diff --git a/doc/content/theory_manual.md b/doc/content/theory_manual.md
index 001996ff..0e70dcd5 100644
--- a/doc/content/theory_manual.md
+++ b/doc/content/theory_manual.md
@@ -110,7 +110,7 @@ At surfaces, atoms and molecules go through dissociations and recombinations, wh
 There are two main dissociation/recombination conditions that TMAP7 offered, namely `ratedep` and `surfdep`.
 These cases are both reproduced in TMAP8 in a more general way, and are detailed below:
 
-### Ratedep conditions
+### Dissociation and recombination reaction kinetics - Ratedep conditions
 
 !style halign=left
 The `ratedep` condition applies when dissociation and recombination reaction kinetics govern the surface reactions [!cite](ambrosek2008verification).
@@ -145,7 +145,7 @@ For example, [ver-1ia](ver-1ia.md) considers the following reaction and model:
 
 !include /ver-1ia.md start=When two species react on a surface to form a third end=This case uses equal starting pressures
 
-### Surfdep conditions
+### Surface energy-driven kinetics - Surfdep conditions
 
 !style halign=left
 The `surfdep` condition applies when recombination is limited by surface energy.
@@ -169,7 +169,7 @@ For example, [ver-1ic](ver-1ic.md) considers the following reaction and model:
 
 !include /ver-1ic.md start=The problem considers the reaction between end=This case uses equal starting pressures
 
-## Surface Equilibrium
+### Surface Equilibrium - Lawdep conditions
 
 !style halign=left
 Both conditions described capture dissociation and recombination reactions, including their kinetics.
diff --git a/doc/content/verification_and_validation/val-2d.md b/doc/content/verification_and_validation/val-2d.md
index 46648e4e..e86f558e 100644
--- a/doc/content/verification_and_validation/val-2d.md
+++ b/doc/content/verification_and_validation/val-2d.md
@@ -102,7 +102,7 @@ The pressures on the upstream and downstream sides are close to vacuum pressures
 C = 0.
 \end{equation}
 
-Due to the high thermal conductivity in Tungsten, the model simplifies the thermal diffusion as a instantaneous process to increase the model efficiency. The temperature inside the Tungsten sample is consistent with the temperature on surface of Tungsten sample. The temperatures is 300 K during implantation, and the temperature after implantation on the upstream and downstream sides are defined as:
+Due to the high thermal conductivity in Tungsten, the model simplifies the thermal diffusion as a instantaneous process to increase the model efficiency. The temperature inside the Tungsten sample is consistent with the temperature on the surface of Tungsten sample. The temperatures is 300 K during implantation, and the temperature after implantation on the upstream and downstream sides are defined as:
 
 \begin{equation} \label{eq:temperature}
 T =
diff --git a/doc/content/verification_and_validation/val-2e.md b/doc/content/verification_and_validation/val-2e.md
index 56855c3e..e2b74502 100644
--- a/doc/content/verification_and_validation/val-2e.md
+++ b/doc/content/verification_and_validation/val-2e.md
@@ -87,7 +87,7 @@ C_i = K_s P_{Ij}^{n},
 
 where $K_s$ is the solubility of hydrogen isotope in the membrane, and $n$ is the exponent for the relation of pressure and concentration.
 
-However, for the kinetics of surface reactions to be captured, the boundary conditions is set as
+However, for the kinetics of surface reactions to be captured, the boundary conditions are set as
 
 \begin{equation} \label{eq:recombination}
 J_{ij} = 2 A (K_r C_i^2 - K_d P_{Ij}),
@@ -118,7 +118,7 @@ $T$ are the temperature.
 
 ## Case and Model Parameters
 
-The pressure history of deuterium on the enclosure 5 for first three simulations (val-2ea, val-2eb, and val-2ec) is presented in [val-2e_abc_pressure_history], as shown in [val-2e_comparison_pressure_history]. The initial pressures on other enclosures are presented in [val-2e_abc_pressure_initial].
+The pressure history of deuterium in enclosure 5 for the first three simulations (val-2ea, val-2eb, and val-2ec) is presented in [val-2e_abc_pressure_history], as shown in [val-2e_comparison_pressure_history]. The initial pressures on other enclosures are presented in [val-2e_abc_pressure_initial].
 
