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1. Shear thickening in dense bidisperse suspensions

   https://doi.org/10.1122/8.0000495  

   Malbranche, Nelya; Chakraborty, Bulbul; Morris, Jeffrey F. (January 2023, Journal of Rheology)

   Discrete-particle simulations of bidisperse shear thickening suspensions are reported. The work considers two packing parameters, the large-to-small particle radius ratio ranging from [Formula: see text] (nearly monodisperse) to [Formula: see text], and the large particle fraction of the total solid loading with values [Formula: see text], 0.5, and 0.85. Particle-scale simulations are performed over a broad range of shear stresses using a simulation model for spherical particles accounting for short-range lubrication forces, frictional interaction, and repulsion between particles. The variation of rheological properties and the maximum packing fraction [Formula: see text] with shear stress [Formula: see text] are reported. At a fixed volume fraction [Formula: see text], bidispersity decreases the suspension relative viscosity [Formula: see text], where [Formula: see text] is the suspension viscosity and [Formula: see text] is the suspending fluid viscosity, over the entire range of shear stresses studied. However, under low shear stress conditions, the suspension exhibits an unusual rheological behavior: the minimum viscosity does not occur as expected at [Formula: see text], but instead decreases with further increase of [Formula: see text] to [Formula: see text]. The second normal stress difference [Formula: see text] acts similarly. This behavior is caused by particles ordering into a layered structure, as is also reflected by the zero slope with respect to time of the mean-square displacement in the velocity gradient direction. The relative viscosity [Formula: see text] of bidisperse rate-dependent suspensions can be predicted by a power law linking it to [Formula: see text], [Formula: see text] in both low and high shear stress regimes. The agreement between the power law and experimental data from literature demonstrates that the model captures well the effect of particle size distribution, showing that viscosity roughly collapses onto a single master curve when plotted against the reduced volume fraction [Formula: see text]. 

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2. Ordered domains in sheared dense suspensions: The link to viscosity and the disruptive effect of friction

   https://doi.org/10.1122/8.0000453  

   Goyal, Abhay; Del Gado, Emanuela; Jones, Scott Z.; Martys, Nicos S. (September 2022, Journal of Rheology)

   Monodisperse suspensions of Brownian colloidal spheres crystallize at high densities, and ordering under shear has been observed at densities below the crystallization threshold. We perform large-scale simulations of a model suspension containing over [Formula: see text] particles to quantitatively study the ordering under shear and to investigate its link to the rheological properties of the suspension. We find that at high rates, for [Formula: see text], the shear flow induces an ordering transition that significantly decreases the measured viscosity. This ordering is analyzed in terms of the development of layering and planar order, and we determine that particles are packed into hexagonal crystal layers (with numerous defects) that slide past each other. By computing local [Formula: see text] and [Formula: see text] order parameters, we determine that the defects correspond to chains of particles in a squarelike lattice. We compute the individual particle contributions to the stress tensor and discover that the largest contributors to the shear stress are primarily located in these lower density, defect regions. The defect structure enables the formation of compressed chains of particles to resist the shear, but these chains are transient and short-lived. The inclusion of a contact friction force allows the stress-bearing structures to grow into a system-spanning network, thereby disrupting the order and drastically increasing the suspension viscosity. 

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3. Average stress in a dilute suspension of rigid spheroids in a second-order fluid in a linear flow

   https://doi.org/10.1103/PhysRevFluids.10.053302  

   Apte, Tanvi Mahendra; Ardekani, Arezoo; Narsimhan, Vivek (May 2025, Physical Review Fluids)

   The microhydrodynamics of particle suspensions in polymeric fluids has a wide range of applications in industry and biology. To discern the dynamics of particles in such systems, it is important to analyze the stress response of the suspension to applied flow fields. While such investigations have been theoretically done for suspensions of rigid spheres in weakly viscoelastic fluids, the effect of nonsphericity of particles on the stress remains relatively unexplored. The interplay between the response of the polymeric fluid and the particle orientation yields rich physics. The viscoelastic torques make the particle inhabit a preferred orientation in a given flow, resulting in time-dependent stresses. In this paper, we determine the average extra stress in a dilute suspension of rigid, non-Brownian spheroids in a second-order fluid subject to shear and extensional flows. We perform this task by examining the flow around a single spheroid in the limit of small Weissenberg number (Wi≪1) and perform an ensemble average of the stress tensor over all particle configurations. There are two contributions to the extra stress: one from the force dipole on the particles (stresslet) and another from the fluctuations in the velocity in the bulk fluid (fluid-induced particle stress), the latter of which does not arise in a zero Reynolds number Newtonian fluid. We present results for the 𝑂⁡(𝜙⁢Wi) corrections to the long-time effective shear viscosity, normal stress coefficients, and extensional viscosities in the suspension in shear, uniaxial extensional, and planar extensional flows, where 𝜙 is the particle volume fraction. To elucidate the effect of particle shape on the effective viscosity, we repeat this analysis for different aspect ratios (𝐴𝑅) for prolate (needlelike) and oblate (disklike) spheroids. 

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4. Understanding the rheology of kaolinite clay suspensions using Bayesian inference

   https://doi.org/10.1122/8.0000556  

   Ran, Ranjiangshang; Pradeep, Shravan; Kosgodagan Acharige, Sébastien; Blackwell, Brendan C.; Kammer, Christoph; Jerolmack, Douglas J.; Arratia, Paulo E. (January 2023, Journal of Rheology)

   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 ([Formula: see text]). 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 [Formula: see text], while being almost inelastic and purely thixotropic at high [Formula: see text]. Overall, our results provide a framework for predictive model fitting to elucidate the rheological behaviors of natural materials and other structured fluids. 

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5. Onset of thermal convection in non-colloidal suspensions

   https://doi.org/10.1017/jfm.2021.59  

   Kang, Changwoo; Yoshikawa, Harunori N.; Mirbod, Parisa (May 2021, Journal of Fluid Mechanics)

   null (Ed.)

   This study explores thermal convection in suspensions of neutrally buoyant, non-colloidal suspensions confined between horizontal plates. A constitutive diffusion equation is used to model the dynamics of the particles suspended in a viscous fluid and it is coupled with the flow equations. We employ a simple model that was proposed by Metzger, Rahli & Yin ( J. Fluid Mech. , vol. 724, 2013, pp. 527–552) for the effective thermal diffusivity of suspensions. This model considers the effect of shear-induced diffusion and gives the thermal diffusivity increasing linearly with the thermal Péclet number ( Pe ) and the particle volume fraction ( ϕ ). Both linear stability analysis and numerical simulation based on the mathematical models are performed for various bulk particle volume fractions $$({\phi _b})$$ ranging from 0 to 0.3. The critical Rayleigh number $$(R{a_c})$$ grows gradually by increasing $${\phi _b}$$ from the critical value $$(R{a_c} = 1708)$$ for a pure Newtonian fluid, while the critical wavenumber $$({k_c})$$ remains constant at 3.12. The transition from the conduction state of suspensions is subcritical, whereas it is supercritical for the convection in a pure Newtonian fluid $$({\phi _b} = 0)$$ . The heat transfer in moderately dense suspensions $$({\phi _b} = 0.2\text{--}0.3)$$ is significantly enhanced by convection rolls for small Rayleigh number ( Ra ) close to $$R{a_c}$$ . We also found a power-law increase of the Nusselt number ( Nu ) with Ra , namely, $$Nu\sim R{a^b}$$ for relatively large values of Ra where the scaling exponent b decreases with $${\phi _b}$$ . Finally, it turns out that the shear-induced migration of particles can modify the heat transfer. 

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