Water Flow Through Nanopore
JULIO MARAÑÓN DI LEO,1 JULIO MARAÑÓN2
1Departamento de Aeronáutica, Facultad de Ingeniería, Universidad Nacional de La Plata, C.C. 67,
La Plata 1900, Argentina
2Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67,
La Plata 1900, Argentina
Received 11 September 2007; accepted 29 October 2007
Published online 10 January 2008 in Wiley InterScience (www.interscience.wiley.com).
DOI 10.1002/qua.21575
ABSTRACT: A molecular dynamics simulation of water flow through a prismatic
surface of van der Waals particles at 300 K is reported. The application of different pressure
gradients to a water produces a large spectrum of average velocities from Poiseuille to
turbulent flow. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem 108: 1623–1628, 2008
Key words: Water flow, skin effect; confinement and molecular dynamics
1. Introduction
I n recent years, there has been a rapid develop-ment of nanoscale technology in a wide range of
applications. Progress in nanotechnology includes
fundamental understanding in areas of biophysics
and materials.
Fluids in micropores are important in many areas
of science and engineering [1, 2]. It should be noted
that the properties of confined fluids differ markedly
from those of the bulk fluid. Many properties of liq-
uids in porous media become inaccessible to experi-
mental measurement when the pore size approaches
molecular dimensions. It is desirable to develop
Correspondence to: J. Marañón; e-mail: maranon@fisica.unlp.
edu.ar
Contract grant sponsor: CONICET, Argentina.
and test molecular theories developed for predict-
ing fluid properties in porous media. Therefore, an
important role for molecular dynamic simulation
(MD) is to explore the assumptions used in exper-
imental results. As a consequence, the macroscopic
flow description must be augmented with the results
of the microscopic physics [3].
The behavior of fluids in confined geometries
is of considerable theoretical interest and practical
importance. There have been many investigations of
the properties of confined liquids using liquid state
theory and computer simulations.
In the case of low-Reynolds-number fluids flow
in a laminar region through a channel has been
described by (MD); the velocity and temperature
profiles found in a good agreement with those
predicted by the hydrodynamics equations [4], by
application of pressure gradient to a single fluid
produces laminar fluid flow and Taylor-Aris hydro-
dynamic dispersion [5], found that small systems
International Journal of Quantum Chemistry, Vol 108, 1623–1628 (2008)
© 2008 Wiley Periodicals, Inc.

DI LEO AND MARAÑÓN
of several thousand molecules exhibit continuum
behavior [6], hydrophobic channels can have sig-
nificant water occupancy despite a reduction in
the number of hydrogen bonds compared to the
bulk fluid [7], the hydrophobicity can close a
sterically open channel to penetration by water,
ions, and small polar solute [8], immiscible fluid
(water/oil) flow through flexible nanotube, the dif-
fusion coefficient of water in the direction of flux,
differs from the quadratic dependence of water
average velocity of Taylor-Aris theory report [9];
and the transport of subcritical Lennard-Jones fluid
in a cylindrical nanopore at low densities can be
explained by hydrodynamic mechanisms alone [10].
Because the constant particle density along the flow
direction, these simulations give limited informa-
tion about diffusive properties of the system, and
calculations of viscosity (from Poiseuille’s equa-
tion) make questionable assumption that contin-
uum hydrodynamics still applies to highly confined
fluids [11].
To this end, we have studied the flow of water
through a prismatic rectangular network of size (a
parallelogram: Lx, Ly, Lz = 3.4, 3.0, 3.0 nm: net con-
stant 0.15 of the quadratic network on the prismatic
surface), of 2,484 single wall van der Waals parti-
cles with MD simulation. The objective of this work
was to study the velocity profiles under different
pressure gradients in a range that goes beyond the
laminar flux and the relation of the self-diffusion
coefficients with the average velocity (Va) of the
hydrodynamic flux.
2. Methods and Models
We carried out NVT nonequilibrium MD sim-
ulation of a water solution, under an external
field, with periodic boundary conditions. The net-
work mentioned earlier acts as reference position
to the van der Waals particles, and it was fixed
by harmonic force to each network node for the
thermal roughness control of the prismatic sur-
face [12]. Deformations of the elastic surface are
important factors that produce instability in the
flux, increasing the probability of wall disintegra-
tion at larger Reynolds number [9]. The harmonic
force restrains the motion of the particles around
this node, which still leaves room for flexibility and
mobility. The van der Waals particles used were
oxygen atoms, and force constant (force constant,
k = 80) was chosen after many simulations, with a
compromise between particle motion flexibility and
simulation stability. These last two conditions have
a strong link with water permeability through the
atomic wall.
This study used detailed representations of the
fluid and the pore walls, which limited the spa-
tial resolutions at which velocity profiles near the
walls could be measured. Since the velocity profiles
were statistical averages over all simulations, the
location of the surface could only be defined in an
average sense. Water density did not become zero
at a precise point, but decayed gradually to zero in
an angstrom-thick region. To eliminate uncertainty
about the location of the fluid boundary and maxi-
mize spatial resolution of the water velocity profile
in the vicinity of the wall, the roughness of the pris-
matic surface was smoothed when water molecules
attempted to cross the surface [10,13–15]. The reflec-
tion gradually heats water molecules near the wall.
Acommon method for removing heat in MD simula-
tion entails the ad hoc rescaling of the instantaneous
velocities of water atoms [14,16].
The prismatic surface confines 800 SPC/E [17]
water molecule (density 0.928 gr/cm3). Periodic
boundary conditions are introduced along the flow
direction (x-direction)in the interest of reducing the
amount of computations needed to obtain useful
results [3].
Forces and configuration energies were com-
puted using the modified GROMOS87 package [18].
Hydrogen atoms and van der Waals particles inter-
act only through coulomb forces. Van der Waals
particles do not interact between them through
Lennard-Jones forces, they interact only with atoms
of the fluid, allowing them to exchange energy
and momentum with the fluid. As regards long-
range electrostatic interaction, it can be assessed
in the GROMOS87 code using the Twin-Range
method [19].
Temperature was controlled by coupling the sys-
tem to thermal bath at 300 K with a time constant
of 0.2 ps. The heat-bath used was developed with a
weak-coupling method, in which the atomic equa-
tions of motion are modified such a manner that the
net result on the system is a first-order relaxation
of the temperature, towards the preset reference
value [20].
The covalent bonds length for water and the
van der Waals particles of the prismatic network
were constrained by the SHAKE procedure (toler-
ance 0.0001 nm). The system was run using a time
step of 3 fs. Trajectories were collected every ten time
steps for further analysis.
1624 INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY DOI 10.1002/qua VOL. 108, NO. 10