Final_Anode_Code.ipynb

{
 "cells": [
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Complete ANODE Model\n",
    "Date :- 12/8/2019\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.sparse import coo_matrix\n",
    "from scipy.sparse.linalg import spsolve\n",
    "from numpy import *\n",
    "from pylab import *\n",
    "import math\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 2\n",
    "NA = 6\n",
    "NJ = 100\n",
    "\n",
    "# Set convergence tolerance and max number of iterations\n",
    "tol = 1e-3\n",
    "itmax = 500"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#constants for the problem\n",
    "I = 1.0             # Amp\n",
    "L = 4.15            # cm\n",
    "rac = 0.09          # cm\n",
    "ra =  0.43          # cm\n",
    "io = 0.06           # Amp/cm^2\n",
    "ao = 50.0\t\t\t# cm-1\n",
    "\n",
    "F = 96487.0         # C/mol\n",
    "R = 8.314           # J/mol-K\n",
    "T = 298.0           # K\n",
    "pi=3.14           \n",
    "epao = 0.74         # initial anode porosity\n",
    "\n",
    "alpha = 0.75        # anodic transfer coeff \n",
    "kappa = 0.6690      # 1/ohm/cm soltn conductivity \n",
    "\n",
    "\n",
    "KOH_o = 0.003       # cm/s OH ions mass transfer coeff\n",
    "KZnOH_o = 0.001     # cm/s ZnOH ions mass transfer coeff\n",
    "\n",
    "COH = 0.007         # moles/cm^3\n",
    "CZnOH = 0.00053     # moles/cm^3\n",
    "\n",
    "DKZnOH=6.9e-6       # cm^2/s\n",
    "DKOH = 2.32e-5      # cm^2/s\n",
    "\n",
    "tOH = 0.74          # transference number\n",
    "tZnOH = 0.04        # transference number\n",
    "\n",
    "Keq = 0.0232        # moles/cm^3\n",
    "kx = 0.005          # cm/s precipitation rate constant\n",
    "\n",
    "\n",
    "VZn = 9.15          # cm^3/mole \n",
    "VZnO = 14.51        # cm^3/mole\n",
    "VKOH = 17.8         # cm^3/mole \n",
    "VZnOH = 67.0        # cm^3/mole\n",
    "VKZnOH = 67.0       # cm^3/mole\n",
    "VH2O = 18.07        # cm^3/mole\n",
    "\n",
    "# Some Cathode properties\n",
    "# properties of cathode\n",
    "rs = 0.45           # cm\n",
    "rc = 0.66           # cm           \n",
    "epc = 0.26          # cathode porosity \n",
    "Vc = 3.14*(rc**2 - ra**2)*L # cathode volume\n",
    "Acat = 2*3.14*(rc-ra)*L     # cathode area\n",
    "VMnO2 = 17.29               # cm^3/mole\n",
    "VMnOOH = 20.45              # cm^3/mole\n",
    "theta = 0.8                 # extent of reaction constant\n",
    "\n",
    "#Make the Mesh\n",
    "xmax = 0.43-0.09\n",
    "h = xmax/(NJ-1)\n",
    "rr = np.linspace(rac,ra,NJ)\n",
    "aio = ao*io"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "ep_Zn_o = 0.26      # initial Zn volume fraction\n",
    "ep_ZnO_o  = 0.0     # initial ZnO volume fraction\n",
    "\n",
    "sigma_Zn = 1.83e5   # /ohm/cm\n",
    "sigma_ZnO = 0.01    # /ohm/cm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# INTERPOLATE\n",
    "# ===========\n",
    "def interpolate( c, h, order ):\n",
    " \n",
    "    ( N, NJ )=c.shape\n",
    "    \n",
    "    cE=np.concatenate( (      c[:,1:NJ], np.zeros((N,1)) ), axis=1 )\n",
    "    cW=np.concatenate( (   np.zeros((N,1)),  c[:,0:NJ-1] ), axis=1 )\n",
    " \n",
    "    dcdx=(cE-cW)/2.0/h;\n",
    "    dcdx[:, 0  ] = ( - 3.0*c[:, 0  ] + 4.0*c[:,1   ] - c[:,2   ] ) /2.0 /h;\n",
    "    dcdx[:,NJ-1] = (   3.0*c[:,NJ-1] - 4.0*c[:,NJ-2] + c[:,NJ-3] ) /2.0 /h;\n",
    " \n",
    "    #if ( order >= 2 ):\n",
    " \n",
    "    d2cdx2= (cE + cW - 2*c)/h**2;\n",
    "    d2cdx2[:,0] = np.zeros((1,N));\n",
    "    d2cdx2[:,NJ-1] = np.zeros((1,N));\n",
    " \n",
    "    return  dcdx , d2cdx2 \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Transfer Current\n",
    "# ===========\n",
    "def transfer(jcold):\n",
    "    \n",
    "    # Calculates the tranfer current j\n",
    "    # Uses the 1st variable in cold, which is i2\n",
    "    \n",
    "    jdcdx, jd2cdx2 = interpolate(jcold,h,2)\n",
    "    trans = jdcdx[0,:] + jcold[0,:]/rr[:]\n",
    "    if abs(trans[1]) <= 1e-5:\n",
    "          trans[0] = trans[1]\n",
    "    trans[NJ-1] = trans[NJ-2]\n",
    "    return trans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def initguess():\n",
    "    \n",
    "    cold = np.ones([N,NJ])\n",
    "    cold[0,:]=-0.05  # i2\n",
    "    cold[1,:]=0.01 # eta\n",
    "    \n",
    "    return cold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Steady State Problem\n",
    "#====================================\n",
    "\n",
    "# Fillmat Matrix function for i2 and eta \n",
    "# =======\n",
    "\n",
    "def fillmat1(cold,dcdx,d2cdx2):\n",
    "\n",
    "    sma = zeros([N,NJ,N])\n",
    "    smb = zeros([N,NJ,N])\n",
    "    smd = zeros([N,NJ,N])\n",
    "    smg = zeros([N,NJ])\n",
    "    \n",
    "    sigma = 20.0\n",
    "    \n",
    "    A1 = (sigma+(epao**1.5)*kappa)/((epao**1.5)*kappa*sigma)\n",
    "    \n",
    "    beta = (1-alpha)*2*F/R/T\n",
    "    betac = -alpha*2*F/R/T\n",
    "\n",
    "    \n",
    "    P1 = aio*exp(beta*cold[1,:])\n",
    "    P2 = aio*exp(betac*cold[1,:])\n",
    "    \n",
    "    smb[0,:,0] = 1\n",
    "    smd[0,:,0] = 1/rr[:]\n",
    "    smd[0,:,1] = -beta*P1 + betac*P2\n",
    "    smg[0,:] = P1 - P2 - dcdx[0,:] - cold[0,:]/rr[:]\n",
    "    \n",
    "    smd[1,:,0] = -A1\n",
    "    smb[1,:,1] = 1\n",
    "    smg[1,:] = -I/(2*pi*rr[:]*L*sigma) + A1*cold[0,:] - dcdx[1,:]\n",
    "\t\n",
    "\t\n",
    "\t# Boundary Condition 1\n",
    "\t\n",
    "    smp = zeros([N,N])\n",
    "    sme = zeros([N,N])\n",
    "    smf = zeros([N,1])\n",
    "\t\n",
    "\t#BC 1 r=rac, i2=0\n",
    "    sme[0,0] = 1\n",
    "    smf[0] = -cold[0,0]\n",
    "\t\n",
    "\t\n",
    "\t#Non BC's\n",
    "    smp[1,1] = 1\n",
    "    sme[1,0] = -A1\n",
    "    smf[1] = -I/(2*pi*rr[0]*L*sigma) + A1*cold[0,0] - dcdx[1,0]\n",
    "    \n",
    "    smb[:,0,:] = smp[:,:]\n",
    "    smd[:,0,:] = sme[:,:]\n",
    "    smg[:,0] = transpose(smf)\n",
    "    \n",
    "\t#____Boundary Condition 2\n",
    "\t\n",
    "    smp = zeros([N,N])\n",
    "    sme = zeros([N,N])\n",
    "    smf = zeros([N,1])\n",
    "\t\n",
    "\t#BC 2 at r=ra, i2 = I/(2pirL)\n",
    "    sme[0,0] = 1\n",
    "    smf[0] = I/(2*pi*ra*L) - cold[0,NJ-1]\n",
    "\t\n",
    "\t#Non BC's\n",
    "    smp[1,1] = 1\n",
    "    sme[1,0] = -A1\n",
    "    smf[1] = -I/(2*pi*rr[NJ-1]*L*sigma) + A1*cold[0,NJ-1] - dcdx[1,NJ-1]\n",
    "\t\t\n",
    "    smb[:,NJ-1,:] = smp[:,:]\n",
    "    smd[:,NJ-1,:] = sme[:,:]\n",
    "    smg[:,NJ-1] = transpose(smf)\n",
    "\t\n",
    "    return sma, smb, smd, smg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def abdgxy(sma, smb, smd, smg):\n",
    "    \n",
    "    sma = transpose(sma, (0, 2, 1))\n",
    "    smb = transpose(smb, (0, 2, 1))\n",
    "    smd = transpose(smd, (0, 2, 1))\n",
    "\n",
    "    A = sma-h/2.0*smb\n",
    "    B = -2.0*sma+h**2*smd\n",
    "    D = sma+h/2.0*smb\n",
    "    G = h**2*smg\n",
    "\n",
    "    B[:,:,0] = h*smd[:,:,0]-1.5*smb[:,:,0]\n",
    "    D[:,:,0] = 2.0*smb[:,:,0]\n",
    "    G[:,0]=h*smg[:,0]\n",
    "    X = -0.5*smb[:,:,0]\n",
    "\n",
    "    A[:,:,NJ-1]=-2.0*smb[:,:,NJ-1]\n",
