L = 1.
nx = 256
cfl = 0.1
initialRadius = L / 4.
k = 1
dx = L / nx
steps = 10 * nx / 8
mesh = Grid2D(dx = dx, dy = dx, nx = nx, ny = nx)
error = CellVariable(mesh=mesh)
distanceVariable = DistanceVariable(
name = 'level set variable',
mesh = mesh,
value = numerix.sqrt((mesh.getCellCenters()[:,0] - L / 2.)**2 + (mesh.getCellCenters()[:,1] - L / 2.)**2) - initialRadius,
hasOld = 1)
initialSurfactantValue = 1.
surfactantVariable = SurfactantVariable(
value = initialSurfactantValue,
distanceVar = distanceVariable
)
velocity = 1.
surfactantEquation = SurfactantEquation(
distanceVar = distanceVariable)
from fipy.variables.cellVariable import CellVariable
L = 1.
nx = 50
cfl = 0.1
initialRadius = L / 4.
k = 1
dx = L / nx
steps = 20
mesh = Grid2D(dx=dx, dy=dx, nx=nx, ny=nx)
distanceVariable = DistanceVariable(
name='level set variable',
mesh=mesh,
value=numerix.sqrt((mesh.getCellCenters()[:, 0] - L / 2.)**2 +
(mesh.getCellCenters()[:, 1] - L / 2.)**2) -
initialRadius,
hasOld=1)
initialSurfactantValue = 1.
surfactantVariable = SurfactantVariable(value=initialSurfactantValue,
distanceVar=distanceVariable)
velocity = CellVariable(
name='velocity',
mesh=mesh,
value=1.,
)
distanceToTravel = L / 5.
boxSize = .2
nx = int(L / dx)
ny = int(L / dx)
steps = int(distanceToTravel / dx / cfl)
timeStepDuration = cfl * dx / velocity
mesh = Grid2D(dx=dx, dy=dx, nx=nx, ny=ny)
x0 = (L - boxSize) / 2
x1 = (L + boxSize) / 2
distanceVariable = DistanceVariable(mesh=mesh, value=1, hasOld=1)
x, y = mesh.getCellCenters()[..., 0], mesh.getCellCenters()[..., 1]
distanceVariable.setValue(-1,
where=((x0 < x) & (x < x1)) & ((x0 < y) & (y < x1)))
surfactantVariable = SurfactantVariable(distanceVar=distanceVariable, value=1.)
surfactantEquation = SurfactantEquation(distanceVar=distanceVariable)
advectionEquation = buildHigherOrderAdvectionEquation(advectionCoeff=velocity)
if __name__ == '__main__':
import fipy.viewers
distanceViewer = fipy.viewers.make(vars=distanceVariable,
limits={
nx = int(L / dx)
ny = int(L / dx)
steps = int(distanceToTravel / dx / cfl)
timeStepDuration = cfl * dx / velocity
mesh = Grid2D(dx = dx, dy = dx, nx = nx, ny = ny)
x0 = (L - boxSize) / 2
x1 = (L + boxSize) / 2
distanceVariable = DistanceVariable(
mesh = mesh,
value = 1,
hasOld = 1
)
x, y = mesh.getCellCenters()[...,0], mesh.getCellCenters()[...,1]
distanceVariable.setValue(-1, where=((x0 < x) & (x < x1)) & ((x0 < y) & (y < x1)))
surfactantVariable = SurfactantVariable(
distanceVar = distanceVariable,
value = 1.
)
surfactantEquation = SurfactantEquation(
distanceVar = distanceVariable)
from fipy.variables.cellVariable import CellVariable
from fipy.models.levelSet.distanceFunction.distanceVariable import DistanceVariable
dx = 0.5
dy = 2.
nx = 5
ny = 5
Lx = nx * dx
Ly = ny * dy
mesh = Grid2D(dx = dx, dy = dy, nx = nx, ny = ny)
var = DistanceVariable(
name = 'level set variable',
mesh = mesh,
value = -1,
hasOld = 1
)
x, y = mesh.getCellCenters()[...,0], mesh.getCellCenters()[...,1]
var.setValue(1, where=((Lx / 3. < x) & (x < 2. * Lx / 3.)) & ((Ly / 3. < y) & (y < 2. * Ly / 3)))
var.calcDistanceFunction()
if __name__ == '__main__':
import fipy.viewers
viewer = fipy.viewers.make(vars = var, limits = {'maxval': -5., 'minval': 5.})
viewer.plot()
raw_input('finished')
dy = 1.
nx = 5
ny = 5
Lx = nx * dx
Ly = ny * dy
mesh = Grid2D(dx = dx, dy = dy, nx = nx, ny = ny)
initialArray = -numerix.ones(nx * ny, 'd')
positiveCells = mesh.getCells(filter = lambda cell: (cell.getCenter()[0] < dx) or (cell.getCenter()[0] > (Lx - dx)) or (cell.getCenter()[1] < dy) or (cell.getCenter()[1] > (Ly - dy)))
for cell in positiveCells:
initialArray[cell.getID()] = 1.
var = DistanceVariable(
name = 'level set variable',
mesh = mesh,
value = initialArray,
hasOld = 1
)
var.calcDistanceFunction()
if __name__ == '__main__':
import fipy.viewers
viewer = fipy.viewers.make(vars = var, limits = {'datamin': -5., 'datamax': 5.})
viewer.plot()
raw_input('finished')
from fipy.models.levelSet.surfactant.surfactantVariable import SurfactantVariable
from fipy.variables.cellVariable import CellVariable
L = 1.
nx = 50
cfl = 0.1
initialRadius = L / 4.
k = 1
dx = L / nx
steps = 20
mesh = Grid2D(dx = dx, dy = dx, nx = nx, ny = nx)
distanceVariable = DistanceVariable(
name = 'level set variable',
mesh = mesh,
value = numerix.sqrt((mesh.getCellCenters()[:,0] - L / 2.)**2 + (mesh.getCellCenters()[:,1] - L / 2.)**2) - initialRadius,
hasOld = 1)
initialSurfactantValue = 1.
