Notes

Bioprocess Engineering — Revision sheet

Every formula and key point across this section, in one scroll — for the daily pass, not the first read.

All Very important (3)

1.0

Fluid Mechanics

Reynolds number for stirred tank

Very important

Re = \frac{d_i^2 N_i \rho}{\mu}

$Re$ — Reynolds number (ratio of inertial to viscous forces), dimensionless
$d_i$ — diameter of the impeller, in metres ( $\text{m}$ )
$N_i$ — frequency of the impeller, in reciprocal seconds ( $\text{s}^{-1}$ )
$\rho$ — density of the fluid, in kilograms per cubic metre ( $\text{kg/m}^3$ )
$\mu$ — viscosity, in pascal-seconds ( $\text{Pa} \cdot \text{s}$ )
$Re < 10$ — laminar
$10 \le Re \le 10{,}000$ — transitional
$Re > 10{,}000$ — turbulent

8.0

Ligand Binding and the Scatchard Plot

The Scatchard equation

Very important

\frac{\Theta}{[L]} = \frac{n}{K_d} - \frac{\Theta}{K_d}

$\Theta$ : fractional saturation, dimensionless
$[L]$ : free (unbound) ligand concentration, $\text{M}$
$n$ : total binding sites per protein molecule, dimensionless
$K_d$ : dissociation constant, $\text{M}$

The Scatchard equation

Very important

\frac{r}{[L]} = nK_a - rK_a = K_a(n - r)

$r$ : average ligand molecules bound per protein molecule, dimensionless
$[L]$ : free ligand concentration, $\text{M}$
$n$ : total binding sites per protein molecule, dimensionless
$K_a$ : association constant, $\text{M}^{-1}$