Table 2.

List of equations and solutions for Logistic‐Monod growth in CSTR culture

Equations and steady state solutions for Logistic‐Monod growth in CSTR culture
$$\frac{dX}{dt}=\mu X-DX=0$$ (11)
$$\frac{dS}{dt}=D(S_F-S)-\frac{\mu X}{Y_{\text{x/s}}}=0$$ (12)
$$S=\frac{K_{S}D}{{\mu }_m-D}$$ (13)
$$X=Y_{\text{x/s}}\left(\left(,S_F-\frac{K_{S}D}{{\mu }_m-D},\right)\right)$$ (14)
$$S=\frac{D{X}_m-X_m{\mu }_m+S_F{Y}_{\text{x/s}}{\mu }_m}{Y_{\text{x/s}}{\mu }_m}$$ (15)
$$X=\frac{X_m{\mu }_m-D{X}_m}{{\mu }_m}$$ (16)
$$S=\frac{\sqrt{{\left(\left(,\left(D-{\mu }_m\right)X_m+S_F{Y}_{\text{x/s}}{\mu }_m,\right)\right)}^2+4K_{S}D{X}_m{Y}_{\text{x/s}}{\mu }_m}-X_m{\mu }_m+D{X}_m+S_F{Y}_{\text{x/s}}{\mu }_m}{2Y_{\text{x/s}}{\mu }_m}$$ (17)
$$X=-\frac{\sqrt{{\left(\left(,\left(D-{\mu }_m\right)X_m+S_F{Y}_{\text{x/s}}{\mu }_m,\right)\right)}^2+4K_{S}D{X}_m{Y}_{\text{x/s}}{\mu }_m}-X_m{\mu }_m+D{X}_m-S_F{Y}_{\text{x/s}}{\mu }_m}{2{\mu }_m}$$ (18)

Abbreviation: CSTR, continuous stirred tank reactor.