surfactantVariable = SurfactantVariable(
value = initialSurfactantValue,
distanceVar = distanceVariable
)
velocity = CellVariable(
name = 'velocity',
mesh = mesh,
value = 1.,
)
def runLeveler(kLeveler=0.018, bulkLevelerConcentration=0.02, cellSize=0.1e-7, rateConstant=0.00026, initialAcceleratorCoverage=0.0, levelerDiffusionCoefficient=5e-10, numberOfSteps=400, displayRate=10, displayViewers=True):
kLevelerConsumption = 0.0005
aspectRatio = 1.5
faradaysConstant = 9.6485e4
gasConstant = 8.314
acceleratorDiffusionCoefficient = 4e-10
siteDensity = 6.35e-6
atomicVolume = 7.1e-6
charge = 2
metalDiffusionCoefficient = 4e-10
temperature = 298.
overpotential = -0.25
bulkMetalConcentration = 250.
bulkAcceleratorConcentration = 50.0e-3
initialLevelerCoverage = 0.
cflNumber = 0.2
numberOfCellsInNarrowBand = 20
cellsBelowTrench = 10
trenchDepth = 0.4e-6
trenchSpacing = 0.6e-6
boundaryLayerDepth = 98.7e-6
i0Suppressor = 0.3
i0Accelerator = 22.5
alphaSuppressor = 0.5
alphaAccelerator = 0.4
alphaAdsorption = 0.62
m = 4
b = 2.65
A = 0.3
Ba = -40
Bb = 60
Vd = 0.098
Bd = 0.0008
etaPrime = faradaysConstant * overpotential / gasConstant / temperature
from fipy import TrenchMesh
from fipy.tools import numerix
mesh = TrenchMesh(cellSize = cellSize,
trenchSpacing = trenchSpacing,
trenchDepth = trenchDepth,
boundaryLayerDepth = boundaryLayerDepth,
aspectRatio = aspectRatio,
angle = numerix.pi * 4. / 180.,
bowWidth = 0.,
overBumpRadius = 0.,
overBumpWidth = 0.)
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
from fipy.models.levelSet.distanceFunction.distanceVariable import DistanceVariable
distanceVar = DistanceVariable(
name = 'distance variable',
mesh = mesh,
value = -1,
narrowBandWidth = narrowBandWidth)
distanceVar.setValue(1, where=mesh.getElectrolyteMask())
distanceVar.calcDistanceFunction(narrowBandWidth = 1e10)
from fipy.models.levelSet.surfactant.surfactantVariable import SurfactantVariable
levelerVar = SurfactantVariable(
name = "leveler variable",
value = initialLevelerCoverage,
distanceVar = distanceVar)
acceleratorVar = SurfactantVariable(
name = "accelerator variable",
value = initialAcceleratorCoverage,
distanceVar = distanceVar)
from fipy.variables.cellVariable import CellVariable
bulkAcceleratorVar = CellVariable(name = 'bulk accelerator variable',
mesh = mesh,
value = bulkAcceleratorConcentration)
bulkLevelerVar = CellVariable(
name = 'bulk leveler variable',
mesh = mesh,
value = bulkLevelerConcentration)
metalVar = CellVariable(
name = 'metal variable',
mesh = mesh,
value = bulkMetalConcentration)
def depositionCoeff(alpha, i0):
expo = numerix.exp(-alpha * etaPrime)
return 2 * i0 * (expo - expo * numerix.exp(etaPrime))
coeffSuppressor = depositionCoeff(alphaSuppressor, i0Suppressor)
coeffAccelerator = depositionCoeff(alphaAccelerator, i0Accelerator)
exchangeCurrentDensity = acceleratorVar.getInterfaceVar() * (coeffAccelerator - coeffSuppressor) + coeffSuppressor
currentDensity = metalVar / bulkMetalConcentration * exchangeCurrentDensity
depositionRateVariable = currentDensity * atomicVolume / charge / faradaysConstant
extensionVelocityVariable = CellVariable(
name = 'extension velocity',
mesh = mesh,
value = depositionRateVariable)
from fipy.models.levelSet.surfactant.adsorbingSurfactantEquation \
import AdsorbingSurfactantEquation
kAccelerator = rateConstant * numerix.exp(-alphaAdsorption * etaPrime)
kAcceleratorConsumption = Bd + A / (numerix.exp(Ba * (overpotential + Vd)) + numerix.exp(Bb * (overpotential + Vd)))
q = m * overpotential + b
levelerSurfactantEquation = AdsorbingSurfactantEquation(
levelerVar,
distanceVar = distanceVar,
bulkVar = bulkLevelerVar,
rateConstant = kLeveler,
consumptionCoeff = kLevelerConsumption * depositionRateVariable)
accVar1 = acceleratorVar.getInterfaceVar()
accVar2 = (accVar1 > 0) * accVar1
accConsumptionCoeff = kAcceleratorConsumption * (accVar2**(q - 1))
acceleratorSurfactantEquation = AdsorbingSurfactantEquation(
acceleratorVar,
distanceVar = distanceVar,
bulkVar = bulkAcceleratorVar,
rateConstant = kAccelerator,
otherVar = levelerVar,
otherBulkVar = bulkLevelerVar,
otherRateConstant = kLeveler,
consumptionCoeff = accConsumptionCoeff)
from fipy.models.levelSet.advection.higherOrderAdvectionEquation \
import buildHigherOrderAdvectionEquation
advectionEquation = buildHigherOrderAdvectionEquation(
advectionCoeff = extensionVelocityVariable)
from fipy.boundaryConditions.fixedValue import FixedValue
from fipy.models.levelSet.electroChem.metalIonDiffusionEquation \
