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Verification and Validation at the Micro and Nanoscale
Harvey ZambranoA. T. Conlisk
ProfessorDirector, Computational Micro and Nanofluidics Laboratory
Department Of Mechanical and Aerospace EngineeringThe Ohio State UniversityColumbus, Ohio 43210
http://www.mecheng.osu.edu/cmnf
Workshop on Verification and Validation in
Copyright @ A. T. Conlisk 2011
Workshop on Verification and Validation in Computational Science
The University of Notre DameOctober 18, 2011
AcknowledgementsDr. J. P. AlarieDr. Lei ChenDr. Subhra Datta K ll E
Dr. Shuvo RoyDr. Reza Sadr (GT)Prof. Sherwin SingerP f Mi i Y d (GT)
National Science FoundationNSEC (CANPB)Army Research Office
Kelly EversDr. Mauro FerrariDr. William FissellProf. Derek Hansford Ankan Kumar Jennifer McFerranDr. Thompson MeffordProf. Susan Olesik
Prof. Minami Yoda (GT)Dr. Zhi ZhengDr. Wei ZhuHarvey ZambranoDr. Andrew Zydney
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Army Research OfficeDARPANIHCCF
Prof. Susan OlesikJessica PengProf. J. Michael RamseyPrashanth Ramesh
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Outline
• Background and motivation (applications)(applications)
• Definitions
• Alternative Plausible Model: Molecular simulation of electroosmotic flow
• Electroosmotic flow: Lennard JonesElectroosmotic flow: Lennard Jones
• Electroosmotic flow: SPC/E water
• Conclusions
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MICROSCALE MEASUREMENTS• Measurement techniques should be nonintrusive
– Little space for probes or connections in microchannels
– Optical techniques tracers– Since most microscale flows steady (and low Re),
temporal resolution not a major issue
• To measure (velocity, temperature, pressure) distributions in microscale flows, need spatial resolutions of O(0.1–1 m)
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( )– Weak signals Low SNR– Optical interference (e.g. glare) at wall
• Interfacial effects important– Relatively large surface area, small volume
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What We Can’t Do
• Measure velocity temperature and• Measure velocity, temperature and concentration profiles in a nanochannel for both liquids and gases.• Development of analytical/computational models become not only necessary but
ti l
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essential.
• iMEDD configuration. All fluid passes directly
Nanopore Membrane
Ports/Ventsfluid passes directly through nanochannels so we consider each one separately and multiply by the number of channels to obtain total system flow rate.
• Working fluid:Phosphate Buffered Saline(PBS)
Nano-channelArray
Electrode
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Buffered Saline(PBS)
Receiver/Donor Chambers withElectrolyte Solutions
Courtesy A. Boiarski, iMEDD
20,000-50,000 channelsChannel heights from 4-50nm
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Synthetic nanochannel membrane for a renal assist device (RAD)
Hindered transport of large (>10,000 Da) sol tes s ch as
Implantable artificialkidney
Da) solutes such as serum albumin in synthetic nanochannel membrane for hemofiltration by a Renal Assist Device(Pressurized)
Copyright @ A. T. Conlisk 2011
Upstream surface Section through AB
4 mthick
Slit-shaped nanopore:~10 nm deep, ~50 mm wide
Conlisk et al., Annals of Biomedical Eng, vol 37, no 4, pp. 722‐726, 2009.
SEM of membrane
Surface/volume ratio
Volume=hWL
Surface area=2WL
181022 mhV
S
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for h=10 nm
Can tailor surfaces for specific application
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Definitions
•AIAA G-077-1998 Guide for the Verification d V lid ti f C t ti l Fl id D i
•W. L. Oberkampf and C. J. Roy, ``Verification And Validation in Scientific Computing’’, Cambridge, 2010
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and Validation of Computational Fluid DynamicsSimulations
Verification
• Reduce the spatial grid size and time step• Manufactured solutions• Unchanged when continuum simulations are performed at the nanoscale
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Validationis the term given to the process ofis the term given to the process of
determining whether the simulation accurately represents the physical problem
of interest. Validation answers the question: Is the computational model an accurate physical representation of the
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p y pactual real-world problem?
