TABLE 1.
Parameters, values, and references of data used for the model
| Parameter | Symbol | Value | Unit | Source |
|---|---|---|---|---|
| Time step | Δt | 10−3 | s | Ad hoc |
| Spatial step | Δx | 10−4 | m | Constrained by CFL numerical condition (34) |
| Grid size, N × N | N | 100 | ||
| Fluid dynamics viscosity | η | 8.9 × 10−4 | kg · m−1 · s−1 | 61 |
| Bacterial vol | Vb | 3 × 10−18 | m3 | Exptl evidence |
| Water mass density | ρ0 | 0.995 × 103 | kg · m−3 | 61 |
| Bacterial mass density | ρb | 1.193 × 103 | kg · m−3 | 57 |
| Cellulose mass density | ρc | 1.5 × 103 | kg · m−3 | Ad hoc |
| Maximal bacterial concn | bsat | 3 × 1014 | Cells · m−3 | Exptl evidence |
| Initial concn of bacteria | b0 | 2 × 1010 | Cells · m−3 | Exptl settings |
| Diffusion coefficient of bacteria | Db | 10−10 | m2 · s−1 | 58 |
| Diffusion coefficient of cellulose | Dc | 5 × 10−11 | m2 · s−1 | Ad hoc |
| Diffusion coefficient of oxygen | Do | 10−9 | m2 · s−1 | 59 |
| Diffusion coefficient of pyoverdin | Dp | 3 × 10−10 | m2 · s−1 | Exptl evidence (data not shown) |
| Initial oxygen concn | o0 | 1.5 × 1023 | Molecules · m−3 | |
| Initial normalized pyoverdin concn | p0 | 3.36 × 10−5 | Exptl fit | |
| Initial normalized cellulose concn | c0 | 10−8 | Ad hoc | |
| Production of pyoverdin | β−1 | 1.22 × 10−4 | s | Exptl fit |
| Production of cellulose | α−1 | 10−3 | s | Ad hoc |
| Growth rate of bacteria | δ | 0.53 | h−1 | Exptl fit |
| Oxygen consumption/bacterium/s | γ | 106 | Molecules · cell−1 · s−1 | 49 |
| Vol of cellulose produced/bacterium | V* = 10 · Vb | 3 × 10−17 | m3 | 60 |
| Minimal bacterial concn for cellulose production | b* = bsat/3 | 1014 | Cells · m−3 | Exptl evidence |
| Boundary condition of oxygen at top | o0 | 1.5 × 1023 | Molecules · m−3 | 49 |
| Acceleration of gravity | g | 9.81 | m · s−2 | |
| Minimal oxygen concn for cellulose and pyoverdin production | o* | o0 × 10−1 | Molecules · m−3 | Ad hoc |