Slurry

A slurry composed of glass beads in silicone oil flowing down an inclined plane Potato starch slurry

A slurry is a mixture of denser solids suspended in liquid, usually water. The most common use of slurry is as a means of transporting solids or separating minerals, 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 micrometre up to hundreds of millimetres. The particles may settle below a certain transport velocity and the mixture can behave like 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

ϕ s l = ρ s ( ρ s l − ρ l ) ρ s l ( ρ s − ρ l ) {\displaystyle \phi _{sl}={\frac {\rho _{s}(\rho _{sl}-\rho _{l})}{\rho _{sl}(\rho _{s}-\rho _{l})}}}

where

ϕ s l {\displaystyle \phi _{sl}} is the solids fraction of the slurry (state by mass) ρ s {\displaystyle \rho _{s}} is the solids density ρ s l {\displaystyle \rho _{sl}} is the slurry density ρ l {\displaystyle \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 specific gravity of water is taken to be 1, this relation is typically written:

ϕ s l = ρ s ( ρ s l − 1 ) ρ s l ( ρ s − 1 ) {\displaystyle \phi _{sl}={\frac {\rho _{s}(\rho _{sl}-1)}{\rho _{sl}(\rho _{s}-1)}}}

even though specific gravity with units tonnes/m3 (t/m3) is used instead of the SI density unit, kg/m3.

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

ϕ s l = M s M s l {\displaystyle \phi _{sl}={\frac {M_{s}}{M_{sl}}}}

therefore

M s l = M s ϕ s l {\displaystyle M_{sl}={\frac {M_{s}}{\phi _{sl}}}}

and

M s + M l = M s ϕ s l {\displaystyle M_{s}+M_{l}={\frac {M_{s}}{\phi _{sl}}}}

then

M l = M s ϕ s l − M s {\displaystyle M_{l}={\frac {M_{s}}{\phi _{sl}}}-M_{s}}

and therefore

M l = 1 − ϕ s l ϕ s l M s {\displaystyle M_{l}={\frac {1-\phi _{sl}}{\phi _{sl}}}M_{s}}

where

ϕ s l {\displaystyle \phi _{sl}} is the solids fraction of the slurry M s {\displaystyle M_{s}} is the mass or mass flow of solids in the sample or stream M s l {\displaystyle M_{sl}} is the mass or mass flow of slurry in the sample or stream M l {\displaystyle M_{l}} is the mass or mass flow of liquid in the sample or stream

Volumetric fraction from mass fraction

ϕ s l , m = M s M s l {\displaystyle \phi _{sl,m}={\frac {M_{s}}{M_{sl}}}}

Equivalently

ϕ s l , v = V s V s l {\displaystyle \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:

ϕ s l , v = M s S G s M s S G s + M l 1 {\displaystyle \phi _{sl,v}={\frac {\frac {M_{s}}{SG_{s}}}{{\frac {M_{s}}{SG_{s}}}+{\frac {M_{l}}{1}}}}}

So

ϕ s l , v = M s M s + M l S G s {\displaystyle \phi _{sl,v}={\frac {M_{s}}{M_{s}+M_{l}SG_{s}}}}

and

ϕ s l , v = 1 1 + M l S G s M s {\displaystyle \phi _{sl,v}={\frac {1}{1+{\frac {M_{l}SG_{s}}{M_{s}}}}}}

Then combining with the first equation:

ϕ s l , v = 1 1 + M l S G s ϕ s l , m M s M s M s + M l {\displaystyle \phi _{sl,v}={\frac {1}{1+{\frac {M_{l}SG_{s}}{\phi _{sl,m}M_{s}}}{\frac {M_{s}}{M_{s}+M_{l}}}}}}

So

ϕ s l , v = 1 1 + S G s ϕ s l , m M l M s + M l {\displaystyle \phi _{sl,v}={\frac {1}{1+{\frac {SG_{s}}{\phi _{sl,m}}}{\frac {M_{l}}{M_{s}+M_{l}}}}}}

Then since

ϕ s l , m = M s M s + M l = 1 − M l M s + M l {\displaystyle \phi _{sl,m}={\frac {M_{s}}{M_{s}+M_{l}}}=1-{\frac {M_{l}}{M_{s}+M_{l}}}}

we conclude that

ϕ s l , v = 1 1 + S G s ( 1 ϕ s l , m − 1 ) {\displaystyle \phi _{sl,v}={\frac {1}{1+SG_{s}({\frac {1}{\phi _{sl,m}}}-1)}}}

where

ϕ s l , v {\displaystyle \phi _{sl,v}} is the solids fraction of the slurry on a volumetric basis ϕ s l , m {\displaystyle \phi _{sl,m}} is the solids fraction of the slurry on a mass basis M s {\displaystyle M_{s}} is the mass or mass flow of solids in the sample or stream M s l {\displaystyle M_{sl}} is the mass or mass flow of slurry in the sample or stream M l {\displaystyle M_{l}} is the mass or mass flow of liquid in the sample or stream S G s {\displaystyle SG_{s}} is the bulk specific gravity of the solids

See also

References

  1. ^ "Shlumberger: Oilfield glossary". Archived from the original on 2012-05-31. Retrieved 2012-05-06.
  2. ^ "Rheonova : Measuring rheological properties of settling slurries". Archived from the original on 2020-04-18. Retrieved 2013-11-30.
  3. ^ "Portland Cement Association: Controlled Low-Strength Material". Archived from the original on 2013-10-17. Retrieved 2012-05-06.
  4. ^ "IRing - Creators of Aegis, an underground drill & blast planning software that helps a mine improve its effectiveness and efficiency". Archived from the original on 2020-08-07. Retrieved 2020-01-02.
  5. ^ Red Valve Company: Coal Slurry Pipeline
  6. ^ Rheonova : Measuring food bolus properties Archived 2013-11-30 at archive.today
  7. ^ Wills, B.A. and Napier-Munn, T.J, Wills' Mineral Processing Technology: an introduction to the practical aspects of ore treatment and mineral recovery, ISBN 978-0-7506-4450-1, Seventh Edition (2006), Elsevier, Great Britain

External links

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