Nanochannel Flow by Quantum MechanicsExplanations of the surprisingly high flow observed in nanochannels by fluid slip at the channel walls are superseded by QED induced ionization of fluid molecules to produce frictionless flow as atoms undergo Coulomb repulsion.
By: QED Radiations Introduction Liquid flow through nanochannels of carbon nanotubes and thin films has been observed [13] to be 25 orders of magnitude higher than predicted by assuming a noslip condition at the channel wall as in the HagenPoiseuille equation of continuum mechanics. To explain this disparity, the fluid is generally thought to slip at the channel wall, but this is questionable because the calculated sliplengths necessary to explain the flow enhancement exceed the typical slip on nonwetting surfaces by 2 to 3 orders of magnitude. Hence, fluid slip at the channel wall is an unlikely explanation for the observed flow enhancement in nanochannels. Instead, flow enhancement is more likely caused by the size effect of QM that causes the viscosity of the fluid to vanish in nanochannels that otherwise does not occur at the macroscale. QM stands for quantum mechanics. Since vanishing viscosity allows the HagenPoiseuille equation to remain valid, MD was performed to show the viscosity does indeed vanish in nanochannels. MD stands for molecular dynamics. Background MD is commonly used [4,5] to explain enhanced nanochannel flow. However, the MD simulations are not valid because QM precludes the atom from having the heat capacity to conserve fluid friction by an increase in temperature. Instead, QED induces atoms in fluid molecules under the TIR confinement of the nanochannel to conserve frictional heat by the creation of EM radiation. QED stands for quantum electrodynamics, TIR for total internal reflection, and EM for electromagnetic. Standard MD computer programs assume the atom has heat capacity, and therefore to obtain valid MD solutions require modification to simulate the QM effect of a vanishing heat capacity on viscosity. See http://www.prlog.org/ Application to Nanochannels In nanochannels, the QM effect during fluid flow is illustrated in the thumbnail. The EM radiation from a laser heats the molecules in the nanochannel while QED conserves the heat by creating EM radiation that ionizes the molecules. However, lasers are not required. Indeed, the fluid molecules flowing through the nanochannel produce viscous frictional heat that is induced by QED to create ionizing EM radiation at the TIR confinement wavelength λ of the nanochannel, Here, λ = 2 nd, where n and d are the refractive index of the fluid and d the tube diameter or thin film thickness. For d < 100 nm,the EM radiation has wavelengths λ in the UV and beyond, i.e., λ < 300 nm. Therefore, QED induced EM radiation in nanochannels has sufficient Planck energy to ionize most fluid molecules having ionization potentials of ~ 10 eV corresponding to λ < 125 nm or d < 45 nm for n = 1.5. What this means is the fluid in nanochannels is charged with Coulomb repulsion between atoms tending to avoid atom contact and reduce viscosity. The reduction in viscosity may be understood by considering the LJ potential between fluid and wall atoms. LJ stands for LennardJones. Here, LJ parameter σ is the repulsive atom core and ε the attractive potential. The Coulomb potential repulses charged atoms to counter the attractive ε potential, and therefore the viscosity is reduced. A similar QM effect occurs as nanocrystals under Joule heating flow through smaller nanopores by Coulomb repulsion of QED induced ionized atoms. See http://www.prlog.org/ MD Simulation and Results The MD simulates a 2D model comprising 100 atoms in a BCC configuration of liquid argon under a constant shear stress. The BCC configuration has atomic spacing of 5.61 Å. The LJ potential is chosen to have σ = 3.45 Å and ε / k = 120, where k is Boltzmann’s constant. The MD computation box is 61.3 Å square. Time steps were < 2 fs. The MD loading imposed a velocity gradient 1.6 x10^{10} / s normal to the flow direction having velocity of 100 m/s over the height of the MD box. After 150000 iterations, the LJ viscosity converged to ~ 80 microPas. Experimentally, the viscosity of liquid argon depends on temperature and varies from 54 to 200 microPas. But agreement between the MD simulation and experiment is not necessary as the purpose was to show the effect of Coulomb repulsion of charged atoms on viscosity. Instead of performing MD for repulsive Coulomb forces between atoms including the attractive LJ potential ε, the Coulomb repulsion was first simulated by neglecting Coulomb repulsion and simply reducing the attractive LJ potential ε by a factor of 100. However, the MD solution diverged in < 20000 iterations suggesting the viscosity did indeed vanish. Because of this, MD solutions including Coulomb repulsion without reducing the attractive potential were not necessary to show frictionless flow in nanochannels. See Nanochannel Flow at http://www.nanoqed.org , 2014. Conclusions 1. Sliplengths [1,2] finding origin in classical physics cannot explain high flow observed in nanochannels. However, arguments [3] that limitless flow observed in nanochannels is precluded by frictional losses at the end of the channel are indeed valid. Ionization of atoms and recombination of charges is very rapid and continually occurring within the nanochannel, but as the atoms leave the channel there is no TIR confinement allowing the atom to regain its classical behavior causing frictional losses to indeed occur. 2. Claims [4] high nanochannel flow can be fully explained in the context of continuum fluid mechanics thereby justifying the lower flow enhancements predicted by MD are not valid. Nanochannel flow does not follow continuum mechanics, but rather QM. In fact, QED induced frictionless flow in nanochannels are likely to produce reported flow enhancements above HagenPoiseuille theory. 3. Under TIR confinement in nanochannels, QM denies the atom the heat capacity to conserve frictional viscous heating by an increase in temperature. Temperature changes simply do not occur in nanochannels. MD solutions [5] showing otherwise are invalid by QM. Instead, the viscous heating is conserved by QED inducing creation of EM radiation that ionizes the atoms to produce Coulomb repulsion that negates the fluid viscosity in the HagenPoiseuille equation to explain the reported flows. References [1] M. Majunder, et al., “Nanoscale hydrodynamics: [2] F. Du, “Membranes of Vertically Aligned Superlong Carbon Nanotubes,” Langmuir, 27, 8437, 2011. [3] T. Sisan and S. Lichter, “The end of nanochannels,” [4] J. Thomas and A. McGaughey, “Reassessing Fast Water Transport Through Carbon Nanotubes. Nano Lett., 8, 2788, 2008. [5] Z. Li, “Surface effects on frictioninduced fluid heating in nanochannel flows,” Phys. Rev. E, 79, 026312, 2009. End
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