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
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.cellCenters distanceVariable.setValue(-1, where=((x0 < x) & (x < x1)) & ((x0 < y) & (y < x1))) surfactantVariable = SurfactantVariable(distanceVar=distanceVariable, value=1.) from fipy.variables.surfactantConvectionVariable import SurfactantConvectionVariable surfactantEquation = TransientTerm() - \ ExplicitUpwindConvectionTerm(SurfactantConvectionVariable(distanceVariable)) advectionEquation = TransientTerm() + AdvectionTerm(velocity) if __name__ == '__main__': distanceViewer = Viewer(vars=distanceVariable, datamin=-.001, datamax=.001) surfactantViewer = Viewer(vars=surfactantVariable, datamin=0., datamax=2.) distanceVariable.calcDistanceFunction() for step in range(steps): print numerix.sum(surfactantVariable)
## build the mesh dx = L / (nx - 1.5) mesh = Grid1D(nx=nx, dx=dx, communicator=serialComm) ## build the distance variable value = mesh.cellCenters[0] - 1.499 * dx ##distanceVar = DistanceVariable(mesh = mesh, value = dx * (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) from .surfactantBulkDiffusionEquation import buildSurfactantBulkDiffusionEquation bulkEqn = buildSurfactantBulkDiffusionEquation(bulkVar, distanceVar=distanceVar, surfactantVar=surfactantVar, diffusionCoeff=diffusion, rateConstant=rateConstant * siteDensity) bulkVar.constrain(cinf, mesh.facesRight) ## Build the surfactant equation surfEqn = AdsorbingSurfactantEquation(surfactantVar=surfactantVar, distanceVar=distanceVar,
distanceVariable = DistanceVariable( name = 'level set variable', mesh = mesh, value = 1., hasOld = 1 ) x, y = mesh.cellCenters cellRadius = numerix.sqrt((x - L / 2.)**2 + (y - L / 2.)**2) distanceVariable.setValue(cellRadius - initialRadius) initialSurfactantValue = 1. surfactantVariable = SurfactantVariable( value = initialSurfactantValue, distanceVar = distanceVariable ) advectionEquation = TransientTerm() + AdvectionTerm(velocity) from fipy.variables.surfactantConvectionVariable import SurfactantConvectionVariable surfactantEquation = TransientTerm() - \ ExplicitUpwindConvectionTerm(SurfactantConvectionVariable(distanceVariable)) if __name__ == '__main__': distanceViewer = Viewer(vars=distanceVariable, datamin=-initialRadius, datamax=initialRadius) surfactantViewer = Viewer(vars=surfactantVariable, datamin=-1., datamax=100.) distanceViewer.plot() surfactantViewer.plot()
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
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 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 mesh = TrenchMesh(cellSize=cellSize, trenchSpacing=trenchSpacing, trenchDepth=trenchDepth, boundaryLayerDepth=boundaryLayerDepth, aspectRatio=aspectRatio, angle=numerix.pi * 4. / 180.) distanceVar = GapFillDistanceVariable(name='distance variable', mesh=mesh, value=-1.) distanceVar.setValue(1., where=mesh.electrolyteMask) distanceVar.calcDistanceFunction() levelerVar = SurfactantVariable(name="leveler variable", value=initialLevelerCoverage, distanceVar=distanceVar) acceleratorVar = SurfactantVariable(name="accelerator variable", value=initialAcceleratorCoverage, distanceVar=distanceVar) 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.interfaceVar * ( coeffAccelerator - coeffSuppressor) + coeffSuppressor currentDensity = metalVar / bulkMetalConcentration * exchangeCurrentDensity depositionRateVariable = currentDensity * atomicVolume / charge / faradaysConstant extensionVelocityVariable = CellVariable(name='extension velocity', mesh=mesh, value=depositionRateVariable) 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.interfaceVar 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) advectionEquation = TransientTerm() + FirstOrderAdvectionTerm( extensionVelocityVariable) metalEquation = buildMetalIonDiffusionEquation( ionVar=metalVar, distanceVar=distanceVar, depositionRate=depositionRateVariable, diffusionCoeff=metalDiffusionCoefficient, metalIonMolarVolume=atomicVolume) metalVar.constrain(bulkMetalConcentration, mesh.facesTop) bulkAcceleratorEquation = buildSurfactantBulkDiffusionEquation( bulkVar=bulkAcceleratorVar, distanceVar=distanceVar, surfactantVar=acceleratorVar, otherSurfactantVar=levelerVar, diffusionCoeff=acceleratorDiffusionCoefficient, rateConstant=kAccelerator * siteDensity) bulkAcceleratorVar.constrain(bulkAcceleratorConcentration, mesh.facesTop) bulkLevelerEquation = buildSurfactantBulkDiffusionEquation( bulkVar=bulkLevelerVar, distanceVar=distanceVar, surfactantVar=levelerVar, diffusionCoeff=levelerDiffusionCoefficient, rateConstant=kLeveler * siteDensity) bulkLevelerVar.constrain(bulkLevelerConcentration, mesh.facesTop) eqnTuple = ((advectionEquation, distanceVar, (), None), (levelerSurfactantEquation, levelerVar, (), None), (acceleratorSurfactantEquation, acceleratorVar, (), None), (metalEquation, metalVar, (), None), (bulkAcceleratorEquation, bulkAcceleratorVar, (), GeneralSolver()), (bulkLevelerEquation, bulkLevelerVar, (), GeneralSolver())) narrowBandWidth = 20 * cellSize levelSetUpdateFrequency = int(0.7 * narrowBandWidth / cellSize / cflNumber / 2) totalTime = 0.0 if displayViewers: try: raise Exception from mayaviSurfactantViewer import MayaviSurfactantViewer viewers = (MayaviSurfactantViewer(distanceVar, acceleratorVar.interfaceVar, zoomFactor=1e6, datamax=0.5, datamin=0.0, smooth=1, title='accelerator coverage'), MayaviSurfactantViewer(distanceVar, levelerVar.interfaceVar, zoomFactor=1e6, datamax=0.5, datamin=0.0, smooth=1, title='leveler coverage')) 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)) viewers = (Viewer(PlotVariable(var=acceleratorVar.interfaceVar)), Viewer(PlotVariable(var=levelerVar.interfaceVar))) for step in range(numberOfSteps): if displayViewers: if step % displayRate == 0: for viewer in viewers: viewer.plot() if step % levelSetUpdateFrequency == 0: distanceVar.calcDistanceFunction() extensionVelocityVariable.setValue(depositionRateVariable) extOnInt = numerix.where( distanceVar.globalValue > 0, numerix.where(distanceVar.globalValue < 2 * cellSize, extensionVelocityVariable.globalValue, 0), 0) dt = cflNumber * cellSize / extOnInt.max() distanceVar.extendVariable(extensionVelocityVariable) for eqn, var, BCs, solver in eqnTuple: eqn.solve(var, boundaryConditions=BCs, dt=dt, solver=solver) totalTime += dt point = ((1.25e-08, ), (3.125e-07, )) value = 2.02815779e-08 return abs(float(distanceVar(point, order=1)) - value) < cellSize / 10.0