import buildMetalIonDiffusionEquation
metalEquation = buildMetalIonDiffusionEquation(
ionVar = metalVar,
distanceVar = distanceVar,
depositionRate = depositionRateVariable,
diffusionCoeff = metalDiffusionCoefficient,
metalIonMolarVolume = atomicVolume)
metalEquationBCs = FixedValue(mesh.getTopFaces(), bulkMetalConcentration)
from fipy.models.levelSet.surfactant.surfactantBulkDiffusionEquation \
import buildSurfactantBulkDiffusionEquation
bulkAcceleratorEquation = buildSurfactantBulkDiffusionEquation(
bulkVar = bulkAcceleratorVar,
distanceVar = distanceVar,
surfactantVar = acceleratorVar,
otherSurfactantVar = levelerVar,
diffusionCoeff = acceleratorDiffusionCoefficient,
rateConstant = kAccelerator * siteDensity)
bulkAcceleratorEquationBCs = (FixedValue(
mesh.getTopFaces(),
bulkAcceleratorConcentration),)
bulkLevelerEquation = buildSurfactantBulkDiffusionEquation(
bulkVar = bulkLevelerVar,
distanceVar = distanceVar,
surfactantVar = levelerVar,
diffusionCoeff = levelerDiffusionCoefficient,
rateConstant = kLeveler * siteDensity)
bulkLevelerEquationBCs = (FixedValue(
mesh.getTopFaces(),
bulkLevelerConcentration),)
eqnTuple = ( (advectionEquation, distanceVar, ()),
(levelerSurfactantEquation, levelerVar, ()),
(acceleratorSurfactantEquation, acceleratorVar, ()),
(metalEquation, metalVar, metalEquationBCs),
(bulkAcceleratorEquation, bulkAcceleratorVar, bulkAcceleratorEquationBCs),
(bulkLevelerEquation, bulkLevelerVar, bulkLevelerEquationBCs))
levelSetUpdateFrequency = int(0.7 * narrowBandWidth / cellSize / cflNumber / 2)
totalTime = 0.0
if displayViewers:
from fipy.viewers.mayaviViewer.mayaviSurfactantViewer import MayaviSurfactantViewer
viewers = (
MayaviSurfactantViewer(distanceVar, acceleratorVar.getInterfaceVar(), zoomFactor = 1e6, limits = { 'datamax' : 0.5, 'datamin' : 0.0 }, smooth = 1, title = 'accelerator coverage'),
MayaviSurfactantViewer(distanceVar, levelerVar.getInterfaceVar(), zoomFactor = 1e6, limits = { 'datamax' : 0.5, 'datamin' : 0.0 }, smooth = 1, title = 'leveler coverage'))
for step in range(numberOfSteps):
if displayViewers:
if step % displayRate == 0:
for viewer in viewers:
viewer.plot()
if step % levelSetUpdateFrequency == 0:
distanceVar.calcDistanceFunction(deleteIslands = True)
extensionVelocityVariable.setValue(depositionRateVariable)
extOnInt = numerix.where(distanceVar > 0,
numerix.where(distanceVar < 2 * cellSize,
extensionVelocityVariable,
0),
0)
dt = cflNumber * cellSize / numerix.max(extOnInt)
id = numerix.max(numerix.nonzero(distanceVar._getInterfaceFlag()))
distanceVar.extendVariable(extensionVelocityVariable, deleteIslands = True)
extensionVelocityVariable[mesh.getFineMesh().getNumberOfCells():] = 0.
for eqn, var, BCs in eqnTuple:
var.updateOld()
for eqn, var, BCs in eqnTuple:
eqn.solve(var, boundaryConditions = BCs, dt = dt)
totalTime += dt
try:
testFile = 'testLeveler.gz'
import os
import examples.levelSet.electroChem
from fipy.tools import dump
data = dump.read(os.path.join(examples.levelSet.electroChem.__path__[0], testFile))
N = mesh.getFineMesh().getNumberOfCells()
print numerix.allclose(data[:N], levelerVar[:N], rtol = 1e-3)
except:
return 0
xCells = int(trenchSpacing / 2 / cellSize)
from fipy.meshes.grid2D import Grid2D
mesh = Grid2D(dx=cellSize, dy=cellSize, nx=xCells, ny=yCells)
bench.stop('mesh')
bench.start()
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
from fipy.models.levelSet.distanceFunction.distanceVariable import \
DistanceVariable
distanceVar = DistanceVariable(name='distance variable',
mesh=mesh,
value=-1,
narrowBandWidth=narrowBandWidth,
hasOld=1)
bottomHeight = cellsBelowTrench * cellSize
trenchHeight = bottomHeight + trenchDepth
trenchWidth = trenchDepth / aspectRatio
sideWidth = (trenchSpacing - trenchWidth) / 2
x, y = mesh.getCellCenters()[..., 0], mesh.getCellCenters()[..., 1]
distanceVar.setValue(1,
where=(y > trenchHeight)
| ((y > bottomHeight)
& (x < xCells * cellSize - sideWidth)))
distanceVar.calcDistanceFunction(narrowBandWidth=1e10)
from fipy.models.levelSet.surfactant.surfactantVariable import \
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
cellsBelowTrench = 10
from fipy.tools import numerix
from fipy import TrenchMesh
mesh = TrenchMesh(cellSize = cellSize,
trenchSpacing = trenchSpacing,
trenchDepth = trenchDepth,
boundaryLayerDepth = boundaryLayerDepth,
aspectRatio = aspectRatio,
angle = numerix.pi * taperAngle / 180.,
bowWidth = 0.,
overBumpRadius = 0.,
overBumpWidth = 0.)
