# Slurry

A slurry is a mixture of solids denser than water suspended in liquid, usually water. The most common use of slurry is as a means of transporting solids, the liquid being a carrier that is pumped on a device such as a centrifugal pump. The size of solid particles may vary from 1 micron up to hundreds of millimeters. The particles may settle below a certain transport velocity and the mixture can behave as a Newtonian or non-Newtonian fluid. Depending on the mixture, the slurry may be abrasive and/or corrosive.

## 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

$\phi _{sl}={\frac {\rho _{s}(\rho _{sl}-\rho _{l})}{\rho _{sl}(\rho _{s}-\rho _{l})}}$

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

$\phi _{sl}={\frac {M_{s}}{M_{sl}}}$

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