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@guyer
Last active June 17, 2019 19:40
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electrolyte notebooks
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Fipy ternary electrolyte"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"At steady-state, For species i=1,2,3:\n",
" \n",
"$$ \\nabla \\cdot(z_i C_i \\nabla \\phi + \\nabla C_i) = 0$$\n",
"\n",
"One species may be eliminated using electroneutrality:\n",
"\n",
"$$ \\sum_i{z_i C_i}=0 $$\n",
"\n",
"Boundary conditions (1D):\n",
" - $ C_1(0)=0 $\n",
" - $ C_1(1)=1.0 $\n",
" - $ \\phi(1)=0 $\n",
" - $ C_2(1)=4/3 $\n",
" - Flux of species 2 and 3:$\\quad z_2 C_2 \\nabla \\phi + \\nabla C_2 = z_3 C_3 \\nabla \\phi + \\nabla C_3 = 0 $"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"ExecuteTime": {
"end_time": "2019-06-17T19:39:17.422579Z",
"start_time": "2019-06-17T19:39:15.875711Z"
}
},
"outputs": [],
"source": [
"%matplotlib inline\n",
"from fipy import *\n",
"from fipy.tools import numerix\n",
"import matplotlib.pyplot as pl\n",
"import numpy as np"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Parameters"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"ExecuteTime": {
"end_time": "2019-06-17T19:39:18.575534Z",
"start_time": "2019-06-17T19:39:18.570181Z"
}
},
"outputs": [],
"source": [
"nx=50\n",
"\n",
"C20=4.0/3.0\n",
"\n",
"z1=+2.\n",
"z2=-2.\n",
"z3=+1."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Mesh"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"ExecuteTime": {
"end_time": "2019-06-17T19:39:19.576892Z",
"start_time": "2019-06-17T19:39:19.549636Z"
}
},
"outputs": [],
"source": [
"mesh = Grid1D(nx=nx, dx=1.0/nx)\n",
"xc=np.asarray(mesh.cellCenters)[0]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Species"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"ExecuteTime": {
"end_time": "2019-06-17T19:39:20.524447Z",
"start_time": "2019-06-17T19:39:20.515356Z"
}
},
"outputs": [],
"source": [
"C1= CellVariable(mesh = mesh, value = 1.0)\n",
"C2= CellVariable(mesh = mesh, value = 4.0/3.0)\n",
"Phi = CellVariable(mesh = mesh, value = 0.0)\n",
"\n",
"# electroneutrality\n",
"C3 = -1/z3 * (z1*C1 + z2*C2)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"ExecuteTime": {
"end_time": "2019-06-17T19:39:22.043788Z",
"start_time": "2019-06-17T19:39:21.490721Z"
}
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pl.plot(xc,C1.value,label='$C_1/C_{10}$')\n",
"pl.plot(xc,C2.value,label='$C_2/C_{10}$')\n",
"pl.plot(xc,C3.value,label='$C_3/C_{10}$')\n",
"pl.plot(xc,Phi.value,label='$f\\phi$')\n",
"\n",
"pl.xlim(0,1)\n",
"pl.xlabel('x / L')\n",
"pl.axhline(0,linestyle=':',color='gray')\n",
"pl.legend(bbox_to_anchor=(1.0, 1.0))\n",
"pl.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Boundary Conditions"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"FiPy doesn't have the means to infer the coupled boundary conditions present here. Instead, we derive the gradient constraints that result from the no-flux conditions on $C_2$:\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"\\vec{J}_{2,\\text{left}} = 0 &= z_2 C_2 \\nabla \\phi + \\nabla C_2 \\\\\n",
"\\nabla\\phi &= -\\frac{1}{z_2}\\frac{\\nabla C_2}{C_2}\\qquad\\text{on left}\n",
"\\end{align*}\n",
"$$\n",
"\n",
"and $C_3$:\n",
"\n",
"$$\n",
"\\begin{align*}\n",
"\\vec{J}_{3,\\text{left}} = 0 &= z_3 C_3 \\nabla \\phi + \\nabla C_3 \\\\\n",
