the ionic current flowing through it.[13]

This concept is an analogy to the structure of a metal-oxide semiconductor field-effect transistor (MOSFET) in electronic circuits. Similar to a MOSFET, a nanofluidic transistor is the fundamental element for building a nanofluidic circuitry. There is possibility to achieve a nanofluidic circuitry, which is capable of logic operation and manipulation for ionic particles.

Since the conductance of ionic current flow is controlled by the gate voltage, using a material with high dielectric constant as the wall of the channel is desired. In this case, there is a stronger field seen within the channel due to a higher gate capacitance. A channel surface with a low surface charge is also desired in order to strengthen the effect of potential tuning by gate electrode. This increases the ability to spatially and temporally tune the ionic and electrostatic environment in the channel.

By introducing an asymmetric field effect along the nanochannel, a field-effect reconfigurable nanofluidic diode is feasible,[15] which features post-fabrication reconfiguration of the diode functions, such as the forward/reverse directions and the rectification degrees. Unlike the nanofluidic field-effect transistor, where only the amount of ions/molecules is regulated by an electrostatic potential, the field-effect reconfigurable diode can be used to control both directions and magnitudes of ion/molecule transport. This device could be deemed as the building blocks for ionic counterpart of the electronic field-programmable gate array.

Ionic bipolar transistors can be made from two conical channels with the smallest opening in nano-scaled dimension. By introducing opposite surface charges at each side, it is able to rectify ionic current as an ionic diode. An ionic bipolar transistor is built by combining two ionic diodes and forming a PNP junction along the inner surface of the channel. While the ionic current is from emitter end to collector end, the strength of the current can be modulated by the base electrode. The surface charge at the channel wall can be modified using chemical methods, by changing the electrolyte concentration or pH value.

Nanofuidic triode is a three-terminal double junction nanofluidic device composed of positive-charged alumina and negative-charged silica nanochannels.[16] The device is essentially a three-terminal bipolar junction transistor. By controlling the voltage across emitter and collector terminals, one can regulate the ion current from base terminal to one of the other two terminals, functioning as an ionic single-pole, double-throw switch.

When surface charges present at the wall of a channel of micro-scaled width, counterions are attracted and co-ions are repelled by electrostatic force. The counterions form a shielding area near the wall. This region penetrate into solution to a certain distance