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
from fipy.models.levelSet.distanceFunction.distanceVariable import DistanceVariable
distanceVar = DistanceVariable(
name = 'distance variable',
mesh = mesh,
value = -1,
narrowBandWidth = narrowBandWidth)
distanceVar.setValue(1, where=mesh.getElectrolyteMask())
distanceVar.calcDistanceFunction(narrowBandWidth = 1e10)
from fipy.models.levelSet.surfactant.surfactantVariable import SurfactantVariable
catalystVar = SurfactantVariable(
name = "catalyst variable",
value = catalystCoverage,
distanceVar = distanceVar)
from fipy.variables.cellVariable import CellVariable
metalVar = CellVariable(
name = 'metal variable',
mesh = mesh,
value = metalConcentration)
exchangeCurrentDensity = currentDensity0 + currentDensity1 * catalystVar.getInterfaceVar()
currentDensity = metalVar / metalConcentration * exchangeCurrentDensity
depositionRateVariable = currentDensity * molarVolume / charge / faradaysConstant
extensionVelocityVariable = CellVariable(
name = 'extension velocity',
mesh = mesh,
value = depositionRateVariable)
from fipy.models.levelSet.surfactant.adsorbingSurfactantEquation \
import AdsorbingSurfactantEquation
catalystSurfactantEquation = AdsorbingSurfactantEquation(
catalystVar,
distanceVar = distanceVar,
bulkVar = 0,
rateConstant = 0,
consumptionCoeff = consumptionRateConstant * extensionVelocityVariable)
from fipy.models.levelSet.advection.higherOrderAdvectionEquation \
import buildHigherOrderAdvectionEquation
advectionEquation = buildHigherOrderAdvectionEquation(
advectionCoeff = extensionVelocityVariable)
from fipy.boundaryConditions.fixedValue import FixedValue
from fipy.models.levelSet.electroChem.metalIonDiffusionEquation \
import buildMetalIonDiffusionEquation
metalEquation = buildMetalIonDiffusionEquation(
ionVar = metalVar,
distanceVar = distanceVar,
depositionRate = depositionRateVariable,
diffusionCoeff = metalDiffusion,
metalIonMolarVolume = molarVolume)
metalEquationBCs = FixedValue(mesh.getTopFaces(), metalConcentration)
if displayViewers:
try:
from fipy.viewers.mayaviViewer.mayaviSurfactantViewer import MayaviSurfactantViewer
viewers = (
MayaviSurfactantViewer(distanceVar, catalystVar.getInterfaceVar(), zoomFactor = 1e6, limits = { 'datamax' : 1.0, 'datamin' : 0.0 }, smooth = 1, title = 'catalyst coverage'),)
except:
class PlotVariable(CellVariable):
def __init__(self, var = None, name = ''):
CellVariable.__init__(self, mesh = mesh.getFineMesh(), name = name)
self.var = self._requires(var)
def _calcValue(self):
return numerix.array(self.var[:self.mesh.getNumberOfCells()])
from fipy.viewers import make
viewers = (
make(PlotVariable(var = distanceVar), limits = {'datamax' : 1e-9, 'datamin' : -1e-9}),
make(PlotVariable(var = catalystVar.getInterfaceVar())))
else:
viewers = ()
levelSetUpdateFrequency = int(0.7 * narrowBandWidth / cellSize / cflNumber / 2)
step = 0
while step < numberOfSteps:
if step % 10 == 0:
for viewer in viewers:
viewer.plot()
if step % levelSetUpdateFrequency == 0:
distanceVar.calcDistanceFunction(deleteIslands = True)
extensionVelocityVariable.setValue(numerix.array(depositionRateVariable))
argmax = numerix.argmax(extensionVelocityVariable)
dt = cflNumber * cellSize / extensionVelocityVariable[argmax]
distanceVar.extendVariable(extensionVelocityVariable, deleteIslands = True)
distanceVar.updateOld()
catalystVar.updateOld()
metalVar.updateOld()
advectionEquation.solve(distanceVar, dt = dt)
catalystSurfactantEquation.solve(catalystVar, dt = dt)
metalEquation.solve(metalVar, boundaryConditions = metalEquationBCs, dt = dt)
step += 1
try:
from fipy.tools import dump
import os
import examples.levelSet.electroChem
data = dump.read(os.path.join(examples.levelSet.electroChem.__path__[0], 'goldData.gz'))
n = mesh.getFineMesh().getNumberOfCells()
print numerix.allclose(catalystVar[:n], data[:n], atol=1.0)
except:
return 0
Ly = ny * dy
mesh = Grid2D(dx=dx, dy=dy, nx=nx, ny=ny)
initialArray = -numerix.ones(nx * ny, 'd')
positiveCells = mesh.getCells(
filter=lambda cell: (cell.getCenter()[0] < dx) or (cell.getCenter()[0] >
(Lx - dx)) or
(cell.getCenter()[1] < dy) or (cell.getCenter()[1] > (Ly - dy)))
for cell in positiveCells:
initialArray[cell.getID()] = 1.
var = DistanceVariable(name='level set variable',
mesh=mesh,
value=initialArray,
hasOld=1)
var.calcDistanceFunction()
if __name__ == '__main__':
import fipy.viewers
viewer = fipy.viewers.make(vars=var,
limits={
'datamin': -5.,
'datamax': 5.
})
viewer.plot()
raw_input('finished')
nx = 50
velocity = 1.
cfl = 0.1
velocity = 1.
distanceToTravel = L / 10.
initialRadius = L / 4.
dx = L / nx
timeStepDuration = cfl * dx / velocity
steps = int(distanceToTravel / dx / cfl)
mesh = Grid2D(dx = dx, dy = dx, nx = nx, ny = nx)
distanceVariable = DistanceVariable(
name = 'level set variable',
mesh = mesh,
value = 1.,
hasOld = 1
)
cellRadius = numerix.sqrt((mesh.getCellCenters()[:,0] - L / 2.)**2 + (mesh.getCellCenters()[:,1] - L / 2.)**2)
distanceVariable.setValue(cellRadius - initialRadius)
initialSurfactantValue = 1.
surfactantVariable = SurfactantVariable(
value = initialSurfactantValue,
distanceVar = distanceVariable
)
advectionEquation = buildHigherOrderAdvectionEquation(
advectionCoeff = velocity)
mesh = Grid2D(dx = cellSize,
dy = cellSize,
nx = xCells,
ny = yCells)
bench.stop('mesh')
bench.start()
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
from fipy.models.levelSet.distanceFunction.distanceVariable import \
DistanceVariable
distanceVar = DistanceVariable(
name = 'distance variable',
mesh = mesh,
value = -1,
narrowBandWidth = narrowBandWidth,
hasOld = 1)
bottomHeight = cellsBelowTrench * cellSize
trenchHeight = bottomHeight + trenchDepth
trenchWidth = trenchDepth / aspectRatio
sideWidth = (trenchSpacing - trenchWidth) / 2
x, y = mesh.getCellCenters()[...,0], mesh.getCellCenters()[...,1]
distanceVar.setValue(1, where=(y > trenchHeight)
| ((y > bottomHeight)
& (x < xCells * cellSize - sideWidth)))
distanceVar.calcDistanceFunction(narrowBandWidth = 1e10)
from fipy.models.levelSet.surfactant.surfactantVariable import \
SurfactantVariable
cinf = 1.
nx = 100
totalTimeSteps = 100
dt = 0.001
## build the mesh
from fipy.meshes.grid1D import Grid1D
dx = L / (nx - 1.5)
mesh = Grid1D(nx=nx, dx=dx)
## build the distance variable
value = mesh.getCellCenters()[:, 0] - 1.499 * dx
##distanceVar = DistanceVariable(mesh = mesh, value = dx * (numerix.arange(nx) - 0.999))
distanceVar = DistanceVariable(mesh=mesh, value=value, hasOld=1)
## Build the bulk diffusion equation
bulkVar = CellVariable(mesh=mesh, value=cinf)
surfactantVar = SurfactantVariable(distanceVar=distanceVar)
bulkEqn = buildSurfactantBulkDiffusionEquation(bulkVar,
distanceVar=distanceVar,
surfactantVar=surfactantVar,
diffusionCoeff=diffusion,
rateConstant=rateConstant *
siteDensity)
bcs = (FixedValue(mesh.getFacesRight(), cinf), )
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
cellsBelowTrench = 10
from fipy.tools import numerix
from fipy import TrenchMesh
mesh = TrenchMesh(cellSize=cellSize,
trenchSpacing=trenchSpacing,
trenchDepth=trenchDepth,
boundaryLayerDepth=boundaryLayerDepth,
aspectRatio=aspectRatio,
angle=numerix.pi * taperAngle / 180.,
bowWidth=0.,
overBumpRadius=0.,
overBumpWidth=0.)
