Third Day Poster Session, 17 June 2010 - NanoTR-VI

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Poster Session, Thursday, June 17
Theme F686 - N1123
Electrokinetic Flow Modeling in a Porous Nanochannel using Curvilinear Coordinates
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UMehdi MostofiUP P*, Davood D. GanjiP Mofid Gorji-BandpyP
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PDepartment of Mechanical Engineering, Noshiravani University of Technology, Babol, Iran
Abstract- In this Paper, it is expected to model the behavior of the electrokinetics driven fluid in porous nanochannel. in this case, continuum
theory is no longer valid. As a result, it is necessary to model the Poisson-Boltzmann and Navier-Stokes using molecular simulation. In
continue, for four typical nano-scale particles, porous media assumption is made and validity of the continuum theory in nano-scale is
investigated.
One of the most important subsystems of the micro- and
nano- fluidic devices is their passage or “Micro- and Nano-
Channel”. Nano-channel term is referred to channels with
hydraulic diameter less than 100 nanometers [1]. By
decrease in size and hydraulic diameter some of the physical
parameters such as surface tension will be more significant
while they are negligible in normal sizes.
Concentrating surface loads in liquid – solid interface makes
the EDL to be existed. If the loads are concentrated in the
end of nano-channels, a potential difference will be
generated that forces the ions in the nano-channel. However,
induced electric field is discharged by electric conduction of
the electrolyte.
Rice and Whitehead [2], Lu and Chan [3] and Ke and Liu
[4] studied the flow in capillary tube. None of them solved
the problem based on the curvilinear coordinates system.
Also, all of them studied the problem with existence of the
pressure gradient while in the modern applications, the
pressure gradient can be eliminated and consequently,
solving the problem considering this fact is necessary. In this
paper, for small zeta potentials without pressure gradient
will be studied based on the curvilinear coordinates in a
capillary tube.
In case of electrokinetic flows in porous media, references
[5] – [7] can be mentioned in order to have some review
about it. In this work, a nano-tube with 15 nm radius will be
investigated. Despite most of the works were done, in this
work, curvilinear coordinates will be employed.
Based on [8], in nano-scale, we should aware of the
compatibility of traditional theories that are used in greater
scales. On the other hand, in nano-scale, there are
experimentally proved limitations that, traditional theories
Table 1. (a) Effect of four typical particle diameters on zeta
potential in a 15 nm radius nano-tube
Normalizes Zeta
Radius (nm)
Potential for Particles
1 0.06
2 0.22
4 0.56
8 0.84
are no longer valid. In this paper, it is tried to trespass those
borders and as a result, molecular simulation has been
employed and the nano-tube is assumed to be porous. In this
case, Poisson-Boltzmann equation must be solved [8].
In simulation phase of the work, first of all, analytical
treatment has been employed in order to have non-porous
media results. Figure (a) shows the result in this case. After
that, some specific particle diameters have been investigated
in order to have achievements about the particle diameter
effect on the zeta potential in nano-tube. In this paper,
diameters of 1, 2, 4 and 8 nm are investigated. Table (a)
shows the results of these four simulations. As the
simulation mentions, the greater the particle, the more
significant the zeta potential. The zeta potential have been
given in Table (a) are normalized by the wall zeta potential
in a non-porous similar nano-tube.
In summary, by considering curvilinear coordinates and
applying it on a nano-tube, no porous media is investigated.
Then, for some specific nano-scale particle diameters,
simulation has been applied. In the case of particles, for
greater particles in comparison of the tube diameter,
significant effects of particles have been occurred and as a
result, continuum mechanics are no longer valid. However,
for smaller particles, it has been shown that, continuum
mechanics are valid at least for diffusion layer. This
achievements are in good agreements with experimental
results in [8].
* Corresponding author: mehdi_mostofi@yahoo.com
Figure 1. (a) Normalized distribution of potential as a function of
normalized radius in a non-porous nano-tube with 30 nm diameter.
[1] S. Kandlikar, et. al, Heat Transfer and Fluid Flow in
Minichannels and Microchannels. Elsevier Limited, Oxford (2006).
[2] Rice, C.L. and Whitehead, R. J. Phys. Chem., 69(11), 4017–
4023 (1965)
[3] W.Y. Lo, and K. Chan. J. Chem. Phys., 143, 339–353 (1994)
[4] H. Keh, and Y.C. Liu, J. Colloids and Interface Surfaces, 172,
222–229 (1995)
[5] Coelho, D. et. al. J. Colloid Interface Sci. 181, 169 (1996).
[6] Coelho, D. et. al. Fractals, 5, 507 (1997).
[7] Marino, S. et. al. J. Colloid Interface Sci. 223, 292 (2000).
[8] G. Karniadakis, et. al. Microflows and Nanoflows. Springer
(2005).
6th Nanoscience and Nanotechnology Conference, zmir, 2010 695