(720g) Explaining Ultra-High Water Flow Rates Observed in Carbon Nanotube Membranes
AIChE Annual Meeting
2013
2013 AIChE Annual Meeting
Separations Division
Carbon Based Nano-Structured Membranes
Thursday, November 7, 2013 - 5:30pm to 5:50pm
Explaining ultra-high water flow rates
observed in carbon nanotube membranes
Davide Mattia,1* Francesco
Calabr?2
1Department of Chemical Engineering, University of
Bath, UK
2 DIEI, Universit? di Cassino, Italy
d.mattia@bath.ac.uk,
www.bath.ac.uk/nanotech
Liquid flow through nanoporous media has been studied in disciplines
as diverse as membrane science, soil permeability and cell physiology. In all
these fields, though, the emphasis has been on the macroscopic outcome, often neglecting the effects of intermolecular
forces and liquid-pore wall physicochemical interactions on liquid behaviour. The availability of carbon nanotubes (CNTs) as a platform for mass
transport studies at the nanoscale has generated a large number of experimental
and molecular dynamics studies which have shown unexpected fluid behaviours
compared to the macroscale. The most striking one has
been the observation of several orders of magnitude higher liquid flow
velocities compared to the no-slip Haagen-Poiseuille equation. ADDIN EN.CITE ADDIN EN.CITE.DATA 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These experimental results have generated an
intense debate about the underlying physical phenomena and whether such flow
can be explained within the continuum model on which traditional fluid
mechanics is based or whether there is a size threshold below which it no
longer applies (Figure 1). These results also hold great promise for filtration
applications in general and water desalination in particular.
ADDIN EN.CITE
<EndNote><Cite><Author>Lee</Author><Year>2011</Year><RecNum>1294</RecNum><DisplayText><style Article">17</ref-type><contributors><authors><author>Lee,
Kah Peng</author><author>Arnot, Tom C.</author><author>Mattia,
D.</author></authors></contributors><titles><title>A
review of reverse osmosis membrane materials for desalination--Development to
date and future potential</title><secondary-title>Journal of Membrane
Science</secondary-title></titles><periodical><full-title>Journal
of Membrane Science</full-title><abbr-1>J. Membr.
Sci.</abbr-1><abbr-2>J Membr
Sci</abbr-2></periodical><pages>1-22</pages><volume>370</volume><number>1-2</number><keywords><keyword>Desalination</keyword><keyword>Reverse
osmosis (RO)</keyword><keyword>Membrane
material</keyword><keyword>Membrane
performance</keyword><keyword>Nano-materials</keyword></keywords><dates><year>2011</year></dates><isbn>0376-7388</isbn><call-num>1294</call-num><urls><related-urls><url>http://www.sciencedirect.com/science/article/B6TGK-51SPS08-2/2/6f8473a09...
10.1016/j.memsci.2010.12.036</electronic-resource-num></record></Cite></EndNote>3
Figure 1.
Water plugs in 40-60 nm and 2-5 nm diameter carbon nanotubes, respectively,
showing a transition from a continuum to a sub-continuum behaviour.
ADDIN EN.CITE ADDIN EN.CITE.DATA 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The micrograph on the left
has been obtained using an environmental SEM by preferential condensation of
water inside a CNT. The micrograph on the right was obtained using high
resolution TEM and shows the coexistence of water liquid and vapor in a capped
CNT.
The attempts made so far to explain these phenomena
have focused on the slip length at the wall and its possible dependencies on a
wide range of parameters, from contact angle to roughness, viscosity and shear
rate. All these solutions are somewhat unsatisfying when slip values in the
order of tens of micrometers for membranes with CNTs with diameters of only few
nanometers are obtained. Moreover, no model has yet been capable of explicitly
relating the flow enhancement with solid-liquid molecular interactions
occurring at the channel walls.
Here a model capable of
explaining the observed dependence of the flow enhancement on the membrane
channels' characteristic dimensions and surface wettability is proposed. The
model can accurately predict the effect of each component for membrane channels
and nanotubes of different sizes, wall surface chemistry and structure.
Comparison with the experimental and modelling data available shows good
agreement (Figure 2).
ADDIN EN.CITE
<EndNote><Cite><Author>Mattia</Author><Year>2012</Year><RecNum>1472</RecNum><DisplayText><style db-id="zsta22rsnd5zpfesz2opddwwttf2sxfsfx09">1472</key></foreign-keys><ref-type
name="Journal
Article">17</ref-type><contributors><authors><author>Mattia,
D.</author><author>Calabr?, F.</author></authors></contributors><titles><title>Explaining
high flow rate of water in carbon nanotubes via solid–liquid molecular
interactions</title><secondary-title>Microfluidics and
Nanofluidics</secondary-title></titles><periodical><full-title>Microfluidics
and Nanofluidics</full-title><abbr-1>Microfluid.
