Particle contact dynamics as the origin for noninteger power expansion rheology in attractive suspension networks

We show that Hertzian particle contacts are the underlying cause of the as-yet-unexplained noninteger power laws in weakly nonlinear rheology. In the medium amplitude oscillatory shear (MAOS) region, the cubic scaling of the leading order nonlinear shear stress (σ 3 ∼ γ 0 m 3, m 3 = 3) is the standard expectation. Expanding on the work by Natalia et al. [J. Rheol. 64, 625-635 (2020)], we report an extensive data set of noncubical, noninteger power law scalings m 3 for particle suspensions in two immiscible fluids with a capillary attractive interaction, known as capillary suspensions. Here, we show that distinct power law exponents are found for the storage and loss moduli and these noninteger scalings occur at every secondary fluid concentration for two different contact angles. These compelling results indicate that the noninteger scalings are related to the underlying microstructure of capillary suspensions. We show that the magnitude of the third harmonic elastic stress scaling m 3, elastic originates from Hertzian-like contacts in combination with the attractive capillary force. The related third harmonic viscous stress scaling m 3, viscous is found to be associated with adhesive-controlled friction. These observations, conducted for a wide range of compositions, can help explain previous reports of noninteger scaling for materials involving particle contacts and offers a new opportunity using the variable power law exponent of MAOS rheology to reveal the physics of particle bonds and friction in the rheological response under low deformation instead of at very high shear rates.