Pass R(x) directly for graded electrodes

CHANGELOG.md

@@ -31,6 +31,7 @@
 
 ## Breaking changes
 
+-    The parameters "Positive/Negative particle distribution in x" and "Positive/Negative surface area per unit volume distribution in x" have been deprecated. Instead, users can provide "Positive/Negative particle radius [m]" and "Positive/Negative surface area per unit volume [m-1]" directly as functions of through-cell position (x [m]) ([#1237](https://github.com/pybamm-team/PyBaMM/pull/1237)) 
 
 # [v0.2.4](https://github.com/pybamm-team/PyBaMM/tree/v0.2.4) - 2020-09-07
 

examples/notebooks/compare-ecker-data.ipynb

@@ -103,8 +103,8 @@
     "    var.x_n: int(parameter_values.evaluate(model.param.L_n / 1e-6)),\n",
     "    var.x_s: int(parameter_values.evaluate(model.param.L_s / 1e-6)),\n",
     "    var.x_p: int(parameter_values.evaluate(model.param.L_p / 1e-6)),\n",
-    "    var.r_n: int(parameter_values.evaluate(model.param.R_n / 1e-7)),\n",
-    "    var.r_p: int(parameter_values.evaluate(model.param.R_p / 1e-7)),\n",
+    "    var.r_n: int(parameter_values.evaluate(model.param.R_n_typ / 1e-7)),\n",
+    "    var.r_p: int(parameter_values.evaluate(model.param.R_p_typ / 1e-7)),\n",
     "}"
    ]
   },
@@ -221,13 +221,6 @@
     "\n",
     "[2] Richardson, Giles, et. al. \"Generalised single particle models for high-rate operation of graded lithium-ion electrodes: Systematic derivation and validation.\" Electrochemica Acta 339 (2020): 135862"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {

examples/notebooks/models/DFN.ipynb

@@ -71,7 +71,7 @@
     "\n",
     "####  Concentration in the electrode active material:\n",
     "\\begin{gather}\n",
-    "N_{\\text{s,k}}\\big|_{r_{\\text{k}}=0} = 0, \\quad \\text{k} \\in \\text{n, p}, \\quad \\ \\ - \\frac{a_{\\text{k}}\\gamma_{\\text{k}}}{\\mathcal{C}_{\\text{k}}} N_{\\text{s,k}}\\big|_{r_{\\text{k}}=1} = j_{\\text{k}}, \\quad \\text{k} \\in \\text{n, p}.\n",
+    "N_{\\text{s,k}}\\big|_{r_{\\text{k}}=0} = 0, \\quad \\text{k} \\in \\text{n, p}, \\quad \\ \\ - \\frac{a_{R, \\text{k}}\\gamma_{\\text{k}}}{\\mathcal{C}_{\\text{k}}} N_{\\text{s,k}}\\big|_{r_{\\text{k}}=1} = j_{\\text{k}}, \\quad \\text{k} \\in \\text{n, p}.\n",
     "\\end{gather}\n",
     "\n",
     "#### Reference potential:\n",
@@ -203,7 +203,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "b72126bb294743c38f4aa5069787b9b6",
+       "model_id": "eceebcfd564d4b53bf56bda5abf066ff",
        "version_major": 2,
        "version_minor": 0
       },
@@ -240,7 +240,7 @@
     "|$\\mathcal{C}_{\\text{k}}$   | $\\tau_{\\text{k}}^*/\\tau_{\\text{d}}^*$   | Ratio of solid diffusion and discharge timescales |\n",
     "|$\\mathcal{C}_{\\text{e}}$   |$\\tau_{\\text{e}}^*/\\tau_{\\text{d}}^*$    |Ratio of electrolyte transport and discharge timescales|\n",
     "|$\\mathcal{C}_{\\text{r,k}}$ |$\\tau_{\\text{r,k}}^*/\\tau_{\\text{d}}^*$  |Ratio of reaction and discharge timescales|\n",
-    "|$a_{\\text{k}}$             |$a_{\\text{k}}^* R_{\\text{k}}^*$          | Product of particle radius and surface area to volume ratio|\n",
+    "|$a_{R, \\text{k}}$             |$a_{\\text{k}}^* R_{\\text{k}}^*$          | Product of particle radius and surface area to volume ratio|\n",
     "|$\\gamma_{\\text{k}}$        |$c_{\\text{k,max}}^*/c_{\\text{n,max}}^*$  |Ratio of maximum lithium concentrations in solid|\n",
     "|$\\gamma_{\\text{e}}$        |$c_{\\text{e,typ}}^*/c_{\\text{n,max}}^*$  |Ratio of maximum lithium concentration in the negative electrode solid and typical electrolyte concentration|\n",
     "\n",