Nanofluid.</abbr-1></periodical><pages>1-6</pages><keywords><keyword>work
of adhesion</keyword><keyword>surface
diffusion</keyword><keyword>slip</keyword><keyword>solid-liquid
interaction</keyword></keywords><dates><year>2012</year></dates><publisher>Springer
Berlin / Heidelberg</publisher><isbn>1613-4982</isbn><call-num>1472</call-num><urls><related-urls><url>http://dx.doi.org/10.1007/s10404-012-0949-z</url></related-urls></urls><...6 The proposed model is based on a two-phase
model for water flow in cylindrical channels with reduced viscosity at the
wall,
, and a non-zero velocity at the wall which is solely
a function of solid-liquid interactions (ex. graphitic carbon and water) and
the applied pressure. By solving the Haagen-Poiseuille equation with this
velocity at the wall term, the following expression for the fluid flow
enhancement,
, at the wall is obtained:
where
and
are the
tube/channel/pore length and radius, respectively;
is the
thickness of the annular region and
is the
liquid bulk density;
is the
surface diffusion term arising from the chemical potential generated by the
pressure gradient, ADDIN EN.CITE
<EndNote><Cite><Author>Ruckenstein</Author><Year>1983</Year><RecNum>1314</RecNum><DisplayText><style no-slip boundary condition of
hydrodynamics</title><secondary-title>Journal of Colloid and
Interface
Science</secondary-title></titles><periodical><full-title>Journal
of Colloid and Interface Science</full-title><abbr-1>J. Colloid
Interface Sci.</abbr-1><abbr-2>J Colloid Interface Sci</abbr-2></periodical><pages>488-491</pages><volume>96</volume><number>2</number><keywords><keyword>slip</keyword><keyword>surface
diffusion</keyword></keywords><dates><year>1983</year></dates><isbn>0021-9797</isbn><call-num>1314</call-num><urls><related-urls><url>http://www.sciencedirect.com/science/article/B6WHR-4CT7DM2-NX/2/a2dbcea1...(83)90050-4</electronic-resource-num></record></Cite></EndNote>7 and
is the
work of adhesion which represents the strength of the solid-liquid interaction
at the tube/channel/pore wall. The two latter terms can be measured
independently and at the macroscale for any solid-liquid couple.
Two recent publications have offered further validation of the
proposed model: First, a molecular dynamics paper of water flow in CNTs of
different lengths has found a linear dependence of the flow enhancement with
the former. ADDIN EN.CITE
<EndNote><Cite><Author>Nicholls</Author><Year>2011</Year><RecNum>1358</RecNum><DisplayText><style Jason</author></authors></contributors><titles><title>Water
transport through (7,7) carbon nanotubes of different lengths using molecular
dynamics</title><secondary-title>Microfluidics and
Nanofluidics</secondary-title></titles><periodical><full-title>Microfluidics
and Nanofluidics</full-title><abbr-1>Microfluid.
Nanofluid.</abbr-1></periodical><pages>257-264</pages><volume>12</volume><number>1-4</number><keywords><keyword>Physics
and
Astronomy</keyword></keywords><dates><year>2011</year></dates><publisher>Springer
Berlin /
Heidelberg</publisher><isbn>1613-4982</isbn><call-num>1358</call-num><urls><related-urls><url>http://dx.doi.org/10.1007/s10404-011-0869-3</url></related-urls></urls><...8
Second, water flow measurements in hydrophilic alumina nanochannels
with diameters ranging from 20 nm to 100 nm have shown to be well represented
by the above equation. For the smallest channels tested, the water permeability
is more than double than the theoretical prediction using the Haagen-Poiseuille
equation. Though such an enhancement is significantly smaller than what has
been measured in hydrophobic carbon nanotubes, it clearly shows that flow enhancement
and water slippage occur on hydrophilic surfaces as well, contrary to existing
theoretical models (Figure 2, red empty circles ○).
ADDIN EN.CITE
<EndNote><Cite><Author>Lee</Author><Year>2012</Year><RecNum>1486</RecNum><DisplayText><style Peng</author><author>Leese,
Hannah</author><author>Mattia, Davide</author></authors></contributors><titles><title>Water
flow enhancement in hydrophilic
nanochannels</title><secondary-title>Nanoscale</secondary-title></titles><periodical><full-title>Nanoscale</full-title></periodical><keywords><keyword>slip</keyword><keyword>flow
enhancement</keyword><keyword>Hagen-poisuille</keyword><keyword>AAO</keyword></keywords><dates><year>2012</year></dates><publisher>The
Royal Society of Chemistry</publisher><isbn>2040-3364</isbn><call-num>1486</call-num><urls><related-urls><url>http://dx.doi.org/10.1039/C2NR30098B</url></related-urls></urls></record...9
Finally, the above equation has been successfully used to model
molecular dynamics simulations of water flow in 2nm diameter silicon carbide
(SiCNTs, yellow diamonds ♦) and boron
nitride (BNNTs, blue squares ■)
nanotubes.10
Figure
2. Normalized flow
enhancement as a function of nanotube radius (dashed curve). Literature:
○ - (Thomas and McGaughey, Nano
Lett, 2009); ● - (Holt et al., Science,
2006); × - (Thomas et al., Int J Therm
Sci, 2010); ▲ - (Majumder et al., Nature, 2005); ♦ - (Du et al., Langmuir, 2011); ■ - (Whitby and Quirke, Nano Lett, 2007). Literature values (open symbols for MD and full
symbols for experimental) are reported as a range between minimum and maximum
possible values. ○ Enhancement values for water flow in alumina nanopores; ♦ SiCNTs; ■ BNNTs; Adapted
from ref.s ADDIN EN.CITE ADDIN EN.CITE.DATA 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
References:
ADDIN EN.REFLIST 1. D.
Mattia and Y. Gogotsi, Microfluid.
Nanofluid., 2008, 5, 289-305.
2. M.
Whitby and N. Quirke, Nat. Nano.,
2007, 2, 87-94.
3. K.
P. Lee, T. C. Arnot and D. Mattia, J.
Membr. Sci., 2011, 370, 1-22.
6. D.
Mattia and F. Calabr?, Microfluid.
Nanofluid., 2012, 1-6.
7. E.
Ruckenstein and P. Rajora, J. Colloid
Interface Sci., 1983, 96,
488-491.
8. W.
Nicholls, M. Borg, D. Lockerby and J. Reese, Microfluid. Nanofluid., 2011, 12,
257-264.
9. K.
P. Lee, H. Leese and D. Mattia, Adv Math
Lett, 2012.
10. K.
Ritos, D. Mattia, F. Calabr? and J. Reese, 2013.