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-phi_right = 0 -rtol = 1e-4 # ! Change back to 1e-8 +p_R = 0 +phi_R = 0 # phi^L domain -Volt_start = 0 -Volt_end = 0.75 +Volt_start = -1.0 +Volt_end = 1.0 # Volt_start = -1.0 # Volt_end = 1.0 -n_Volts = 25 # ! Change back to 101 +n_Volts = 10_001 Phi_Pot_Diff_dim = np.linspace(Volt_start, Volt_end, n_Volts) Phi_Pot_Diff_dimless = Phi_Pot_Diff_dim * e0/(k*T) -y_A, y_C, y_S, phi, p, x, n_sol = [], [], [], [], [], [], [] -for index, K_ in enumerate(K_vec): - print('-------------------------------------------------------------------') - print('K: ', str(K_)) - print('-------------------------------------------------------------------') - phi_inner, y_A_inner, y_C_inner, y_S_inner, p_inner,x_inner, n_inner = [], [], [], [], [], [], [] - for i, phi_bcs in enumerate(Phi_Pot_Diff_dimless): - print('-------------------------------------------------------------------') - print('K: ', str(K_)) - print('phi_bcs: ', phi_bcs) - print('-------------------------------------------------------------------') - relax_param = 0.05 - if phi_bcs > 20: - relax_param = 0.02 - if phi_bcs > 25: - relax_param = 0.01 - y_A_, y_C_, phi_, p_, x_ = solve_System_2eq(phi_bcs, phi_right, p_right, z_A, z_C, y_R, y_R, K_, Lambda2, a2, number_cells, relax_param=relax_param, refinement_style='hard_log', rtol=rtol, max_iter=10_000, return_type='Vector') - y_A_inner.append(y_A_) - y_C_inner.append(y_C_) - y_S_inner.append(1 - y_A_ - y_C_) - phi_inner.append(phi_*(k*T/e0)) - p_inner.append(p_) - n_inner.append(n(p_, K_)) - x_inner.append(x_) - y_A.append(y_A_inner) - y_C.append(y_C_inner) - y_S.append(y_S_inner) - phi.append(phi_inner) - p.append(p_inner) - x.append(x_inner) - n_sol.append(n_inner) - +# K +K_vec = ['incompressible', 50_000, 40_000, 30_000, 20_000] - -# Charge +Q_DL_dim_ = [] Q_DL_dimless_ = [] -for i in range(len(K_vec)): - Q_inner = [] - for j in range(len(Phi_Pot_Diff_dimless)): - # ToDo: nR_m -> n - Q_inner.append(Q_num_(y_A[i][j], y_C[i][j], n_sol[i][j], x[i][j])) - Q_DL_dimless_.append(Q_inner) -Q_DL_dimless_ = np.array(Q_DL_dimless_) -Q_DL_dim_ = Q_DL_dimless_ * nR_m * e0 * LR * 1e+6 * 1/(1e+4) # [µF/cm³] +for K in K_vec: + y_A_R, y_C_R = Molarity / nR_mol, Molarity / nR_mol + y_N_R = 1 - y_A_R - y_C_R + Q_DL_dimless_.append(Q_DL_dimless_ana(y_A_R, y_C_R, y_N_R, z_A, z_C, Phi_Pot_Diff_dimless, phi_R, p_R, K, Lambda2, a2, kappa)) + Q_DL_dim_.append(Q_DL_dim_ana(y_A_R, y_C_R, y_N_R, z_A, z_C, Phi_Pot_Diff_dimless, phi_R, p_R, K, Lambda2, a2, nR_m, e0, LR, kappa)) # Double layer capacity C_DL_dim = [C_dl(q_dl, Phi_Pot_Diff_dim) for q_dl in Q_DL_dim_] @@ -119,70 +82,117 @@ Phi_pot_center_array_dimless = Phi_pot_center(Phi_Pot_Diff_dimless) Phi_pot_center_array_dim = Phi_pot_center(Phi_Pot_Diff_dim) -# Visualizations +# Plotting # Charge -plt.figure() -[plt.plot(Phi_Pot_Diff_dimless, Q_DL_dimless_[i], label=f'K = {K_vec[i]}') for i in range(len(K_vec))] -plt.grid() -plt.legend() -plt.xlabel('$\delta \\varphi$ [-]') -plt.ylabel('Q $[-]$') -plt.tight_layout() -plt.show() - -# Double layer capacity -plt.figure() -[plt.plot(Phi_pot_center_array_dimless, C_DL_dimless[i], label=f'K = {K_vec[i]}') for i in range(len(K_vec))] -plt.grid() -plt.legend() -plt.xlabel('$\delta \\varphi$ [-]') -plt.ylabel('$C_{dl} [-]$') -plt.tight_layout() -plt.show() - -# y_alpha_L -y_A_np, y_C_np, y_S_np = np.array(y_A), np.array(y_C), np.array(y_S) -markers = ['--', '-', ':'] +fig = plt.figure() colors = ['tab:blue', 'tab:orange', 'tab:green', 'tab:red', 'tab:purple'] -plt.figure() -for i in range(len(K_vec)): - clr = colors[i] - plt.plot(Phi_Pot_Diff_dimless, y_A_np[i,:,0], '--', color=clr) - plt.plot(Phi_Pot_Diff_dimless, y_C_np[i,:,0], '-', color=clr) - plt.plot(Phi_Pot_Diff_dimless, y_S_np[i,:,0], ':', color=clr) -dummy, = plt.plot(0, 0, color='grey', linestyle='--', label='$y_A$') -dummy, = plt.plot(0, 0, color='grey', linestyle='-', label='$y_C$') -dummy, = plt.plot(0, 0, color='grey', linestyle=':', label='$y_S$') -for index, K_ in enumerate(K_vec): - dummy, = plt.plot(0, 0, color=colors[index], linestyle='-', label=f'K = {K_}') -plt.grid() -plt.legend() -plt.xlabel('$\delta \\varphi$ [-]') -plt.ylabel('$y_\\alpha^L$') -plt.tight_layout() -plt.show() - -n_sol_np = np.array(n_sol) -n_A_np, n_C_np, n_S_np = y_A_np * n_sol_np, y_C_np * n_sol_np, y_S_np * n_sol_np -plt.figure() -clr = colors[0] -for i in range(len(K_vec)): - clr = colors[i] - plt.plot(Phi_Pot_Diff_dimless, n_A_np[i,:,0], '--', color=clr) - plt.plot(Phi_Pot_Diff_dimless, n_C_np[i,:,0], '-', color=clr) - plt.plot(Phi_Pot_Diff_dimless, n_S_np[i,:,0], ':', color=clr) -dummy, = plt.plot(0, 0, color='grey', linestyle='--', label='$n_A$') -dummy, = plt.plot(0, 0, color='grey', linestyle='-', label='$n_C$') -dummy, = plt.plot(0, 0, color='grey', linestyle=':', label='$n_S$') -for index, K_ in enumerate(K_vec): - dummy, = plt.plot(0, 0, color=colors[index], linestyle='-', label=f'K = {K_}') -plt.grid() -plt.legend() -plt.xlabel('$\delta \\varphi$ [-]') -plt.ylabel('$n_\\alpha^L [-]$') -plt.tight_layout() -plt.show() +color_dimless = 'tab:purple' +color_dim = 'tab:red' +ax = fig.add_subplot(111, label="1") +ax2 = fig.add_subplot(111, label="2", frame_on=False) + +# Plot dimensional data +for i, q_dl in enumerate(Q_DL_dim_): + ax.plot(Phi_Pot_Diff_dim, q_dl, color=colors[i], label=f'$K$: {K_vec[i]}') +ax.grid() +ax.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) +ax.set_ylabel('$Q$ [\u03bc$F/cm^3]$', color=color_dim) +ax.tick_params(axis='x', colors=color_dim) +ax.tick_params(axis='y', colors=color_dim) + +for i, q_dl in enumerate(Q_DL_dimless_): + ax2.plot(Phi_Pot_Diff_dimless, q_dl, color=colors[i]) +ax2.xaxis.tick_top() +ax2.yaxis.tick_right() +ax2.