    "    B[:,:,NJ-1]=h*smd[:,:,NJ-1]+1.5*smb[:,:,NJ-1]\n",
    "    G[:,NJ-1]=h*smg[:,NJ-1]\n",
    "    Y=0.5*smb[:,:,NJ-1]\n",
    "\n",
    "    ABD = concatenate((A, B, D), axis=1)\n",
    "    BC1 = concatenate((B[:,:,0] , D[:,:,0] , X), axis=1)\n",
    "    BC2 = concatenate((Y , A[:,:,NJ-1] , B[:,:,NJ-1]), axis=1)\n",
    "    ABD[:,:,0] = BC1\n",
    "    ABD[:,:,NJ-1] = BC2\n",
    "\n",
    "    return ABD, G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def band(ABD, G):\n",
    "    \n",
    "    BMrow = reshape(arange(1,N*NJ+1), (NJ,N))\n",
    "    BMrow = BMrow[:, :, newaxis]\n",
    "    BMrow = transpose(BMrow, (1, 2, 0))\n",
    "    BMrow = BMrow[:,[0 for i in range(3*N)],:]\n",
    "    \n",
    "    a = arange(1,3*N+1)\n",
    "    a = a[newaxis,:]\n",
    "    a = repeat(a,N,0)\n",
    "    a = a[:,:,newaxis]\n",
    "    a = repeat(a,NJ,2)\n",
    "\n",
    "    b = arange(0,(N)*(NJ-3)+N,N)\n",
    "    b = hstack((b[0], b, b[len(b)-1]))\n",
    "    b = b[newaxis,newaxis,:]\n",
    "    b = repeat(b,N,0)\n",
    "    b = repeat(b,3*N,1)\n",
    "    \n",
    "    BMcol = a + b\n",
    "    BMcol = BMcol - 1\n",
    "    BMrow = BMrow - 1\n",
    "    BMrow = ravel(BMrow)\n",
    "    BMcol = ravel(BMcol)\n",
    "    ABD = ravel(ABD)\n",
    "    BigMat = coo_matrix((ABD, (BMrow, BMcol)), shape=(N*NJ, N*NJ)).tocsc()\n",
    "    BigG = transpose(G)\n",
    "    BigG = ravel(BigG)\n",
    "    # print BigMat.todense()\n",
    "    delc = spsolve(BigMat, BigG)\n",
    "    \n",
    "    return delc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 , 0.13923265272614674\n",
      "2 , 0.003114580298810513\n",
      "3 , 9.182488032908424e-05\n",
      "Converged in 3 steps.\n"
     ]
    }
   ],
   "source": [
    "# MAIN PROGRAM\n",
    "# ===========\n",
    "\n",
    "cold = initguess()\t\n",
    "\n",
    "it = 1\n",
    "did = False \n",
    "\n",
    "for it in range(1,itmax):\n",
    "        \n",
    "        \n",
    "    dcdx, d2cdx2 = interpolate(cold,h,2)\n",
    "    sma, smb, smd, smg = fillmat1(cold,dcdx,d2cdx2)\n",
    "    ABD, G = abdgxy(sma, smb, smd, smg)\n",
    "    delc = band(ABD, G)\n",
    "    delc = delc.reshape((NJ, N))\n",
    "    delc = transpose(delc)\n",
    "    maxerror = amax(abs(delc))\n",
    "    print(it,',',maxerror)\n",
    "    cold = cold + delc\n",
    "    if maxerror < tol:\n",
    "        did = True\n",
    "        print ('Converged in ' +str(it)+ ' steps.')\n",
    "        break\n",
    "\n",
    "if not did:\n",
    "    print ('The program did not converge.')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "j_1 = transfer(cold)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ===========\n",
    "# PLOT RESULTS\n",
    "# ===========\n",
    "\n",
    "fig,ax = plt.subplots(1,1,figsize=(6, 6))\n",
    "\n",
    "params = {'mathtext.default': 'regular' }\n",
    "rcParams.update(params)\n",
    "\n",
    "\n",
    "xs = linspace(0,ra,NJ)\n",
    "c1 = j_1\n",
    "c2 = cold[1,:]\n",
    "ax.plot(xs,c1)\n",
    "ax.plot(xs,c2)\n",
    "ax.legend(['$i2$','$eta$'],loc='center right')\n",
    "ax.set_ylabel('$i2\\/(A/cm^{2})$')\n",
    "ax.set_xlabel('$r\\/(cm)$')\n",
    "ax.set_xlim(0, ra)\n",
    "savefig('CD.png', dpi=300)\n",
    "plt.show()\n",
    "\n",
    "close('all')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Time Step\n",
    "tstep = 10         # sec\n",
    "total_time = 3200  # sec\n",
    "total_steps = int(total_time/tstep)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cathode(catprop,tstep):\n",
    "        \n",
    "    # Evolves the cathode properties\n",
    "    # 0 = cathode porosity\n",
    "    # 1 = cathode OH- concentration\n",
    "    # 2 = convection velocity from cathode\n",
    "    # 3 = OH- conc at anode interface (unchanged here)\n",
    "    # 4 = overpotential at anode interface (unchanged here) \n",
    "    # 5 = OH- flux from anode (unchanged here)\n",
    "    # 6 = OH- flux to cathode (unchanged here)\n",
    "    \n",
    "    \n",
    "    newcatprop = np.zeros_like(catprop)\n",
    "    newcatprop[0] = I*(-VMnO2 + 0.1*VMnOOH)*tstep/Vc/F + catprop[0]\n",
    "    newcatprop[1] = ((Acat*catprop[6] + 0.1*I/F)*tstep/Vc + catprop[0]*catprop[1] )/newcatprop[0]\n",
    "    newcatprop[2] = -(newcatprop[0]-catprop[0])*Vc/Acat/tstep\n",
    "    \n",
    "    if newcatprop[1] <= 0.0:\n",
    "        newcatprop[1] = 0.0\n",
    "    \n",
    "    newcatprop[3] = catprop[3]\n",
    "    newcatprop[4] = catprop[4]\n",
    "    newcatprop[5] = catprop[5]\n",
    "    newcatprop[6] = catprop[6]\n",
    "    \n",
    "    return newcatprop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fluxes(fcold):\n",
    "    \n",
    "    dcdr, d2cdr2 = interpolate(fcold,h,2)\n",
    "    \n",
    "    cE=np.concatenate((fcold[:,1:NJ], np.zeros((N,1)) ), axis=1 )\n",
    "    cW=np.concatenate(( np.zeros((N,1)), fcold[:,0:NJ-1] ), axis=1 )\n",
    "    \n",
    "    dcdr=(cE-cW)/2.0/h\n",
    "    dcdr[:,0] = (-3.0*fcold[:,0] + 4.0*fcold[:,1] - fcold[:,2] ) /2.0 /h\n",
    "    dcdr[:,NJ-1] = (3.0*fcold[:,NJ-1] - 4.0*fcold[:,NJ-2] + fcold[:,NJ-3] ) /2.0 /h\n",
    "    \n",
    "    L_flux_OH = -DKOH*dcdr[2,0]*fcold[3,0]**1.5 - tOH/F*fcold[0,0] + fcold[2,0]*fcold[4,0]\n",
    "    R_flux_OH = -DKOH*dcdr[2,NJ-1]*fcold[3,NJ-1]**1.5 - tOH/F*fcold[0,NJ-1] + fcold[2,NJ-1]*fcold[4,NJ-1]\n",
    "    \n",
    "   \n",
    "    \n",
    "    return L_flux_OH,R_flux_OH"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def properties(Znprop,pcold,tstep):\n",
    "    \n",
    "\n",
    "    dcdxpcold, d2cdx2pcold = interpolate(pcold,h,2)\n",
    "    \n",
    "    new_prop = np.zeros_like(Znprop)\n",
    "    \n",
    "    #aa\n",
    "    new_prop[0,:] = ao*((1 - pcold[3,:])/(1-epao))**(2/3)\n",
    "    \n",
    "    #am\n",
    "    new_prop[1,:] = new_prop[0,:]*(Znprop[5,:]**(2/3)/(Znprop[5,:]**(2/3) + Znprop[6,:]**(2/3)))\n",
    "    \n",
    "   \n",
    "    for u in new_prop[0,:]:\n",
    "        for i in new_prop[1,:]:\n",
    "            if i == u:\n",
    "                new_prop[2,:] = KOH_o\n",
    "                new_prop[3,:] = KZnOH_o\n",
    "                new_prop[4,:] = kx\n",
    "                \n",
    "            else:\n",
    "                #KOH\n",
    "                new_prop[2,:] = KOH_o/new_prop[0,:]*(new_prop[0,:] - new_prop[1,:])/(np.log(new_prop[0,:]/new_prop[1,:]))\n",
    "                \n",
    "                #KZnOH\n",
    "                new_prop[3,:] = KZnOH_o/new_prop[0,:]*(new_prop[0,:] - new_prop[1,:])/(np.log(new_prop[0,:]/new_prop[1,:]))\n",
    "                \n",
    "                #ks\n",
    "                X = 1/((new_prop[3,:]*new_prop[1,:])/np.log(new_prop[0,:]/(new_prop[0,:] - new_prop[1,:])))\n",
    "                Y = 1/(((new_prop[0,:]-new_prop[1,:])*kx)/new_prop[0,:])\n",
    "                Z = X + Y\n",
    "                new_prop[4,:] = 1/Z\n",
    "                \n",
    "               \n",
    "    \"formula for volume fraction change from sunnu paper\"\n",
    "    \n",
    "    vol_change = np.zeros_like(coldA)\n",
    "    \n",