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
from fipy.models.levelSet.distanceFunction.distanceVariable import DistanceVariable
distanceVar = DistanceVariable(name='distance variable',
mesh=mesh,
value=-1,
narrowBandWidth=narrowBandWidth)
distanceVar.setValue(1, where=mesh.getElectrolyteMask())
distanceVar.calcDistanceFunction(narrowBandWidth=1e10)
from fipy.models.levelSet.surfactant.surfactantVariable import SurfactantVariable
catalystVar = SurfactantVariable(name="catalyst variable",
value=catalystCoverage,
distanceVar=distanceVar)
from fipy.variables.cellVariable import CellVariable
metalVar = CellVariable(name='metal variable',
mesh=mesh,
value=metalConcentration)
exchangeCurrentDensity = currentDensity0 + currentDensity1 * catalystVar.getInterfaceVar(
)
currentDensity = metalVar / metalConcentration * exchangeCurrentDensity
depositionRateVariable = currentDensity * molarVolume / charge / faradaysConstant
extensionVelocityVariable = CellVariable(name='extension velocity',
mesh=mesh,
value=depositionRateVariable)
from fipy.models.levelSet.surfactant.adsorbingSurfactantEquation \
import AdsorbingSurfactantEquation
catalystSurfactantEquation = AdsorbingSurfactantEquation(
catalystVar,
distanceVar=distanceVar,
bulkVar=0,
rateConstant=0,
consumptionCoeff=consumptionRateConstant * extensionVelocityVariable)
from fipy.models.levelSet.advection.higherOrderAdvectionEquation \
import buildHigherOrderAdvectionEquation
advectionEquation = buildHigherOrderAdvectionEquation(
advectionCoeff=extensionVelocityVariable)
from fipy.boundaryConditions.fixedValue import FixedValue
from fipy.models.levelSet.electroChem.metalIonDiffusionEquation \
import buildMetalIonDiffusionEquation
metalEquation = buildMetalIonDiffusionEquation(
ionVar=metalVar,
distanceVar=distanceVar,
depositionRate=depositionRateVariable,
diffusionCoeff=metalDiffusion,
metalIonMolarVolume=molarVolume)
metalEquationBCs = FixedValue(mesh.getTopFaces(), metalConcentration)
if displayViewers:
try:
from fipy.viewers.mayaviViewer.mayaviSurfactantViewer import MayaviSurfactantViewer
viewers = (MayaviSurfactantViewer(distanceVar,
catalystVar.getInterfaceVar(),
zoomFactor=1e6,
limits={
'datamax': 1.0,
'datamin': 0.0
},
smooth=1,
title='catalyst coverage'), )
except:
class PlotVariable(CellVariable):
def __init__(self, var=None, name=''):
CellVariable.__init__(self,
mesh=mesh.getFineMesh(),
name=name)
self.var = self._requires(var)
def _calcValue(self):
return numerix.array(
self.var[:self.mesh.getNumberOfCells()])
from fipy.viewers import make
viewers = (make(PlotVariable(var=distanceVar),
limits={
'datamax': 1e-9,
'datamin': -1e-9
}),
make(PlotVariable(var=catalystVar.getInterfaceVar())))
else:
viewers = ()
levelSetUpdateFrequency = int(0.7 * narrowBandWidth / cellSize /
cflNumber / 2)
step = 0
while step < numberOfSteps:
if step % 10 == 0:
for viewer in viewers:
viewer.plot()
if step % levelSetUpdateFrequency == 0:
distanceVar.calcDistanceFunction(deleteIslands=True)
extensionVelocityVariable.setValue(
numerix.array(depositionRateVariable))
argmax = numerix.argmax(extensionVelocityVariable)
dt = cflNumber * cellSize / extensionVelocityVariable[argmax]
distanceVar.extendVariable(extensionVelocityVariable,
deleteIslands=True)
distanceVar.updateOld()
catalystVar.updateOld()
metalVar.updateOld()
advectionEquation.solve(distanceVar, dt=dt)
catalystSurfactantEquation.solve(catalystVar, dt=dt)
metalEquation.solve(metalVar,
boundaryConditions=metalEquationBCs,
dt=dt)
step += 1
try:
from fipy.tools import dump
import os
import examples.levelSet.electroChem
data = dump.read(
os.path.join(examples.levelSet.electroChem.__path__[0],
'goldData.gz'))
n = mesh.getFineMesh().getNumberOfCells()
print numerix.allclose(catalystVar[:n], data[:n], atol=1.0)
except:
return 0
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.meshes.grid2D import Grid2D
mesh = Grid2D(dx=cellSize, dy=cellSize, nx=xCells, ny=yCells)
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
from fipy.models.levelSet.distanceFunction.distanceVariable import \
DistanceVariable
distanceVar = DistanceVariable(name='distance variable',
mesh=mesh,
value=-1,
narrowBandWidth=narrowBandWidth,
hasOld=1)
bottomHeight = cellsBelowTrench * cellSize
trenchHeight = bottomHeight + trenchDepth
trenchWidth = trenchDepth / aspectRatio
sideWidth = (trenchSpacing - trenchWidth) / 2
x, y = mesh.getCellCenters()[..., 0], mesh.getCellCenters()[..., 1]
distanceVar.setValue(1,
where=(y > trenchHeight) |
((y > bottomHeight) &
(x < xCells * cellSize - sideWidth)))
distanceVar.calcDistanceFunction(narrowBandWidth=1e10)
from fipy.models.levelSet.surfactant.surfactantVariable import \
SurfactantVariable
catalystVar = SurfactantVariable(name="catalyst variable",