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) +ax2.set_ylabel('$Q [-]$', color=color_dimless) +ax2.xaxis.set_label_position('top') +ax2.yaxis.set_label_position('right') +ax2.tick_params(axis='x', colors=color_dimless) +ax2.tick_params(axis='y', colors=color_dimless) + +fig.legend() +fig.tight_layout() +fig.show() + + +# Double Layer Capacity +Phi_pot_center_array_dimless = Phi_pot_center(Phi_Pot_Diff_dimless) +Phi_pot_center_array_dim = Phi_pot_center(Phi_Pot_Diff_dim) +fig = plt.figure() +color_dimless = 'tab:purple' +color_dim = 'tab:red' +ax = fig.add_subplot(111, label="1") +ax2 = fig.add_subplot(111, label="2", frame_on=False) + +# Plot dimensional data +for i, c_dl in enumerate(C_DL_dim): + ax.plot(Phi_pot_center_array_dim, c_dl, color=colors[i], label=f'$K$: {K_vec[i]}') +ax.grid() +ax.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) +ax.set_ylabel('$C_{dl}$ [\u03bc$F/cm^2]$', color=color_dim) +ax.tick_params(axis='x', colors=color_dim) +ax.tick_params(axis='y', colors=color_dim) + +for i, c_dl in enumerate(C_DL_dimless): + ax2.plot(Phi_pot_center_array_dimless, c_dl, color=colors[i]) +# ax2.grid() +ax2.xaxis.tick_top() +ax2.yaxis.tick_right() +ax2.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) +ax2.set_ylabel('$Q [-]$', color=color_dimless) +ax2.xaxis.set_label_position('top') +ax2.yaxis.set_label_position('right') +ax2.tick_params(axis='x', colors=color_dimless) +ax2.tick_params(axis='y', colors=color_dimless) + +fig.legend() +fig.tight_layout() +fig.show() + +# # y_alpha_L +# y_A_np, y_C_np, y_S_np = np.array(y_A), np.array(y_C), np.array(y_S) +# markers = ['--', '-', ':'] +# colors = ['tab:blue', 'tab:orange', 'tab:green', 'tab:red', 'tab:purple'] +# plt.figure() +# for i in range(len(K_vec)): +# clr = colors[i] +# plt.plot(Phi_Pot_Diff_dimless, y_A_np[i,:,0], '--', color=clr) +# plt.plot(Phi_Pot_Diff_dimless, y_C_np[i,:,0], '-', color=clr) +# plt.plot(Phi_Pot_Diff_dimless, y_S_np[i,:,0], ':', color=clr) +# dummy, = plt.plot(0, 0, color='grey', linestyle='--', label='$y_A$') +# dummy, = plt.plot(0, 0, color='grey', linestyle='-', label='$y_C$') +# dummy, = plt.plot(0, 0, color='grey', linestyle=':', label='$y_S$') +# for index, K_ in enumerate(K_vec): +# dummy, = plt.plot(0, 0, color=colors[index], linestyle='-', label=f'K = {K_}') +# plt.grid() +# plt.legend() +# plt.xlabel('$\delta \\varphi$ [-]') +# plt.ylabel('$y_\\alpha^L$') +# plt.tight_layout() +# plt.show() + +# n_sol_np = np.array(n_sol) +# n_A_np, n_C_np, n_S_np = y_A_np * n_sol_np, y_C_np * n_sol_np, y_S_np * n_sol_np +# plt.figure() +# clr = colors[0] +# for i in range(len(K_vec)): +# clr = colors[i] +# plt.plot(Phi_Pot_Diff_dimless, n_A_np[i,:,0], '--', color=clr) +# plt.plot(Phi_Pot_Diff_dimless, n_C_np[i,:,0], '-', color=clr) +# plt.plot(Phi_Pot_Diff_dimless, n_S_np[i,:,0], ':', color=clr) +# dummy, = plt.plot(0, 0, color='grey', linestyle='--', label='$n_A$') +# dummy, = plt.plot(0, 0, color='grey', linestyle='-', label='$n_C$') +# dummy, = plt.plot(0, 0, color='grey', linestyle=':', label='$n_S$') +# for index, K_ in enumerate(K_vec): +# dummy, = plt.plot(0, 0, color=colors[index], linestyle='-', label=f'K = {K_}') +# plt.grid() +# plt.legend() +# plt.xlabel('$\delta \\varphi$ [-]') +# plt.ylabel('$n_\\alpha^L [-]$') +# plt.tight_layout() +# plt.show() # Store data -np.savez('../../Data/DoubleLayerCapacity/DLKap_Compressibility.npz', Lambda2=Lambda2, a2=a2, K_vec=K_vec, kappa=kappa, Molarity=Molarity, y_R=y_R, z_A=z_A, z_C=z_C, number_cells=number_cells, p_right=p_right, phi_right=phi_right, rtol=rtol, Volt_start=Volt_start, Volt_end=Volt_end, n_Volts=n_Volts, Phi_Pot_Diff_dimless=Phi_Pot_Diff_dimless, Phi_Pot_Diff_dim=Phi_Pot_Diff_dim, Phi_pot_center_array_dim=Phi_pot_center_array_dim, Phi_pot_center_array_dimless=Phi_pot_center_array_dimless, y_A=y_A, y_C=y_C, y_S=y_S, phi=phi, p=p, x=x, n_sol=n_sol, Q_DL_dimless_=Q_DL_dimless_, Q_DL_dim_ =Q_DL_dim_, C_DL_dimless=C_DL_dimless, C_DL_dim=C_DL_dim, y_A_np=y_A_np, y_C_np=y_C_np, y_S_np=y_S_np, n_sol_np=n_sol_np, n_A_np=n_A_np, n_C_np=n_C_np, n_S_np=n_S_np) +np.savez('../../Data/DoubleLayerCapacity/DLKap_Compressibility.npz', Lambda2=Lambda2, a2=a2, K_vec=K_vec, kappa=kappa, Molarity=Molarity, y_A_R=y_A_R, y_C_R=y_C_R, z_A=z_A, z_C=z_C, p_R=p_R, phi_R=phi_R, Volt_start=Volt_start, Volt_end=Volt_end, n_Volts=n_Volts, Phi_Pot_Diff_dimless=Phi_Pot_Diff_dimless, Phi_Pot_Diff_dim=Phi_Pot_Diff_dim, Phi_pot_center_array_dim=Phi_pot_center_array_dim, Phi_pot_center_array_dimless=Phi_pot_center_array_dimless, Q_DL_dimless_=Q_DL_dimless_, Q_DL_dim_ =Q_DL_dim_, C_DL_dimless=C_DL_dimless, C_DL_dim=C_DL_dim) diff --git a/examples/ReproducableCode/DoubleLayerCapacity/IncompressibleValidationAnalyticalMethod.py b/examples/ReproducableCode/DoubleLayerCapacity/IncompressibleValidationAnalyticalMethod.py index cf633d74c996677331b7514f712ba88733078ea0..cd0ec8a03b34e1bf99594e9e21812474160977a9 100644 --- a/examples/ReproducableCode/DoubleLayerCapacity/IncompressibleValidationAnalyticalMethod.py +++ b/examples/ReproducableCode/DoubleLayerCapacity/IncompressibleValidationAnalyticalMethod.py @@ -44,7 +44,7 @@ chi = 80 # [-] Lambda2 = (k*T*epsilon0*(1+chi))/(e0**2 * nR_m * (LR)**2) a2 = (pR)/(nR_m * k * T) K = 'incompressible' -kappa = 5 +kappa = 0 Molarity = 0.01 y_R = Molarity / nR_mol z_A, z_C = -1.0, 1.0 diff --git a/examples/ReproducableCode/DoubleLayerCapacity/Molarity.py b/examples/ReproducableCode/DoubleLayerCapacity/Molarity.py index 101b6c889728d38cec9b0e29c89c7f87579d3f39..fe785f8d726ec709f934c1dc01033aab83bcb2e2 100644 --- a/examples/ReproducableCode/DoubleLayerCapacity/Molarity.py +++ b/examples/ReproducableCode/DoubleLayerCapacity/Molarity.py @@ -29,7 +29,7 @@ T = 293.75 # [K] epsilon0 = 8.85e-12 #[F/m] F = 9.65e+4 # [As/mol] NA = 6.022e+23 # [1/mol] - Avogadro constant -nR_mol = 55 +nR_mol = 55 # [mol/m^3] nR_m = nR_mol * NA * 1/(1e-3)# [1/m^3] pR = 1.01325 * 1e+5 # [Pa] LR = 20e-8 @@ -56,7 +56,7 @@ Phi_Pot_Diff_dimless = Phi_Pot_Diff_dim * e0/(k*T) # Molarity -Molarity = np.array([0.01, 0.1, 1]) +Molarity = np.array([0.01, 0.1, 1]) # [mol/m^3] Q_DL_dim_ = [] Q_DL_dimless_ = [] diff --git a/examples/ReproducableCode/ElectrolyticDiode/BackwardBias.py b/examples/ReproducableCode/ElectrolyticDiode/BackwardBias.py index b4cf41ccb7314d99c917d4ec984c70f8791d9f6b..c0744f3af0825a74a86aaf056fc2d7cad002f8d7 100644 --- a/examples/ReproducableCode/ElectrolyticDiode/BackwardBias.py +++ b/examples/ReproducableCode/ElectrolyticDiode/BackwardBias.py @@ -25,13 +25,14 @@ import numpy as np # Parameter phi_bias = 10 Bias_type = 'BackwardBias' -g_phi = 5 +g_phi = 10 y_fixed = 0.01 z_A = -1.0 z_C = 1.0 K = 'incompressible' -Lambda2 = 8.553e-2 # ! e-6 -a2 = 7.5412e-2 # ! e-4 +Lambda2 = 3e-2 # 8.553e-2 # ! e-6 +a2 = 7.5412e-4 # ! e-4 +solvation = 0 number_cells = [20,100] # ! [40, 400] Lx = 2 Ly = 10 @@ -44,7 +45,7 @@ relax_param = 0.05 max_iter = 15_000 # Solve the system -y_A, y_C, phi, p, X, u = ElectrolyticDiode(Bias_type, phi_bias, g_phi, z_A, z_C, y_fixed, y_fixed, K, Lambda2, a2, number_cells, relax_param=relax_param, Lx=Lx, Ly=Ly, rtol=rtol, max_iter=max_iter, return_type='Extended') +y_A, y_C, phi, p, X, u = ElectrolyticDiode(Bias_type, phi_bias, g_phi, z_A, z_C, y_fixed, y_fixed, K, Lambda2, a2, number_cells, relax_param=relax_param, Lx=Lx, Ly=Ly, solvation=solvation, rtol=rtol, max_iter=max_iter, return_type='Extended') x, y = X[0], X[1] y_S = 1 - y_A - y_C diff --git a/examples/ReproducableCode/ElectrolyticDiode/ForwardBias.py b/examples/ReproducableCode/ElectrolyticDiode/ForwardBias.py index d265e41360dbd5f992121d31a9367c7dcfccc9bc..dd9d6f272ff6bd677b0a1e33a4cb5d87e18d4351 100644 --- a/examples/ReproducableCode/ElectrolyticDiode/ForwardBias.py +++ b/examples/ReproducableCode/ElectrolyticDiode/ForwardBias.py @@ -25,13 +25,14 @@ import numpy as np # Parameter phi_bias = 10 Bias_type = 'ForwardBias' -g_phi = 5 +g_phi = 10 y_fixed = 0.01 z_A = -1.0 z_C = 1.0 K = 'incompressible' -Lambda2 = 8.553e-2 # ! e-6 -a2 = 7.5412e-2 # !e-4 +Lambda2 = 3e-2 # 8.553e-2 # ! e-6 +a2 = 7.5412e-4 # !e-4 +solvation = 0 number_cells = [20, 100] # ! [40, 400] Lx = 2 Ly = 10 @@ -44,7 +45,7 @@ relax_param = 0.05 max_iter = 15_000 # Solve the system -y_A, y_C, phi, p, X, u = ElectrolyticDiode(Bias_type, phi_bias, g_phi, z_A, z_C, y_fixed, y_fixed, K, Lambda2, a2, number_cells, relax_param=relax_param, Lx=Lx, Ly=Ly, rtol=rtol, max_iter=max_iter, return_type='Extended') +y_A, y_C, phi, p, X, u = ElectrolyticDiode(Bias_type, phi_bias, g_phi, z_A, z_C, y_fixed, y_fixed, K, Lambda2, a2, number_cells, relax_param=relax_param, Lx=Lx, Ly=Ly, rtol=rtol, solvation=solvation, max_iter=max_iter, return_type='Extended') x, y = X[0], X[1] y_S = 1 - y_A - y_C diff --git a/examples/ReproducableCode/ElectrolyticDiode/NoBias.py b/examples/ReproducableCode/ElectrolyticDiode/NoBias.py index fd1ac9daf8c94302773ff08cf21c236d20afbbe4..ac228cbc26d34d7641407021e6811cac90f9b2a2 100644 --- a/examples/ReproducableCode/ElectrolyticDiode/NoBias.py +++ b/examples/ReproducableCode/ElectrolyticDiode/NoBias.py @@ -25,13 +25,14 @@ import numpy as np # Parameter phi_bias = 10 # Doesn't matter, as set to zero in the function Bias_type = 'NoBias' -g_phi = 5 +g_phi = 10 y_fixed = 0.01 z_A = -1.0 z_C = 1.0 K = 'incompressible' -Lambda2 = 8.553e-2 # ! e-6 -a2 = 7.5412e-2 # ! e-4 +Lambda2 = 3e-2 # 8.553e-2 # ! e-6 +a2 = 7.5412e-4 # ! e-4 +solvation = 0 number_cells = [20, 100] # ! [40, 400] Lx = 2 Ly = 10 @@ -44,7 +45,7 @@ relax_param = 0.05 max_iter = 15_000 # Solve the system -y_A, y_C, phi, p, X, u = ElectrolyticDiode(Bias_type, phi_bias, g_phi, z_A, z_C, y_fixed, y_fixed, K, Lambda2, a2, number_cells, relax_param=relax_param, Lx=Lx, Ly=Ly, rtol=rtol, max_iter=max_iter, return_type='Extended') +y_A, y_C, phi, p, X, u = ElectrolyticDiode(Bias_type, phi_bias, g_phi, z_A, z_C, y_fixed, y_fixed, K, Lambda2, a2, number_cells, relax_param=relax_param, Lx=Lx, Ly=Ly, solvation=solvation, rtol=rtol, max_iter=max_iter, return_type='Extended') x, y = X[0], X[1] y_S = 1 - y_A - y_C diff --git a/examples/ReproducableCode/ParameterAnalysis/ChargeNumbers.py b/examples/ReproducableCode/ParameterAnalysis/ChargeNumbers.py new file mode 100644 index 0000000000000000000000000000000000000000..5074381c340989c8c82681b6f2097f8767c8ffdb --- /dev/null +++ b/examples/ReproducableCode/ParameterAnalysis/ChargeNumbers.py @@ -0,0 +1,83 @@ +''' +Jan Habscheid +Jan.Habscheid@rwth-aachen.de +''' +# import the src file needed to solve the system of equations +import sys +import os + + +# Add the src directory to the sys.path +src_path = os.path.join(os.path.dirname(os.path.abspath(__file__)), '../../..', 'src') +sys.path.insert(0, src_path) + +from Eq04 import solve_System_4eq + +# Remove the src directory from sys.path after import +del sys.path[0] + +# Import plotting library +import matplotlib.pyplot as plt +import numpy as np + +# Define Parameter and buondary conditions +phi_left = 4.0 +phi_right = 0.0 +p_right = 0.0 +y_A_R_1, y_C_R_1 = 1/6, 2/6 +y_A_R_2, y_C_R_2 = 2/6, 1/6 +z_A_1, z_C_1 = -2.0, 1.0 +z_A_2, z_C_2 = -1.0, 2.0 +K = 'incompressible' +a2 = 7.5412e-4 +number_cells = 1024*8 +refinement_style = 'hard_log' +rtol = 1e-8 +max_iter = 10_000 + +# Define left values of electric potential and values for lambda^2 +Lambda2 = 8.553e-6 + +# Solve the system +y_A_1, y_C_1, phi_1, p_1, x_1 = solve_System_4eq(phi_left, phi_right, p_right, z_A_1, z_C_2, y_A_R_1, y_C_R_1, K, Lambda2, a2, number_cells, relax_param=0.05, x0=0, x1=1, refinement_style=refinement_style, return_type='Vector', max_iter=max_iter, rtol=rtol) + +y_A_2, y_C_2, phi_2, p_2, x_2 = solve_System_4eq(phi_left, phi_right, p_right, z_A_2, z_C_2, y_A_R_2, y_C_R_2, K, Lambda2, a2, number_cells, relax_param=0.05, x0=0, x1=1, refinement_style=refinement_style, return_type='Vector', max_iter=max_iter, rtol=rtol) + + +# Visualize the results +plt.figure() +plt.plot(x_1, phi_1, label='z_A = -2, z_C = 1') +plt.plot(x_2, phi_2, label='z_A = -1, z_C = 