examples/notebooks/models/SPMe.ipynb

@@ -33,7 +33,7 @@
     "\\mathcal{C}_{\\text{k}} \\frac{\\partial c_{\\text{s,k}}}{\\partial t} &= -\\frac{1}{r_{\\text{k}}^2} \\frac{\\partial}{\\partial r_{\\text{k}}} \\left(r_{\\text{k}}^2 N_{\\text{s,k}}\\right), \\\\\n",
     "N_{\\text{s,k}} &= -D_{\\text{s,k}}(c_{\\text{s,k}}) \\frac{\\partial c_{\\text{s,k}}}{\\partial r_{\\text{k}}}, \\quad \\text{k} \\in \\text{n, p}, \\end{align}\n",
     "$$\n",
-    "N_{\\text{s,k}}\\big|_{r_{\\text{k}}=0} = 0, \\quad \\text{k} \\in \\text{n, p}, \\quad \\ \\ - \\frac{a_{\\text{k}}\\gamma_{\\text{k}}}{\\mathcal{C}_{\\text{k}}} N_{\\text{s,k}}\\big|_{r_{\\text{k}}=1} = \n",
+    "N_{\\text{s,k}}\\big|_{r_{\\text{k}}=0} = 0, \\quad \\text{k} \\in \\text{n, p}, \\quad \\ \\ - \\frac{a_{R, \\text{k}}\\gamma_{\\text{k}}}{\\mathcal{C}_{\\text{k}}} N_{\\text{s,k}}\\big|_{r_{\\text{k}}=1} = \n",
     "\\begin{cases}\n",
     "\t\t  \\frac{I}{L_{\\text{n}}}, \\quad &\\text{k}=\\text{n}, \\\\ \n",
     "\t\t  -\\frac{I}{L_{\\text{p}}}, \\quad &\\text{k}=\\text{p}, \n",
@@ -155,7 +155,7 @@
     {
      "data": {
       "text/plain": [
-       "<pybamm.solvers.solution.Solution at 0x7f69f08dd2e8>"
+       "<pybamm.solvers.solution.Solution at 0x7f5cd829b4a8>"
       ]
      },
      "execution_count": 3,
@@ -183,7 +183,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "47ee8d1901bd4bdd87fba1d347da16ec",
+       "model_id": "5f19fdea006d4f22ae77a584c87d5eb3",
        "version_major": 2,
        "version_minor": 0
       },
@@ -218,7 +218,7 @@
     "|$\\mathcal{C}_{\\text{k}}$   | $\\tau_{\\text{k}}^*/\\tau_{\\text{d}}^*$   | Ratio of solid diffusion and discharge timescales |\n",
     "|$\\mathcal{C}_{\\text{e}}$   |$\\tau_{\\text{e}}^*/\\tau_{\\text{d}}^*$    |Ratio of electrolyte transport and discharge timescales|\n",
     "|$\\mathcal{C}_{\\text{r,k}}$ |$\\tau_{\\text{r,k}}^*/\\tau_{\\text{d}}^*$  |Ratio of reaction and discharge timescales|\n",
-    "|$a_{\\text{k}}$             |$a_{\\text{k}}^* R_{\\text{k}}^*$          | Product of particle radius and surface area to volume ratio|\n",
+    "|$a_{R, \\text{k}}$             |$a_{\\text{k}}^* R_{\\text{k}}^*$          | Product of particle radius and surface area to volume ratio|\n",
     "|$\\gamma_{\\text{k}}$        |$c_{\\text{k,max}}^*/c_{\\text{n,max}}^*$  |Ratio of maximum lithium concentrations in solid|\n",
     "|$\\gamma_{\\text{e}}$        |$c_{\\text{e,typ}}^*/c_{\\text{n,max}}^*$  |Ratio of maximum lithium concentration in the negative electrode solid and typical electrolyte concentration|\n",
     "\n",