value=catalystCoverage,
distanceVar=distanceVar)
from fipy.variables.cellVariable import CellVariable
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.getInterfaceVar()
exchangeCurrentDensity = currentDensity0 + tmp
import fipy.tools.numerix as numerix
expo = numerix.exp(expoConstant * overpotential)
currentDensity = expo * exchangeCurrentDensity * metalVar \
/ metalConcentration
depositionRateVariable = currentDensity * molarVolume \
/ (charge * faradaysConstant)
extensionVelocityVariable = CellVariable(name='extension velocity',
mesh=mesh,
value=depositionRateVariable)
from fipy.models.levelSet.surfactant.adsorbingSurfactantEquation \
import AdsorbingSurfactantEquation
surfactantEquation = AdsorbingSurfactantEquation(
surfactantVar=catalystVar,
distanceVar=distanceVar,
bulkVar=bulkCatalystVar,
rateConstant=rateConstant0 + rateConstant3 * overpotential**3)
from fipy.models.levelSet.advection.higherOrderAdvectionEquation \
import buildHigherOrderAdvectionEquation
advectionEquation = buildHigherOrderAdvectionEquation(
advectionCoeff=extensionVelocityVariable)
from fipy.boundaryConditions.fixedValue import FixedValue
from fipy.models.levelSet.electroChem.metalIonDiffusionEquation \
import buildMetalIonDiffusionEquation
metalEquation = buildMetalIonDiffusionEquation(
ionVar=metalVar,
distanceVar=distanceVar,
depositionRate=depositionRateVariable,
diffusionCoeff=metalDiffusion,
metalIonMolarVolume=molarVolume,
)
metalEquationBCs = FixedValue(mesh.getFacesTop(), metalConcentration)
from fipy.models.levelSet.surfactant.surfactantBulkDiffusionEquation \
import buildSurfactantBulkDiffusionEquation
bulkCatalystEquation = buildSurfactantBulkDiffusionEquation(
bulkVar=bulkCatalystVar,
distanceVar=distanceVar,
surfactantVar=catalystVar,
diffusionCoeff=catalystDiffusion,
rateConstant=rateConstant0 * siteDensity)
catalystBCs = FixedValue(mesh.getFacesTop(), catalystConcentration)
if displayViewers:
try:
from fipy.viewers.mayaviViewer.mayaviSurfactantViewer import MayaviSurfactantViewer
viewers = (MayaviSurfactantViewer(distanceVar,
catalystVar.getInterfaceVar(),
zoomFactor=1e6,
limits={
'datamax': 0.5,
'datamin': 0.0
},
smooth=1,
title='catalyst coverage'), )
except:
from fipy.viewers import make
viewers = (make(distanceVar,
limits={
'datamin': -1e-9,
'datamax': 1e-9
}), make(catalystVar.getInterfaceVar()))
else:
viewers = ()
levelSetUpdateFrequency = int(0.8 * narrowBandWidth \
/ (cellSize * cflNumber * 2))
for step in range(numberOfSteps):
if step % 5 == 0:
for viewer in viewers:
viewer.plot()
if step % levelSetUpdateFrequency == 0:
distanceVar.calcDistanceFunction()
extensionVelocityVariable.setValue(depositionRateVariable())
distanceVar.updateOld()
catalystVar.updateOld()
metalVar.updateOld()
bulkCatalystVar.updateOld()
distanceVar.extendVariable(extensionVelocityVariable)
dt = cflNumber * cellSize / numerix.max(extensionVelocityVariable)
advectionEquation.solve(distanceVar, dt=dt)
surfactantEquation.solve(catalystVar, dt=dt)
metalEquation.solve(metalVar,
dt=dt,
boundaryConditions=metalEquationBCs)
bulkCatalystEquation.solve(bulkCatalystVar,
dt=dt,
boundaryConditions=catalystBCs)
try:
import os
import examples.levelSet.electroChem
filepath = os.path.join(examples.levelSet.electroChem.__path__[0],
'test.gz')
from fipy.tools import dump
from fipy.tools import numerix
print catalystVar.allclose(numerix.array(dump.read(filepath)),
rtol=1e-4)
except:
return 0
def runLeveler(kLeveler=0.018,
bulkLevelerConcentration=0.02,
cellSize=0.1e-7,
rateConstant=0.00026,
initialAcceleratorCoverage=0.0,
levelerDiffusionCoefficient=5e-10,
numberOfSteps=400,
displayRate=10,
displayViewers=True):
kLevelerConsumption = 0.0005
aspectRatio = 1.5
faradaysConstant = 9.6485e4
gasConstant = 8.314
acceleratorDiffusionCoefficient = 4e-10
siteDensity = 6.35e-6
atomicVolume = 7.1e-6
charge = 2
metalDiffusionCoefficient = 4e-10
temperature = 298.
overpotential = -0.25
bulkMetalConcentration = 250.
bulkAcceleratorConcentration = 50.0e-3
initialLevelerCoverage = 0.
cflNumber = 0.2
numberOfCellsInNarrowBand = 20
cellsBelowTrench = 10
trenchDepth = 0.4e-6
trenchSpacing = 0.6e-6
boundaryLayerDepth = 98.7e-6
i0Suppressor = 0.3
i0Accelerator = 22.5
alphaSuppressor = 0.5
alphaAccelerator = 0.4
alphaAdsorption = 0.62
m = 4
b = 2.65
A = 0.3
Ba = -40
Bb = 60
Vd = 0.098
Bd = 0.0008
etaPrime = faradaysConstant * overpotential / gasConstant / temperature
from fipy import TrenchMesh
from fipy.tools import numerix
mesh = TrenchMesh(cellSize=cellSize,
trenchSpacing=trenchSpacing,
trenchDepth=trenchDepth,
boundaryLayerDepth=boundaryLayerDepth,
aspectRatio=aspectRatio,
angle=numerix.pi * 4. / 180.,
bowWidth=0.,
overBumpRadius=0.,
overBumpWidth=0.)
