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1 | 1 | # ChromoSim |
2 | 2 |
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3 | | -1D ion-exchange chromatography column simulator (mechanistic; multi-species; gradient; FPLC-style outputs) |
| 3 | +1D ion-exchange chromatography column simulator (mechanistic model; multi-species; with gradient; FPLC-style outputs) |
4 | 4 |
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5 | 5 | **ChromoSim** simulates axial convection–dispersion with competitive Langmuir binding. Affinity can be constant (e.g., proteins) or mapped to a per-species property (e.g., surface potential) with salt-dependent screening. Outputs: breakthrough curves, in-column heatmaps, and an FPLC-style trace (mL / pseudo-mAU) with a %B overlay. |
6 | 6 |
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@@ -51,25 +51,16 @@ Edit parameters in **`scripts/main_ev_aex.py`** (or create your own script): |
51 | 51 |
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52 | 52 | ## What the model solves |
53 | 53 |
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54 | | -**Mobile phase for species \(i\):** |
55 | | -$$ |
56 | | -\partial_t C_i \;=\; -u\,\partial_z C_i \;+\; D_{\mathrm{ax}}\,\partial_{zz} C_i |
57 | | -\;-\; \frac{1-\varepsilon}{\varepsilon}\,\partial_t Q_i . |
58 | | -$$ |
| 54 | +**Mobile phase for species i:** |
| 55 | +$$\partial_t C_i = -u \partial_z C_i + D_{\mathrm{ax}} \partial_{zz} C_i - \frac{1-\varepsilon}{\varepsilon} \partial_t Q_i$$ |
59 | 56 |
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60 | 57 | **Wall phase (competitive Langmuir):** |
61 | | -$$ |
62 | | -\partial_t Q_i \;=\; k_{a,i}\,C_i\Big(Q_{\max}-\sum_j Q_j\Big) \;-\; k_{d,i}\,Q_i . |
63 | | -$$ |
| 58 | +$$\partial_t Q_i = k_{a,i} C_i\Big(Q_{\max}-\sum_j Q_j\Big) - k_{d,i}Q_i$$ |
64 | 59 |
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65 | 60 | **Optional affinity map:** |
66 | | -$$ |
67 | | -K_i \;\equiv\; \frac{k_{a,i}}{k_{d,i}} |
68 | | -\;=\; K^\circ \exp\!\big(\gamma\,|P_i|\,f(I)\big). |
69 | | -$$ |
70 | | - |
71 | | -Use constant \(K_i\) by setting \(\gamma=0\). |
| 61 | +$$K_i \equiv \frac{k_{a,i}}{k_{d,i}} = K^\circ \exp\big(\gamma\,|P_i|\,f(I)\big)$$ |
72 | 62 |
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| 63 | +(Use constant $K_i$ by setting $\gamma=0$.) |
73 | 64 |
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74 | 65 | ## Repo layout |
75 | 66 |
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