    "    vol_change[0,:] = 1/2/F*(dcdxpcold[0,:] + pcold[0,:]/rr[:])*(VZn + 4*VKOH - VKZnOH - 2*(VKOH*tOH + tZnOH*VKZnOH/2))*tstep\n",
    "    vol_change[1,:] = new_prop[0,:]*new_prop[4,:]*(pcold[5,:] - pcold[2,:]**2/Keq)*VZnO*tstep\n",
    "    \n",
    "    \n",
    "    new_prop[5,:] = (Znprop[5,:] + vol_change[0,:]) \n",
    "    \n",
    "    \n",
    "    vg = np.zeros_like(vol_change)\n",
    "    vg = vol_change[1,:]\n",
    "    if (vg>0).all() == True:\n",
    "        new_prop[6,:] = (Znprop[6,:] + vg)\n",
    "    else:\n",
    "        new_prop[6,:] = Znprop[6,:]\n",
    "\n",
    "    #sigma\n",
    "    new_prop[7,:] = sigma_Zn*(Znprop[5,:]**(1/5)) + sigma_ZnO*Znprop[6,:]**(1/5)\n",
    "    \n",
    "    return new_prop\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def volume_change(vcold,tstep,prop_zinc,init_volume):\n",
    "    \n",
    "    dcdxvcold, d2cdx2vcold = interpolate(vcold,h,2)\n",
    "    new_volume_change = np.zeros_like(vcold)\n",
    "    \n",
    "    new_volume_change[0,:] =  1/2/F*(dcdxvcold[0,:] + vcold[0,:]/rr[:])*(VZn + 4*VKOH - VKZnOH - 2*(VKOH*tOH + tZnOH*VKZnOH/2))*tstep\n",
    "    new_volume_change[1,:] =  -(prop_zinc[0,:]*prop_zinc[4,:]*(vcold[5,:] - vcold[2,:]**2/Keq)*(2*VKOH + VH2O - VKZnOH + VZnO)*tstep)\n",
    "    \n",
    "    return new_volume_change"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rate_equation(rcold,tstep,prop_zinc):\n",
    "    \n",
    "    rate_equation = np.zeros_like(rcold)\n",
    "    \n",
    "    dcdxrcold, d2cdx2rcold = interpolate(rcold,h,2)\n",
    "    \n",
    "    # rate equation for OH ions\n",
    "    rate_equation[0,:] = 2*prop_zinc[0,:]*prop_zinc[4,:]*(rcold[5,:] - rcold[2,:]**2/Keq)\n",
    "    \n",
    "    # rate equation for ZnOH ions\n",
    "    rate_equation[1,:] = -prop_zinc[0,:]*prop_zinc[4,:]*(rcold[5,:] - rcold[2,:]**2/Keq)\n",
    "    \n",
    "    rate_equation[2,:] = (2*tOH - 4)/2/F*(dcdxrcold[0,:] + rcold[0,:]/rr[:])\n",
    "    \n",
    "    rate_equation[3,:] = (tZnOH + 1)/2/F*(dcdxrcold[0,:] + rcold[0,:]/rr[:])\n",
    "    \n",
    "    return rate_equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fillmat Matrix function for i2 and eta \n",
    "# =======\n",
    "\n",
    "def fillmat2(cold,dcdx,d2cdx2,cprev,tstep,catprop,zinc):\n",
    "    \n",
    "    ([N,NJ]) = cold.shape\n",
    "    \n",
    "    sma = zeros([N,NJ,N])\n",
    "    smb = zeros([N,NJ,N])\n",
    "    smd = zeros([N,NJ,N])\n",
    "    smg = zeros([N,NJ])\n",
    "\n",
    "    \n",
    "    \n",
    "    OHs = catprop[1]\n",
    "    velo = catprop[2]\n",
    "     \n",
    "    aa = zinc[0,:]\n",
    "    KOH = zinc[2,:]\n",
    "    KZnOH = zinc[3,:]\n",
    "    ks = zinc[4,:]\n",
    "    sigma = zinc[7,:]\n",
    "    \n",
    "    C1 = 2*F*aa*KOH\n",
    "    C2 = 2*F*aa*KZnOH \n",
    "    \n",
    "    beta = (1-alpha)*2*F/R/T\n",
    "    betac = -alpha*2*F/R/T\n",
    "    \n",
    "    B1 = cold[2,:] - dcdx[0,:]/C1 - cold[0,:]/rr[:]/C1\n",
    "    B2 = cold[5,:] + dcdx[0,:]/C2 + cold[0,:]/rr[:]/C2\n",
    "    P1 = aa*io*exp(beta*cold[1,:])\n",
    "    P2 = aa*io*exp(betac*cold[1,:])\n",
    "    \n",
    "    \n",
    "    # Equation for i2\n",
    "    \n",
    "    smb[0,:,0] = 1 - 1/(CZnOH)**0.06/(COH)**2.59*(-2.59*(B1)**1.59*(B2)**0.06*(P1)/C1 + 0.06*(B1)**2.59*(B2)**-0.94*(P1)/C2) +\\\n",
    "                1/(CZnOH)**0.94/(COH)**-0.92*(0.94*(B1)**-0.92*(B2)**-0.06*(P2)/C2 + 0.92*(B1)**-1.92*(B2)**0.94*(P2)/C1)\n",
    "    smd[0,:,0] = 1/rr[:] - 1/(CZnOH)**0.06/(COH)**2.59*(-2.59*(B1)**1.59*(B2)**0.06*(P1)/C1/rr[:] + 0.06*(B1)**2.59*(B2)**-0.94*(P1)/C2/rr[:]) +\\\n",
    "                1/(CZnOH)**0.94/(COH)**-0.92*(0.94*(B1)**-0.92*(B2)**-0.06*(P2)/C2/rr[:] + 0.92*(B1)**-1.92*(B2)**0.94*(P2)/C1/rr[:])\n",
    "    smd[0,:,1] = -1/(CZnOH)**0.06/(COH)**2.59*((B1)**2.59*(B2)**0.06*beta*(P1)) + 1/(CZnOH)**0.94/(COH)**-0.92*((B1)**-0.92*(B2)**0.94*betac*(P2))\n",
    "    smd[0,:,2] = - 1/(CZnOH)**0.06/(COH)**2.59*(2.59*(B2)**0.06*(B1)**1.59*(P1)) +\\\n",
    "                1/(CZnOH)**0.94/(COH)**-0.92*(-0.92*(B1)**-1.92*(B2)**0.94*(P2))\n",
    "    smd[0,:,5] = - 1/(CZnOH)**0.06/(COH)**2.59*(0.06*(B2)**-0.94*(B1)**2.59*(P1)) +\\\n",
    "                1/(CZnOH)**0.94/(COH)**-0.92*(0.94*(B1)**-0.92*(B2)**-0.06*(P2))\n",
    "\n",
    "    smg[0,:] = (- dcdx[0,:] - cold[0,:]/rr[:])+ 1/(CZnOH)**0.06/(COH)**2.59*((B1)**2.59*(B2)**0.06*(P1)) -\\\n",
    "                1/(CZnOH)**0.94/(COH)**-0.92*((B1)**-0.92*(B2)**0.94*(P2))\n",
    "    \n",
    "    \n",
    "    # Equation for eta\n",
    "    \n",
    "    smd[1,:,0] = -1/kappa*cold[5,:]*cold[2,:] - 1/sigma*cold[2,:]*cold[3,:]**1.5*cold[5,:]\n",
    "    smb[1,:,1] = cold[2,:]*cold[3,:]**1.5*cold[5,:]\n",
    "    smb[1,:,2] = -2*R*T/F*(2-tOH)*cold[3,:]**1.5*cold[5,:]\n",
    "    smd[1,:,2] = cold[3,:]**1.5*dcdx[1,:]*cold[5,:] -\\\n",
    "                1/kappa*cold[0,:]*cold[5,:] -\\\n",
    "                1/sigma*cold[3,:]**1.5*cold[0,:]*cold[5,:] +\\\n",
    "                I/(2*pi*rr[:]*L*sigma)*cold[3,:]**1.5*cold[5,:] -\\\n",
    "                3*R*T/F*(-1/2 - tZnOH/2)*cold[3,:]**1.5*dcdx[5,:]\n",
    "    smd[1,:,3] = 1.5*cold[2,:]*cold[3,:]**0.5*dcdx[1,:]*cold[5,:] -\\\n",
    "                1/sigma*1.5*cold[2,:]*cold[3,:]**0.5*cold[0,:]*cold[5,:] +\\\n",
    "                I/(2*pi*rr[:]*L*sigma)*1.5*cold[2,:]*cold[3,:]**0.5*cold[5,:] -\\\n",
    "                2*R*T/F*(2-tOH)*1.5*cold[3,:]**0.5*dcdx[2,:]*cold[5,:] -\\\n",
    "                3*R*T/F*(-1/2-tZnOH/2)*1.5*cold[3,:]**0.5*cold[2,:]*dcdx[5,:]\n",
    "    smb[1,:,5] = -3*R*T/F*(-1/2 - tZnOH/2)*cold[3,:]**1.5*cold[2,:]\n",
    "    smd[1,:,5] = cold[3,:]**1.5*dcdx[1,:]*cold[2,:] -\\\n",
    "                1/kappa*cold[0,:]*cold[2,:] -\\\n",
    "                1/sigma*cold[3,:]**1.5*cold[0,:]*cold[2,:] +\\\n",
    "                I/(2*pi*rr[:]*L*sigma)*cold[3,:]**1.5*cold[2,:] -\\\n",
    "                2*R*T/F*(2 - tOH)*cold[3,:]**1.5*dcdx[2,:]\n",
    "    \n",
    "    smg[1,:] =  1/kappa*cold[0,:]*cold[2,:]*cold[5,:] +\\\n",
    "                1/sigma*cold[0,:]*cold[2,:]*cold[3,:]**1.5*cold[5,:] -\\\n",
    "                I/(2*pi*rr[:]*L*sigma)*cold[2,:]*(cold[3,:])**1.5*cold[5,:] +\\\n",
    "                2*R*T/F*(2-tOH)*(cold[3,:])**1.5*dcdx[2,:]*cold[5,:]+\\\n",
    "                3*R*T/F*(-1/2 - tZnOH/2)*cold[2,:]*cold[3,:]**1.5*dcdx[5,:] -\\\n",
    "                cold[3,:]**1.5*cold[2,:]*dcdx[1,:]*cold[5,:]\n",
    "                \n",
    "    # Equation for COH\n",
    "    \n",
    "    smb[2,:,0] = (-2*tOH+4)/2/F\n",
    "    smd[2,:,0] = (-2*tOH+4)/2/F/rr[:]\n",
    "    sma[2,:,2] = -cold[3,:]**1.5*DKOH\n",
    "    smb[2,:,2] = -cold[3,:]**1.5*DKOH/rr[:] -\\\n",
    "                1.5*DKOH*cold[3,:]**0.5*dcdx[3,:] +\\\n",
    "                cold[4,:] \n",
    "    smd[2,:,2] = 4*aa*ks*cold[2,:]/Keq +\\\n",
    "                dcdx[4,:] +\\\n",
    "                cold[4,:]/rr[:] +\\\n",
    "                2*cold[3,:]/tstep - cprev[3,:]/tstep\n",
    "    smb[2,:,3] = -1.5*DKOH*cold[3,:]**0.5*dcdx[2,:]\n",
    "    smd[2,:,3] = -DKOH*1.5*cold[3,:]**0.5*d2cdx2[2,:] -\\\n",