"&= z_3 C_3 \\nabla \\phi - \\frac{z_1}{z_3} \\nabla C_1 - \\frac{z_2}{z_3} \\nabla C_2 \\\\\n",
"\\nabla \\phi &= \\frac{z_1}{z_3^2}\\frac{\\nabla C_1}{C_3} + \\frac{z_2}{z_3^2}\\frac{\\nabla C_2}{C_3}\\qquad\\text{on left}\n",
"\\end{align*}\n",
"$$\n",
"\n",
"We can combine these results to eliminate $\\nabla\\phi$ and solve for $\\nabla C_2$ in terms of $\\nabla C_1$:\n",
"$$\\nabla C_2 = -\\frac{z_1 z_2 C_2}{z_2^2 C_2 + z_3^2 C_3}\\nabla C_1$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Note that relying on FiPy's natural no-flux boundary condition on $C_2$ does not work in this case. The reason is that, without a constraint and because FiPy doesn't upwind, `C2.faceGrad` is zero at the boundary, leading to either $\\nabla\\phi = 0$ or $\\nabla \\phi = (z_1/z_3^2)\\nabla C_1 / C_3$, depending on which condition we use. Instead, it is necessary to obtain constraints on $C_2$ and $\\phi$ in terms of the known constraint on $C_1$."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"ExecuteTime": {
"end_time": "2019-06-17T19:39:25.461497Z",
"start_time": "2019-06-17T19:39:25.399780Z"
}
},
"outputs": [],
"source": [
"## Concentration BC's\n",
"C1.constrain(1.0, mesh.facesRight)\n",
"C1.constrain(0.0, mesh.facesLeft)\n",
"\n",
"C2.constrain(C20, mesh.facesRight)\n",
"C2.faceGrad.constrain((-z1 * z2 * C2.faceValue / (z2**2 * C2.faceValue + z3**2 * C3.faceValue)) * C1.faceGrad, mesh.facesLeft)\n",
"\n",
"Phi.constrain(0, mesh.facesRight)\n",
"Phi.faceGrad.constrain(-(1/z2) * C2.faceGrad / C2.faceValue, where=mesh.facesLeft)\n",
"\n",
"# Other boundary conditions are:\n",
"# - Flux of species 2 = 0 \n",
"# - Flux of species 3 = 0"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Governing Equations"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"ExecuteTime": {
"end_time": "2019-06-17T19:39:27.709004Z",
"start_time": "2019-06-17T19:39:27.683454Z"
}
},
"outputs": [],
"source": [
"migr_coeff_1 = z1*C1\n",
"migr_coeff_3 = z3*C3\n",
"migr_coeff_2 = z2*C2 \n",
"\n",
"Eq1 = + DiffusionTerm(coeff=z1*C1, var=Phi) + DiffusionTerm(coeff=1.0, var=C1)\n",
"Eq2 = + DiffusionTerm(coeff=z2*C2, var=Phi) + DiffusionTerm(coeff=1.0, var=C2)\n",
"Eq3 = + DiffusionTerm(coeff=z3*C3, var=Phi) + DiffusionTerm(coeff=-z1/z3, var=C1) + DiffusionTerm(coeff=-z2/z3, var=C2)\n",
"\n",
"Eqns = Eq1 & Eq2 & Eq3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Solution"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"ExecuteTime": {
"end_time": "2019-06-17T19:39:33.455470Z",
"start_time": "2019-06-17T19:39:30.179272Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"166.66666666666669\n",
"8111.914864637596\n",
"19.689769346243416\n",
"0.527796339963467\n",
"0.4183480266876322\n",
"0.18091047223695744\n",
"0.09259998165657486\n",
"0.04006704973560209\n",
"0.018576714225317793\n",
"0.008142953142658605\n",
"0.0036638057933016757\n",
"0.001617273663271697\n",
"0.0007209662189310841\n",
"0.00031928083121372954\n",
"0.00014191049661706125\n",
"6.292827496441198e-05\n",
"2.7941861626831995e-05\n",
"1.2396704922369395e-05\n",
"5.5025843225439935e-06\n",
"2.4417388447566056e-06\n",
"1.0836956718221162e-06\n",
"4.809164486551736e-07\n",
"2.1343189918070662e-07\n",
"9.471795023257837e-08\n",
"4.203536760276676e-08\n",
"1.8654906263127136e-08\n",
"8.27893004198873e-09\n",
"3.6740929744445703e-09\n",
"1.6305296459790902e-09\n",
"7.23614259584439e-10\n",
"3.211694650383402e-10\n",
"1.4253347855072822e-10\n",
