Bingham Plastic — Viscoplastic Flow

Bingham Model

A Bingham plastic flows only when the applied stress τ exceeds the yield stress τ_y. Below τ_y, the material moves as a rigid plug. The constitutive law:

τ = τ_y + μ_p · (du/dy) if |τ| > τ_y
du/dy = 0 if |τ| ≤ τ_y

This gives a characteristic plug flow region near the channel centerline where shear stress is lowest.

Controls

Yield stress τ_y 0.30 Plastic viscosity μ_p 0.20 Pressure gradient G 1.00 Fluid type Bingham Plastic Newtonian (compare) Power-law (shear-thinning) Power-law index n 0.5

Key Results

Bingham number Bn = τ_y·H / (μ_p·V_max) quantifies yield dominance. Large Bn → mostly plug flow.