Magnetic body force on the medium

How hard does the coil's fringe pull on the magnetised medium?

The formula

fm = μ_{0} M G, Δp = fm ℓg

fm: Body force per unit volume, N/m³
M: Medium magnetisation, A/m
G: Field gradient ∇H, A/m²
Δp: Pressure across the fringe, Pa
ℓg: Length of the gradient region, m

LaTeX

fm = \mu_0 \cdot M \cdot G, \qquad Δp = fm \cdot ℓg

Work it out

M Medium magnetisation

kA/m

The magnetisation of the medium as a whole, per unit volume of slurry — for a 5 % micron-iron slurry in a 50 kA/m field, about 7.5 kA/m. Negative for a diamagnetic medium.

G Field gradient

A/m²

How fast H changes along the tube at the coil's end, ∇H. A 50 kA/m field falling off over 25 mm is 2 × 10⁶ A/m².

ℓg Length of the gradient region

How far along the tube the gradient extends — roughly the coil's radius at either end.

or see a worked example with typical numbers

Method

Convert the magnetisation to A/m and the gradient region to metres.
The Kelvin force on a magnetised volume is μ₀·M·∇H: the magnetisation times the gradient of the field, times the permeability of free space (4π × 10⁻⁷ H/m). Its direction is toward the stronger field for a paramagnetic or ferromagnetic medium, away from it for a diamagnetic one.
A force per unit volume acting over a length is a pressure. Multiply by the length of the gradient region for the pressure difference the fringe can sustain.

Assumptions

M is taken as given and uniform across the gradient region. In reality M is induced by the very field whose gradient is doing the pulling — M = χ·H — so it falls as H does across the fringe, and the force here is the force at the stated M, an upper figure for the region.
The gradient is along the tube. The radial gradient at a coil's end pulls the medium toward the wall as well, which is a mixing and a settling question rather than a pumping one.
The medium is a continuum. For a dilute slurry the force acts on the particles and they drag the carrier with them through viscous coupling; at micron sizes that coupling is tight and the continuum picture holds.
Nothing here is Meyer's. The Kelvin force is nineteenth-century magnetostatics; the magnetisation and gradient are the reader's, and the estate specifies neither.