Supplementary material from "Unified torque scaling in counter-rotating suspension Taylor–Couette flow"

Torque measurements are reported for the Taylor–Couette flow of a neutrally buoyant non-colloidal suspension in the counter-rotation regime upto a particle volume fraction of ϕ =0.2. A unified scaling relation for the dimensionless torque (the pseudo-Nusselt number) of the form Nu_ω0=(α₀+α₁ Ta₁^*α₂) Ta(0)^kμ_r(ϕ)ⁿ is shown to hold over a range of Taylor number Ta^c1≤ Ta ≤ ~10⁶ that covers primary, secondary and tertiary bifurcating states; here, Ta₁^*= Ta(ϕ)/Ta^c1(ϕ) is the reduced Taylor number, Ta^c1 is the critical Taylor number at primary bifurcation and μ_r(ϕ) = μ(ϕ)/μ(0) is the relative viscosity of the suspension. Possible effects of flow transitions and inhomogeneous distribution of particles on torque scaling are discussed.This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical Transactions paper (Part 1)’.