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RemDelaporteMathurin
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Nov 4, 2025
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First pass on the Concentration part.
… into chirag-bcs
RemDelaporteMathurin
requested changes
Feb 23, 2026
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| ## Understanding math behind concentration and flux boundary conditions |
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Since this applies to all BCs (H transport and heat transfer) should this live in an introduction section?
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| ## Recombination and dissociation | ||
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| Hydrogen recombination or dissociation can be modeled with `SurfaceReactionBC`, e.g.: | ||
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| $$ | ||
| \mathrm{H + H} \quad \overset{K_r}{\underset{K_d}{\rightleftharpoons}} \quad \mathrm{H_2} | ||
| $$ | ||
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| ### Mathematical formulation | ||
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| Let: | ||
| - $c_H$ be the surface concentration of atomic hydrogen | ||
| - $P_{H_2}$ the partial pressure of molecular hydrogen | ||
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| The net reaction rate is: | ||
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| $$ | ||
| K = K_r \, c_H^2 - K_d \, P_{H_2} | ||
| $$ | ||
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| The corresponding flux of atomic hydrogen is: | ||
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| $$ | ||
| \mathbf{J}_H \cdot \mathbf{n} = - 2 K | ||
| $$ | ||
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| #### Weak form contribution | ||
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| The weak form contribution of recombination flux is: | ||
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| $$ | ||
| \int_{\Gamma_s} \mathbf{J}_H \cdot \mathbf{n} \, v \, d\Gamma = | ||
| - \int_{\Gamma_s} 2 K \, v \, d\Gamma | ||
| $$ | ||
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| --- | ||
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| ### Modeling recombination and dissociation | ||
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| Recombination and dissociation can also be modeled using `SurfaceReactionBC`, where the forward and backward rates of this reaction correspond to recombination and dissociation, respectively. | ||
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| To model the reaction: | ||
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| $$ \mathrm{H} + \mathrm{H} \rightleftharpoons \mathrm{H_2}$$ | ||
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| where $ \text{Species A} = \text{Species B} = \text{H} $, assign your `reactants` list accordingly: | ||
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| ```{code-cell} ipython3 | ||
| H = F.Species("H") | ||
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| my_recombination_bc = F.SurfaceReactionBC( | ||
| reactant=[A, A], | ||
| gas_pressure=1e5, | ||
| k_r0=1, | ||
| E_kr=0.1, | ||
| k_d0=1e-5, | ||
| E_kd=0.1, | ||
| subdomain=boundary, | ||
| ) | ||
| ``` |
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All of this is redundant with the previous section
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moved recombination and dissociation discussion to under "surface reactions" , I think it may be a helpful snippet for users that are skimming through and looking for that specifically
| figure = plotter.screenshot("concentration.png") | ||
| ``` | ||
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| The results without isotopic exchange show virtually no diffusion for a given inlet concentration, indicating that isotopic exchange helps enchance diffusion! |
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I see the exact same concentration fields
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fixed by using the same colorbar range
…, removed weak formulation discussions)
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Boundary conditions chapter: