PhD Thesis Defence: Mohammed Tabish Khan

Rheology of dense non-Brownian suspensions.

Suspensions are ubiquitous in nature and industry, ranging from magma, blood, and mud to cement, paint, and molten chocolate. Despite the Newtonian nature of the suspending fluid and the expectation of linearity in the absence of inertia, these suspensions display a diverse array of non-linear rheological behaviours. The origin of these behaviours is puzzling, particularly in the case of non-Brownian particles, because of the absence of a time scale in the system other than the inverse of the shear rate. By combining experimental rheology, atomic force microscopy to determine the interaction forces between particles and phenomenological modelling, we show that the macroscopic rheology of non-Brownian suspensions can be predicted from the non-hydrodynamic interactions between two particles. 

The first part of the thesis explores shear-thickening suspensions, showing a discontinuous rise in shear viscosity at a critical shear rate ̇γ for particle volume fractions ϕ above random loose packing. Unlike conventional practices involving prolonged pre-shearing at constant ̇γ without justification, this study performs shear stress sweeps on freshly loaded samples. The protocol reveals the transition from continuous to discontinuous shear thickening, leading to a non-monotonic ‘S-shaped’ curve with increasing sweeps, thus establishing shear strain as a crucial variable in the rheology of dense suspensions. Two shear stress scales are identified, contributing to the proposal of a phenomenological model. The model incorporates the mean coordination number z as a microstructural variable, successfully predicting the shear strain-dependent rheology. Particle imaging velocimetry on the top surface shows the gradual change in velocity profile from Newtonian prediction to shear localization with increasing strain, substantiating the above inferences.

The second part investigates shear-thinning suspensions, displaying discontinuous shear thinning at a ϕ-dependent critical stress. The nature of shear thinning is influenced by the strength of attractive forces, resulting in non-monotonic behaviour observed in shear rate sweeps for strongly attractive suspensions. The proposed model predicts the qualitative rheological features for such suspensions as well. Finally, we identify a particle-fluid combination exhibiting quasi-Newtonian behaviour for volume fractions up to ϕ = 0.55. The absence of non-hydrodynamic interactions between particles is confirmed using atomic force microscopy, supporting our argument that analyzing particle-particle interactions enables predicting the rheology of dense non-Brownian suspension.