Microbial Growth Curves

OD600: --

Growth Rate μ: -- h⁻¹

Doubling Time: -- h

Substrate: -- g/L

Phase: --

FPS: --

Parameters

μmax 0.5 h⁻¹

Ks (Monod) 0.5 g/L

Initial Biomass X₀ 0.05 g/L

Initial Substrate S₀ 10 g/L

Yield Yx/s 0.5 g/g

Culture Mode

Dilution Rate D 0.2 h⁻¹

Feed Rate 0.5 g/L/h

LagLogStationaryDeath

Governing Equations

Monod Kinetics:
  μ = μmax × S / (Ks + S)

Biomass Growth (Batch):
  dX/dt = μ × X
  dS/dt = -(μ × X) / Yx/s

Fed-Batch:
  dX/dt = μ × X - (F/V) × X
  dS/dt = (F/V) × (Sin - S) - (μ × X) / Yx/s

Continuous (Chemostat):
  dX/dt = (μ - D) × X
  dS/dt = D × (S0 - S) - (μ × X) / Yx/s

Doubling Time:
  td = ln(2) / μ ≈ 0.693 / μ

OD600 conversion: OD600 ≈ 0.3 × X (g/L) + 0.02