Centrifuge simulation

solid + liquor inlets -> cake + filtrate (Sigma-theory sizing)

Governing equations

The exact equations the solver works for a centrifuge — the same math shown in the app's "Theory" panel, not a black box.

$R$

solids recovery to the cake [0..1]

$\dot n_s$

solids molar flow [mol/s]

$\dot n_{liq,ret}$

liquid retained in the cake [mol/s]

$m$

cake moisture fraction

$v_g$

gravitational settling velocity [m/s] (Stokes)

$G$

g-force multiple — the whole point of a centrifuge: it multiplies settling velocity

$g$

gravitational acceleration

$\rho_s, \rho_l$

solid and liquid densities [kg/m³]

$d$

particle diameter [m]

$\mu$

liquid viscosity [Pa·s]

$\Sigma$

sigma factor [m²] — the equivalent settling area used to size/scale machines

$Q_f$

feed volumetric flow [m³/s]

Parameters

solids_recovery [0..1, default 0.98], cake_moisture [0..1, default 0.2] (same split as filter); Sigma-theory sizing: g_factor [default 2000], viscosity [Pa.s, default 1e-3], solid_density [kg/m^3, default 1500], liquid_density [kg/m^3, default 1000], liquid_molar_volume [m^3/mol, default 1.8e-5]

Example flowsheets that use it