Flow of Fluids and Solids
at the Nanoscale
Thomas Prevenslik
QED Radiations
Discovery Bay, Hong Kong, China
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Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
Introduction
(Fluids)
The Hagen-Poiseuille equation of classical fluid flow that
assumes a no-slip condition at the wall cannot explain the
dramatic increase in flow found in nanochannels.
Even if slip is assumed at the wall, the calculated slip-lengths
are found exceed the slip on non-wetting surfaces by 2 to 3
orders of magnitude.
Similarly, MD simulations of nanochannel flow cannot explain
the flow enhancement.
MD = molecular dynamics.
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Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
Introduction
(Solids)
In solids, classical kMC cannot explain how crystals in a
nanotube under the influence of an electric current flow
through a constriction that is smaller than the crystal
kMC = kinetic Monte Carlo.
However, QM and not classical physics governs the
nanoscale.
QM = quantum mechanics.
At the nanocale, fluid and solid atoms are placed under
EM confinement that by QM requires their heat capacity
to vanish.
EM = electromagnetic.
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Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
QM v. Classical Physics
Unlike classical physics, QM precludes the conservation of
viscous and frictional heat in fluid and solid atoms by the
usual increase in temperature.
MD and kMC based in classical physics therefore require
modification for QM at the nanoscale.
Conservation of viscous and frictional heat proceeds by
QED inducing creation of EM radiation that ionizes the
atoms to cause atomic separation under
Coulomb charge repulsion.
QED = quantum electrodynamics.
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Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
Approach
MD simulations of liquid argon flow in a nanochannel show the
viscosity to vanish suggesting the flow is upper bound by the
frictionless Bernoulli equation
Simplified extension of Bernoulli equation to the flow of a solid
crystal through a nanotube suggests cohesion to vanish,
Fluid and solid at the nanoscale flow as a loosely bound
collection of atoms under Coulomb repulsion
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Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
Theory
Heat capacity of the atom
TIR Confinement of Nanostructures
Conservation of energy and momentum
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Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
Planck Energy - E - eV
Heat Capacity of the Atom
0.1
Classical
Physics
(MD,
Comsol)
Classical
Physics
(MD,
Comsol)
0.01
hc
l
E
  hc  
exp  lkT   1
 
 
QM
(kT = 0)
0.001
kT
0.0258 eV
0.0001
0.00001
1
10
100
1000
Thermal Wavelength - l - microns
At the nanoscale, the atom has no heat capacity by QM
Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
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TIR Confinement
Nanostructures have high surface to volume ratio 
Absorbed EM energy temporarily confines itself to the surface
to form the TIR confinement
QED converts absorbed EM energy to standing waves that
ionize the nanostructure or escape to surroundings
Heat
QED
QED
Surface
Ionization
ld/ 2
Absorption
Radiation
Radiation
f = ( c/n) / l
Standing Wave
l/2=d
E=hf
Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
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Conservation of Energy
Lack of heat capacity by QM precludes EM energy
conservation in discrete molecules and nanostructures
by an increase in temperature, but how does
conservation proceed?
Proposal
Absorbed EM energy is conserved by creating QED
induced excitons (holon and electron pairs) at the TIR
resonance
Upon recombination, the excitons emit EM radiation that
charges the molecule and nanostructure or is lost to the
surroundings.
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Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
Conservation of Momentum
Absorption of EM energy  photon velocities vanish
Excitons are created at zero velocity
Momentum of photons = Momentum of excitons = 0
Momentum is conserved because EM energy is absorbed
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Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
Potentials
Frictionless Fluids / Solids
Atom + QED Charge
QED
Charge
Zero

Atom
QED charge makes atomic attraction vanish   = 0
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Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
MD v. QM
MD assumes the atoms have thermal kT energy or the
heat capacity to conserve EM energy by an increase in
temperature, but QM does not
QM requires the Nose-Hoover thermostat to maintain
the model at constant absolute zero temperature.
Classically, temperature creates pressure. QM requires
the temperature to create excitons and charge that
produces repulsive Coulomb forces between atoms.
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Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
MD Simulation
Usually, MD solutions of nanochannel flow are performed with
Lees and Edwards periodic boundary conditions.
But charging the atoms requires long range corrections that
may be avoided by using a discrete MD model and
considering all atoms without a cut-off in force computations
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Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
Lennard-Jones Potential
The L-J simulation of the atomic potential
𝑈𝐿𝐽 = 4

