r

m

Radial distance to rotation axis in centrifuge

$\overline{r}$

m

Average radial distance in centrifuge

r₀

m

Radial reference distance in centrifuge at z = 0 (base of sediment or top of cream)

RGF

-

Relative Gravity Force = acceleration factor in centrifuge with respect to free fall (RGF = 1 in earth’s gravity)

$\text{RGF}=\left|g/g_{grav}\right|$

s

-

Structured fabric phase containing dispersed solids and emulsion droplets

t

s

Time

T

-

Dimensionless time

$T=t/\tau$

v

m/s

Speed

$U\left(\varphi \right)$

-

Dimensionless fluid flow speed

$U\left(\varphi \right)=-\delta {\varphi }^2/\left(1-\varphi \right)$

V

m³/(m²s)

The volume per unit time per unit lateral area

WE

-

whole egg

x

m

Spatial coordinate, often horizontal

z

m

Spatial coordinate, often vertical. Increases with height

Z

m

Horizontal distance from bottom vessel in centrifuge

$Z=r_0-r$

δ

-

Dimensionless number for relative importance of gravity over elasticity in earth’s gravity (RGF = 1) and in centrifuge

$\delta =-\text{RGF}\left(\Delta \rho g_{grav}H/{\epsilon }_0\right){\left(1-{\varphi }_0\right)}^3/{\varphi }_0^4$

ε

N/m²

Elasticity

$\varphi$

-

Porosity, here fractional volume available for fluid

$\varphi ={\varphi }_w$

${\varphi }_s$

-

Volume fraction dispersed phase (solids, air, oil, and structurant)

${\varphi }_w$

-

Porosity = local fractional volume available for fluid

${\varphi }_w+{\varphi }_s=1$

${\varphi }_0$

-

Initial porosity, initial volume fraction available for fluid

μ

Pas

Viscosity of a fluid, μ_w for aqueous phase

p

-

pi

p = 3.141592654

P

-

Dimensionless Pi number

ρ

kg/m³

Density, mass per unit volume; ρ_s for dispersed, ρ_w for fluid

τ

s

Relaxation time

$\tau =\left(\left(1-{\varphi }_0\right)/{\varphi }_0\right)2\mu H^2/\left(k_0{\epsilon }_0\right)$

ω

rad/s

Cyclic frequency

$\omega =2\text{π}f$

ξ

-

Dimensionless vertical distance from bottom of vessel

$\xi =z/H$

Θ

-

Dimensionless height of depleted zone

$\Theta =\Omega /H$

Ω

m

Height of depleted zone

Δρ

kg/m³

Average density difference between dispersed and fluid phase, positive in sedimentation

$\Delta \rho ={\rho }_s-{\rho }_w$