Validation
• Compare with experimental data• But, profiles can’t be measured in nanoscale channels• Compare integrated quantities• Or use an Alternative Plausible
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Model
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Alternative Plausible Model
N t ll i d lid ti b t• Not really viewed as validation, but is a measure of predictive capability• APM provides information on the sensitivity of the problem to entirely different model constructions
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different model constructions
Adjust ionic concentration:
Dimensional Analysis
jNanoscale computations
can be validated usingmicroscale experiments
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Alternative Plausible Model
C t t i d d t
APM example: nuclear waste
Create two or more independent models of the same phenomenon
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burial (time scale)
Oberkampf and Roy 2010
Alternative Plausible ModelMolecular Dynamics Model of
Electroosmotic Flow in aElectroosmotic Flow in aNanochannel
Zhu, Singer, Zheng and Conlisk, Phys. Rev. E, vol. 71, 2005
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• Ions are charged Lennard-Jones particles
• Uniform negative wall charge
• Lennard-Jones solvent with large ion-solvent
Molecular dynamics simulation
• Lennard-Jones solvent, with large ion-solvent attractions mimics solvation in a polar solvent
• Objective: Compare MD with existing continuum theory -Does continuum theory apply at the nanometer scale?
• 31 cations (.22M), 12 anions (.085M), 7757 solvent (*=0.8)
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Does continuum theory apply at the nanometer scale?
• Verified for Poiseuille Flow (pressure driven)
Zhu, Singer, Zheng and Conlisk, Phys. Rev. E(2005)
Electroosmotic flow
Charged walls create charge
Walls are negatively charged.
Charged walls create charge imbalance in the fluid
+ cations
direction of electric field and flow
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Electrolyte flows in response to electric field
anions
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cation
anion
solvent
• The fluid is layered near the walls.
MD simulation of electroosmotic flow
y
• Anions are in the center.
• Cations move most rapidly to the right, faster than the solvent.
• Anions net motion is to the right, but slower than cations or solvent.
O i ll ti d i ill
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• Occasionally a cation and ion will form a temporary bound pair.
Velocity (mobility) profile =5
When y=1, velocity profile calculated from modified PB theory best agrees with simulation; no continuum breakdown
Travis and Giddens (2000): breakdown for ~5 mol diameters
Move lots of excess chargefrom the wall!
2e
y = 1
y = 2
e
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e
e
y = 0
(unmodified PB)
y
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Alternative Plausible ModelMolecular Dynamics Simulations
of a Silica Surface with Discontinuous Charged Patches
in a Chloride-Water FilmZambrano, Pinti, Prakash and Conlisk
To be submitted
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charged patches
electric field
free surface
Electroosmotic Flow: SPC/E water
Periodic boundary conditions in
X and Y directions
charged patches
Amorphous silicasubstrate
b c d
h
X
Y
ZEOF
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Silica slab: 22.8nm x 3.2nm x 2.32nm (17300 atoms)Water molecules: 14000
Cl ions: 150 (0.55 M), Debye length is 0.41nmTotal atoms = 59450
a = 3.5 nmb = 3.5 nmc = 8.0 nmd = 7.8 nmh = ~6.0nm
electrolyte solution
a b c d
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System with and without charged patches with external EF of 0.05 V/nm
no patches σpatches/σ = -0.5EF EF
a b
σpatches/σ = -1 EF EF
EOF
σpatches/σ = -2
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c d
System with and without charged patches with external EF of 0.3 V/nm no patches σpatches/σ = -0.5EF EF
a b
σpatches/σ = -1 EF EF
EOF
σpatches/σ = -2
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c d
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Chloride packing density along Z- direction calculated between the electrodes
Copyright @ A. T. Conlisk 2011EF = 0.1V/nmoutermost atom
layer
Chlorides are in bulk between electrodes
Chloride packing density along Z-direction on the largest electrode
EF = 0.1V/nm
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a boutermost wall atom layer
Chlorides collect on electrodes
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Water packing density along Z-direction on the largest electrode
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EF = 0.1V/nm
Layering at surface
Water axial velocity profiles for systems with patches
σp/σ = -1.0 σp/σ = -0.5
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Inflection pt in velocity due to roughness
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Water velocity profiles for the system without patches
Center of first layer of immobile waters
region where molecular structure, water
orientation and surface roughness are not
of immobile waters
Copyright @ A. T. Conlisk 2011MD and Continuum Approach enforcing
Stick Boundary Condition
roughness are not negligible
Conclusions
• Verification procedures are unchanged for ti l l ti t th lcontinuum calculations at the nanoscale.
• Nanoscale computations can be validated by microscale experiments• MD simulations and the continuum analysis can be used as an Alternative
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Plausible Model to estimate the sensitivity of electroosmotic flow in a nanochannel to different model paradigms.