    "                DKOH/rr[:]*1.5*cold[3,:]**0.5*dcdx[2,:] -\\\n",
    "                1.5*DKOH*0.5*dcdx[2,:]*cold[3,:]**-0.5*dcdx[3,:] +\\\n",
    "                2*cold[2,:]/tstep - cprev[2,:]/tstep\n",
    "    smb[2,:,4] = cold[2,:]\n",
    "    smd[2,:,4] = dcdx[2,:] + cold[2,:]/rr[:] \n",
    "    smd[2,:,5] = -2*aa*ks\n",
    "    smg[2,:] = 2*aa*ks*(cold[5,:] - cold[2,:]**2/Keq) +\\\n",
    "                DKOH*cold[3,:]**1.5*d2cdx2[2,:] +\\\n",
    "                DKOH/rr[:]*cold[3,:]**1.5*dcdx[2,:]+\\\n",
    "                DKOH*1.5*cold[3,:]**0.5*dcdx[2,:]*dcdx[3,:] +\\\n",
    "                (2*tOH - 4)/2/F*(dcdx[0,:] + cold[0,:]/rr[:]) - dcdx[2,:]*cold[4,:] -\\\n",
    "                dcdx[4,:]*cold[2,:] - cold[4,:]*cold[2,:]/rr[:] -\\\n",
    "                2*cold[2,:]*cold[3,:]/tstep + cold[2,:]*cprev[3,:]/tstep + cold[3,:]*cprev[2,:]/tstep\n",
    "    \n",
    "    # Equation for porosity\n",
    "    \n",
    "    smb[3,:,0] = -VZn/2/F\n",
    "    smd[3,:,0] = -VZn/2/F/rr[:]\n",
    "    smd[3,:,2] = -2*VZnO*aa*ks*cold[2,:]/Keq\n",
    "    smd[3,:,3] = 1/tstep\n",
    "    smd[3,:,5] = VZnO*aa*ks\n",
    "    smg[3,:] = VZn/2/F*(dcdx[0,:] + cold[0,:]/rr[:]) -\\\n",
    "                VZnO*aa*ks*(cold[5,:] - cold[2,:]**2/Keq) -\\\n",
    "                cold[3,:]/tstep + cprev[3,:]/tstep \n",
    "    \n",
    "    # Equation for volume average velocity\n",
    "    \n",
    "    V1 = 1/2/F*(VKOH*(2*tOH - 4) + VKZnOH*(2*tZnOH + 2)/2)\n",
    "    V2 = (2*VKOH + VH2O - VZnOH)\n",
    "    \n",
    "    smb[4,:,0] = -V1\n",
    "    smd[4,:,0] = -V1/rr[:]\n",
    "    smd[4,:,2] = 2*cold[2,:]/Keq*aa*ks*V2\n",
    "    smd[4,:,3] = 1/tstep\n",
    "    smb[4,:,4] = 1\n",
    "    smd[4,:,4] = 1/rr[:]\n",
    "    smd[4,:,5] = -aa*ks*V2\n",
    "    smg[4,:] = aa*ks*V2*(cold[5,:] - cold[2,:]**2/Keq) +\\\n",
    "                V1*(dcdx[0,:] + cold[0,:]/rr[:]) - dcdx[4,:] - cold[4,:]/rr[:] -\\\n",
    "                cold[3,:]/tstep + cprev[3,:]/tstep \n",
    "    \n",
    "    # Equation for CZnOH\n",
    "    \n",
    "    smb[5,:,0] = (-tZnOH-1)/2/F\n",
    "    smd[5,:,0] = (-tZnOH-1)/2/F/rr[:]\n",
    "    smd[5,:,2] = -2*aa*ks*cold[2,:]/Keq\n",
    "    smb[5,:,3] = -1.5*DKZnOH*cold[3,:]**0.5*dcdx[5,:]\n",
    "    smd[5,:,3] = -DKZnOH*1.5*cold[3,:]**0.5*d2cdx2[5,:] -\\\n",
    "                DKZnOH/rr[:]*1.5*cold[3,:]**0.5*dcdx[5,:] -\\\n",
    "                1.5*DKZnOH*0.5*dcdx[5,:]*cold[3,:]**-0.5*dcdx[3,:] +\\\n",
    "                2*cold[5,:]/tstep - cprev[5,:]/tstep\n",
    "    smb[5,:,4] = cold[5,:]\n",
    "    smd[5,:,4] = dcdx[5,:] + cold[5,:]/rr[:]\n",
    "    sma[5,:,5] = -DKZnOH*cold[3,:]**1.5\n",
    "    smb[5,:,5] = -cold[3,:]**1.5*DKZnOH/rr[:] -\\\n",
    "                1.5*DKZnOH*cold[3,:]**0.5*dcdx[3,:] + cold[4,:]\n",
    "    smd[5,:,5] = dcdx[4,:] + cold[4,:]/rr[:] + aa*ks + 2*cold[3,:]/tstep - cprev[3,:]/tstep\n",
    "\n",
    "    smg[5,:] = DKZnOH*(cold[3,:]**1.5*d2cdx2[5,:]) +\\\n",
    "                DKZnOH/rr[:]*cold[3,:]**1.5*dcdx[5,:] +\\\n",
    "                1.5*DKZnOH*cold[3,:]**0.5*dcdx[5,:]*dcdx[3,:] -\\\n",
    "                cold[4,:]*dcdx[5,:]- dcdx[4,:]*cold[5,:] -\\\n",
    "                1/rr[:]*cold[4,:]*cold[5,:] + aa*ks*cold[2,:]**2/Keq - aa*ks*cold[5,:] -\\\n",
    "                2*cold[3,:]*cold[5,:]/tstep + cold[3,:]*cprev[5,:]/tstep + cold[5,:]*cprev[3,:]/tstep +\\\n",
    "                (tZnOH + 1)/2/F*(dcdx[0,:] + cold[0,:]/rr[:])\n",
    "\n",
    "    \n",
    "    # __________Boundary condition 1\n",
    "\n",
    "    smp = zeros([N,N])\n",
    "    sme = zeros([N,N])\n",
    "    smf = zeros([N,1])\n",
    "    \n",
    "    sme[0,0] = 1\n",
    "    smf[0] = -cold[0,0]\n",
    "    smp[2,2] = 1\n",
    "    smf[2] = -dcdx[2,0]\n",
    "    sme[4,4] = 1\n",
    "    smf[4] = -cold[4,0]\n",
    "    smp[5,5] = 1\n",
    "    smf[5] = -dcdx[5,0]\n",
    "    \n",
    "    # Equation for eta\n",
    "    \n",
    "    sme[1,0] = -1/kappa*cold[5,0]*cold[2,0] - 1/sigma[0]*cold[2,0]*cold[3,0]**1.5*cold[5,0]\n",
    "    smp[1,1] = cold[2,0]*cold[3,0]**1.5*cold[5,0]\n",
    "    smp[1,2] = -2*R*T/F*(2-tOH)*cold[3,0]**1.5*cold[5,0]\n",
    "    sme[1,2] = cold[3,0]**1.5*dcdx[1,0]*cold[5,0] -\\\n",
    "                1/kappa*cold[0,0]*cold[5,0] -\\\n",
    "                1/sigma[0]*cold[3,0]**1.5*cold[0,0]*cold[5,0] +\\\n",
    "                I/(2*pi*rr[0]*L*sigma[0])*cold[3,0]**1.5*cold[5,0] -\\\n",
    "                3*R*T/F*(-1/2 - tZnOH/2)*cold[3,0]**1.5*dcdx[5,0]\n",
    "    sme[1,3] = 1.5*cold[2,0]*cold[3,0]**0.5*dcdx[1,0]*cold[5,0] -\\\n",
    "                1/sigma[0]*1.5*cold[2,0]*cold[3,0]**0.5*cold[0,0]*cold[5,0] +\\\n",
    "                I/(2*pi*rr[0]*L*sigma[0])*1.5*cold[2,0]*cold[3,0]**0.5*cold[5,0] -\\\n",
    "                2*R*T/F*(2-tOH)*1.5*cold[3,0]**0.5*dcdx[2,0]*cold[5,0] -\\\n",
    "                3*R*T/F*(-1/2-tZnOH/2)*1.5*cold[3,0]**0.5*cold[2,0]*dcdx[5,0]\n",
    "    smp[1,5] = -3*R*T/F*(-1/2 - tZnOH/2)*cold[3,0]**1.5*cold[2,0]\n",
    "    sme[1,5] = cold[3,0]**1.5*dcdx[1,0]*cold[2,0] - 1/kappa*cold[0,0]*cold[2,0] - 1/sigma[0]*cold[3,0]**1.5*cold[0,0]*cold[2,0] +\\\n",
    "                I/(2*pi*rr[0]*L*sigma[0])*cold[3,0]**1.5*cold[2,0] - 2*R*T/F*(2 - tOH)*cold[3,0]**1.5*dcdx[2,0]\n",
    "    \n",
    "    smf[1] =  1/kappa*cold[0,0]*cold[2,0]*cold[5,0] + 1/sigma[0]*cold[0,0]*cold[2,0]*(cold[3,0])**1.5*cold[5,0] -\\\n",
    "                I/(2*pi*rr[0]*L*sigma[0])*cold[2,0]*(cold[3,0])**1.5*cold[5,0] +\\\n",
    "                2*R*T/F*(2-tOH)*(cold[3,0])**1.5*dcdx[2,0]*cold[5,0]\\\n",
    "                + 3*R*T/F*(-1/2 - tZnOH/2)*cold[2,0]*cold[3,0]**1.5*dcdx[5,0] -\\\n",
    "                cold[3,0]**1.5*cold[2,0]*dcdx[1,0]*cold[5,0]\n",
    "    \n",
    "    smp[3,0] = -VZn/2/F\n",
    "    sme[3,0] = -VZn/2/F/rr[0]\n",
    "    sme[3,2] = -2*VZnO*aa[0]*ks[0]*cold[2,0]/Keq\n",
    "    sme[3,3] = 1/tstep\n",
    "    sme[3,5] = VZnO*aa[0]*ks[0]\n",
    "    smf[3] = VZn/2/F*(dcdx[0,0] + cold[0,0]/rr[0]) -\\\n",
    "            VZnO*aa[0]*ks[0]*(cold[5,0] - cold[2,0]**2/Keq) -\\\n",
    "            cold[3,0]/tstep + cprev[3,0]/tstep\n",
    "\n",
    "    #smp[4,0] = -V1\n",
    "    #sme[4,0] = -V1/rr[0]\n",
    "    #sme[4,2] = 2*cold[2,0]/Keq*V2*aa[0]*ks[0]\n",
    "    #sme[4,3] = 1/tstep\n",
    "    #smp[4,4] = 1\n",
    "    #sme[4,4] = 1/rr[0]\n",
    "    #sme[4,5] = -V2*aa[0]*ks[0]\n",
    "    #smf[4] = aa[0]*ks[0]*V2*(cold[5,0] - cold[2,0]**2/Keq) + V1*(dcdx[0,0] + cold[0,0]/rr[0]) - dcdx[4,0] - cold[4,0]/rr[0] - cold[3,0]/tstep + cprev[3,0]/tstep \n",
    "    \n",
    "    # Equation for CZnOH\n",
    "    \n",
    "    #smp[5,0] = (-tZnOH-1)/2/F\n",
    "    #sme[5,0] = (-tZnOH-1)/2/F/rr[0]\n",
    "    #sme[5,2] = -2*ao*ks*cold[2,0]/Keq\n",
    "    #smp[5,3] = -1.5*DKZnOH*cold[3,0]**0.5*dcdx[5,0]\n",
    "    #sme[5,3] = -DKZnOH*1.5*cold[3,0]**0.5*d2cdx2[5,0] - DKZnOH/rr[0]*1.5*cold[3,0]**0.5*dcdx[5,0] - 1.5*DKZnOH*0.5*dcdx[5,0]*cold[3,0]**-0.5*dcdx[3,0] +\\\n",
    "                #2*cold[5,0]/tstep - cprev[5,0]/tstep\n",
    "    #smp[5,4] = cold[5,0]\n",
    "    #sme[5,4] = dcdx[5,0] + cold[5,0]/rr[0]\n",