examples/notebooks/models/pouch-cell-model.ipynb

@@ -91,7 +91,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/home/user/Documents/PyBaMM/pybamm/models/full_battery_models/base_battery_model.py:361: UserWarning: 1+1D Thermal models are only valid if both tabs are placed at the top of the cell.\n",
+      "/home/user/Documents/PyBaMM/pybamm/models/full_battery_models/base_battery_model.py:375: UserWarning: 1+1D Thermal models are only valid if both tabs are placed at the top of the cell.\n",
       "  \"1+1D Thermal models are only valid if both tabs are \"\n"
      ]
     }
@@ -339,7 +339,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We then add the solution object from the 1+1D model. This is just so that PyBaMM uses the same times behind the scenes when dealing with COMSOL model and the reduced-order models: the variables in `comsol_model.variables` are functions of time only that return the (interpolated in space) COMSOL solution."
+    "We then add the solution object from the 1+1D model. This is just so that PyBaMM uses the same (dimensionless) times behind the scenes when dealing with COMSOL model and the reduced-order models: the variables in `comsol_model.variables` are functions of time only that return the (interpolated in space) COMSOL solution. We also need to update the time and length scales for the COMSOL model so that any dimensionless variables are scaled correctly. "
    ]
   },
   {

examples/scripts/compare_lithium_ion_particle_distribution.py

@@ -16,17 +16,22 @@
 params = [models[0].default_parameter_values, models[1].default_parameter_values]
 
 
-def negative_distribution(x):
-    return 1 + 2 * x / models[1].param.l_n
+def negative_radius(x):
+    "Negative particle radius as a function of through-cell position (x_n [m])"
+    R_n_0 = params[0]["Negative particle radius [m]"]
+    grading = 1 + 2 * x / models[1].param.L_n
+    return grading * R_n_0
 
 
-def positive_distribution(x):
-    return 1 + 2 * (1 - x) / models[1].param.l_p
+def positive_radius(x):
+    "Positive particle radius as a function of through-cell position (x_p [m])"
+    R_p_0 = params[0]["Positive particle radius [m]"]
+    grading = 1 + 2 * (models[1].param.L_x - x) / models[1].param.L_p
+    return grading * R_p_0
 
 
-params[1]["Negative particle distribution in x"] = negative_distribution
-params[1]["Positive particle distribution in x"] = positive_distribution
-
+params[1]["Negative particle radius [m]"] = negative_radius
+params[1]["Positive particle radius [m]"] = positive_radius
 
 # set up and solve simulations
 t_eval = np.linspace(0, 3600, 100)
@@ -45,8 +50,8 @@ def positive_distribution(x):
     "Electrolyte potential [V]",
     "Positive electrode potential [V]",
     "Terminal voltage [V]",
-    "Negative particle distribution in x",
-    "Positive particle distribution in x",
+    "Negative particle radius",
+    "Positive particle radius",
 ]
 
 # plot

examples/scripts/compare_particle_shape.py

@@ -27,8 +27,6 @@
             {
                 "Negative electrode surface area to volume ratio [m-1]": 170000,
                 "Positive electrode surface area to volume ratio [m-1]": 200000,
-                "Negative surface area per unit volume distribution in x": 1,
-                "Positive surface area per unit volume distribution in x": 1,
             },
             check_already_exists=False,
         )

pybamm/input/parameters/lithium-ion/anodes/graphite_Chen2020/parameters.csv

@@ -11,7 +11,6 @@ Negative electrode OCP [V],[data]graphite_LGM50_ocp_Chen2020,Chen 2020,
 Negative electrode porosity,0.25,Chen 2020,
 Negative electrode active material volume fraction,0.75,Chen 2020,
 Negative particle radius [m],5.86E-6,Chen 2020,
-Negative particle distribution in x,1,default,
 Negative electrode Bruggeman coefficient (electrolyte),1.5,Chen 2020,theoretical
 Negative electrode Bruggeman coefficient (electrode),1.5,default,
 ,,,