 !table id=val-2e_abc_pressure_history caption=Values of deuterium pressure on enclosure 5 during simulations val-2ea, val-2eb, and val-2ec [!citep](ambrosek2008verification).
 | time (s)      | Pressure $P_{D_2,5}$ (Pa)      |
@@ -152,7 +152,7 @@ The pressure history of deuterium on the enclosure 5 for first three simulations
 | $P_{D_2,3}$ | Deuterium pressure in enclosure 3    | 1 $\times 10^{-6}$                                          | Pa                    |
 | $P_{D_2,4}$ | Deuterium pressure in enclosure 4    | 1 $\times 10^{-10}$                                         | Pa                    |
 
-The pressure history of D$_2$ on the enclosure 5 for next two simulations (val-2ed and val-2ee) is presented in [val-2e_de_pressure_history], as shown in [val-2e_comparison_mixture_pressure_history]. The initial pressures on other enclosures are presented in [val-2e_de_pressure_initial].
+The pressure history of D$_2$ in enclosure 5 for the next two simulations (val-2ed and val-2ee) is presented in [val-2e_de_pressure_history], as shown in [val-2e_comparison_mixture_pressure_history]. The initial pressures on other enclosures are presented in [val-2e_de_pressure_initial].
 
 !table id=val-2e_de_pressure_history caption=Values of deuterium pressure on enclosure 5 during simulations val-2ed and val-2ee [!citep](ambrosek2008verification).
 | time (s)      | Pressure $P_{D_2,5}$ (Pa)      |
@@ -192,7 +192,7 @@ The pressure history of D$_2$ on the enclosure 5 for next two simulations (val-2
 
 
 !alert note title=Updates of times and initial pressures in val-2ee to be consistent with val-2ed.
-In [!cite](ambrosek2008verification), the times and initial pressures in val-2ee are different from the values used in val-2ed. However, we use the same values from val-2ed in val-2ee for consistency. The trivial difference in times and initial pressures do not impact the final results.
+In [!cite](ambrosek2008verification), the times and initial pressures in val-2ee are different from the values used in val-2ed. However, we use the same values from val-2ed in val-2ee for consistency. The trivial differences in times and initial pressures do not impact the final results.
 
 Other case and model parameters used in TMAP8 are listed in [val-2e_parameters]:
 
@@ -223,7 +223,7 @@ Other case and model parameters used in TMAP8 are listed in [val-2e_parameters]:
 | $K_{d,HD}$ | HD dissociation coefficient | 2.1897$\times 10^{22} / \sqrt{3T}$     | molecular/m$^2$/Pa              | [!cite](ambrosek2008verification) |
 
 !alert warning title=Typo in [!cite](ambrosek2008verification)
-There are typos on the equations for hydrogen diffusivity, recombination and dissociation coefficients in the input files from TMAP7 in val-2ed and val-2ee. The correct values are provided in [val-2e_parameters] and used in TMAP8. The pre-factor for hydrogen diffusivity used in TMAP8 is 3.728 $\times 10^{-4}$ m$^2$/s instead of 2.636 $\times 10^{-4}$ m$^2$/s as used in the input file published in [!cite](ambrosek2008verification). The activation energy for recombination coefficient used in TMAP8 is -11836 K (making the term in the exponential positive) instead of the 11836 K value used in the input file in [!cite](ambrosek2008verification) - note that the value listed in Eq. (71) in [!cite](ambrosek2008verification) is correct. The values of the species molecular weight in amu are also updated from the input files shown in [!cite](ambrosek2008verification).
+There are typos in the equations for hydrogen diffusivity, recombination and dissociation coefficients in the input files from TMAP7 in val-2ed and val-2ee. The correct values are provided in [val-2e_parameters] and used in TMAP8. The pre-factor for hydrogen diffusivity used in TMAP8 is 3.728 $\times 10^{-4}$ m$^2$/s instead of 2.636 $\times 10^{-4}$ m$^2$/s as used in the input file published in [!cite](ambrosek2008verification). The activation energy for recombination coefficient used in TMAP8 is -11836 K (making the term in the exponential positive) instead of the 11836 K value used in the input file in [!cite](ambrosek2008verification) - note that the value listed in Eq. (71) in [!cite](ambrosek2008verification) is correct. The values of the species molecular weight in amu are also updated from the input files shown in [!cite](ambrosek2008verification).
 
