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Mud is a suspension of fine-grained particles (sand, silt, and clay) in water. The interaction of clay minerals in mud gives rise to complex rheological behaviors, such as yield stress, thixotropy, and viscoelasticity. Here, we experimentally examine the flow behaviors of kaolinite clay suspensions, a model mud, using steady shear rheometry. The flow curves exhibit both yield stress and rheological hysteresis behaviors for various kaolinite volume fractions (ϕk). Further understanding of these behaviors requires fitting to existing constitutive models, which is challenging due to numerous fitting parameters. To this end, we employ a Bayesian inference method, Markov chain Monte Carlo, to fit the experimental flow curves to a microstructural viscoelastic model. The method allows us to estimate the rheological properties of the clay suspensions, such as viscosity, yield stress, and relaxation time scales. The comparison of the inherent relaxation time scales suggests that kaolinite clay suspensions are strongly viscoelastic and weakly thixotropic at relatively low ϕk, while being almost inelastic and purely thixotropic at high ϕk. Overall, our results provide a framework for predictive model fitting to elucidate the rheological behaviors of natural materials and other structured fluids.

We investigate the rheological behavior of athermal particle suspensions using experiments and theory. A generalized version of the homogenization estimates of Ponte Castañeda and Willis [J. Mech. Phys. Solids, 43(12), 1919–1951 (1995)] is presented for the effective viscosity of athermal suspensions accounting for additional microstructural features (e.g., polydispersity) via an empirical parameter, [Formula: see text]. For the case of identically sized spheres dispersed with statistical isotropy in a Newtonian fluid, the parameter [Formula: see text] is estimated from the results of Batchelor and Green [J. Fluid Mech. 56(2), 375–400 (1972)] for the Huggins coefficient. Predictions for the macroscopic viscosity are found to be in good agreement with measurements for monodisperse polymethyl methacrylate (PMMA) spheres in glycerol, as well as for the empirical Krieger–Dougherty equation for the shear viscosity. The proposed estimates have the added benefit that they can also be used to get information on the statistics of the stress and strain-rate fields in the fluid and particle phases. In addition, results for the effective shear viscosity are used in combination with the linear comparison method of Ponte Castañeda [J. Mech. Phys. Solids 39(1), 45–71 (1991)] to generate the corresponding estimates for the effective macroscopic behavior and field statistics of particle suspensions in (viscoplastic) yield stress fluids. Good agreement is also found between the theoretical estimates and experimental results for the effective yield and flow stress of suspensions with monodisperse PMMA spheres in Carbopol. Finally, it is argued that the results for the phase averages and fluctuations of the stress and strain-rate fields can be used to provide a physical interpretation for the parameter [Formula: see text] in terms of the polydispersity of the suspension and its implications for the percolation threshold.