pybamm/input/parameters/lithium-ion/anodes/graphite_Ecker2015/parameters.csv

@@ -13,7 +13,6 @@ Negative electrode OCP [V],[function]graphite_ocp_Ecker2015_function,,
 Negative electrode porosity,0.329,,
 Negative electrode active material volume fraction, 0.372403,,
 Negative particle radius [m],1.37E-05,,
-Negative particle distribution in x,1,,
 Negative electrode Bruggeman coefficient (electrolyte),1.6372789338386007,Solve for permeability factor B=0.162=eps^b,
 Negative electrode Bruggeman coefficient (electrode),0,No Bruggeman correction to the solid conductivity,
 ,,,

pybamm/input/parameters/lithium-ion/anodes/graphite_Kim2011/parameters.csv

@@ -11,7 +11,6 @@ Negative electrode OCP [V],[function]graphite_ocp_Kim2011,
 Negative electrode porosity,0.4,,
 Negative electrode active material volume fraction,0.51,,
 Negative particle radius [m],5.083E-7,,
-Negative particle distribution in x,1,,
 Negative electrode Bruggeman coefficient (electrolyte),2,,
 Negative electrode Bruggeman coefficient (electrode),2,,
 ,,,

pybamm/input/parameters/lithium-ion/anodes/graphite_Ramadass2004/parameters.csv

@@ -11,7 +11,6 @@ Negative electrode OCP [V],[function]graphite_ocp_Ramadass2004,
 Negative electrode porosity,0.485,Ramadass,electrolyte volume fraction
 Negative electrode active material volume fraction,0.49,Ramadass,
 Negative particle radius [m],2e-06,Ramadass,
-Negative particle distribution in x,1,,
 Negative electrode Bruggeman coefficient (electrolyte),4,Guess,
 Negative electrode Bruggeman coefficient (electrode),4,Ramadass,
 ,,,

pybamm/input/parameters/lithium-ion/anodes/graphite_UMBL_Mohtat2020/parameters.csv

@@ -12,7 +12,6 @@ Negative electrode OCP [V],[function]graphite_ocp_PeymanMPM,Peyman MPM,
 Negative electrode porosity,0.3,Peyman MPM,
 Negative electrode active material volume fraction,0.61,Peyman MPM,rest is binder
 Negative particle radius [m],2.5E-06,Peyman MPM,
-Negative particle distribution in x,1,,
 Negative electrode Bruggeman coefficient (electrode),1.5,Peyman MPM,
 Negative electrode Bruggeman coefficient (electrolyte),1.5,Peyman MPM,
 Negative electrode tortuosity, 0.16,

pybamm/input/parameters/lithium-ion/anodes/graphite_mcmb2528_Marquis2019/parameters.csv

@@ -11,7 +11,6 @@ Negative electrode OCP [V],[function]graphite_mcmb2528_ocp_Dualfoil1998,
 Negative electrode porosity,0.3,Scott Moura FastDFN,electrolyte volume fraction
 Negative electrode active material volume fraction,0.6,,
 Negative particle radius [m],1E-05,Scott Moura FastDFN,
-Negative particle distribution in x,1,,
 Negative electrode Bruggeman coefficient (electrolyte),1.5,Scott Moura FastDFN,
 Negative electrode Bruggeman coefficient (electrode),1.5,Scott Moura FastDFN,
 ,,,

pybamm/input/parameters/lithium-ion/cathodes/LFP_Prada2013/parameters.csv

@@ -11,7 +11,6 @@ Positive electrode OCP [V],[function]LFP_ocp_ashfar2017,,
 Positive electrode porosity,0.12728395,Calculation minimized to Severson,
 Positive electrode active material volume fraction,0.28485556,Calculation minimized to Severson,
 Positive particle radius [m],1.00E-08,Calculation minimized to Severson,
-Positive particle distribution in x,1,,
 Positive electrode Bruggeman coefficient (electrode),1.5,,
 Positive electrode Bruggeman coefficient (electrolyte),1.5,,
 ,,,

pybamm/input/parameters/lithium-ion/cathodes/LiNiCoO2_Ecker2015/parameters.csv

@@ -13,7 +13,6 @@ Positive electrode OCP [V],[function]nco_ocp_Ecker2015_function,,
 Positive electrode porosity,0.296,,
 Positive electrode active material volume fraction, 0.40832,,
 Positive particle radius [m],6.5E-06,,
-Positive particle distribution in x,1,,
 Positive electrode Bruggeman coefficient (electrolyte),1.5442267190786427,Solve for permeability factor B=0.1526=eps^b,
 Positive electrode Bruggeman coefficient (electrode),0,No Bruggeman correction to solid conductivity,
 Positive electrode exchange-current density [A.m-2],[function]nco_electrolyte_exchange_current_density_Ecker2015,,

pybamm/input/parameters/lithium-ion/cathodes/NMC_UMBL_Mohtat2020/parameters.csv

@@ -11,7 +11,6 @@ Positive electrode OCP [V],[function]NMC_ocp_PeymanMPM,,
 Positive electrode porosity,0.3,Peyman MPM,
 Positive electrode active material volume fraction,0.445,Peyman MPM,rest is binder
 Positive particle radius [m],3.5E-06,Peyman MPM,
-Positive particle distribution in x,1,,
 Positive electrode Bruggeman coefficient (electrode),1.5,Peyman MPM,
 Positive electrode Bruggeman coefficient (electrolyte),1.5,Peyman MPM,
 Positive electrode tortuosity,0.16,

pybamm/input/parameters/lithium-ion/cathodes/lico2_Marquis2019/parameters.csv

@@ -11,7 +11,6 @@ Positive electrode OCP [V],[function]lico2_ocp_Dualfoil1998,,
 Positive electrode porosity,0.3,Scott Moura FastDFN,electrolyte volume fraction
 Positive electrode active material volume fraction,0.5,,
 Positive particle radius [m],1E-05,Scott Moura FastDFN,
-Positive particle distribution in x,1,,
 Positive electrode Bruggeman coefficient (electrolyte),1.5,Scott Moura FastDFN,
 Positive electrode Bruggeman coefficient (electrode),1.5,Scott Moura FastDFN,
 ,,,

pybamm/input/parameters/lithium-ion/cathodes/lico2_Ramadass2004/parameters.csv

@@ -11,7 +11,6 @@ Positive electrode OCP [V],[function]lico2_ocp_Ramadass2004,,
 Positive electrode porosity,0.385,Ramadass,electrolyte volume fraction
 Positive electrode active material volume fraction,0.59,Ramadass,
 Positive particle radius [m],2e-06,Ramadass,
-Positive particle distribution in x,1,,
 Positive electrode Bruggeman coefficient (electrolyte),4,Ramadass,
 Positive electrode Bruggeman coefficient (electrode),4,Ramadass,
 ,,,

pybamm/input/parameters/lithium-ion/cathodes/nca_Kim2011/parameters.csv

@@ -11,7 +11,6 @@ Positive electrode OCP [V],[data]nca_ocp_Kim2011_data,
 Positive electrode porosity,0.4,,
 Positive electrode active material volume fraction,0.41,,
 Positive particle radius [m],1.633E-6,,
-Positive particle distribution in x,1,,
 Positive electrode Bruggeman coefficient (electrolyte),2,,
 Positive electrode Bruggeman coefficient (electrode),2,,
 ,,,

pybamm/input/parameters/lithium-ion/cathodes/nmc_Chen2020/parameters.csv

@@ -11,7 +11,6 @@ Positive electrode OCP [V],[data]nmc_LGM50_ocp_Chen2020,Chen 2020,
 Positive electrode porosity,0.335,Chen 2020,
 Positive electrode active material volume fraction,0.665,Chen 2020,
 Positive particle radius [m],5.22E-6,Chen 2020,
-Positive particle distribution in x,1,default,
 Positive electrode Bruggeman coefficient (electrolyte),1.5,Chen 2020,theoretical
 Positive electrode Bruggeman coefficient (electrode),1.5,default,
 ,,,

