Parth Ajmera

Catalytic efficiency

Very important

\text{Catalytic efficiency} = \frac{k_{cat}}{K_M}

$k_{cat}$ — turnover number ( $\text{s}^{-1}$ )
$K_M$ — Michaelis constant ( $\text{mol L}^{-1}$ )

Turnover number (k_cat)

Very important

In notes →

k_{cat} = \frac{V_{max}}{[E]_{total}}

$V_{max}$ — maximum reaction velocity
$[E]_{total}$ — total enzyme concentration

Overall reaction free energy from half-reactions

Very important

In notes →

\Delta G_{rxn} = \Delta G_{donor\,(oxidation)} + \Delta G_{acceptor\,(reduction)}

$\Delta G_{donor}$ — the electron-donor half-reaction, written as an oxidation
$\Delta G_{acceptor}$ — the electron-acceptor half-reaction, written as a reduction

First-order process step response

Very important

In notes →

y(t) = MK_p\left(1-e^{-t/\tau_p}\right)

$M$ — step input magnitude
$K_p$ — process gain
$\tau_p$ — process time constant

Newtonian fluid constitutive law

Very important

In notes →

\tau = \mu\dot\gamma

$\tau$ — shear stress
$\mu$ — viscosity
$\dot\gamma$ — shear rate

Reynolds number

Very important

In notes →

Re = \frac{\rho v D}{\mu}

$\rho$ — fluid density
$v$ — velocity
$D$ — pipe diameter
$\mu$ — viscosity

Equilibrium constant from Gibbs free energy

Very important

In notes →

K_{eq} = e^{-\Delta G/RT}

$\Delta G$ — standard Gibbs free energy change
$R$ — gas constant
$T$ — absolute temperature

Newton's law of cooling

Very important

In notes →

T(t) = T_{env} + (T_0-T_{env})e^{-kt}

$T_{env}$ — ambient/final temperature
$T_0$ — initial temperature
$k$ — cooling rate constant

Monod kinetics with endogenous decay

Very important

In notes →

\mu_{net} = \mu_{max}\frac{S}{K_S+S} - k_d

$\mu_{max}$ — maximum specific growth rate
$K_S$ — Monod (half-saturation) constant
$S$ — limiting substrate concentration
$k_d$ — endogenous decay rate

Mean cell retention time (MCRT)

Very important

In notes →

\theta_c = \frac{V\,X}{Q\,X_e}

$V$ — reactor volume
$X$ — in-reactor biomass concentration
$Q$ — flow rate of the stream leaving the system
$X_e$ — biomass concentration in that leaving stream

First-order thermal death (sterilization design)

Very important

In notes →

N(t) = N_0\,e^{-k_dt}

$N_0$ — initial viable count
$k_d$ — death rate constant
$t$ — time

Zero-order reaction kinetics

Very important

In notes →

C(t) = C_0 - kt, \qquad t_{complete} = \frac{C_0}{k}

$C_0$ — initial concentration
$k$ — zero-order rate constant

Chemostat washout condition

Very important

In notes →

D_{crit} = \mu_{max}\frac{S_0}{K_S+S_0}

$D_{crit}$ — critical (washout) dilution rate
$S_0$ — feed substrate concentration

Superficial vs. interstitial velocity (packed bed)

Very important

In notes →

v_{interstitial} = \frac{v_{superficial}}{\varepsilon}, \qquad v_{superficial}=\frac{Q}{A}

$\varepsilon$ — bed void fraction
$Q$ — volumetric flow rate
$A$ — empty-column cross-sectional area