 !alert warning title=Solubility values for val-2ea, val-2eb, val-2ec differ from those for val-2ed, val-2ee
 To achieve a lower RMSPE in [val-2e_comparison_diffusion], the solubility values for val-2ea, val-2eb, and val-2ec were taken from the simulation input files in [!cite](ambrosek2008verification), rather than using the values provided in the documentation in [!cite](ambrosek2008verification).
diff --git a/doc/content/verification_and_validation/ver-1dc.md b/doc/content/verification_and_validation/ver-1dc.md
index d79fbb78..788e52db 100644
--- a/doc/content/verification_and_validation/ver-1dc.md
+++ b/doc/content/verification_and_validation/ver-1dc.md
@@ -18,8 +18,8 @@ and, for $i=1$, $i=2$, and $i=3$:
     \frac{dC_{T_i}}{dt} = \alpha_t^i  \frac {C_{T_i}^{empty} C_M } {(N \cdot \text{trap\_per\_free})} - \alpha_r^i C_{T_i},
 \end{equation}
 and
-\begin{equation} \label{eqn:trapping_empty}
-    C_{T_i}^{empty} = (C_{{T_i}0} \cdot N - \text{trap\_per\_free} \cdot C_{T_i}  ) ,
+\begin{equation}  \label{eqn:trapping_empty}
+    C_{T_i}^{empty} = C_{{T_i}0} \cdot N - \text{trap\_per\_free} \cdot C_{T_i} ,
 \end{equation}
 where $C_M$ is the concentrations of the mobile, $C_{T_i}$ is the trapped species in trap $i$, $D$ is the diffusivity of the mobile species, $\alpha_t^i$ and $\alpha_r^i$ are the trapping and release rate coefficients for trap $i$, $\text{trap\_per\_free}$ is a factor scaling $C_{T_i}$ to be closer to $C_M$ for better numerical convergence, $C_{{T_i}0}$ is the fraction of host sites $i$ that can contribute to trapping, $C_{T_i}^{empty}$ is the concentration of empty trapping sites, and $N$ is the host density.
 
@@ -33,7 +33,7 @@ where
 
 $\lambda$ = lattice parameter
 
-$\nu$ = Debye frequency ($\approx$ $10^{13} \; s^{-1}$)
+$\nu$ = Debye frequency ($\approx$ $10^{13}$; s$^{-1}$)
 
 $\rho$ = trapping site fraction
 
@@ -62,7 +62,7 @@ Three traps that are relatively weak are assumed to be active in a slab. The tra
 \label{eqn:Jp}
     J_p = \frac{C_0 D}{l} \left\{ 1 + 2 \sum_{m=1}^{\infty} \left[ (-1)^m \exp \left( -m^2 \frac{t}{2 \; \tau_{b_e}} \right) \right] \right\},
 \end{equation}
-where $C_0$ is the steady dissolved gas concentration at the upstream (x = 0) side, $l$ is the thickness of the slab, $D$ is the diffusivity of the gas through the material, and $\tau_{b_e}$, the breakthrough time, is defined as
+where $C_0$ is the steady dissolved gas concentration at the upstream ($x =$ 0) side, $l$ is the thickness of the slab, $D$ is the diffusivity of the gas through the material, and $\tau_{b_e}$, the breakthrough time, is defined as
 
 \begin{equation}
 \label{eqn:tau_be}
diff --git a/doc/content/verification_and_validation/ver-1dd.md b/doc/content/verification_and_validation/ver-1dd.md
index 9eddabd5..9007bb92 100644
--- a/doc/content/verification_and_validation/ver-1dd.md
+++ b/doc/content/verification_and_validation/ver-1dd.md
@@ -22,7 +22,7 @@ where $C_M$ is the concentrations of the mobile, $D$ is the diffusivity of the m
 \label{eqn:Jp}
     J_p = \frac{C_0 D}{l} \left\{ 1 + 2 \sum_{m=1}^{\infty} \left[ (-1)^m \exp \left( -m^2 \frac{t}{2 \; \tau_{b_e}} \right) \right] \right\},
 \end{equation}
-where $C_0$ is the steady dissolved gas concentration at the upstream (x = 0) side, $l$ is the thickness of the slab, $D$ is the diffusivity of the gas through the material, and $\tau_{b_e}$, the breakthrough time, is defined as
+where $C_0$ is the steady dissolved gas concentration at the upstream ($x =$ 0) side, $l$ is the thickness of the slab, $D$ is the diffusivity of the gas through the material, and $\tau_{b_e}$, the breakthrough time, is defined as
 
