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Stan’s Legacy

Design an EPG slurry: density, viscosity, flow and permittivity

What does this mix of carrier, metal and surfactant weigh, how thick is it, does it flow smoothly at this pump rate, and what does it do to the water's permittivity?

The formula
Re=ρvDη
Re
Reynolds number
ρ
Slurry density, kg/m³
v
Mean velocity, m/s
D
Tube diameter, m
η
Slurry viscosity, Pa·s
LaTeX
Re = \frac{ρ \cdot v \cdot D}{η}

Work it out

The liquid the particulate is carried in.

The particulate.

%

The metal's share of the volume.

%

The surfactant's share of the volume.

mm

The bore the slurry is pumped through.

L/min

What the pump delivers.

For the permittivity step, when the carrier is water: which water.

°C

The medium's temperature.

Method

  1. Weight the carrier's, the metal's and the surfactant's densities by their volume fractions and add them — the slurry density calculation.
  2. Thicken the carrier's viscosity by Einstein's and Batchelor's terms in the metal fraction — the slurry viscosity calculation.
  3. Take that density and viscosity, the bore and the pump rate, and find the mean velocity and the Reynolds number — the flow regime calculation.
  4. Apply the Maxwell Garnett rule to the water at temperature with this metal fraction — the metal-loaded permittivity calculation.
  5. Each step is its own calculation with its own page; every formula is shown below with these numbers in it, and links to that page pre-filled.

Assumptions

  • Every assumption of every constituent applies: volumes add, particles are dilute rigid spheres, the tube is straight and smooth and the flow steady, the inclusions are well-separated conductors in a dielectric host.
  • The permittivity step assumes the carrier is water. If the carrier is oil or glycerol the density, viscosity and flow steps are right and the permittivity step is not — it is computed against the chosen water profile regardless, and should be read as "if this were in water".
  • The density and viscosity steps use handbook values at 20 °C for the carrier; only the permittivity step uses the temperature entered.
  • Nothing here is Meyer's. The estate material specifies how fast the medium moves and says nothing about its recipe.