TABLE 1

Parameters, values, and references of data used for the model

ParameterSymbolValueUnitSource
Time stepΔt10−3sAd hoc
Spatial stepΔx10−4mConstrained by CFL numerical condition (34)
Grid size, N × NN100
Fluid dynamics viscosityη8.9 × 10−4kg · m−1 · s−161
Bacterial volVb3 × 10−18m3Exptl evidence
Water mass densityρ00.995 × 103kg · m−361
Bacterial mass densityρb1.193 × 103kg · m−357
Cellulose mass densityρc1.5 × 103kg · m−3Ad hoc
Maximal bacterial concnbsat3 × 1014Cells · m−3Exptl evidence
Initial concn of bacteriab02 × 1010Cells · m−3Exptl settings
Diffusion coefficient of bacteriaDb10−10m2 · s−158
Diffusion coefficient of celluloseDc5 × 10−11m2 · s−1Ad hoc
Diffusion coefficient of oxygenDo10−9m2 · s−159
Diffusion coefficient of pyoverdinDp3 × 10−10m2 · s−1Exptl evidence (data not shown)
Initial oxygen concno01.5 × 1023Molecules · m−3
Initial normalized pyoverdin concnp03.36 × 10−5Exptl fit
Initial normalized cellulose concnc010−8Ad hoc
Production of pyoverdinβ−11.22 × 10−4sExptl fit
Production of celluloseα−110−3sAd hoc
Growth rate of bacteriaδ0.53h−1Exptl fit
Oxygen consumption/bacterium/sγ106Molecules · cell−1 · s−149
Vol of cellulose produced/bacteriumV* = 10 · Vb3 × 10−17m360
Minimal bacterial concn for cellulose productionb* = bsat/31014Cells · m−3Exptl evidence
Boundary condition of oxygen at topo01.5 × 1023Molecules · m−349
Acceleration of gravityg9.81m · s−2
Minimal oxygen concn for cellulose and pyoverdin productiono*o0 × 10−1Molecules · m−3Ad hoc