 \begin{equation}
 \label{eqn:tau_be}
diff --git a/doc/content/verification_and_validation/ver-1fc.md b/doc/content/verification_and_validation/ver-1fc.md
index 79b358c4..be7ac322 100644
--- a/doc/content/verification_and_validation/ver-1fc.md
+++ b/doc/content/verification_and_validation/ver-1fc.md
@@ -4,16 +4,16 @@
 
 ## General Case Description
 
-This third heat transfer problem is taken from [!cite](ambrosek2008verification) and builds on the capabilities verified in [ver-1fa](ver-1fa.md) and [ver-1fb](ver-1fb.md). 
+This third heat transfer problem is taken from [!cite](ambrosek2008verification) and builds on the capabilities verified in [ver-1fa](ver-1fa.md) and [ver-1fb](ver-1fb.md).
 The configuration is the same as in [ver-1fb](ver-1fb.md), except that, the current case is in a composite structure with constant surface temperature. This case is simulated in [/ver-1fc.i] with both transient and steady state solutions.
 
-The composite is a 40 cm thick layer of Copper (Cu) followed by a 40 cm layer of iron (Fe) ([!citep](ambrosek2008verification)). The temperature of both layers is initially 0 K, but at time t = 0, the outside face of the Cu is held at 600 K while the outside face of the Fe is maintained at 0 K.
-The thermal conductivities of Cu and Fe are set to 401 W/m/K and 80.2 W/m/K, respectively. The TMAP7 documentation does not specify the materials' density $\rho$ or the specific heat $C_p$, but the TMAP7 input file lists $\rho C_p = 3.4392 \times 10^6$ J$\cdot$m$^{-3}\cdot$K$^{-1}$ for Cu and $3.5179 \times 10^6$ J$\cdot$m$^{-3}\cdot$K$^{-1}$ for Fe [!citep](ambrosek2008verification). TMAP8 uses $\rho = 8960$ kg/m$^{3}$ and $C_p =  383.8$ J$\cdot$kg$^{-1}\cdot$K$^{-1}$ for Cu and $\rho = 7870$ kg/m$^{3}$ and $C_p = 447.0$ J$\cdot$kg$^{-1}\cdot$K$^{-1}$ for Fe. The densities are from [!cite](Haynes2015), and the specific heat capacities are calculated to match the $\rho C_p$ values from TMAP7 in [!cite](ambrosek2008verification), which closely match values from [!cite](Haynes2015) ($C_p =  385$ J$\cdot$kg$^{-1}\cdot$K$^{-1}$ for Cu and $C_p =  449$ J$\cdot$kg$^{-1}\cdot$K$^{-1}$ for Fe).
+The composite is a 40 cm thick layer of Copper (Cu) followed by a 40 cm layer of iron (Fe) ([!cite](ambrosek2008verification)). The temperature of both layers is initially 0 K, but at time $t = 0$ s, the outside face of the Cu is held at 600 K while the outside face of the Fe is maintained at 0 K.
+The thermal conductivities of Cu and Fe are set to 401 W/m/K and 80.2 W/m/K, respectively. The TMAP7 documentation does not specify the materials' density $\rho$ or the specific heat $C_p$, but the TMAP7 input file lists $\rho C_p = 3.4392 \times 10^6$ J$\cdot$m$^{-3}\cdot$K$^{-1}$ for Cu and $3.5179 \times 10^6$ J$\cdot$m$^{-3}\cdot$K$^{-1}$ for Fe ([!cite](ambrosek2008verification)). TMAP8 uses $\rho = 8960$ kg/m$^{3}$ and $C_p =  383.8$ J$\cdot$kg$^{-1}\cdot$K$^{-1}$ for Cu and $\rho = 7870$ kg/m$^{3}$ and $C_p = 447.0$ J$\cdot$kg$^{-1}\cdot$K$^{-1}$ for Fe. The densities are from [!cite](Haynes2015), and the specific heat capacities are calculated to match the $\rho C_p$ values from TMAP7 in [!cite](ambrosek2008verification), which closely match values from [!cite](Haynes2015) ($C_p =  385$ J$\cdot$kg$^{-1}\cdot$K$^{-1}$ for Cu and $C_p =  449$ J$\cdot$kg$^{-1}\cdot$K$^{-1}$ for Fe).
 