"6.319440158577929e-11\n",
"2.8100778259830832e-11\n",
"1.2411462126423729e-11\n",
"5.5270203470827115e-12\n",
"2.4898494346740138e-12\n",
"1.0844728298219362e-12\n",
"5.67706035720192e-13\n"
]
}
],
"source": [
"res = 1e+10\n",
"restol= 1e-12\n",
"\n",
"while res > restol:\n",
" res = Eqns.sweep()\n",
" print(res)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plot Solution"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"ExecuteTime": {
"end_time": "2019-06-17T19:39:36.361795Z",
"start_time": "2019-06-17T19:39:35.927892Z"
},
"scrolled": false
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pl.plot(xc,C1.value,label='$C_1/C_{10}$')\n",
"pl.plot(xc,C2.value,label='$C_2/C_{10}$')\n",
"pl.plot(xc,C3.value,label='$C_3/C_{10}$')\n",
"pl.plot(xc,Phi.value,label='$f\\phi$')\n",
"\n",
"pl.xlim(0,1)\n",
"pl.xlabel('x / L')\n",
"pl.axhline(0,linestyle=':',color='gray')\n",
"pl.legend(bbox_to_anchor=(1.0, 1.0))\n",
"pl.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Analytical Solution\n",
"From West Section 5.7\n",
"\n",
"A. C. West, Electrochemistry and Electrochemical Engineering: An Introduction (CreateSpace Independent Publishing Platform, 2012)."
]
},
{
"attachments": {
"image.png": {
"image/png": 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"
}
},
"cell_type": "markdown",
"metadata": {},
"source": [
"![image.png](attachment:image.png)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"ExecuteTime": {
"end_time": "2019-06-17T19:39:44.449887Z",
"start_time": "2019-06-17T19:39:44.241331Z"
}
},
"outputs": [
{
"data": {
"image/png": 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M+bdL3lpV6/6/pk7yfuDVwOYkZ4F3As+D6T2v+V9MSFJzV9JbQ5Kky2AIJKk5QyBJzRkCSWrOEEhSc4ZAkpozBJLU3P8CxEHzLf0vucoAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rho= z1*C1 + z2*C2 + z3*C3\n",
"pl.plot(xc,rho.value)\n",
"pl.show()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"ExecuteTime": {
"end_time": "2019-06-17T19:39:45.696150Z",
"start_time": "2019-06-17T19:39:45.298037Z"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"flux1 = z1*C1.faceValue * Phi.faceGrad + C1.faceGrad\n",
"flux2 = z2*C2.faceValue * Phi.faceGrad + C2.faceGrad\n",
"flux3 = z3*C3.faceValue * Phi.faceGrad + C3.faceGrad\n",
"\n",
"x=np.asarray(mesh.faceCenters)[0]\n",
"\n",
"pl.plot(x,flux1.value[0],label='$J_1$')\n",
"pl.plot(x,flux2.value[0],label='$J_2$')\n",
"pl.plot(x,flux3.value[0],label='$J_3$')\n",
"\n",
"pl.legend(bbox_to_anchor=(1.0, 1.0))\n",
"\n",
"pl.show()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"hide_input": false,
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
},
"toc": {
"base_numbering": 1,
"nav_menu": {},
"number_sections": false,
"sideBar": true,
"skip_h1_title": false,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {},
"toc_section_display": "block",
"toc_window_display": false
},
"varInspector": {
"cols": {
"lenName": 16,
"lenType": 16,
"lenVar": 40
},
"kernels_config": {
"python": {
"delete_cmd_postfix": "",
"delete_cmd_prefix": "del ",
"library": "var_list.py",
"varRefreshCmd": "print(var_dic_list())"
},
"r": {
"delete_cmd_postfix": ") ",
"delete_cmd_prefix": "rm(",
"library": "var_list.r",
"varRefreshCmd": "cat(var_dic_list()) "
}
},
"types_to_exclude": [
"module",
"function",
"builtin_function_or_method",
"instance",
"_Feature"
],
"window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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