temperature, viscosity, and charge density effects on …
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US Army Corps of EngineersBUILDING STRONG®
TEMPERATURE, VISCOSITY, AND CHARGE DENSITY EFFECTS ON THE VELOCITY PROFILEOF A NANOCHANNEL ELECTRO-OSMOTIC FLOW
Paul F. Mlakar, John F. PetersSenior Research Scientists
GSL, U.S. Army ERDC Vicksburg, MS
Bohumir JelinekPostdoctoral Fellow
CAVS, Mississippi State University
Sergio FelicelliProfessor, Mechanical Engineering
CAVS, Mississippi State University
( ) ( )[ ] extClNad EzczcezF
−+ −=)(
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Electrokinetic process - definitionsElectorkinetic phenomena: electric field related effects
occurring in heterogeneous fluids in porous materialsElectroosmosis: motion of fluid under the influence of
electric fieldElectrophoresis: motion of particles under the influence of
electric fieldStreaming potential: electric potential generated by
moving fluidCause: Double layer of charges on solid-liquid interface
Applications: dewatering of concrete structures, decontamination, nanoscale devices, even source of electric energy?
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Na+ and Cl- ions solvated in water,confined between two negatively charged Si walls
Applied electric field parallel to the wallsMeasured velocity profiles and ionic concentrationsFinal goal: obtain effective diffusion coefficients and ionic
mobilities to supplement continuum level model
References:R. Qiao and N. R. Aluru: Charge Inversion and Flow Reversal in a Nanochannel Electro-osmotic Flow,
PRL 92 (19) 2004R. Qiao and N. R. Aluru: Multiscale Simulation of Electroosmotic Transport Using Embedding
Techniques, International Journal for Multiscale Computational Engineering 2 (2) 2004
Atomic system configuration
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Construction of simulation cell
Channel walls of silicon crystal surface in (111) direction
Dimensions 4.66x4.22x3.49 nmUniform negative charge on inner
surface layersWalls: 924 uncharged Si atoms
308 neg. charged Si atoms
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Construction of simulation cellPeriodic boundary
conditions in x and y directions => slab with infinite surface area
Studied variation along z direction
Solvation:Randomly inserted 2290 water moleculesAvoided overlap, even across PBC boundaries
xyz
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Construction of simulation cellInsertion of ions:
Replaced random water molecules with Na+ and Cl- ions
Ionic solution:2144 water molecules108 Na+ ions38 Cl- ions
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Energy minimization
Molecules reorient and settle to local minimum of energy position
H from H2O molecules points to the negative surface
Na+ ions move slightly closer to the negatively charged surface
Cl- ions move slightly away from the negatively charged surface
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Pressure adjustment
Bottom wall is fixedExternal force is applied on
the top wall atoms in the downward direction
Magnitude of the external force is calculated so that the total force on each atom corresponds to the desired pressure
External force is balanced by the fluid pressure
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Equilibration of atomic systemEquilibration:
MD simulation, t = 2 nswithout ext. electric fieldT = 300 K
Result:ionic concentration profile is formed along the z direction
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Simulation with applied electric fieldElectric field applied in the +x
direction (to the right)
extE
Na+ ions (dark blue):move in the direction of
or adsorb at the negatively charged surface
Cl- ions (light blue):move opposite to
xyz
extE
extE
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Simulation with applied electric field
E Electric field
extE
Na+ adsorb at the negatively charged surface or move in the direction of
Cl- move opposite to extE
extE
zy
x
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Velocity profiles
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Selective thermostat
Themostating of velocity component in the field direction (x) slightly influences velocity profile – we chose to apply selective (yz) thermostat
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Mass flux areal density profiles
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Concentration profiles
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Temperature dependenceFlux Velocity
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Temperature effects on concentrations
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Temperature effects on driving force( ) ( )[ ] extClNad EzczcezF
−+ −=)(
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ViscosityStokes equation:
Integrated:
Velocity approximation:
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Velocity predicted from charge densityStokes equation:
Blue:inverse power viscosity
Red:constant viscosity
Black:Molecular Dynamics
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Lennard-Jones and Coulomb interactionRGBLennard-Jones
BlackElectrostatic (Coulomb)
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Concentration profiles
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Lennard-Jones and Coulomb interactionRGBLennard-Jones
BlackElectrostatic (Coulomb)
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Adsorption sites
The nearest-to-wall peak of high Na+ concentration corresponds to the favorable adsorption sites on the silicon surface
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Potential energy profile
Potential energy profile of an ions was measured along the line perpendicular to the surface
The line passed through different adsorption sites
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PPPM Ewald sum
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Effects of ionic concentrations
Surface charge:-70 e
Na+:108
Cl-:38
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Effects of ionic concentrations
Surface charge:-70 e
Na+:100
Cl-:30
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Effects of ionic concentrations
Surface charge:-70 e
Na+:93
Cl-:23
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Effects of ionic concentrations
Surface charge:-70 e
Na+:78
Cl-:8
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Effects of surface charge density
Surface charge:-70 e
Na+:100
Cl-:30
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Effects of surface charge density
Surface charge:-60 e
Na+:100
Cl-:40
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Effects of surface charge density
Surface charge:-50 e
Na+:100
Cl-:50
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Effects of surface charge density
Surface charge:-40 e
Na+:100
Cl-:60
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Low surface charge density flow
Surface charge:-4 e
Na+:108
Cl-:104
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Low surface charge density flow
Surface charge:-4 e
Na+:44
Cl-:40
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Low surface charge density flow
Surface charge:-4 e
Na+:28
Cl-:24
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Low surface charge density flow
Surface charge:-4 e
Na+:12
Cl-:8
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Conclusions
Studied temperature, viscosity, and charge density effects on a nanochannel electroosmotic flow by MD simulations
Obtained velocity, mass flux, ionic concentration, and viscosity profiles
Justified temperature dependence of water flow direction by thermal release of adsorbed Na+ ions and spatial variation of viscosity
Demonstrated an improved prediction of velocity profile from charge density using non-constant viscosity
Revealed the dependence of the flow on surface charge density and ionic concentrations