Theory
In 1965, Rice and Whitehead published the seminal contribution to the theory of the transport of electrolyte solutions in long (ideally infinite) nanometer-diameter capillaries. Briefly, the potential, ϕ, at a radial distance, r, is given by the Poisson-Boltzmann equation,
where κ is the inverse Debye length,
determined by the ion number density, n, the dielectric constant, ε, the Boltzmann constant, k, and the temperature, T. Knowing the potential, φ(r), the charge density can then be recovered from the Poisson equation, whose solution may be expressed as a modified Bessel function of the first kind, I0, and scaled to the capillary radius, a. An equation of motion under combined pressure and electrically-driven flow can then be written,
where η is the viscosity, dp/dz is the pressure gradient, and Fz is the body force driven by the action of the applied electric field, Ez, on the net charge density in the double layer. When there is no applied pressure, the radial distribution of the velocity is given by,
From the equation above, it follows that fluid flow in nanocapillaries is governed by the κa product, that is, the relative sizes of the Debye length and the pore radius. By adjusting these two parameters and the surface charge density of the nanopores, fluid flow can be manipulated as desired.
Read more about this topic: Nanofluidics
Famous quotes containing the word theory:
“If my theory of relativity is proven correct, Germany will claim me as a German and France will declare that I am a citizen of the world. Should my theory prove untrue, France will say that I am a German and Germany will declare that I am a Jew.”
—Albert Einstein (1879–1955)
“A theory of the middle class: that it is not to be determined by its financial situation but rather by its relation to government. That is, one could shade down from an actual ruling or governing class to a class hopelessly out of relation to government, thinking of gov’t as beyond its control, of itself as wholly controlled by gov’t. Somewhere in between and in gradations is the group that has the sense that gov’t exists for it, and shapes its consciousness accordingly.”
—Lionel Trilling (1905–1975)
“The things that will destroy America are prosperity-at-any- price, peace-at-any-price, safety-first instead of duty-first, the love of soft living, and the get-rich-quick theory of life.”
—Theodore Roosevelt (1858–1919)