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Slurry density

How dense is the medium once the metal particulate and surfactant are in it?

The formula
ρ=1−φ−s⁢ρc+φ⁢ρm+s⁢ρs
ρ
Mixture density, kg/m³
φ
Metal volume fraction, %
s
Surfactant volume fraction, %
ρc
Carrier density, kg/m³
ρm
Metal density, kg/m³
ρs
Surfactant density, kg/m³
LaTeX 
ρ = (1 - φ - s) \cdot ρc + φ \cdot ρm + s \cdot ρs

Work it out

The liquid the particulate is carried in. Handbook density at 20 °C.

The particulate. Sets its density.

%

The particulate's share of the total volume. Not mass — by mass the same slurry is far more metal than this.

%

The surfactant's share of the volume. Small, and near water's density, so it barely moves this answer — it is here so the fractions add up honestly.

or see a worked example with typical numbers

Method

  1. Convert the two percentages to fractions by dividing by 100. What is left after the metal and surfactant fractions is the carrier's share.
  2. Look up the three densities: the carrier's and the metal's from the handbook values, and a typical surfactant's of about 1050 kg/m³.
  3. Weight each density by its volume fraction and add them up. Density is mass per volume, and volume fractions of an ideal mixture simply add, so this is exact for components that do not react or dissolve into one another.
  4. For the mass fraction, take the metal's contribution — its fraction times its density — and divide by the mixture density.

Assumptions

  • Volumes add. They do not quite, for a solid suspended in a liquid with a surfactant dissolved in it, but the departure is well under a per cent and far smaller than the uncertainty in how much metal actually went in.
  • The particulate is solid metal at its bulk density. An oxidised or porous powder is lighter than this; a loading quoted for one will overstate the mixture density.
  • The surfactant is taken at 1050 kg/m³. Real surfactants run from about 1000 to 1100, and at the fractions used here the difference is in the third figure.
  • Nothing here is Meyer's. The estate material specifies how fast the medium moves and says nothing about its recipe; the carriers and metals offered are the plausible candidates, and the page says which was chosen.