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
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 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=298.0, overpotential=-0.3, metalConcentration=250.0, catalystConcentration=5e-3, catalystCoverage=0.0, currentDensity0=0.26, currentDensity1=45.0, cellSize=0.1e-7, trenchDepth=0.5e-6, aspectRatio=2.0, 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=-1.0, hasOld=1) bottomHeight = cellsBelowTrench * cellSize trenchHeight = bottomHeight + trenchDepth trenchWidth = trenchDepth / aspectRatio sideWidth = (trenchSpacing - trenchWidth) / 2 x, y = mesh.cellCenters distanceVar.setValue(1.0, 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 == 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