2') +plt.legend() +plt.xlabel('x') +plt.ylabel('$\\varphi$') +plt.grid() +plt.show() + +plt.figure() +plt.plot(x_1, y_A_1, label='z_A = -2, z_C = 1') +plt.plot(x_2, y_A_2, label='z_A = -1, z_C = 2') +plt.legend() +plt.xlabel('x') +plt.ylabel('$y_A$') +plt.grid() +plt.show() + +plt.figure() +plt.plot(x_1, y_C_1, label='z_A = -2, z_C = 1') +plt.plot(x_2, y_C_2, label='z_A = -1, z_C = 2') +plt.legend() +plt.xlabel('x') +plt.ylabel('$y_C$') +plt.grid() +plt.show() + +plt.figure() +plt.plot(x_1, p_1, label='z_A = -2, z_C = 1') +plt.plot(x_2, p_2, label='z_A = -1, z_C = 2') +plt.legend() +plt.xlabel('x') +plt.ylabel('p') +plt.grid() +plt.show() + diff --git a/examples/ReproducableCode/ValidationDreyer.py b/examples/ReproducableCode/ValidationDreyer.py new file mode 100644 index 0000000000000000000000000000000000000000..ce5de1624a22e510a3f6332a1b705671f91f7c04 --- /dev/null +++ b/examples/ReproducableCode/ValidationDreyer.py @@ -0,0 +1,104 @@ +''' +Jan Habscheid +Jan.Habscheid@rwth-aachen.de + +This script is used to validate the implemetation with: +Wolfgang Dreyer, Clemens Guhlke, and Rüdiger Müller. Bulk-surface electrothermodynamics and applications to electrochemistry. Entropy, 20(12), 2018 +''' + +# import the src file needed to solve the system of equations +import sys +import os + +# Add the src directory to the sys.path +src_path = os.path.join(os.path.dirname(os.path.abspath(__file__)), '../..', 'src') +sys.path.insert(0, src_path) + +from Eq04 import solve_System_4eq + +# Remove the src directory from sys.path after import +del sys.path[0] + +# Further imports +import matplotlib.pyplot as plt +import matplotlib.ticker as ticker +import numpy as np + +# Define the parameters and boundary conditions +e0 = 1.602e-19 # [As] +k = 1.381e-23 # [J/K] +T = 293.75#298#293.15 # [K] +epsilon0 = 8.85e-12 #[F/m] +F = 9.65e+4 # [As/mol] +NA = 6.022e+23 # [1/mol] - Avogadro constant +p_ref = 1.01325 * 1e+5 # [Pa] +L_ref = 10e-9#20e-9#20e-9 # [m] +chi = 80 # [-] + +# BCS according to Fuhrmann - FuelCells +nRef = 55.4 # [mol/L] +Molarity = 0.5 +y_A_R, y_C_R = Molarity / nRef, Molarity / nRef #0.01, 0.01 +pR = 0 +z_A, z_C = -1.0, 1.0 +nR_m = nRef * NA * 1/(1e-3) # [1/m^3] +phi_L_dim = 0.6 # [V] -> 500 mV # ! Change back to 0.5 for Fuhrmann Fuel-Cells, 0.6 for Dereyer - Bulk-Surface +phi_R_dim = 0.0 # [V] +phi_L_dimless = phi_L_dim * e0 / (k * T) +phi_R_dimless = phi_R_dim * e0 / (k * T) +phi_L_dimless, phi_R_dimless + +# Parameters +K = 'incompressible' +Lambda2 = (k*T*epsilon0*(1+chi))/(e0**2 * nR_m * (L_ref)**2) +a2 = (p_ref)/(nR_m * k * T) +Lambda2, a2 # values not sure, as T, chi and L_ref not given in Fuhrmann paper + +# Solver parameters +number_cells = 1028*16#1024*4#128 +relax_param = 0.005#0.001##0.01 +refinement_style = 'log' +max_iter = 100_000 +return_type = 'Vector' +rtol = 1e-8 # ! Change back to 1e-8 + + +y_A_dimless, y_C_dimless, y_S_dimless, phi_dimless, p_dimless, x_dimless = [], [], [], [], [], [] +y_A_, y_C_, phi_, p_, x_ = solve_System_4eq(phi_L_dimless, phi_R_dimless, pR, z_A, z_C, y_A_R, y_C_R, K, Lambda2, a2, number_cells, solvation=0, PoissonBoltzmann=True, relax_param=relax_param, refinement_style=refinement_style, return_type=return_type, max_iter=max_iter, rtol=rtol) +y_A_dimless.append(y_A_) +y_C_dimless.append(y_C_) +y_S_dimless.append(1 - y_A_ - y_C_) +phi_dimless.append(phi_) +p_dimless.append(p_) +x_dimless.append(x_) + +y_A_, y_C_, phi_, p_, x_ = solve_System_4eq(phi_L_dimless, phi_R_dimless, pR, z_A, z_C, y_A_R, y_C_R, K, Lambda2, a2, number_cells=1024, solvation=0, PoissonBoltzmann=False, relax_param=relax_param, refinement_style=refinement_style, return_type=return_type, max_iter=max_iter, rtol=rtol) +y_A_dimless.append(y_A_) +y_C_dimless.append(y_C_) +y_S_dimless.append(1 - y_A_ - y_C_) +phi_dimless.append(phi_) +p_dimless.append(p_) +x_dimless.append(x_) + +y_A_, y_C_, phi_, p_, x_ = solve_System_4eq(phi_L_dimless, phi_R_dimless, pR, z_A, z_C, y_A_R, y_C_R, K, Lambda2, a2, number_cells=1024, solvation=8, PoissonBoltzmann=False, relax_param=relax_param, refinement_style=refinement_style, return_type=return_type, max_iter=max_iter, rtol=rtol) +y_A_dimless.append(y_A_) +y_C_dimless.append(y_C_) +y_S_dimless.append(1 - y_A_ - y_C_) +phi_dimless.append(phi_) +p_dimless.append(p_) +x_dimless.append(x_) + +# Rescale to physical values +y_A_dimless, y_C_dimless, y_S_dimless, phi_dimless, p_dimless, x_dimless = np.array(y_A_dimless), np.array(y_C_dimless), np.array(y_S_dimless), np.array(phi_dimless), np.array(p_dimless), np.array(x_dimless) +phi_dim = phi_dimless * k * T / e0 +p_dim = p_dimless * p_ref +x_dim = x_dimless * L_ref +y_A_dim = y_A_dimless +y_C_dim = y_C_dimless +y_S_dim = y_S_dimless +n_A_dim = y_A_dim * nRef +n_C_dim = y_C_dim * nRef +n_S_dim = y_S_dim * nRef + +# Store the results +np.savez('../Data/Validation_Dreyer_BulkSurface.npz', y_A_dimless=y_A_dimless, y_C_dimless=y_C_dimless, y_S_dimless=y_S_dimless, phi_dimless=phi_dimless, p_dimless=p_dimless, x_dimless=x_dimless, y_A_dim=y_A_dim, y_C_dim=y_C_dim, y_S_dim=y_S_dim, n_A_dim=n_A_dim, n_C_dim=n_C_dim, n_S_dim=n_S_dim, phi_dim=phi_dim, p_dim=p_dim, x_dim=x_dim) \ No newline at end of file diff --git a/examples/Visualizations/DoubleLayerCapacity.py/VisCompressibility.py b/examples/Visualizations/DoubleLayerCapacity.py/VisCompressibility.py index 310270cb301c76e58341d84c25c4a637a05f2e58..97cbf78777474e06b102a31e1865a174cda03a21 100644 --- a/examples/Visualizations/DoubleLayerCapacity.py/VisCompressibility.py +++ b/examples/Visualizations/DoubleLayerCapacity.py/VisCompressibility.py @@ -18,14 +18,14 @@ Q_DL_dimless_ = data['Q_DL_dimless_'] Q_DL_dim_ = data['Q_DL_dim_'] C_DL_dim = data['C_DL_dim'] C_DL_dimless = data['C_DL_dimless'] -y_A = data['y_A'] -y_C = data['y_C'] -y_S = data['y_S'] +# y_A = data['y_A'] +# y_C = data['y_C'] +# y_S = data['y_S'] Phi_Pot_Diff_dim = data['Phi_Pot_Diff_dim'] Phi_Pot_Diff_dimless = data['Phi_Pot_Diff_dimless'] Phi_pot_center_array_dim = data['Phi_pot_center_array_dim'] Phi_pot_center_array_dimless = data['Phi_pot_center_array_dimless'] -n_sol = data['n_sol'] +# n_sol = data['n_sol'] K_vec = data['K_vec'] @@ -39,25 +39,26 @@ color_dim = 'tab:red' ax = fig.add_subplot(111, label="1") ax2 = fig.add_subplot(111, label="2", frame_on=False) -# Plot dimensional data -for i, q_dl in enumerate(Q_DL_dim_): - ax.plot(Phi_Pot_Diff_dim, q_dl, color=colors[i], label=f'K: {K_vec[i]}') +# Plot dimensionless data +for i, q_dl in enumerate(Q_DL_dimless_): + ax.plot(Phi_Pot_Diff_dimless, q_dl, color=colors[i], label=f'K: {K_vec[i]}') ax.grid() -ax.