Flow of Fluids and Solids at the Nanoscale Thomas Prevenslik QED Radiations Discovery Bay, Hong Kong, China Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 1

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. Introduction (Fluids) Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 2

Introduction (Solids) Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 3 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.

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. Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 4

Approach Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 5 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

Heat capacity of the atom TIR Confinement of Nanostructures Conservation of energy and momentum Theory Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 6

Heat Capacity of the Atom 7 kT eV Classical Physics (MD, Comsol) Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona Classical Physics (MD, Comsol) QM (kT = 0) At the nanoscale, the atom has no heat capacity by QM

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 f = ( c/n) / / 2 = d E = h f TIR Confinement 8 Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona Heat d Ionization QED Radiation QED Radiation Surface Absorption / 2 Standing Wave

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. Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 9

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 Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 10

Frictionless Fluids / Solids Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona QED charge makes atomic attraction vanish   = 0 11

MD v. QM Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 12 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.

MD Simulation Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 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 13

Lennard-Jones Potential Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 14

Electrostatic Force Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 15 The electrostatic energy U ES from the QED induced charge The fraction  c of U ES to counter the attractive potential  The electrostatic repulsion force F between atoms

Temperature Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 16 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 K to avoid temperature dependent atom velocities.

Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona The BCC configuration assumed a discrete 2D model of 100 atoms of liquid argon in a 32.6 A configuration. 17 Model

Loading Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 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 iterations (Solution iterations) 18

MD Solution 19 Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona

MD Results Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 20 MD solutions were obtained for various  to determine the optimum at which the viscosity vanished  = <  c = Collectively, 4 pairs of atoms participated in reducing 2 atom friction

Experimental Data Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 21 = Q M / Q M, 0 Q M is the actual flow Q M,0 is the Bernoulli equation

Conclusions 22 Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 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.

Flow of Solids Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona Iron crystals under an electric current fit through a constriction in the nanochannel that is smaller than the crystal itself ? 23

Classical kMC  atom has kT energy  invalid by QM But as kT  0, V  0, the crystal does not move. kMC Solutions Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona Flow of metal crystals through smooth uniform nanochannels is generally thought caused by electromigration based on kMC 24

Analysis Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 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, 25

Bernoulli Equation Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona The pressure P across the atom is, P = F / b 2 giving the atom velocity V Experiment  V = 1.4 micron/s, L=2 micron,  V* = 0.2 Volts For iron, b =0.22 nm,  = 7880 kg/m 3  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 ? 26

Questions & Papers Proc. 2nd Conference on Heat Transfer Fluid Flow, HTTF'2015, July, Barcelona 27