Slurry viscosity

How much does suspending the particulate thicken the carrier?

The formula

η = η0 (1 + 2.5 φ + 6.2 φ^{2})

LaTeX

η = η0 \left( 1 + 2.5 \cdot φ + 6.2 \cdot φ^2 \right)

Work it out

c Carrier fluid

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

φ Particulate loading

The solid's share of the total volume.

or see a worked example with typical numbers

Look up the carrier's viscosity at 20 °C — about 1 mPa·s for water, 30 for a light mineral oil, 1400 for glycerol.
Convert the loading to a fraction by dividing by 100.
Einstein's term: each particle disturbs the flow around it, and for dilute rigid spheres the viscosity rises by 2.5 times the volume fraction. Batchelor's term, 6.2 φ², accounts for pairs of particles interacting, and matters from a few per cent upward.
Multiply the carrier's viscosity by the bracket. The ratio itself — the bracket — is the relative viscosity.

Rigid, spherical, non-interacting particles in a dilute suspension. Einstein's coefficient is exact for isolated spheres and Batchelor's extends it to about 10 % by volume. Beyond that the formula falls increasingly short of the real thickening, and above roughly 40 % the suspension stops behaving as a Newtonian liquid at all.
Particles far larger than molecules and far smaller than the tube — the continuum picture. Iron filings in a two-centimetre tube qualify; a coarse grit does not.
The carrier's viscosity is its 20 °C value. Water thins by about 2 % per degree of warming, oils by more; a medium running warm is thinner than this.
No magnetic field. A magnetised slurry of ferromagnetic particles thickens sharply along the field — the magnetorheological effect — which is a large part of what an EPG does to its medium and is outside this formula.