Symbol  Dimension  Description  Formula 
A  m^{2}  Total area, often perpendicular to flow 

D  m  Width of vessel 

D_{s }  m^{2}/s  Coefficient of consolidation  ${D}_{s}={k}_{0}{\epsilon}_{0}/(2\mu )$ 
$D\left(\varphi \right)$  ^{ }  Dimensionless dispersion coefficient  $D\left(\varphi \right)=\left(1\varphi \right)/\varphi $ 
E  N/m^{2}  Young’s elastic modulus for compression 

f  Hz  Frequency 

f    Fluid phase 

g  m^{2}/s  Acceleration of free fall or radial acceleration in centrifuge  g_{grav} or ω^{2}r 
g_{grav}  m^{2}/s  Acceleration of free fall  9.8125 m/s^{2} 
H  m  Height of vessel (along the flow direction) 

k  m^{2}  Permeability 

L  m  Length, often of the caked zone 

m  kg  Mass 

P,p  N/m^{2}  Pressure, p_{w} in fluid, p_{s} in solids phase 

q  m^{3}/(m^{2}s)  Volume displaced per unit time through a unit lateral area 


 Darcy’s law  ${q}_{w}=\left(k/{m}_{w}\right)\text{d}{P}_{w}/\text{d}z$ 
q_{w}_{ }  m^{3}/(m^{2}s)  Darcy speed of fluid phase 

q_{s}_{ }  m^{3}/(m^{2}s)  Darcy speed of dispersed phase 

Q’    Darcy speed of fluid scaled dimensionless  ${Q}^{\prime}={q}_{w}\left(\tau /H\right)\left(1{\varphi}_{0}\right)/{\varphi}_{0}$ 