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
from fipy.models.levelSet.distanceFunction.distanceVariable import DistanceVariable
distanceVar = DistanceVariable(name='distance variable',
mesh=mesh,
value=-1,
narrowBandWidth=narrowBandWidth)
distanceVar.setValue(1, where=mesh.getElectrolyteMask())
distanceVar.calcDistanceFunction(narrowBandWidth=1e10)
from fipy.models.levelSet.surfactant.surfactantVariable import SurfactantVariable
levelerVar = SurfactantVariable(name="leveler variable",
value=initialLevelerCoverage,
distanceVar=distanceVar)
acceleratorVar = SurfactantVariable(name="accelerator variable",
value=initialAcceleratorCoverage,
distanceVar=distanceVar)
from fipy.variables.cellVariable import CellVariable
bulkAcceleratorVar = CellVariable(name='bulk accelerator variable',
mesh=mesh,
value=bulkAcceleratorConcentration)
bulkLevelerVar = CellVariable(name='bulk leveler variable',
mesh=mesh,
value=bulkLevelerConcentration)
metalVar = CellVariable(name='metal variable',
mesh=mesh,
value=bulkMetalConcentration)
def depositionCoeff(alpha, i0):
expo = numerix.exp(-alpha * etaPrime)
return 2 * i0 * (expo - expo * numerix.exp(etaPrime))
coeffSuppressor = depositionCoeff(alphaSuppressor, i0Suppressor)
coeffAccelerator = depositionCoeff(alphaAccelerator, i0Accelerator)
exchangeCurrentDensity = acceleratorVar.getInterfaceVar() * (
coeffAccelerator - coeffSuppressor) + coeffSuppressor
currentDensity = metalVar / bulkMetalConcentration * exchangeCurrentDensity
depositionRateVariable = currentDensity * atomicVolume / charge / faradaysConstant
extensionVelocityVariable = CellVariable(name='extension velocity',
mesh=mesh,
value=depositionRateVariable)
from fipy.models.levelSet.surfactant.adsorbingSurfactantEquation \
import AdsorbingSurfactantEquation
kAccelerator = rateConstant * numerix.exp(-alphaAdsorption * etaPrime)
kAcceleratorConsumption = Bd + A / (numerix.exp(Ba *
(overpotential + Vd)) +
numerix.exp(Bb * (overpotential + Vd)))
q = m * overpotential + b
levelerSurfactantEquation = AdsorbingSurfactantEquation(
levelerVar,
distanceVar=distanceVar,
bulkVar=bulkLevelerVar,
rateConstant=kLeveler,
consumptionCoeff=kLevelerConsumption * depositionRateVariable)
accVar1 = acceleratorVar.getInterfaceVar()
accVar2 = (accVar1 > 0) * accVar1
accConsumptionCoeff = kAcceleratorConsumption * (accVar2**(q - 1))
acceleratorSurfactantEquation = AdsorbingSurfactantEquation(
acceleratorVar,
distanceVar=distanceVar,
bulkVar=bulkAcceleratorVar,
rateConstant=kAccelerator,
otherVar=levelerVar,
otherBulkVar=bulkLevelerVar,
otherRateConstant=kLeveler,
consumptionCoeff=accConsumptionCoeff)
from fipy.models.levelSet.advection.higherOrderAdvectionEquation \
import buildHigherOrderAdvectionEquation
advectionEquation = buildHigherOrderAdvectionEquation(
advectionCoeff=extensionVelocityVariable)
from fipy.boundaryConditions.fixedValue import FixedValue
from fipy.models.levelSet.electroChem.metalIonDiffusionEquation \
import buildMetalIonDiffusionEquation
metalEquation = buildMetalIonDiffusionEquation(
ionVar=metalVar,
distanceVar=distanceVar,
depositionRate=depositionRateVariable,
diffusionCoeff=metalDiffusionCoefficient,
metalIonMolarVolume=atomicVolume)
metalEquationBCs = FixedValue(mesh.getTopFaces(), bulkMetalConcentration)
from fipy.models.levelSet.surfactant.surfactantBulkDiffusionEquation \
import buildSurfactantBulkDiffusionEquation
bulkAcceleratorEquation = buildSurfactantBulkDiffusionEquation(
bulkVar=bulkAcceleratorVar,
distanceVar=distanceVar,
surfactantVar=acceleratorVar,
otherSurfactantVar=levelerVar,
diffusionCoeff=acceleratorDiffusionCoefficient,
rateConstant=kAccelerator * siteDensity)
bulkAcceleratorEquationBCs = (FixedValue(mesh.getTopFaces(),
bulkAcceleratorConcentration), )
bulkLevelerEquation = buildSurfactantBulkDiffusionEquation(
bulkVar=bulkLevelerVar,
distanceVar=distanceVar,
surfactantVar=levelerVar,
diffusionCoeff=levelerDiffusionCoefficient,
rateConstant=kLeveler * siteDensity)
bulkLevelerEquationBCs = (FixedValue(mesh.getTopFaces(),
bulkLevelerConcentration), )
eqnTuple = ((advectionEquation, distanceVar,
()), (levelerSurfactantEquation, levelerVar,
()), (acceleratorSurfactantEquation, acceleratorVar,
()), (metalEquation, metalVar, metalEquationBCs),
(bulkAcceleratorEquation, bulkAcceleratorVar,
bulkAcceleratorEquationBCs),
(bulkLevelerEquation, bulkLevelerVar, bulkLevelerEquationBCs))
levelSetUpdateFrequency = int(0.7 * narrowBandWidth / cellSize /
cflNumber / 2)
totalTime = 0.0
if displayViewers:
from fipy.viewers.mayaviViewer.mayaviSurfactantViewer import MayaviSurfactantViewer
viewers = (MayaviSurfactantViewer(distanceVar,
acceleratorVar.getInterfaceVar(),
zoomFactor=1e6,
limits={
'datamax': 0.5,
'datamin': 0.0
},
smooth=1,
title='accelerator coverage'),
MayaviSurfactantViewer(distanceVar,
levelerVar.getInterfaceVar(),
zoomFactor=1e6,
limits={
'datamax': 0.5,
'datamin': 0.0
},
smooth=1,
title='leveler coverage'))
for step in range(numberOfSteps):
if displayViewers:
if step % displayRate == 0:
for viewer in viewers:
viewer.plot()
if step % levelSetUpdateFrequency == 0:
distanceVar.calcDistanceFunction(deleteIslands=True)
extensionVelocityVariable.setValue(depositionRateVariable)
extOnInt = numerix.where(
distanceVar > 0,
numerix.where(distanceVar < 2 * cellSize,
extensionVelocityVariable, 0), 0)
dt = cflNumber * cellSize / numerix.max(extOnInt)
id = numerix.max(numerix.nonzero(distanceVar._getInterfaceFlag()))
distanceVar.extendVariable(extensionVelocityVariable,
deleteIslands=True)
extensionVelocityVariable[mesh.getFineMesh().getNumberOfCells():] = 0.