 This case provides both a verification (comparison against an analytical solution) and a benchmarking (code-to-code comparison) exercise. The steady state solution (called ver-1fcs in [!cite](ambrosek2008verification)) is compared against an analytical solution, and the transient solution is compared against ABAQUS. ABAQUS is a finite element analysis (FEA) program that has been validated for both transient and steady state solutions in heat transfer modeling applications. The ABAQUS code was setup and run by R. G. Ambrosek and presented in [!cite](ambrosek2008verification).
 
 !alert warning title=Typo in [!cite](ambrosek2008verification) - confusion between ABAQUS and TMAP7 results
-In [!cite](ambrosek2008verification), Table 11 for TMAP7 and ABAQUS transient results and Table 13 for TMAP7 and ABAQUS steady-state results are identical, even though they should be different. Given the nature of the data, it corresponds to transient conditions and has been used as such for comparison below. As a result, no ABAQUS and TMAP7 data was used in the steady state case, only TMAP8 predictions and the analytical solution.
+In [!cite](ambrosek2008verification), Table 11 for TMAP7 and ABAQUS transient results and Table 13 for TMAP7 and ABAQUS steady-state results are identical, even though they should be different. Given the nature of the data, it corresponds to transient conditions and has been used as such for comparison below. As a result, no ABAQUS and TMAP7 data was used in the steady-state case, only TMAP8 predictions and the analytical solution.
 Another issue is that the column labels for ABAQUS and TMAP7 are reversed in Table 11 and Table 13, casting doubt on which results correspond to ABAQUS and which to TMAP7. In this benchmarking exercise, we therefore refer to these results as `ABAQUS or TMAP7 (1)` and `ABAQUS or TMAP7 (2)`. Since they are close, we still consider the benchmarking exercise successful.
 
 ## Steady State solution and results
@@ -38,8 +38,8 @@ At steady state, the flux in and out of any section of the slab are equal. The t
 
 The interface temperature at steady state is therefore equal to $T_I = 500$ K. The temperature profile for conduction in steady state, with constant physical properties, is linear. The temperature profile of A and B can therefore be found through linear interpolation.
 
-With TMAP8, the steady state solution can be obtained in different ways: by using the [steady state solve](source/executioners/Steady.md) or by running a [transient simulation](source/executioners/Transient.md) until steady state is reached. 
-[!cite](ambrosek2008verification) indicates that the steady state solution was obtained by running the transient solution until $t=10,000$ s, which is what is reproduced with TMAP8 here. 
+With TMAP8, the steady state solution can be obtained in different ways: by using the [steady state solve](source/executioners/Steady.md) or by running a [transient simulation](source/executioners/Transient.md) until steady state is reached.
+[!cite](ambrosek2008verification) indicates that the steady state solution was obtained by running the transient solution until $t=10,000$ s, which is what is reproduced with TMAP8 here.
 TMAP8 predictions were found to be identical to the analytical solution with a root mean square percentage error (RMSPE) of 0.23 %, as shown in [ver-1fc_comparison_temperature_steady_state].
 
 !media comparison_ver-1fc.py
@@ -52,8 +52,8 @@ TMAP8 predictions were found to be identical to the analytical solution with a r
 
 For the transient case, TMAP8 predictions are compared against ABAQUS predictions from [!cite](ambrosek2008verification). This is therefore a benchmarking case.
 
-The transient solution was compared in two ways: where time, $t$, is held constant and where distance, $x$, through the structure is held constant. 
-The constant time comparison between ABAQUS and TMAP8 was made at time $t = 150$ s. 
+The transient solution was compared in two ways: where time, $t$, is held constant and where distance, $x$, through the structure is held constant.
+The constant time comparison between ABAQUS and TMAP8 was made at time $t = 150$ s.
 The constant time values are shown in [ver-1fc_comparison_temperature_transient_t150], and the comparison is satisfactory.
 