    "    #smp[5,5] = -cold[3,0]**1.5*DKZnOH/rr[0] - 1.5*DKZnOH*cold[3,0]**0.5*dcdx[3,0] + cold[4,0]\n",
    "    #sme[5,5] = dcdx[4,0] + cold[4,0]/rr[0] + ao*ks + 2*cold[3,0]/tstep - cprev[3,0]/tstep\n",
    "\n",
    "    #smf[5] = #DKZnOH*(cold[3,0]**1.5*d2cdx2[5,0]) + DKZnOH/rr[0]*cold[3,0]**1.5*dcdx[5,0] + 1.5*DKZnOH*cold[3,0]**0.5*dcdx[5,0]*dcdx[3,0] -\\\n",
    "                #cold[4,0]*dcdx[5,0]- dcdx[4,0]*cold[5,0] - 1/rr[0]*cold[4,0]*cold[5,0] + ao*ks*cold[2,0]**2/Keq - ao*ks*cold[5,0] -\\\n",
    "                #2*cold[3,0]*cold[5,0]/tstep + cold[3,0]*cprev[5,0]/tstep + cold[5,0]*cprev[3,0]/tstep + (tZnOH + 1)/2/F*(dcdx[0,:] + cold[0,:]/rr[:])\n",
    "    \n",
    "    # Insert (sme smp smf) into (smb smd smg)\n",
    "\n",
    "    smb[:,0,:] = smp[:,:]\n",
    "    smd[:,0,:] = sme[:,:]\n",
    "    smg[:,0] = transpose(smf)\n",
    "\n",
    "    # __________Boundary condition 2\n",
    "\n",
    "    smp = zeros([N,N])\n",
    "    sme = zeros([N,N])\n",
    "    smf = zeros([N,1])\n",
    "    \n",
    "    sme[0,0] = 1\n",
    "    smf[0] = I/(2*pi*rr[NJ-1]*L) - cold[0,NJ-1]\n",
    "    sme[2,2] = 1\n",
    "    smf[2] = OHs - cold[2,NJ-1]  \n",
    "    sme[4,4] = 1\n",
    "    smf[4] = velo - cold[4,NJ-1] \n",
    "    smp[5,5] = 1\n",
    "    smf[5] = -dcdx[5,NJ-1]\n",
    "    # Equation for eta\n",
    "    \n",
    "    sme[1,0] = -1/kappa*cold[5,NJ-1]*cold[2,NJ-1] - 1/sigma[NJ-1]*cold[2,NJ-1]*cold[3,NJ-1]**1.5*cold[5,NJ-1]\n",
    "    smp[1,1] = cold[2,NJ-1]*cold[3,NJ-1]**1.5*cold[5,NJ-1]\n",
    "    smp[1,2] = -2*R*T/F*(2-tOH)*cold[3,NJ-1]**1.5*cold[5,NJ-1]\n",
    "    sme[1,2] = cold[3,NJ-1]**1.5*dcdx[1,NJ-1]*cold[5,NJ-1] -\\\n",
    "                1/kappa*cold[0,NJ-1]*cold[5,NJ-1] -\\\n",
    "                1/sigma[NJ-1]*cold[3,NJ-1]**1.5*cold[0,NJ-1]*cold[5,NJ-1] +\\\n",
    "                I/(2*pi*rr[NJ-1]*L*sigma[NJ-1])*cold[3,NJ-1]**1.5*cold[5,NJ-1] -\\\n",
    "                3*R*T/F*(-1/2 - tZnOH/2)*cold[3,NJ-1]**1.5*dcdx[5,NJ-1]\n",
    "    sme[1,3] = 1.5*cold[2,NJ-1]*cold[3,NJ-1]**0.5*dcdx[1,NJ-1]*cold[5,NJ-1] -\\\n",
    "                1/sigma[NJ-1]*1.5*cold[2,NJ-1]*cold[3,NJ-1]**0.5*cold[0,NJ-1]*cold[5,NJ-1] +\\\n",
    "                I/(2*pi*rr[NJ-1]*L*sigma[NJ-1])*1.5*cold[2,NJ-1]*cold[3,NJ-1]**0.5*cold[5,NJ-1] -\\\n",
    "                2*R*T/F*(2-tOH)*1.5*cold[3,NJ-1]**0.5*dcdx[2,NJ-1]*cold[5,NJ-1] -\\\n",
    "                3*R*T/F*(-1/2-tZnOH/2)*1.5*cold[3,NJ-1]**0.5*cold[2,NJ-1]*dcdx[5,NJ-1]\n",
    "    smp[1,5] = -3*R*T/F*(-1/2 - tZnOH/2)*cold[3,NJ-1]**1.5*cold[2,NJ-1]\n",
    "    sme[1,5] = cold[3,NJ-1]**1.5*dcdx[1,NJ-1]*cold[2,NJ-1] -\\\n",
    "                1/kappa*cold[0,NJ-1]*cold[2,NJ-1] -\\\n",
    "                1/sigma[NJ-1]*cold[3,NJ-1]**1.5*cold[0,NJ-1]*cold[2,NJ-1] +\\\n",
    "                I/(2*pi*rr[NJ-1]*L*sigma[NJ-1])*cold[3,NJ-1]**1.5*cold[2,NJ-1] -\\\n",
    "                2*R*T/F*(2 - tOH)*cold[3,NJ-1]**1.5*dcdx[2,NJ-1]\n",
    "    \n",
    "    smf[1] =  1/kappa*cold[0,NJ-1]*cold[2,NJ-1]*cold[5,NJ-1] +\\\n",
    "            1/sigma[NJ-1]*cold[0,NJ-1]*cold[2,NJ-1]*(cold[3,NJ-1])**1.5*cold[5,NJ-1] -\\\n",
    "            I/(2*pi*rr[NJ-1]*L*sigma[NJ-1])*cold[2,NJ-1]*(cold[3,NJ-1])**1.5*cold[5,NJ-1] +\\\n",
    "            2*R*T/F*(2-tOH)*(cold[3,NJ-1])**1.5*dcdx[2,NJ-1]*cold[5,NJ-1]\\\n",
    "            + 3*R*T/F*(-1/2 - tZnOH/2)*cold[2,NJ-1]*cold[3,NJ-1]**1.5*dcdx[5,NJ-1] -\\\n",
    "            cold[3,NJ-1]**1.5*cold[2,NJ-1]*dcdx[1,NJ-1]*cold[5,NJ-1]\n",
    "    \n",
    "    \n",
    "    smp[3,0] = -VZn/2/F\n",
    "    sme[3,0] = -VZn/2/F/rr[NJ-1]\n",
    "    sme[3,2] = -2*VZnO*aa[NJ-1]*ks[NJ-1]*cold[2,NJ-1]/Keq\n",
    "    sme[3,3] = 1/tstep\n",
    "    sme[3,5] = VZnO*aa[NJ-1]*ks[NJ-1]\n",
    "    smf[3] = VZn/2/F*(dcdx[0,NJ-1] + cold[0,NJ-1]/rr[NJ-1]) -\\\n",
    "            VZnO*aa[NJ-1]*ks[NJ-1]*(cold[5,NJ-1] - cold[2,NJ-1]**2/Keq) -\\\n",
    "            cold[3,NJ-1]/tstep + cprev[3,NJ-1]/tstep\n",
    "\n",
    "        \n",
    "    #smp[4,0] = -V1\n",
    "    #sme[4,0] = -V1/rr[NJ-1]\n",
    "    #sme[4,2] = 2*cold[2,NJ-1]/Keq*aa[NJ-1]*ks[NJ-1]*V2\n",
    "    #sme[4,3] = 1/tstep\n",
    "    #smp[4,4] = 1\n",
    "    #sme[4,4] = 1/rr[NJ-1]\n",
    "    #sme[4,5] = -aa[NJ-1]*ks[NJ-1]*V2\n",
    "    #smf[4] = aa[NJ-1]*ks[NJ-1]*V2*(cold[5,NJ-1] - cold[2,NJ-1]**2/Keq) +\\\n",
    "                #V1*(dcdx[0,NJ-1] + cold[0,NJ-1]/rr[NJ-1]) - dcdx[4,NJ-1] - cold[4,NJ-1]/rr[NJ-1] -\\\n",
    "     #       cold[3,NJ-1]/tstep + cprev[3,NJ-1]/tstep\n",
    "\n",
    "    # Equation for CZnOH\n",
    "    \n",
    "    #smp[5,0] = (-tZnOH-1)/2/F\n",
    "    #sme[5,0] = (-tZnOH-1)/2/F/rr[NJ-1]\n",
    "    #sme[5,2] = -2*aa[NJ-1]*ks[NJ-1]*cold[2,NJ-1]/Keq\n",
    "    #smp[5,3] = -1.5*DKZnOH*cold[3,NJ-1]**0.5*dcdx[5,NJ-1]\n",
    "    #sme[5,3] = -DKZnOH*1.5*cold[3,NJ-1]**0.5*d2cdx2[5,NJ-1] - DKZnOH/rr[NJ-1]*1.5*cold[3,NJ-1]**0.5*dcdx[5,NJ-1] -\\\n",
    "    #            1.5*DKZnOH*0.5*dcdx[5,NJ-1]*cold[3,NJ-1]**-0.5*dcdx[3,NJ-1] +\\\n",
    "    #            2*cold[5,NJ-1]/tstep - cprev[5,NJ-1]/tstep\n",
    "    #smp[5,4] = cold[5,NJ-1]\n",
    "    #sme[5,4] = dcdx[5,NJ-1] + cold[5,NJ-1]/rr[NJ-1]\n",
    "    #smp[5,5] = -cold[3,NJ-1]**1.5*DKZnOH/rr[NJ-1] - 1.5*DKZnOH*cold[3,NJ-1]**0.5*dcdx[3,NJ-1] + cold[4,NJ-1]\n",
    "    #sme[5,5] = dcdx[4,NJ-1] + cold[4,NJ-1]/rr[NJ-1] + aa[NJ-1]*ks[NJ-1] + 2*cold[3,NJ-1]/tstep - cprev[3,NJ-1]/tstep\n",
    "\n",
    "    #smf[5] = DKZnOH*(cold[3,NJ-1]**1.5*d2cdx2[5,NJ-1]) +\\\n",
    "    #        DKZnOH/rr[NJ-1]*cold[3,NJ-1]**1.5*dcdx[5,NJ-1] +\\\n",
    "    #        1.5*DKZnOH*cold[3,NJ-1]**0.5*dcdx[5,NJ-1]*dcdx[3,NJ-1] -\\\n",
    "     #       cold[4,NJ-1]*dcdx[5,NJ-1]- dcdx[4,NJ-1]*cold[5,NJ-1] -\\\n",
    "     #       1/rr[NJ-1]*cold[4,NJ-1]*cold[5,NJ-1] +\\\n",
    "     #       aa[NJ-1]*ks[NJ-1]*cold[2,NJ-1]**2/Keq - aa[NJ-1]*ks[NJ-1]*cold[5,NJ-1] -\\\n",
    "     #       2*cold[3,NJ-1]*cold[5,NJ-1]/tstep + cold[3,NJ-1]*cprev[5,NJ-1]/tstep + cold[5,NJ-1]*cprev[3,NJ-1]/tstep +\\\n",
    "     #       (tZnOH + 1)/2/F*(dcdx[0,NJ-1] + cold[0,NJ-1]/rr[NJ-1])\n",
    "\n",
    "    \n",
    "    smb[:,NJ-1,:] = smp[:,:]\n",
    "    smd[:,NJ-1,:] = sme[:,:]\n",
    "    smg[:,NJ-1] = transpose(smf)\n",
    "    \n",
    "    return sma, smb, smd, smg\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "COH = 0.007\n",
    "epao = 0.74\n",
    "v = 0\n",
    "CZnOH = 0.00053"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = NA\n",
    "# Transfer initial result to cprevA\n",
    "cprevA = np.zeros([N,NJ])\n",
    "cprevA[0,:] = cold[0,:]\n",
    "cprevA[1,:] = cold[1,:]       \n",
    "cprevA[2,:] = COH\n",
    "cprevA[3,:] = epao\n",
    "cprevA[4,:] = v\n",
    "cprevA[5,:] = CZnOH\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# Expand coldC for time-dependent problem\n",
    "coldA = np.zeros([N,NJ])\n",
    "coldA[:] = cprevA\n",
    "j = transfer(coldA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.59516355e-01 7.02527007e-03 2.63586430e-05 7.00000000e-03\n",
      " 9.92011644e-03 0.00000000e+00 0.00000000e+00]\n"
     ]
    }
   ],
   "source": [
    "# initial cathode properties\n",
