A new frequency-dependent threshold for irreversibility in non-Brownian suspensions

Non-Brownian suspensions of smooth spherical particles behave as Newtonian fluids under steady shear, yet exhibit complex responses under oscillatory shear, including a transition to absorbing state. In this state, particles align with the shear direction, reducing interactions and lowering the complex viscosity. Classical theory predicts this transition to a reversible absorbing state to be strain-rate independent, occurring below a strain amplitude threshold that depends only on particle volume fraction, γ0 < γcl(ϕ). However, recent simulations by Ge et al. showed that weak van der Waals interactions introduce a frequency dependence under oscillatory shear, giving rise to a new critical strain amplitude threshold γ0 > γcr (ω, ϕ). In this study, we experimentally validate this frequency-dependent threshold through time-sweep oscillatory shear tests on suspensions of hollow glass spheres in a Newtonian matrix. Our results confirm that γcr is inversely proportional to frequency. This complements the classical, volume-fraction-dependent threshold and defines a bounded regime in which the system can reach a reversible absorbing state. Outside this regime, the suspension remains in an irreversible state, governed by particle collisions, either due to high strain amplitudes inducing steady-shear-like interactions, or due to particle clustering at low amplitudes, where collisions persist within clusters. Importantly, at sufficiently low frequencies, the absorbing state becomes inaccessible, as γcr exceeds γcl. This behavior is here confirmed by experiments at very low frequencies, further validating our findings. These results enhance the understanding of microstructural dynamics in dense suspensions and highlight the critical roles of strain amplitude and frequency in governing the reversible-to-irreversible transition.