 !media comparison_ver-1fc.py
diff --git a/doc/content/verification_and_validation/ver-1fd.md b/doc/content/verification_and_validation/ver-1fd.md
index 763f099f..4b023eb7 100644
--- a/doc/content/verification_and_validation/ver-1fd.md
+++ b/doc/content/verification_and_validation/ver-1fd.md
@@ -4,9 +4,9 @@
 
 ## General Case Description
 
-The fourth heat transfer problem taken from [!cite](ambrosek2008verification) builds on the capabilities verified in [ver-1fa](ver-1fa.md), [ver-1fb](ver-1fb.md), and [ver-1fc](ver-1fc.md). The configuration is the same as in [ver-1fb](ver-1fb.md), except that, the current case has a convection boundary. This case is simulated in [/ver-1fd.i]
+The fourth heat transfer problem taken from [!cite](ambrosek2008verification) builds on the capabilities verified in [ver-1fa](ver-1fa.md), [ver-1fb](ver-1fb.md), and [ver-1fc](ver-1fc.md). The configuration is the same as in [ver-1fb](ver-1fb.md), except that, the current case has a convection boundary. This case is simulated in [/ver-1fd.i].
 
-The case focuses on the heating of a semi-infinite slab by convection at the boundary. The slab is initially configured with a constant temperature of 100 K throughout the slab. A convection boundary is activated at the surface from time $t = 0$ s. The convection temperature is in the enclosure is $T_{\infty} = 500$ K. In the slab, the conduction coefficient is $h = 200$ W, the thermal conductivity is $k = 801$ W/m/K, and the thermal diffusivity is $\alpha = 1.17 \times 10^{-4}$ m$^2$/s.
+The case focuses on the heating of a semi-infinite slab by convection at the boundary. The slab is initially configured with a constant temperature of 100 K throughout the slab. A convection boundary is activated at the surface from time $t = 0$ s. The convection temperature in the enclosure is $T_{\infty} = 500$ K. In the slab, the conduction coefficient is $h = 200$ W, the thermal conductivity is $k = 801$ W/m/K, and the thermal diffusivity is $\alpha = 1.17 \times 10^{-4}$ m$^2$/s.
 
 ## Analytical solution
 
@@ -21,15 +21,15 @@ where $T_i = 100$ K is the initial temperature, $T_{\infty} = 500$ K is the temp
 \end{equation}
 is the thermal diffusivity. The volumetric specific heat is defined as $\rho C_p = 3.439 \times 10^6$ J/m$^3$/K, which gives us $\alpha \approx 1.17 \times 10^{-4}$ m$^2$/s.
 
-Note that the simulated length of the semi-infinite slab is not explicitely specified in [!cite](ambrosek2008verification). In TMAP8, a length of $l=100$ cm with a zero-flux boundary condition at the end was found to be sufficient to match the analytical solution (i.e., the temperature at the desired position $x = 5$ cm is not affected by the boundary condition at position $l$), as shown in [ver-1fd_comparison_convective_heating].
+Note that the simulated length of the semi-infinite slab is not explicitly specified in [!cite](ambrosek2008verification). In TMAP8, a length of $l=100$ cm with a zero-flux boundary condition at the end was found to be sufficient to match the analytical solution (i.e., the temperature at the desired position $x = 5$ cm is not affected by the boundary condition at position $l$), as shown in [ver-1fd_comparison_convective_heating].
 