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) -ax.set_ylabel('$Q$ [\u03bc$F/cm^3]$', color=color_dim) -ax.tick_params(axis='x', colors=color_dim) -ax.tick_params(axis='y', colors=color_dim) +ax.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) +ax.set_ylabel('$Q [-]$', color=color_dimless) +ax.tick_params(axis='x', colors=color_dimless) +ax.tick_params(axis='y', colors=color_dimless) -for i, q_dl in enumerate(Q_DL_dimless_): - ax2.plot(Phi_Pot_Diff_dimless, q_dl, color=colors[i]) +# Plot dimensional data +for i, q_dl in enumerate(Q_DL_dim_): + ax2.plot(Phi_Pot_Diff_dim, q_dl, color=colors[i]) ax2.xaxis.tick_top() ax2.yaxis.tick_right() -ax2.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) -ax2.set_ylabel('$Q [-]$', color=color_dimless) +ax2.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) +ax2.set_ylabel('$Q$ [\u03bc$F/cm^3]$', color=color_dim) ax2.xaxis.set_label_position('top') ax2.yaxis.set_label_position('right') -ax2.tick_params(axis='x', colors=color_dimless) -ax2.tick_params(axis='y', colors=color_dimless) +ax2.tick_params(axis='x', colors=color_dim) +ax2.tick_params(axis='y', colors=color_dim) fig.legend() fig.tight_layout() @@ -73,25 +74,25 @@ ax = fig.add_subplot(111, label="1") ax2 = fig.add_subplot(111, label="2", frame_on=False) # Plot dimensional data -for i, c_dl in enumerate(C_DL_dim): - ax.plot(Phi_pot_center_array_dim, c_dl, color=colors[i], label=f'K: {K_vec[i]}') +for i, c_dl in enumerate(C_DL_dimless): + ax.plot(Phi_pot_center_array_dimless, c_dl, color=colors[i], label=f'K: {K_vec[i]}') ax.grid() -ax.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) -ax.set_ylabel('$C_{dl}$ [\u03bc$F/cm^2]$', color=color_dim) -ax.tick_params(axis='x', colors=color_dim) -ax.tick_params(axis='y', colors=color_dim) +ax.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) +ax.set_ylabel('$C_{dl} [-]$', color=color_dimless) +ax.tick_params(axis='x', colors=color_dimless) +ax.tick_params(axis='y', colors=color_dimless) -for i, c_dl in enumerate(C_DL_dimless): - ax2.plot(Phi_pot_center_array_dimless, c_dl, color=colors[i]) +for i, c_dl in enumerate(C_DL_dim): + ax2.plot(Phi_pot_center_array_dim, c_dl, color=colors[i]) # ax2.grid() ax2.xaxis.tick_top() ax2.yaxis.tick_right() -ax2.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) -ax2.set_ylabel('$Q [-]$', color=color_dimless) +ax2.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) +ax2.set_ylabel('$C_{dl}$ [\u03bc$F/cm^2]$', color=color_dim) ax2.xaxis.set_label_position('top') ax2.yaxis.set_label_position('right') -ax2.tick_params(axis='x', colors=color_dimless) -ax2.tick_params(axis='y', colors=color_dimless) +ax2.tick_params(axis='x', colors=color_dim) +ax2.tick_params(axis='y', colors=color_dim) fig.legend() fig.tight_layout() diff --git a/examples/Visualizations/DoubleLayerCapacity.py/VisIncompressible.py b/examples/Visualizations/DoubleLayerCapacity.py/VisIncompressible.py index fafdfa60f5a9c2919205cce2aecbe061313ff931..ce63cfe4f9d220220a83b4811eee1ee5e15ed7d1 100644 --- a/examples/Visualizations/DoubleLayerCapacity.py/VisIncompressible.py +++ b/examples/Visualizations/DoubleLayerCapacity.py/VisIncompressible.py @@ -28,31 +28,32 @@ C_DL_dimless = data_Molarity['C_DL_dimless'] # Plotting # Charge fig = plt.figure() -colors = ['tab:blue', 'tab:orange', 'tab:green'] +colors = ['tab:blue', 'tab:orange', 'tab:green', 'tab:red', 'tab:purple'] color_dimless = 'tab:purple' color_dim = 'tab:red' ax = fig.add_subplot(111, label="1") ax2 = fig.add_subplot(111, label="2", frame_on=False) -# Plot dimensional data -for i, q_dl in enumerate(Q_DL_dim_): - ax.plot(Phi_Pot_Diff_dim, q_dl, color=colors[i], label=f'M: {Molarity[i]}') +# Plot dimensionless data +for i, q_dl in enumerate(Q_DL_dimless_): + ax.plot(Phi_Pot_Diff_dimless, q_dl, color=colors[i], label=f'M: {Molarity[i]}') ax.grid() -ax.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) -ax.set_ylabel('$Q$ [\u03bc$F/cm^3]$', color=color_dim) -ax.tick_params(axis='x', colors=color_dim) -ax.tick_params(axis='y', colors=color_dim) +ax.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) +ax.set_ylabel('$Q [-]$', color=color_dimless) +ax.tick_params(axis='x', colors=color_dimless) +ax.tick_params(axis='y', colors=color_dimless) -for i, q_dl in enumerate(Q_DL_dimless_): - ax2.plot(Phi_Pot_Diff_dimless, q_dl, color=colors[i]) +# Plot dimensional data +for i, q_dl in enumerate(Q_DL_dim_): + ax2.plot(Phi_Pot_Diff_dim, q_dl, color=colors[i]) ax2.xaxis.tick_top() ax2.yaxis.tick_right() -ax2.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) -ax2.set_ylabel('$Q [-]$', color=color_dimless) +ax2.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) +ax2.set_ylabel('$Q$ [\u03bc$F/cm^3]$', color=color_dim) ax2.xaxis.set_label_position('top') ax2.yaxis.set_label_position('right') -ax2.tick_params(axis='x', colors=color_dimless) -ax2.tick_params(axis='y', colors=color_dimless) +ax2.tick_params(axis='x', colors=color_dim) +ax2.tick_params(axis='y', colors=color_dim) fig.legend() fig.tight_layout() @@ -68,25 +69,25 @@ ax = fig.add_subplot(111, label="1") ax2 = fig.add_subplot(111, label="2", frame_on=False) # Plot dimensional data -for i, c_dl in enumerate(C_DL_dim): - ax.plot(Phi_pot_center_array_dim, c_dl, color=colors[i], label=f'M: {Molarity[i]}') +for i, c_dl in enumerate(C_DL_dimless): + ax.plot(Phi_pot_center_array_dimless, c_dl, color=colors[i], label=f'M: {Molarity[i]}') ax.grid() -ax.