Slurry

For the settlement in the North West province of South Africa, see Slurry, North West.
A slurry composed of glass beads in silicone oil flowing down an inclined plane

A slurry is a thin sloppy mud or cement or, in extended use, any fluid mixture of a pulverized solid with a liquid (usually water), often used as a convenient way of handling solids in bulk.[1] Slurries behave in some ways like thick fluids, flowing under gravity but are also capable of being pumped if not too thick.

Examples

Examples of slurries include:

Calculations

Determining solids fraction

To determine the percent solids (or solids fraction) of a slurry from the density of the slurry, solids and liquid[7]

$\phi_{sl}=\frac{\rho_{s}(\rho_{sl} - \rho_{l})}{\rho_{sl}(\rho_{s} - \rho_{l})}$

where

$\phi_{sl}$ is the solids fraction of the slurry (state by mass)
$\rho_{s}$ is the solids density
$\rho_{sl}$ is the slurry density
$\rho_{l}$ is the liquid density

In aqueous slurries, as is common in mineral processing, the specific gravity of the species is typically used, and since $SG_{water}$ is taken to be 1, this relation is typically written:

$\phi_{sl}=\frac{\rho_{s}(\rho_{sl} - 1)}{\rho_{sl}(\rho_{s} - 1)}$

even though specific gravity with units tonnes/m^3 (t/m^3) is used instead of the SI density unit, kg/m^3.

Liquid mass from mass fraction of solids

To determine the mass of liquid in a sample given the mass of solids and the mass fraction: By definition

$\phi_{sl}=\frac{M_{s}}{M_{sl}}$*100

therefore

$M_{sl}=\frac{M_{s}}{\phi_{sl}}$

and

$M_{s}+M_{l}=\frac{M_{s}}{\phi_{sl}}$

then

$M_{l}=\frac{M_{s}}{\phi_{sl}}-M_{s}$

and therefore

$M_{l}=\frac{1-\phi_{sl}}{\phi_{sl}}M_{s}$

where

$\phi_{sl}$ is the solids fraction of the slurry
$M_{s}$ is the mass or mass flow of solids in the sample or stream
$M_{sl}$ is the mass or mass flow of slurry in the sample or stream
$M_{l}$ is the mass or mass flow of liquid in the sample or stream

Volumetric fraction from mass fraction

$\phi_{sl,m}=\frac{M_{s}}{M_{sl}}$

Equivalently

$\phi_{sl,v}=\frac{V_{s}}{V_{sl}}$

and in a minerals processing context where the specific gravity of the liquid (water) is taken to be one:

$\phi_{sl,v}=\frac{\frac{M_{s}}{SG_{s}}}{\frac{M_{s}}{SG_{s}}+\frac{M_{l}}{1}}$

So

$\phi_{sl,v}=\frac{M_{s}}{M_{s}+M_{l}SG_{s}}$

and

$\phi_{sl,v}=\frac{1}{1+\frac{M_{l}SG_{s}}{M_{s}}}$

Then combining with the first equation:

$\phi_{sl,v}=\frac{1}{1+\frac{M_{l}SG_{s}}{\phi_{sl,m}M_{s}}\frac{M_{s}}{M_{s}+M_{l}}}$

So

$\phi_{sl,v}=\frac{1}{1+\frac{SG_{s}}{\phi_{sl,m}}\frac{M_{l}}{M_{s}+M_{l}}}$

Then since

$\phi_{sl,m}=\frac{M_{s}}{M_{s}+M_{l}}=1-\frac{M_{l}}{M_{s}+M_{l}}$

we conclude that

$\phi_{sl,v}=\frac{1}{1+SG_{s}(\frac{1}{\phi_{sl,m}}-1)}$

where

$\phi_{sl,v}$ is the solids fraction of the slurry on a volumetric basis
$\phi_{sl,m}$ is the solids fraction of the slurry on a mass basis
$M_{s}$ is the mass or mass flow of solids in the sample or stream
$M_{sl}$ is the mass or mass flow of slurry in the sample or stream
$M_{l}$ is the mass or mass flow of liquid in the sample or stream
$SG_{s}$ is the bulk specific gravity of the solids