前述の概要で、流加培養の利点は培養液中の流加基質濃度を任意に制御できること、と述べた。このことを簡単な数式で以下に示す。 今、ただ1種類の基質Sを流加し、ある微生物を好気培養して、二酸化炭素のみが生成物であるという最も単純な流加培養を考える。培養液量はほぼ変わらないと仮定すると、ある時間 t におけるSの微分物質収支式は、
ただし、s は培養液中の流加基質濃度[g/L]、t は培養時間[h]、fvol は流加液の体積流量[L/h]、sin は流加液中の流加基質濃度[g/L]、v はバイオリアクター内の培養液量[L]、μ は微生物の比増殖速度[h-1]、Yx/s は菌体収率[g-DCW/g-substrate]、qCO2 は二酸化炭素生成速度[h-1]、YCO2/s はS由来の二酸化炭素生成収率[g-CO2/g-substrate]、x は菌体濃度[g-DCW/L]である。右辺第1項は単位培養液当たりのSの流加流量、第2項(2つの細分項から成り立っている)は x から見たSの消費速度である。
もし、f が高くて右辺第1項>右辺第2項ならば、ds/dt > 0 となり s は増加し、逆に f が低くて第1項<第2項ならば、ds/dt < 0 となり s は減少する。そして、f が適切で丁度、第1項=第2項であれば、ds/dt = 0 となり s は変わらない(一定である)。よって、f を人間の手で、あるいは自動的に、変動させることによって、s を人為的に任意に変えることができるのである。
なお、流量(flow rate)とは単位時間当たりの流体の移動量であり、国際単位系では体積流量[m3/s](上式では、国際単位系でなく、[L/h]としている)、質量流量[kg/s]、モル流量[mol/s]があり、流速(flow velocity)とは区別されねばならない。流速とは、文字通り、流体の流れの速度(速さ)であり、単位は例えば[m/h]である(国際単位系では[m/s])。
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