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) -ax.set_ylabel('$C_{dl}$ [\u03bc$F/cm^2]$', color=color_dim) -ax.tick_params(axis='x', colors=color_dim) -ax.tick_params(axis='y', colors=color_dim) +ax.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) +ax.set_ylabel('$C_{dl} [-]$', color=color_dimless) +ax.tick_params(axis='x', colors=color_dimless) +ax.tick_params(axis='y', colors=color_dimless) -for i, c_dl in enumerate(C_DL_dimless): - ax2.plot(Phi_pot_center_array_dimless, c_dl, color=colors[i]) +for i, c_dl in enumerate(C_DL_dim): + ax2.plot(Phi_pot_center_array_dim, c_dl, color=colors[i]) # ax2.grid() ax2.xaxis.tick_top() ax2.yaxis.tick_right() -ax2.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) -ax2.set_ylabel('$Q [-]$', color=color_dimless) +ax2.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) +ax2.set_ylabel('$C_{dl}$ [\u03bc$F/cm^2]$', color=color_dim) ax2.xaxis.set_label_position('top') ax2.yaxis.set_label_position('right') -ax2.tick_params(axis='x', colors=color_dimless) -ax2.tick_params(axis='y', colors=color_dimless) +ax2.tick_params(axis='x', colors=color_dim) +ax2.tick_params(axis='y', colors=color_dim) fig.legend() fig.tight_layout() @@ -112,31 +113,32 @@ kappa_vec = data_Solvation['kappa_vec'] # Plotting # Charge fig = plt.figure() -colors = ['tab:blue', 'tab:orange', 'tab:green', 'tab:cyan'] +colors = ['tab:blue', 'tab:orange', 'tab:green', 'tab:red', 'tab:purple'] color_dimless = 'tab:purple' color_dim = 'tab:red' ax = fig.add_subplot(111, label="1") ax2 = fig.add_subplot(111, label="2", frame_on=False) -# Plot dimensional data -for i, q_dl in enumerate(Q_DL_dim_): - ax.plot(Phi_Pot_Diff_dim, q_dl, color=colors[i], label=f'$\kappa$: {kappa_vec[i]}') +# Plot dimensionless data +for i, q_dl in enumerate(Q_DL_dimless_): + ax.plot(Phi_Pot_Diff_dimless, q_dl, color=colors[i], label=f'$\kappa$: {kappa_vec[i]}') ax.grid() -ax.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) -ax.set_ylabel('$Q$ [\u03bc$F/cm^3]$', color=color_dim) -ax.tick_params(axis='x', colors=color_dim) -ax.tick_params(axis='y', colors=color_dim) +ax.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) +ax.set_ylabel('$Q [-]$', color=color_dimless) +ax.tick_params(axis='x', colors=color_dimless) +ax.tick_params(axis='y', colors=color_dimless) -for i, q_dl in enumerate(Q_DL_dimless_): - ax2.plot(Phi_Pot_Diff_dimless, q_dl, color=colors[i]) +# Plot dimensional data +for i, q_dl in enumerate(Q_DL_dim_): + ax2.plot(Phi_Pot_Diff_dim, q_dl, color=colors[i]) ax2.xaxis.tick_top() ax2.yaxis.tick_right() -ax2.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) -ax2.set_ylabel('$Q [-]$', color=color_dimless) +ax2.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) +ax2.set_ylabel('$Q$ [\u03bc$F/cm^3]$', color=color_dim) ax2.xaxis.set_label_position('top') ax2.yaxis.set_label_position('right') -ax2.tick_params(axis='x', colors=color_dimless) -ax2.tick_params(axis='y', colors=color_dimless) +ax2.tick_params(axis='x', colors=color_dim) +ax2.tick_params(axis='y', colors=color_dim) fig.legend() fig.tight_layout() @@ -152,25 +154,25 @@ ax = fig.add_subplot(111, label="1") ax2 = fig.add_subplot(111, label="2", frame_on=False) # Plot dimensional data -for i, c_dl in enumerate(C_DL_dim): - ax.plot(Phi_pot_center_array_dim, c_dl, color=colors[i], label=f'$\kappa$: {kappa_vec[i]}') +for i, c_dl in enumerate(C_DL_dimless): + ax.plot(Phi_pot_center_array_dimless, c_dl, color=colors[i], label=f'$\kappa$: {kappa_vec[i]}') ax.grid() -ax.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) -ax.set_ylabel('$C_{dl}$ [\u03bc$F/cm^2]$', color=color_dim) -ax.tick_params(axis='x', colors=color_dim) -ax.tick_params(axis='y', colors=color_dim) +ax.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) +ax.set_ylabel('$C_{dl} [-]$', color=color_dimless) +ax.tick_params(axis='x', colors=color_dimless) +ax.tick_params(axis='y', colors=color_dimless) -for i, c_dl in enumerate(C_DL_dimless): - ax2.plot(Phi_pot_center_array_dimless, c_dl, color=colors[i]) +for i, c_dl in enumerate(C_DL_dim): + ax2.plot(Phi_pot_center_array_dim, c_dl, color=colors[i]) # ax2.grid() ax2.xaxis.tick_top() ax2.yaxis.tick_right() -ax2.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) -ax2.set_ylabel('$Q [-]$', color=color_dimless) +ax2.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) +ax2.set_ylabel('$C_{dl}$ [\u03bc$F/cm^2]$', color=color_dim) ax2.xaxis.set_label_position('top') ax2.yaxis.set_label_position('right') -ax2.tick_params(axis='x', colors=color_dimless) -ax2.tick_params(axis='y', colors=color_dimless) +ax2.tick_params(axis='x', colors=color_dim) +ax2.tick_params(axis='y', colors=color_dim) fig.legend() fig.tight_layout() @@ -196,31 +198,32 @@ C_DL_dimless = data_Lambda['C_DL_dimless'] # Plotting # Charge fig = plt.figure() -colors = ['tab:blue', 'tab:orange', 'tab:green'] +colors = ['tab:blue', 'tab:orange', 'tab:green', 'tab:red', 'tab:purple'] color_dimless = 'tab:purple' color_dim = 'tab:red' ax = fig.add_subplot(111, label="1") ax2 = fig.add_subplot(111, label="2", frame_on=False) -# Plot dimensional data -for i, q_dl in enumerate(Q_DL_dim_): - ax.plot(Phi_Pot_Diff_dim, q_dl, color=colors[i], label=f'$\lambda^2$: {Lambda2_vec[i]}') +# Plot dimensionless data +for i, q_dl in enumerate(Q_DL_dimless_): + ax.plot(Phi_Pot_Diff_dimless, q_dl, color=colors[i], label=f'$\lambda^2$: {Lambda2_vec[i]}') ax.grid() -ax.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) -ax.set_ylabel('$Q$ [\u03bc$F/cm^3]$', color=color_dim) -ax.tick_params(axis='x', colors=color_dim) -ax.tick_params(axis='y', colors=color_dim) +ax.