def runSimpleTrenchSystem(faradaysConstant=9.6e4,
gasConstant=8.314,
transferCoefficient=0.5,
rateConstant0=1.76,
rateConstant3=-245e-6,
catalystDiffusion=1e-9,
siteDensity=9.8e-6,
molarVolume=7.1e-6,
charge=2,
metalDiffusion=5.6e-10,
temperature=298.,
overpotential=-0.3,
metalConcentration=250.,
catalystConcentration=5e-3,
catalystCoverage=0.,
currentDensity0=0.26,
currentDensity1=45.,
cellSize=0.1e-7,
trenchDepth=0.5e-6,
aspectRatio=2.,
trenchSpacing=0.6e-6,
boundaryLayerDepth=0.3e-6,
numberOfSteps=5,
displayViewers=True):
cflNumber = 0.2
numberOfCellsInNarrowBand = 10
cellsBelowTrench = 10
yCells = cellsBelowTrench \
+ int((trenchDepth + boundaryLayerDepth) / cellSize)
xCells = int(trenchSpacing / 2 / cellSize)
from fipy.tools import serialComm
mesh = Grid2D(dx=cellSize,
dy=cellSize,
nx=xCells,
ny=yCells,
communicator=serialComm)
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
distanceVar = DistanceVariable(name='distance variable',
mesh=mesh,
value=-1.,
hasOld=1)
bottomHeight = cellsBelowTrench * cellSize
trenchHeight = bottomHeight + trenchDepth
trenchWidth = trenchDepth / aspectRatio
sideWidth = (trenchSpacing - trenchWidth) / 2
x, y = mesh.cellCenters
distanceVar.setValue(1.,
where=(y > trenchHeight) |
((y > bottomHeight) &
(x < xCells * cellSize - sideWidth)))
distanceVar.calcDistanceFunction(order=2)
catalystVar = SurfactantVariable(name="catalyst variable",
value=catalystCoverage,
distanceVar=distanceVar)
bulkCatalystVar = CellVariable(name='bulk catalyst variable',
mesh=mesh,
value=catalystConcentration)
metalVar = CellVariable(name='metal variable',
mesh=mesh,
value=metalConcentration)
expoConstant = -transferCoefficient * faradaysConstant \
/ (gasConstant * temperature)
tmp = currentDensity1 * catalystVar.interfaceVar
exchangeCurrentDensity = currentDensity0 + tmp
expo = numerix.exp(expoConstant * overpotential)
currentDensity = expo * exchangeCurrentDensity * metalVar \
/ metalConcentration
depositionRateVariable = currentDensity * molarVolume \
/ (charge * faradaysConstant)
extensionVelocityVariable = CellVariable(name='extension velocity',
mesh=mesh,
value=depositionRateVariable)
surfactantEquation = AdsorbingSurfactantEquation(
surfactantVar=catalystVar,
distanceVar=distanceVar,
bulkVar=bulkCatalystVar,
rateConstant=rateConstant0 + rateConstant3 * overpotential**3)
advectionEquation = TransientTerm() + AdvectionTerm(
extensionVelocityVariable)
metalEquation = buildMetalIonDiffusionEquation(
ionVar=metalVar,
distanceVar=distanceVar,
depositionRate=depositionRateVariable,
diffusionCoeff=metalDiffusion,
metalIonMolarVolume=molarVolume,
)
metalVar.constrain(metalConcentration, mesh.facesTop)
from surfactantBulkDiffusionEquation import buildSurfactantBulkDiffusionEquation
bulkCatalystEquation = buildSurfactantBulkDiffusionEquation(
bulkVar=bulkCatalystVar,
distanceVar=distanceVar,
surfactantVar=catalystVar,
diffusionCoeff=catalystDiffusion,
rateConstant=rateConstant0 * siteDensity)
bulkCatalystVar.constrain(catalystConcentration, mesh.facesTop)
if displayViewers:
try:
from mayaviSurfactantViewer import MayaviSurfactantViewer
viewer = MayaviSurfactantViewer(distanceVar,
catalystVar.interfaceVar,
zoomFactor=1e6,
datamax=0.5,
datamin=0.0,
smooth=1,
title='catalyst coverage')
except:
viewer = MultiViewer(
viewers=(Viewer(distanceVar, datamin=-1e-9, datamax=1e-9),
Viewer(catalystVar.interfaceVar)))
else:
viewer = None
levelSetUpdateFrequency = int(0.8 * narrowBandWidth \
/ (cellSize * cflNumber * 2))
for step in range(numberOfSteps):
if step > 5 and step % 5 == 0 and viewer is not None:
viewer.plot()
if step % levelSetUpdateFrequency == 0:
distanceVar.calcDistanceFunction(order=2)
extensionVelocityVariable.setValue(depositionRateVariable())
distanceVar.updateOld()
distanceVar.extendVariable(extensionVelocityVariable, order=2)