for eqn, var, BCs in eqnTuple:
var.updateOld()
for eqn, var, BCs in eqnTuple:
eqn.solve(var, boundaryConditions=BCs, dt=dt)
totalTime += dt
try:
testFile = 'testLeveler.gz'
import os
import examples.levelSet.electroChem
from fipy.tools import dump
data = dump.read(
os.path.join(examples.levelSet.electroChem.__path__[0], testFile))
N = mesh.getFineMesh().getNumberOfCells()
print numerix.allclose(data[:N], levelerVar[:N], rtol=1e-3)
except:
return 0
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.meshes.grid2D import Grid2D
mesh = Grid2D(dx = cellSize,
dy = cellSize,
nx = xCells,
ny = yCells)
narrowBandWidth = numberOfCellsInNarrowBand * cellSize
from fipy.models.levelSet.distanceFunction.distanceVariable import \
DistanceVariable
distanceVar = DistanceVariable(
name = 'distance variable',
mesh = mesh,
value = -1,
narrowBandWidth = narrowBandWidth,
hasOld = 1)
bottomHeight = cellsBelowTrench * cellSize
trenchHeight = bottomHeight + trenchDepth
trenchWidth = trenchDepth / aspectRatio
sideWidth = (trenchSpacing - trenchWidth) / 2
x, y = mesh.getCellCenters()[...,0], mesh.getCellCenters()[...,1]
distanceVar.setValue(1, where=(y > trenchHeight) | ((y > bottomHeight) & (x < xCells * cellSize - sideWidth)))
distanceVar.calcDistanceFunction(narrowBandWidth = 1e10)
from fipy.models.levelSet.surfactant.surfactantVariable import \
SurfactantVariable
catalystVar = SurfactantVariable(
name = "catalyst variable",
value = catalystCoverage,
distanceVar = distanceVar)
from fipy.variables.cellVariable import CellVariable
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.getInterfaceVar()
exchangeCurrentDensity = currentDensity0 + tmp
import fipy.tools.numerix as numerix
expo = numerix.exp(expoConstant * overpotential)
currentDensity = expo * exchangeCurrentDensity * metalVar \
/ metalConcentration
depositionRateVariable = currentDensity * molarVolume \
/ (charge * faradaysConstant)
extensionVelocityVariable = CellVariable(
name = 'extension velocity',
mesh = mesh,
value = depositionRateVariable)
from fipy.models.levelSet.surfactant.adsorbingSurfactantEquation \
import AdsorbingSurfactantEquation
surfactantEquation = AdsorbingSurfactantEquation(
surfactantVar = catalystVar,
distanceVar = distanceVar,
bulkVar = bulkCatalystVar,
rateConstant = rateConstant0 + rateConstant3 * overpotential**3)
from fipy.models.levelSet.advection.higherOrderAdvectionEquation \
import buildHigherOrderAdvectionEquation
advectionEquation = buildHigherOrderAdvectionEquation(
advectionCoeff = extensionVelocityVariable)
from fipy.boundaryConditions.fixedValue import FixedValue
from fipy.models.levelSet.electroChem.metalIonDiffusionEquation \
import buildMetalIonDiffusionEquation
metalEquation = buildMetalIonDiffusionEquation(
ionVar = metalVar,
distanceVar = distanceVar,
depositionRate = depositionRateVariable,
diffusionCoeff = metalDiffusion,
metalIonMolarVolume = molarVolume,
)
metalEquationBCs = FixedValue(mesh.getFacesTop(), metalConcentration)
from fipy.models.levelSet.surfactant.surfactantBulkDiffusionEquation \
import buildSurfactantBulkDiffusionEquation
bulkCatalystEquation = buildSurfactantBulkDiffusionEquation(
bulkVar = bulkCatalystVar,
distanceVar = distanceVar,
surfactantVar = catalystVar,
diffusionCoeff = catalystDiffusion,
rateConstant = rateConstant0 * siteDensity
)
catalystBCs = FixedValue(mesh.getFacesTop(), catalystConcentration)
if displayViewers:
try:
from fipy.viewers.mayaviViewer.mayaviSurfactantViewer import MayaviSurfactantViewer
viewers = (MayaviSurfactantViewer(distanceVar, catalystVar.getInterfaceVar(), zoomFactor = 1e6, limits = { 'datamax' : 0.5, 'datamin' : 0.0 }, smooth = 1, title = 'catalyst coverage'),)
except:
from fipy.viewers import make
viewers = (
make(distanceVar, limits = { 'datamin' :-1e-9 , 'datamax' : 1e-9 }),
make(catalystVar.getInterfaceVar()))
else:
viewers = ()
levelSetUpdateFrequency = int(0.8 * narrowBandWidth \
/ (cellSize * cflNumber * 2))
for step in range(numberOfSteps):
if step % 5 == 0:
for viewer in viewers:
viewer.plot()
if step % levelSetUpdateFrequency == 0:
distanceVar.calcDistanceFunction()
extensionVelocityVariable.setValue(depositionRateVariable())
distanceVar.updateOld()
catalystVar.updateOld()
metalVar.updateOld()
bulkCatalystVar.updateOld()
distanceVar.extendVariable(extensionVelocityVariable)
dt = cflNumber * cellSize / numerix.max(extensionVelocityVariable)
advectionEquation.solve(distanceVar, dt = dt)
surfactantEquation.solve(catalystVar, dt = dt)
metalEquation.solve(metalVar, dt = dt,
boundaryConditions = metalEquationBCs)
bulkCatalystEquation.solve(bulkCatalystVar, dt = dt,
boundaryConditions = catalystBCs)
try:
import os
import examples.levelSet.electroChem
filepath = os.path.join(examples.levelSet.electroChem.__path__[0], 'test.gz')
from fipy.tools import dump
from fipy.tools import numerix
print catalystVar.allclose(numerix.array(dump.read(filepath)), rtol = 1e-4)
except:
return 0