Barite Jig - 2D Pulsating Bed Stratification and Hindered Settling Lab

Why a jig sorts by density

A grain in water settles at the terminal velocity where drag balances apparent weight, (ρ_p - ρ_w) g πd³/6 = ½ ρ_w C_d(Re) πd²/4 v², with the Clift-Gauvin drag law C_d(Re). For the same size, barite (ρ = 4.4 g/cm³) falls faster than quartz (2.65 g/cm³); in the Stokes limit v = (ρ_p - ρ_w) g d²/(18 μ), in the Newton limit v ∝ √(d (ρ_p - ρ_w)).

Pulsation and hindered settling

The jig drives the water up and down, u(t) = A ω cos ωt. On the upstroke the bed dilates and grains are carried up; on the downstroke they settle, so the grain velocity is u(t) - v_t multiplied by a hindrance factor (1 - φ/φ_max)^2.5 that grows as the local solid fraction φ approaches random close packing (0.6). Dense grains sink more per cycle, quartz is left on top; the dilation makes the bed loose enough to rearrange.

Honest simplifications: a one-dimensional mean-field model with 140 tracer grains, no explicit collisions, a tiny random jitter standing in for turbulence, equal grain sizes, and an assumed dilation rule. It illustrates the mechanism, not a plant design.

• Run the Well-tuned jig for 30 seconds and read the layer bars: barite concentrates in the lowest layers.
• Choose Too gentle: the bed never dilates and the grains stay mixed.
• Choose Too violent: the bed is thrown up and sorting gets worse.
• Make grains finer (1 mm): settling is slower, so it takes longer to sort.