𝑅
12

−
𝑅
6
 = repulsive
 = attractive
The L-J potential minimum occurs at R = 21/6 
ULJ = - .
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Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
Electrostatic Force
The electrostatic energy UES from the QED induced charge
𝑈𝐸𝑆
𝑒2
=
4𝑜 𝑅
The fraction c of UES to counter the attractive potential 
𝑈𝐿𝐽
421/6 𝑜 
𝑐 =
=
𝑈𝐸𝑆
𝑒2
The electrostatic repulsion force F between atoms
e2
F=
4 𝑜 𝑅 2
,  < c
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Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
Temperature
MD simulations valid by QM require the viscous heat is not
conserved by an increase in temperature
MD solutions are therefore made near absolute zero
temperature, say 0.001 K to avoid temperature dependent
atom velocities.
Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
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Model
The BCC configuration assumed a discrete 2D model of 100
atoms of liquid argon in a 32.6 A configuration.
Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
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Loading
The MD loading was a velocity gradient normal to the
flow of 100 m/s over the height of the MD box.
Unlike Lees-Edwards, the MD computation box is
distorted after 25000 iterations
(Solution 150000 iterations)
Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
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MD Solution
The fraction c of the available electrostatic energy UES to
counter the attractive potential  is,
c =
ULJ
UES
=
4 21/6 𝑜 
𝑒2
Taking  = 120  k for argon, the fraction c = 0.0027.
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Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
MD Results
MD solutions were obtained for various  to determine the
optimum at which the viscosity vanished
Viscosity [ Pa-s]
4.0E-04
2.0E-04
0.0E+00
-2.0E-04
 = 0.0006 < c = 0.0027
-4.0E-04
-6.0E-04
Collectively, 4 pairs of atoms
participated
in reducing 2 atom friction
-8.0E-04
-1.0E-03
-1.2E-03
-1.4E-03
0
50000
100000
150000
Iteration
Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
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Experimental Data
 = QM / QM, 0
QM is the actual flow QM,0 is the Bernoulli equation
Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
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Conclusions
High flow in nanochannels is the consequence of QM that
requires the heat capacity of the atom under EM confinement
to vanish and negate the conservation of viscous heat by an
increase in temperature.
Instead, the viscous heat is conserved by QED inducing the
creation of EM radiation that ionizes the fluid molecules to
produce a state of Coulomb repulsion that overcomes the
attractive potential between atoms.
Nanochannels produce frictionless Bernoulli flow as the fluid
viscosity vanishes and reasonably supports experiments.
Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
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Flow of Solids
Iron crystals under an electric current fit through a constriction
in the nanochannel that is smaller than the crystal itself ?
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Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
kMC Solutions
Flow of metal crystals through smooth uniform nanochannels is
generally thought caused by electromigration based on kMC
Classical kMC  atom has kT energy  invalid by QM
But as kT  0, V  0, the crystal does not move.
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Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
Analysis
Instead of temperature changes, QED conserves the Joule
heat to charge all atoms in crystal
For a voltage difference V* acting across nanotube length L,
the force F across a crystal atom of cubical dimension b
having charge q = unit electron charge,
V ∗
F=q
b
L
Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
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Bernoulli Equation
The pressure P across the atom is, P = F / b2
giving the atom velocity V
V=
2P
=

qV ∗
2
bL
Experiment  V = 1.4 micron/s , L=2 micron, V* = 0.2 Volts
For iron, b =0.22 nm,  = 7880 kg/m3  V = 135 microns/s
2 orders of magnitude higher !!!
Only 1% of crystal atoms are charged ?
Fe (n=1.25) < CNT graphite (n=2.5) 
Rerun tests with Si (n=3.2) crystal ?
Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona
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Questions & Papers
Email: nanoqed@gmail.com
http://www.nanoqed.org
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Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, 20-21 July, Barcelona