Symbol

Dimension

Description

Formula

A

m²

Total area, often perpendicular to flow

D

m

Width of vessel

D_s

m²/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/m²

Young’s elastic modulus for compression

f

Hz

Frequency

f

-

Fluid phase

g

m²/s

Acceleration of free fall or radial acceleration in centrifuge

g_grav or -ω²r

g_grav

m²/s

Acceleration of free fall

-9.8125 m/s²

H

m

Height of vessel (along the flow direction)

k

m²

Permeability

L

m

Length, often of the caked zone

m

kg

Mass

P,p

N/m²

Pressure, p_w in fluid, p_s in solids phase

q

m³/(m²s)

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

m³/(m²s)

Darcy speed of fluid phase

q_s

m³/(m²s)

Darcy speed of dispersed phase

Q’

-

Darcy speed of fluid scaled dimensionless

$Q^{\prime }=q_w\left(\tau /H\right)\left(1-{\varphi }_0\right)/{\varphi }_0$