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) +ax.set_ylabel('$Q [-]$', color=color_dimless) +ax.tick_params(axis='x', colors=color_dimless) +ax.tick_params(axis='y', colors=color_dimless) -for i, q_dl in enumerate(Q_DL_dimless_): - ax2.plot(Phi_Pot_Diff_dimless, q_dl, color=colors[i]) +# Plot dimensional data +for i, q_dl in enumerate(Q_DL_dim_): + ax2.plot(Phi_Pot_Diff_dim, q_dl, color=colors[i]) ax2.xaxis.tick_top() ax2.yaxis.tick_right() -ax2.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) -ax2.set_ylabel('$Q [-]$', color=color_dimless) +ax2.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) +ax2.set_ylabel('$Q$ [\u03bc$F/cm^3]$', color=color_dim) ax2.xaxis.set_label_position('top') ax2.yaxis.set_label_position('right') -ax2.tick_params(axis='x', colors=color_dimless) -ax2.tick_params(axis='y', colors=color_dimless) +ax2.tick_params(axis='x', colors=color_dim) +ax2.tick_params(axis='y', colors=color_dim) fig.legend() fig.tight_layout() @@ -236,25 +239,25 @@ ax = fig.add_subplot(111, label="1") ax2 = fig.add_subplot(111, label="2", frame_on=False) # Plot dimensional data -for i, c_dl in enumerate(C_DL_dim): - ax.plot(Phi_pot_center_array_dim, c_dl, color=colors[i], label=f'$\lambda^2$: {Lambda2_vec[i]}') +for i, c_dl in enumerate(C_DL_dimless): + ax.plot(Phi_pot_center_array_dimless, c_dl, color=colors[i], label=f'$\lambda^2$: {Lambda2_vec[i]}') ax.grid() -ax.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) -ax.set_ylabel('$C_{dl}$ [\u03bc$F/cm^2]$', color=color_dim) -ax.tick_params(axis='x', colors=color_dim) -ax.tick_params(axis='y', colors=color_dim) +ax.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) +ax.set_ylabel('$C_{dl} [-]$', color=color_dimless) +ax.tick_params(axis='x', colors=color_dimless) +ax.tick_params(axis='y', colors=color_dimless) -for i, c_dl in enumerate(C_DL_dimless): - ax2.plot(Phi_pot_center_array_dimless, c_dl, color=colors[i]) +for i, c_dl in enumerate(C_DL_dim): + ax2.plot(Phi_pot_center_array_dim, c_dl, color=colors[i]) # ax2.grid() ax2.xaxis.tick_top() ax2.yaxis.tick_right() -ax2.set_xlabel('$\delta \\varphi [-]$', color=color_dimless) -ax2.set_ylabel('$Q [-]$', color=color_dimless) +ax2.set_xlabel('$\delta \\varphi [nm]$', color=color_dim) +ax2.set_ylabel('$C_{dl}$ [\u03bc$F/cm^2]$', color=color_dim) ax2.xaxis.set_label_position('top') ax2.yaxis.set_label_position('right') -ax2.tick_params(axis='x', colors=color_dimless) -ax2.tick_params(axis='y', colors=color_dimless) +ax2.tick_params(axis='x', colors=color_dim) +ax2.tick_params(axis='y', colors=color_dim) fig.legend() fig.tight_layout() diff --git a/examples/Visualizations/VisElectrolyticDiode.py b/examples/Visualizations/VisElectrolyticDiode.py index 3394d1af6dcec9300b7df6c9e08071fd00a949c4..7aaf0c01e9ddf638ac979315d473a7f97fe74280 100644 --- a/examples/Visualizations/VisElectrolyticDiode.py +++ b/examples/Visualizations/VisElectrolyticDiode.py @@ -101,4 +101,12 @@ axs[0,3].set_title('$y_S [-]$', fontsize=labelsize) axs[0,4].set_title('$p [-]$', fontsize=labelsize) fig.tight_layout() fig.savefig('../Figures/ElectrolyticDiode.svg') -fig.show() \ No newline at end of file +fig.show() + +print('np.max(y_A_Forward):', np.max(y_A_Forward)) +print('np.max(y_A_NoBias):', np.max(y_A_NoBias)) +print('np.max(y_A_Backward):', np.max(y_A_Backward)) + +print('np.max(y_C_Forward):', np.max(y_C_Forward)) +print('np.max(y_C_NoBias):', np.max(y_C_NoBias)) +print('np.max(y_C_Backward):', np.max(y_C_Backward)) \ No newline at end of file diff --git a/examples/Visualizations/VisNConstituentMixture.py b/examples/Visualizations/VisNConstituentMixture.py index 4266b96ee85450eb9bd6acb0451e9f1004103a7c..f4d0817a8c3853e370e5db927ca31d98c94a6f21 100644 --- a/examples/Visualizations/VisNConstituentMixture.py +++ b/examples/Visualizations/VisNConstituentMixture.py @@ -37,6 +37,8 @@ for i in range(2): # Concentrations for species in range(len(z[plotting_index])): axs[i,j].plot(x[plotting_index], y[plotting_index][species], label=f'z = {z[plotting_index][species]}', lw=lw, color=colors[species]) + y_S_ = 1 - np.sum(y[plotting_index], axis=0) + axs[i,j].plot(x[plotting_index], y_S_, label=f'z = {0}', lw=lw, color=colors[-1]) lgnd = axs[i,j].legend(fontsize=labelsize) for line in lgnd.get_lines(): line.set_linewidth(legend_width) @@ -89,4 +91,7 @@ for line in lgnd.get_lines(): line.set_linewidth(legend_width) fig.show() -fig.savefig('../Figures/NConstituentMixture_ElectricPotential.svg', bbox_inches='tight') \ No newline at end of file +fig.savefig('../Figures/NConstituentMixture_ElectricPotential.svg', bbox_inches='tight') + +for p_ in p: + print(np.max(p_)) \ No newline at end of file diff --git a/src/ElectrolyticDiode.py b/src/ElectrolyticDiode.py index 7d3b3702696e6c732092cba8484620ee25453eac..2dd690a77bbf8da54f433370d1f9b2d19cf87a20 100644 --- a/src/ElectrolyticDiode.py +++ b/src/ElectrolyticDiode.py @@ -189,9 +189,25 @@ def ElectrolyticDiode(Bias_type:str, phi_bias:float, g_phi:float, z_A:float, z_C # Collect boundary conditions bcs = [bc_bottom_phi, bc_top_phi, bc_bottom_y_A, bc_top_y_A, bc_bottom_y_C, bc_top_y_C] + # def p_bottom_(x): + # return np.full_like(x[1], 0) + # def p_top_(x): + # return np.full_like(x[1], 0) + # p_bottom_bcs = fem.Function(W3) + # p_bottom_bcs.interpolate(p_bottom_) + # p_top_bcs = fem.Function(W3) + # p_top_bcs.interpolate(p_top_) + # facet_bottom_dofs = fem.locate_dofs_geometrical((W.sub(3), W.sub(3).collapse()[0]), Bottom) + # facet_top_dofs = fem.locate_dofs_geometrical((W.sub(3), W.sub(3).collapse()[0]), Top) + # bc_bottom_p = fem.dirichletbc(p_bottom_bcs, facet_bottom_dofs, W.sub(3)) + # bc_top_p = fem.dirichletbc(p_top_bcs, facet_top_dofs, W.sub(3)) + # bcs.append(bc_bottom_p) + # bcs.append(bc_top_p) + # Variational formulation if K == 'incompressible': def nF(y_A, y_C): + # n = const = 1 return (z_C * y_C + z_A * y_A) def J_A(y_A, y_C, phi, p): @@ -217,8 +233,6 @@ def ElectrolyticDiode(Bias_type:str, phi_bias:float, g_phi:float, z_A:float, z_C ) + ( inner(J_A(y_A, y_C, phi, p), grad(v_A)) * dx + inner(J_C(y_A, y_C, phi, p), grad(v_C)) * dx - # inner(grad(ln(y_A) + a2 * solvation * p - ln(1-y_A-y_C) + z_A * phi), grad(v_A)) * dx - # + inner(grad(ln(y_C) + a2 * solvation * p- ln(1-y_A-y_C) + z_C * phi), grad(v_C)) * dx ) # Define Neumann boundaries @@ -298,7 +312,7 @@ if __name__ == '__main__': K = 'incompressible' Lambda2 = 8.553e-2 # ! Change back to 1e-6 # g_phi *= np.sqrt(Lambda2) # ! Unsure about this scaling - a2 = 7.5412e-2 + a2 = 7.5412e-4 number_cells = [20, 100] Lx = 2 Ly = 10 diff --git a/src/Eq04.py b/src/Eq04.py index d5b332cfb5b063ed3f9106a6081baf71176343e1..eba9ca177de8d96206b5917490a15c1731ae146c 100644 --- a/src/Eq04.py +++ b/src/Eq04.py @@ -307,23 +307,24 @@ def solve_System_4eq(phi_left:float, phi_right:float, p_right:float, z_A:float, if __name__ == '__main__': # Define the parameters - phi_left = 5.0 + phi_left = 10.0 phi_right = 0.0 p_right = 0.0 - y_A_R = 1/3 - y_C_R = 1/3 + y_A_R = 0.01#1/3 + y_C_R = 0.01#1/3 z_A = -1.0 z_C = 1.0 K = 'incompressible' Lambda2 = 8.553e-6 a2 = 7.5412e-4 + solvation = 0 number_cells = 1024 relax_param = .1 rtol = 1e-4 max_iter = 500 # Solve the system - y_A, y_C, phi, p, x = solve_System_4eq(phi_left, phi_right, p_right, z_A, z_C, y_A_R, y_C_R, K, Lambda2, a2, number_cells, relax_param=relax_param, x0=0, x1=1, refinement_style='uniform', return_type='Vector', max_iter=max_iter, rtol=rtol) + y_A, y_C, phi, p, x = solve_System_4eq(phi_left, phi_right, p_right, z_A, z_C, y_A_R, y_C_R, K, Lambda2, a2, number_cells, solvation=solvation, relax_param=relax_param, x0=0, x1=1, refinement_style='uniform', return_type='Vector', max_iter=max_iter, rtol=rtol) # Plot the solution plt.plot(x, phi) diff --git a/src/Helper_DoubleLayerCapacity.py b/src/Helper_DoubleLayerCapacity.py index 6fa7ab41a37ab09a4f46e03bb961c83ac4e137e2..7721b6e985ec55509984b3ca2b8260b40f714d66 100644 --- a/src/Helper_DoubleLayerCapacity.py +++ b/src/Helper_DoubleLayerCapacity.py @@ -160,22 +160,24 @@ def Q_DL_dimless_ana(y_A_R:float, y_C_R:float, y_N_R:float, z_A:float, z_C:float D_C = y_C_R / (np.exp(-(solvation+1)*a2*p_R-z_C*phi_R)) D_N = y_N_R / (np.exp(-a2*p_R)) - Q_DL = [] - dx_phi_L = 0 - for phi_L_ in phi_L: - def func(p_L): - # A_Term = D_A * np.exp(-z_A*phi_L) - A_Term = D_A * np.exp(-(solvation+1)*a2*p_L-z_A*phi_L_) - C_Term = D_C * np.exp(-(solvation+1)*a2*p_L-z_C*phi_L_) - N_Term = D_N * np.exp(-a2*p_L) - - return (A_Term + C_Term + N_Term) - 1 - p_L = fsolve(func, dx_phi_L) - dx_phi_L = np.sqrt(p_L - E_p) * np.sqrt(2*a2/Lambda2) - Q_DL_ = Lambda2 * dx_phi_L - Q_DL.append(Q_DL_) - Q_DL = np.array(Q_DL) - + # fsolve method + # Q_DL = [] + # dx_phi_L = 0 + # for phi_L_ in phi_L: + # def func(p_L): + # # A_Term = D_A * np.exp(-z_A*phi_L) + # A_Term = D_A * np.exp(-(solvation+1)*a2*p_L-z_A*phi_L_) + # C_Term = D_C * np.exp(-(solvation+1)*a2*p_L-z_C*phi_L_) + # N_Term = D_N * np.exp(-a2*p_L) + + # return (A_Term + C_Term + N_Term) - 1 + # p_L = fsolve(func, dx_phi_L) + # dx_phi_L = np.sqrt(p_L - E_p) * np.sqrt(2*a2/Lambda2) + # Q_DL_ = Lambda2 * dx_phi_L + # Q_DL.append(Q_DL_) + # Q_DL = np.array(Q_DL) + + # Fixed Point Iteration # def func_L(p_L): # CLambda = D_A * np.exp(-z_A * phi_L - solvation*a2*p_L) + D_C * np.exp(-z_C * phi_L - solvation*a2*p_L) + D_N # return np.log(CLambda)/a2 @@ -186,7 +188,13 @@ def Q_DL_dimless_ana(y_A_R:float, y_C_R:float, y_N_R:float, z_A:float, z_C:float # Q_DL = np.sqrt(2) * Lambda * a * np.sqrt(p_L - E_p) # ! ToDo: Implement full analytical for solvation == 0 - + # Analytical method + E_p = p_R + CLambda_L = np.log(D_A * np.exp(-z_A * phi_L - (solvation+1) * E_p) + D_C * np.exp(-z_C * phi_L - (solvation+1) * E_p) + D_N * np.exp(-z_N * phi_L - (solvation+1) * E_p)) + # CLambda_R = np.log(D_A * np.exp(-z_A * phi_R + E_p * a2) + D_C * np.exp(-z_C * phi_R + E_p * a2) + D_N * np.exp(-z_N * phi_R + E_p * a2)) + Lambda = np.sqrt(Lambda2) + Q_DL = (phi_L-phi_R) / np.abs(phi_L-phi_R) * Lambda * np.sqrt(2/(solvation+1)) * (np.sqrt(CLambda_L))# - np.sqrt(CLambda_R)) # dx_phi_R -> 0 + return Q_DL else: C_A = y_A_R / ((K + p_R - 1)**(-1*a2*K)*np.exp(-z_A*phi_R)) C_C = y_C_R / ((K + p_R - 1)**(-1*a2*K)*np.exp(-z_C*phi_R)) @@ -201,9 +209,9 @@ def Q_DL_dimless_ana(y_A_R:float, y_C_R:float, y_N_R:float, z_A:float, z_C:float Lambda = np.sqrt(Lambda2) a = np.sqrt(a2) - Q_DL = Lambda * a * np.sqrt(2) * (Left)# - Right) - - return Q_DL + Q_DL = (phi_L-phi_R) / np.abs(phi_L-phi_R) * Lambda * a * np.sqrt(2) * (Left)# - Right) + return Q_DL + raise ValueError('Invalid input for K') def Q_DL_dim_ana(y_A_R:float, y_C_R:float, y_N_R:float, z_A:float, z_C:float, phi_L:float, phi_R:float, p_R:float, K:str|float, Lambda2:float, a2:float, nR_m:float, e0:float, LR:float, solvation:float) -> float: ''' diff --git a/src/__pycache__/ElectrolyticDiode.cpython-312.pyc b/src/__pycache__/ElectrolyticDiode.cpython-312.pyc index 66c24c7393adaac517d32d2b149c471a6fa11dba..85cfcd62eece31a7fb8129feeeeabfc0a79cee2e 100644 Binary files a/src/__pycache__/ElectrolyticDiode.cpython-312.pyc and b/src/__pycache__/ElectrolyticDiode.cpython-312.pyc differ diff --git a/src/__pycache__/Eq02.cpython-312.pyc b/src/__pycache__/Eq02.cpython-312.pyc index 22914ed1a5ac4beb0cd95fb993ee210cac42c52d..db7936e73aa933adfe164ec1a59346d55a066edb 100644 Binary files a/src/__pycache__/Eq02.cpython-312.pyc and b/src/__pycache__/Eq02.cpython-312.pyc differ diff --git a/src/__pycache__/Eq04.cpython-312.pyc b/src/__pycache__/Eq04.cpython-312.pyc index 4fcbdc9745e29e883aed5afc77b94d4200e0387f..9aa38d17942f24cbc3817ab838bd70c4ce01cfd8 100644 Binary files a/src/__pycache__/Eq04.cpython-312.pyc and b/src/__pycache__/Eq04.cpython-312.pyc differ diff --git a/src/__pycache__/Helper_DoubleLayerCapacity.cpython-312.pyc b/src/__pycache__/Helper_DoubleLayerCapacity.cpython-312.pyc index 7fcfd455a306d8842cf22799aa1f0ea7210cd3a3..7f5cfd18fef9a21e18cc874a502b752456687826 100644 Binary files a/src/__pycache__/Helper_DoubleLayerCapacity.cpython-312.pyc and b/src/__pycache__/Helper_DoubleLayerCapacity.cpython-312.pyc differ