 !alert warning title=Typo in [!cite](ambrosek2008verification)
-In [!cite](ambrosek2008verification), the value of $k = 801$ W/m/K is provided, whereas the input file lists $k = 401$ W/m/K. In TMAP8, we have decided to use $k = 401$ W/m/K since it provides the same results as those shown in Figure 9 in [!cite](ambrosek2008verification), and provides the appropriate value for $\alpha$. Moreover, [!cite](ambrosek2008verification) lists $\alpha = 1.17 \times 10^{-4}$ m$^2$/s in the documentation, but the input file lists $\rho C_p = 3.439 \times 10^6$ instead of $\alpha$. TMAP8 assumes a density and specific heat value to match $\rho C_p = 3.439 \times 10^6$ to reproduce TMAP7's input file rather than documentation.
+In [!cite](ambrosek2008verification), the value of $k = 801$ W/m/K is provided, whereas the input file lists $k = 401$ W/m/K. In TMAP8, we have decided to use $k = 401$ W/m/K since it provides the same results as those shown in Figure 9 in [!cite](ambrosek2008verification), and provides the appropriate value for $\alpha$. Moreover, [!cite](ambrosek2008verification) lists $\alpha = 1.17 \times 10^{-4}$ m$^2$/s in the documentation, but the input file lists $\rho C_p = 3.439 \times 10^6$ instead of $\alpha$. TMAP8 assumes a density and specific heat value to match $\rho C_p = 3.439 \times 10^6$ to reproduce TMAP7's input file rather than its documentation.
 
 ## Results
 
-The comparison between TMAP8 predictions and the analytical solution is performed at depth $x = 5$ cm. 
-These results are shown in [ver-1fd_comparison_convective_heating]. 
+The comparison between TMAP8 predictions and the analytical solution is performed at depth $x = 5$ cm.
+These results are shown in [ver-1fd_comparison_convective_heating].
 They show great agreement between TMAP8 and the analytical solution with a root mean square percentage error of RMSPE = 0.29 %.
 
 !media comparison_ver-1fd.py
diff --git a/doc/content/verification_and_validation/ver-1gc.md b/doc/content/verification_and_validation/ver-1gc.md
index 0b1fd1b1..402b6a0f 100644
--- a/doc/content/verification_and_validation/ver-1gc.md
+++ b/doc/content/verification_and_validation/ver-1gc.md
@@ -45,7 +45,7 @@ where $t$ is the time in s, $c_{A0} = 2.415 \times 10^{14}$ atoms/m$^3$ is the i
 
 
 The concentration of $C$ was found by applying a mass balance over the system in [!cite](ambrosek2008verification). From the
-stoichiometry of this reaction it was found that
+stoichiometry of this reaction, it was found that
 \begin{equation} \label{eq:chemical_reaction_solution_C}
 c_C(t) = c_{A0} - c_A(t) - c_B(t).
 \end{equation}
diff --git a/doc/content/verification_and_validation/ver-1hb.md b/doc/content/verification_and_validation/ver-1hb.md
index e77e9457..3fe664a9 100644
--- a/doc/content/verification_and_validation/ver-1hb.md
+++ b/doc/content/verification_and_validation/ver-1hb.md
@@ -20,7 +20,7 @@ and for gas $D_2$ are given by
 \end{equation}
 where $Q$ is the volumetric flow rate (m$^3 \cdot$s$^{-1}$), $V$ is the volume (m$^3$), $P^i_j$ is the pressure in enclosure $i$ of gas species $j$ ($j$ = $T_2$ or $D_2$).
 
-We solve these time evolution equations for the T$_2$ and D$_2$ pressures in the two enclosures using TMAP8 with $t$ the time and with the initial condition set to $P^1_{T_2} = P^2_{D_2} = 1$ Pa, and $P^2_{T_2} = P^1_{D_2} = 0$ Pa. We use $V = 1$ m$^3$ and $Q = 0.1$ m$^3$s$^-1$.
+We solve these time evolution equations for the T$_2$ and D$_2$ pressures in the two enclosures using TMAP8 with $t$ the time and with the initial condition set to $P^1_{T_2} = P^2_{D_2} = 1$ Pa, and $P^2_{T_2} = P^1_{D_2} = 0$ Pa. We use $V = 1$ m$^3$ and $Q = 0.1$ m$^3\cdot $s$^{-1}$.
 