    "propC = np.zeros([7])\n",
    "\n",
    "propC[0] = epc\n",
    "propC[1] = COH\n",
    "propC[3] = coldA[2,NJ-1]\n",
    "propC[4] = coldA[1,NJ-1]\n",
    "propC = cathode(propC,tstep)\n",
    "print(propC)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "zincp = np.zeros([8,NJ]) \n",
    "zincp[0,:] = 50        #aa\n",
    "zincp[1,:] = 50        #am\n",
    "zincp[2,:] = KOH_o     #KOH\n",
    "zincp[3,:] = KZnOH_o   #KZnOH\n",
    "zincp[4,:] = kx        #ks\n",
    "zincp[5,:] = 0.26      #volume fraction of Zn\n",
    "zincp[6,:] = 0.        #volume fraction of ZnO\n",
    "zincp[7,:] = 20        #conductivity\n",
    "\n",
    "\n",
    "zincp = properties(zincp,coldA,tstep)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "init_vol = np.zeros([2,NJ])\n",
    "init_vol[0,:] = 0.26\n",
    "init_vol[1,:] = 0\n",
    "init_vol = volume_change(coldA,tstep,zincp,init_vol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "# MAIN PROGRAM\n",
    "# ===========\n",
    "\n",
    "def time_step(cold,cprev,tstep,catprop,Znprop):\n",
    "    it = 1\n",
    "    did = False \n",
    "    j = transfer(cold)\n",
    "    for it in range(1,itmax):\n",
    "        \n",
    "        \n",
    "        #Znprop = properties(zincp,coldA,tstep,vol_frac)\n",
    "        dcdx, d2cdx2 = interpolate(cold,h,2)\n",
    "        sma, smb, smd, smg = fillmat2(cold,dcdx,d2cdx2,cprev,tstep,catprop,Znprop)\n",
    "        ABD, G = abdgxy(sma, smb, smd, smg)\n",
    "        delc = band(ABD, G)\n",
    "        delc = delc.reshape((NJ, N))\n",
    "        delc = transpose(delc)\n",
    "        maxerror = amax(abs(delc))\n",
    "        #print(it,',',maxerror)\n",
    "        \n",
    "        cold = cold + delc\n",
    "        if maxerror < tol:\n",
    "            did = True\n",
    "            \n",
    "            print ('Converged in ' +str(it)+ ' steps.')\n",
    "            return cold\n",
    "\n",
    "    if not did:\n",
    "        print ('The program did not converge.')\n",
    "    print(\"code ended\")  \n",
    "    return cold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TIME STEP: 1\n",
      "Anode\n",
      "Converged in 3 steps.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Shreeram\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:25: RuntimeWarning: invalid value encountered in true_divide\n",
      "C:\\Users\\Shreeram\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:28: RuntimeWarning: invalid value encountered in true_divide\n",
      "C:\\Users\\Shreeram\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:31: RuntimeWarning: divide by zero encountered in true_divide\n",
      "C:\\Users\\Shreeram\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:32: RuntimeWarning: divide by zero encountered in true_divide\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TIME STEP: 2\n",
      "Anode\n",
      "Converged in 3 steps.\n",
      "TIME STEP: 3\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 4\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 5\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 6\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 7\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 8\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 9\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 10\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 11\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 12\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 13\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 14\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 15\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 16\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 17\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 18\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 19\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 20\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 21\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 22\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 23\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 24\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 25\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 26\n",
      "Anode\n",
      "Converged in 2 steps.\n",
      "TIME STEP: 27\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 28\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 29\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 30\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 31\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 32\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 33\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 34\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 35\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 36\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 37\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 38\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 39\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 40\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 41\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 42\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 43\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 44\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 45\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 46\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 47\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 48\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 49\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 50\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 51\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 52\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 53\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 54\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 55\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 56\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 57\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 58\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 59\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 60\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 61\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 62\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 63\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 64\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 65\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 66\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 67\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 68\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 69\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 70\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 71\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 72\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 73\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 74\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 75\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 76\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 77\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 