# Slurry

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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. 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:

• Cement slurry, a mixture of cement, water, and assorted dry and liquid additives used in the petroleum and other industries
• Soil/cement slurry, also called Controlled Low-Strength Material (CLSM), flowable fill, controlled density fill, flowable mortar, plastic soil-cement, K-Krete, and other names
• A mixture of thickening agent, oxidizers, and water used to form a gel explosive{{ safesubst:#invoke:Unsubst||date=__DATE__ |\$B=

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## 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

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