dt = cflNumber * cellSize / extensionVelocityVariable.max()
advectionEquation.solve(distanceVar, dt=dt)
surfactantEquation.solve(catalystVar, dt=dt)
metalEquation.solve(metalVar, dt=dt)
bulkCatalystEquation.solve(bulkCatalystVar,
dt=dt,
solver=GeneralSolver(tolerance=1e-15,
iterations=2000))
try:
import os
filepath = os.path.splitext(__file__)[0] + '.gz'
print catalystVar.allclose(numerix.loadtxt(filepath), rtol=1e-4)
except:
return 0
def runGold(faradaysConstant=9.6e4,
consumptionRateConstant=2.6e+6,
molarVolume=10.21e-6,
charge=1.0,
metalDiffusion=1.7e-9,
metalConcentration=20.0,
catalystCoverage=0.15,
currentDensity0=3e-2 * 16,
currentDensity1=6.5e-1 * 16,
cellSize=0.1e-7,
trenchDepth=0.2e-6,
aspectRatio=1.47,
trenchSpacing=0.5e-6,
boundaryLayerDepth=90.0e-6,
numberOfSteps=10,
taperAngle=6.0,
displayViewers=True):
cflNumber = 0.2
numberOfCellsInNarrowBand = 20
mesh = TrenchMesh(cellSize=cellSize,
trenchSpacing=trenchSpacing,
trenchDepth=trenchDepth,
boundaryLayerDepth=boundaryLayerDepth,
aspectRatio=aspectRatio,
angle=numerix.pi * taperAngle / 180.)
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
distanceVar = GapFillDistanceVariable(name='distance variable',
mesh=mesh,
value=-1.)
distanceVar.setValue(1., where=mesh.electrolyteMask)
distanceVar.calcDistanceFunction()
catalystVar = SurfactantVariable(name="catalyst variable",
value=catalystCoverage,
distanceVar=distanceVar)
metalVar = CellVariable(name='metal variable',
mesh=mesh,
value=metalConcentration)
exchangeCurrentDensity = currentDensity0 + currentDensity1 * catalystVar.interfaceVar
currentDensity = metalVar / metalConcentration * exchangeCurrentDensity
depositionRateVariable = currentDensity * molarVolume / charge / faradaysConstant
extensionVelocityVariable = CellVariable(name='extension velocity',
mesh=mesh,
value=depositionRateVariable)
catalystSurfactantEquation = AdsorbingSurfactantEquation(
catalystVar,
distanceVar=distanceVar,
bulkVar=0,
rateConstant=0,
consumptionCoeff=consumptionRateConstant * extensionVelocityVariable)
advectionEquation = TransientTerm() + FirstOrderAdvectionTerm(
extensionVelocityVariable)
metalEquation = buildMetalIonDiffusionEquation(
ionVar=metalVar,
distanceVar=distanceVar,
depositionRate=depositionRateVariable,
diffusionCoeff=metalDiffusion,
metalIonMolarVolume=molarVolume)
metalVar.constrain(metalConcentration, mesh.facesTop)
if displayViewers:
try:
from .mayaviSurfactantViewer import MayaviSurfactantViewer
viewer = MayaviSurfactantViewer(distanceVar,
catalystVar.interfaceVar,
zoomFactor=1e6,
datamax=1.0,
datamin=0.0,
smooth=1,
title='catalyst coverage',
animate=True)
except:
class PlotVariable(CellVariable):
def __init__(self, var=None, name=''):
CellVariable.__init__(self, mesh=mesh.fineMesh, name=name)
self.var = self._requires(var)
def _calcValue(self):
return numerix.array(self.var(self.mesh.cellCenters))
viewer = MultiViewer(
viewers=(Viewer(
PlotVariable(
var=distanceVar), datamax=1e-9, datamin=-1e-9),
Viewer(PlotVariable(var=catalystVar.interfaceVar))))
else:
viewer = None
levelSetUpdateFrequency = int(0.7 * narrowBandWidth / cellSize /
cflNumber / 2)
step = 0
while step < numberOfSteps:
if step % 10 == 0 and viewer is not None:
viewer.plot()
if step % levelSetUpdateFrequency == 0:
distanceVar.calcDistanceFunction()
extensionVelocityVariable.setValue(
numerix.array(depositionRateVariable))
dt = cflNumber * cellSize / max(extensionVelocityVariable.globalValue)
distanceVar.extendVariable(extensionVelocityVariable)
advectionEquation.solve(distanceVar, dt=dt)
catalystSurfactantEquation.solve(catalystVar, dt=dt)
metalEquation.solve(metalVar, dt=dt)
step += 1
point = ((5e-09, ), (1.15e-07, ))
value = 1.45346701e-09
return abs(float(distanceVar(point, order=1)) - value) < cellSize / 10.0