78\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 79\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 80\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 81\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 82\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 83\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 84\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 85\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 86\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 87\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 88\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 89\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 90\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 91\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 92\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 93\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 94\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 95\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 96\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 97\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 98\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 99\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 100\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 101\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 102\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 103\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 104\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 105\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 106\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 107\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 108\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 109\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 110\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 111\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 112\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 113\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 114\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 115\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 116\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 117\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 118\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 119\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 120\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 121\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 122\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 123\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 124\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 125\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 126\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 127\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 128\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 129\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 130\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 131\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 132\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 133\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 134\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 135\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 136\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 137\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 138\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 139\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 140\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 141\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 142\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 143\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 144\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 145\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 146\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 147\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 148\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 149\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 150\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 151\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 152\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 153\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 154\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 155\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 156\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 157\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 158\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 159\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 160\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 161\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 162\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 163\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 164\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 165\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 166\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 167\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 168\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 169\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 170\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 171\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 172\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 173\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 174\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 175\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 176\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 177\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 178\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 179\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 180\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 181\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 182\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 183\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 184\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 185\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 186\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 187\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 188\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 189\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 190\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 191\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 192\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 193\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 194\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 195\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 196\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 197\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 198\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 199\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 200\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 201\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 202\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 203\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 204\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 205\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 206\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 207\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 208\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 209\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 210\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 211\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 212\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 213\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 214\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 215\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 216\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 217\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 218\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 219\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 220\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 221\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 222\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 223\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 224\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 225\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 226\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 227\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 228\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 229\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 230\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 231\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 232\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 233\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 234\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 235\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 236\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 237\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 238\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 239\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 240\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 241\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 242\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 243\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 244\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 245\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 246\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 247\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 248\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 249\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 250\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 251\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 252\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 253\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 254\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 255\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 256\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 257\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 258\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 259\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 260\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 261\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 262\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 263\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 264\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 265\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 266\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 267\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 268\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 269\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 270\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 271\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 272\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 273\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 274\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 275\n",
      "Anode\n",
      "Converged in 1 steps.\n",
      "TIME STEP: 276\n",
      "Anode\n",
      "Converged in 1 steps.\n"
     ]
    },
    {
     "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": [
    "for step in range(1,total_steps+1):\n",
    "    \n",
    "    print\n",
    "    print ('TIME STEP:', step)\n",
    "    print ('Anode')\n",
    "    \n",
    "    \n",
    "    \n",
    "    coldA = time_step(coldA,cprevA,tstep,propC,zincp)\n",
    "    zincp = properties(zincp,coldA,tstep)\n",
    "    rate_eq = rate_equation(coldA,tstep,zincp)\n",
    "    vol_chg = volume_change(coldA,tstep,zincp,init_vol)\n",
    "    init_vol = vol_chg\n",
    "    j = transfer(coldA)\n",
    "    \n",
    "    \n",
    "    \n",
    "    junk,right_flux = fluxes(coldA)\n",
    "    propC[0] = epc\n",
    "    propC[3] = coldA[2,NJ-1]\n",
    "    propC[4] = coldA[1,NJ-1]\n",
    "    propC[6] = right_flux\n",
    "    #print(zincp[6,:])\n",
    "    propC = cathode(propC,tstep)\n",
    "    cprevA = coldA\n",
    "    \n",
    "     \n",
    "    #if step ==10 or step == 75 or step == 120 or step == 170 or step == 200 or step == 250 or step == 276:\n",
    "    #if step < 11:   \n",
    "    plt.plot(xs,coldA[3,:],label = int(step*10/60))\n",
    "        #plt.plot(xs,zincp[6,:],label = int(step*10/60))\n",
    "    plt.ylabel('porosity')\n",
    "    plt.xlabel('radius (cm)')\n",
    "        #plt.legend(loc='lower left',shadow=True, ncol=2)\n",
    "        #savefig('porosity', dpi=1200)\n",
    "    \n",
    "    \n",
    "    if (zincp[5,:] <= 0).any()==True:\n",
    "        break    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ===========\n",
    "# PLOT RESULTS\n",
    "# ===========\n",
    "\n",
    "fig,ax = plt.subplots(1,1,figsize=(6, 6))\n",
    "\n",
    "params = {'mathtext.default': 'regular' }\n",
    "rcParams.update(params)\n",
    "\n",
    "\n",
    "xs = linspace(0,ra,NJ)\n",
    "c1 = j\n",
    "c2 = coldA[1,:]\n",
    "c3 = coldA[2,:]\n",
    "c4 = coldA[3,:]\n",
    "c5 = coldA[4,:]\n",
    "c6 = coldA[5,:]\n",
    "ax.plot(xs,c1)\n",
    "ax.plot(xs,c2)\n",
    "ax.plot(xs,c3)\n",
    "ax.plot(xs,c4,'g^')\n",
    "ax.plot(xs,c5)\n",
    "ax.plot(xs,c6)\n",
    "ax.legend(['$i_{2}$','$eta$','$COH$','$ep$','$v$','$CZnOH$'],loc='upper left')\n",
    "ax.set_ylabel('$j\\/(A/cm^{3})$')\n",
    "ax.set_xlabel('$r\\/(cm)$')\n",
    "ax.set_xlim(0, ra)\n",
    "savefig('All_V.png', dpi=300)\n",
    "plt.show()\n",
    "\n",
    "close('all')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "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"
    },
    {
     "data": {
      "text/plain": [
       "0.9300914506257905"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.plot(xs,zincp[5,:],label='ZnOH')\n",
    "#plt.plot(xs,zincp[4,:],label='OHe')\n",
    "plt.xlabel('radius (cm)')\n",
    "plt.ylabel('porosity')\n",
    "plt.legend()\n",
    "#savefig('ep.png', dpi=1200)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}