pybamm/models/full_battery_models/base_battery_model.py

@@ -801,9 +801,7 @@ def set_voltage_variables(self):
         # Battery-wide variables
         V_dim = self.variables["Terminal voltage [V]"]
         eta_e_av = self.variables.get("X-averaged electrolyte ohmic losses", 0)
-        eta_c_av = self.variables.get(
-            "X-averaged concentration overpotential", 0
-        )
+        eta_c_av = self.variables.get("X-averaged concentration overpotential", 0)
         eta_e_av_dim = self.variables.get("X-averaged electrolyte ohmic losses [V]", 0)
         eta_c_av_dim = self.variables.get(
             "X-averaged concentration overpotential [V]", 0
@@ -844,8 +842,13 @@ def set_voltage_variables(self):
         i_cc_dim = self.variables["Current collector current density [A.m-2]"]
         # Gather all overpotentials
         v_ecm = -(eta_ocv + eta_r_av + eta_c_av + eta_e_av + delta_phi_s_av)
-        v_ecm_dim = -(eta_ocv_dim + eta_r_av_dim + eta_c_av_dim + eta_e_av_dim +
-                      delta_phi_s_av_dim)
+        v_ecm_dim = -(
+            eta_ocv_dim
+            + eta_r_av_dim
+            + eta_c_av_dim
+            + eta_e_av_dim
+            + delta_phi_s_av_dim
+        )
         # Current collector area for turning resistivity into resistance
         A_cc = self.param.A_cc
         self.variables.update(

pybamm/models/full_battery_models/lithium_ion/base_lithium_ion_model.py

@@ -25,8 +25,8 @@ def __init__(self, options=None, name="Unnamed lithium-ion model", build=False):
             "negative electrode": self.param.L_x,
             "separator": self.param.L_x,
             "positive electrode": self.param.L_x,
-            "negative particle": self.param.R_n,
-            "positive particle": self.param.R_p,
+            "negative particle": self.param.R_n_typ,
+            "positive particle": self.param.R_p_typ,
             "current collector y": self.param.L_y,
             "current collector z": self.param.L_z,
         }
@@ -40,9 +40,9 @@ def set_standard_output_variables(self):
         self.variables.update(
             {
                 "r_n": var.r_n,
-                "r_n [m]": var.r_n * self.param.R_n,
+                "r_n [m]": var.r_n * self.param.R_n_typ,
                 "r_p": var.r_p,
-                "r_p [m]": var.r_p * self.param.R_p,
+                "r_p [m]": var.r_p * self.param.R_p_typ,
             }
         )
 

pybamm/models/full_battery_models/lithium_ion/basic_dfn.py

@@ -167,14 +167,18 @@ def __init__(self, name="Doyle-Fuller-Newman model"):
         self.boundary_conditions[c_s_n] = {
             "left": (pybamm.Scalar(0), "Neumann"),
             "right": (
-                -param.C_n * j_n / param.a_n / param.D_n(c_s_surf_n, T),
+                -param.C_n * j_n / param.a_R_n / param.D_n(c_s_surf_n, T),
                 "Neumann",
             ),
         }
         self.boundary_conditions[c_s_p] = {
             "left": (pybamm.Scalar(0), "Neumann"),
             "right": (
-                -param.C_p * j_p / param.a_p / param.gamma_p / param.D_p(c_s_surf_p, T),
+                -param.C_p
+                * j_p
+                / param.a_R_p
+                / param.gamma_p
+                / param.D_p(c_s_surf_p, T),
                 "Neumann",
             ),
         }

pybamm/models/full_battery_models/lithium_ion/basic_dfn_half_cell.py

@@ -32,11 +32,7 @@ class BasicDFNHalfCell(BaseModel):
     **Extends:** :class:`pybamm.lithium_ion.BaseModel`
     """
 
-    def __init__(
-        self,
-        name="Doyle-Fuller-Newman half cell model",
-        options=None,
-    ):
+    def __init__(self, name="Doyle-Fuller-Newman half cell model", options=None):
         super().__init__({}, name)
         pybamm.citations.register("marquis2019asymptotic")
         # `param` is a class containing all the relevant parameters and functions for
@@ -237,7 +233,7 @@ def __init__(
             self.boundary_conditions[c_s_n] = {
                 "left": (pybamm.Scalar(0), "Neumann"),
                 "right": (
-                    -param.C_n * j_n / param.a_n / param.D_n(c_s_surf_n, T),
+                    -param.C_n * j_n / param.a_R_n / param.D_n(c_s_surf_n, T),
                     "Neumann",
                 ),
             }
@@ -273,7 +269,7 @@ def __init__(
                 "right": (
                     -param.C_p
                     * j_p
-                    / param.a_p
+                    / param.a_R_p
                     / param.gamma_p
                     / param.D_p(c_s_surf_p, T),
                     "Neumann",