 ## Analytical solution
 
diff --git a/doc/content/verification_and_validation/ver-1if.md b/doc/content/verification_and_validation/ver-1if.md
index 3cfebd05..607eb4ca 100644
--- a/doc/content/verification_and_validation/ver-1if.md
+++ b/doc/content/verification_and_validation/ver-1if.md
@@ -12,7 +12,7 @@ This verification problem is taken from [!cite](ambrosek2008verification) and bu
 
 ## Analytical solution
 
-Similar with [ver-1ie](ver-1ie.md), the governing equation becomes
+Similar to [ver-1ie](ver-1ie.md), the governing equation becomes
 
 \begin{equation}
 \label{eq:lawdep:equation_p_ab_final}
diff --git a/doc/content/verification_and_validation/ver-1ja.md b/doc/content/verification_and_validation/ver-1ja.md
index 826d602d..b5d15e02 100644
--- a/doc/content/verification_and_validation/ver-1ja.md
+++ b/doc/content/verification_and_validation/ver-1ja.md
@@ -30,7 +30,7 @@ and
 where $t$ is the time in seconds, concentrations are in atoms/m$^3$, and $k= 0.693/t_{1/2}$ is the decay rate constant in 1/s.
 
 !alert warning title=TMAP8 uses different model parameters than TMAP7
-The initial tritium concentration in TMAP7 was defined as $C_T^0 = 1.5$ atoms/m$^3$. To use a more realistic values, TMAP8 uses $C_T^0 = 1.5 \times 10^{5}$ atoms/m$^3$.
+The initial tritium concentration in TMAP7 was defined as $C_T^0 = 1.5$ atoms/m$^3$. To use more realistic values, TMAP8 uses $C_T^0 = 1.5 \times 10^{5}$ atoms/m$^3$.
 Moreover, $k$ is defined as $k=0.693/t_{1/2} \approx 1.78199 \times 10^{-9}$ 1/s instead of $1.78241 \times 10^{-9}$ 1/s to be fully consistent with the half-life value (assuming 365.25 days in a year).
 
 ## Analytical Solution
diff --git a/doc/content/verification_and_validation/ver-1ka.md b/doc/content/verification_and_validation/ver-1ka.md
index 2755d595..6442fa51 100644
--- a/doc/content/verification_and_validation/ver-1ka.md
+++ b/doc/content/verification_and_validation/ver-1ka.md
@@ -16,7 +16,7 @@ The rise in pressure of T$_2$ molecules in the first enclosure can be monitored
 \end{equation}
 
 where $S$ represents the volumetric T$_2$ source rate, $V$ is the volume of the enclosure, $k$ is the Boltzmann constant, and $T$ is the temperature of the enclosure.
-In this case, $S$ is set to 10$^{20}$ molecules/m$^{-3}$/s, $V = 1$ m$^3$, and the temperature of the enclosure is constant at $T = 500$ K.
+In this case, $S$ is set to 10$^{20}$ molecules/m$^{3}$/s, $V = 1$ m$^3$, and the temperature of the enclosure is constant at $T = 500$ K.
 
 ## Analytical Solution
 
@@ -35,7 +35,7 @@ Comparison of the TMAP8 results and the analytical solution is shown in
        image_name=ver-1ka_comparison_time.png
        style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto
        id=ver-1ka_comparison_time
-       caption=Comparison of T$_2$ partial pressure in an enclosure with no loss pathways as function of time calculated through TMAP8 and analytically. TMAP8 matches the analytical solution.
+       caption=Comparison of T$_2$ partial pressure in an enclosure with no loss pathways as a function of time calculated through TMAP8 and analytically. TMAP8 matches the analytical solution.
 
 ## Input files
 
diff --git a/doc/content/verification_and_validation/ver-1kc-2.md b/doc/content/verification_and_validation/ver-1kc-2.md
index 74dedaf0..b14881ae 100644
--- a/doc/content/verification_and_validation/ver-1kc-2.md
+++ b/doc/content/verification_and_validation/ver-1kc-2.md
@@ -91,7 +91,7 @@ As shown in [ver-1kc-2_mass_conservation_k10], mass is conserved between the two
        image_name=ver-1kc-2_comparison_time_k10.png
        style=width:50%;margin-bottom:2%;margin-left:auto;margin-right:auto
        id=ver-1kc-2_comparison_time_k10
-       caption=Evolution of species concentration over time governed by Sieverts' law with $K = 10/\sqrt{RT}$ and $\eta = \sqrt{2K_1/K_2}$.
+       caption=Evolution of species pressure over time governed by Sieverts' law with $K = 10/\sqrt{RT}$ and $\eta = \sqrt{2K_1/K_2}$.
 
 !media comparison_ver-1kc-2.py
        image_name=ver-1kc-2_equilibrium_constant_k10.png