import matplotlib.pyplot as plt import numpy as np import openpnm as op # Get Deff w/o including Knudsen effect shape = np.array([10, 10, 10]) spacing = 1.0 net = op.network.Cubic(shape=[10, 10, 10], spacing=spacing) geom = op.geometry.SpheresAndCylinders(network=net, pores=net.Ps, throats=net.Ts) air = op.phase.Air(network=net) phys = op.physics.Standard(network=net, geometry=geom, phase=air) odiff = op.models.physics.diffusive_conductance.ordinary_diffusion phys.add_model(propname="throat.diffusive_conductance", model=odiff) fd = op.algorithms.FickianDiffusion(network=net, phase=air) fd.set_value_BC(pores=net.pores("left"), values=1.0) fd.set_value_BC(pores=net.pores("right"), values=0.0) fd.run() L = (shape * spacing)[1] A = (shape * spacing)[[0, 2]].prod() Mdot = fd.rate(pores=net.pores("left")).squeeze() Deff0 = Mdot * L / A # Get Deff w/ including Knudsen effect mdiff = op.models.physics.diffusive_conductance.mixed_diffusion phys.add_model(propname="throat.diffusive_conductance", model=mdiff) spacings = np.linspace(1e-9, 1e-4, 20) spacings = np.logspace(-9, -3, 25) Deff = [] for spacing in spacings: np.random.seed(10) net = op.network.Cubic(shape=[10, 10, 10], spacing=spacing) geom = op.geometry.SpheresAndCylinders(network=net, pores=net.Ps, throats=net.Ts) air = op.phase.Air(network=net) phys = op.physics.Standard(network=net, geometry=geom, phase=air) phys.add_model(propname="throat.diffusive_conductance", model=mdiff) fd = op.algorithms.FickianDiffusion(network=net, phase=air) fd.set_value_BC(pores=net.pores("left"), values=1.0) fd.set_value_BC(pores=net.pores("right"), values=0.0) fd.run() L = (shape * spacing)[1] A = (shape * spacing)[[0, 2]].prod() Mdot = fd.rate(pores=net.pores("left")).squeeze() Deff.append(Mdot * L / A) # Plot ratio of Deff w/ Knudsen to that w/o Deff = np.array(Deff) plt.figure() plt.plot(spacings, Deff/Deff0) plt.xscale("log") plt.xlabel("spacing (m)") plt.ylabel("Deff/Deff0")