r

m

Radial distance to rotation axis in centrifuge

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)

RGF = | g / g g r a v |

s

-

Structured fabric phase containing dispersed solids and emulsion droplets

t

s

Time

T

-

Dimensionless time

T = t / τ

v

m/s

Speed

U ( ϕ )

-

Dimensionless fluid flow speed

U ( ϕ ) = δ ϕ 2 / ( 1 ϕ )

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

δ = RGF ( Δ ρ g g r a v H / ε 0 ) ( 1 ϕ 0 ) 3 / ϕ 0 4

ε

N/m2

Elasticity

ϕ

-

Porosity, here fractional volume available for fluid

ϕ = ϕ w

ϕ s

-

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

ϕ w

-

Porosity = local fractional volume available for fluid

ϕ w + ϕ s = 1

ϕ 0

-

Initial porosity, initial volume fraction available for fluid

μ

Pas

Viscosity of a fluid, μw for aqueous phase

p

-

pi

p = 3.141592654

P

-

Dimensionless Pi number

ρ

kg/m3

Density, mass per unit volume; ρs for dispersed, ρw for fluid

τ

s

Relaxation time

τ = ( ( 1 ϕ 0 ) / ϕ 0 ) 2 μ H 2 / ( k 0 ε 0 )

ω

rad/s

Cyclic frequency

ω = 2 π f

ξ

-

Dimensionless vertical distance from bottom of vessel

ξ = z / H

Θ

-

Dimensionless height of depleted zone

Θ = Ω / H

Ω

m

Height of depleted zone

Δρ

kg/m3

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

Δ ρ = ρ s ρ w