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1. A stabilized computational nonlocal poromechanics model for dynamic analysis of saturated porous media

   https://doi.org/10.1002/nme.6762  

   Menon, Shashank; Song, Xiaoyu (June 2021, International Journal for Numerical Methods in Engineering)

   Abstract In this article we formulate a stable computational nonlocal poromechanics model for dynamic analysis of saturated porous media. As a novelty, the stabilization formulation eliminates zero‐energy modes associated with the original multiphase correspondence constitutive models in the coupled nonlocal poromechanics model. The two‐phase stabilization scheme is formulated based on an energy method that incorporates inhomogeneous solid deformation and fluid flow. In this method, the nonlocal formulations of skeleton strain energy and fluid flow dissipation energy equate to their local formulations. The stable coupled nonlocal poromechanics model is solved for dynamic analysis by an implicit time integration scheme. As a new contribution, we validate the coupled stabilization formulation by comparing numerical results with analytical and finite element solutions for one‐dimensional and two‐dimensional dynamic problems in saturated porous media. Numerical examples of dynamic strain localization in saturated porous media are presented to demonstrate the efficacy of the stable coupled poromechanics framework for localized failure under dynamic loads. 

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2. Shear Thinning and Stress-Dependent Viscosity Activation Volumes: Combining Eyring and Carreau

   https://doi.org/10.1007/s11249-025-02047-3  

   Hopper, Nicholas; Bennett, Dennis_W; Espinosa-Marzal, Rosa_M; Tysoe, Wilfred (July 2025, Tribology Letters)

   Abstract The viscosity of fluids and their dependence on shear rate, known as shear thinning, plays a critical role in applications ranging from lubricants and coatings to biomedical and food-processing industries. Traditional models such as the Carreau and Eyring theories offer competing explanations for shear-thinning behavior. The Carreau model attributes viscosity reduction to molecular distortions, while the Eyring model describes shear thinning as a stress-induced transition over an activation energy barrier. This work proposes an extended-Eyring model that incorporates stress-dependent activation volumes, bridging key aspects of both theories. In modifying transition-state theory by using an Evans-Polanyi perturbation analysis, we derive a generalized viscosity equation that accounts for the molecular-scale rearrangements governing fluid flow. The model is validated against computational and experimental data, including shear-thinning behavior of pure squalane and polyethylene oxide (PEO) aqueous solutions. Comparative analysis with Carreau-Yasuda and conventional Eyring models demonstrates excellent accuracy in predicting viscosity trends over a wide range of shear rates. The introduction of stress-dependent activation volumes provides a description of molecular exchange kinetics accounting for structural reorganization under shear. These findings offer a unified framework for modeling shear thinning and have broad implications for designing advanced lubricants, polymer solutions, and complex fluids with tailored flow properties. Graphical Abstract 

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3. A homogenization model for the rheology and local field statistics of suspensions of particles in yield stress fluids

   https://doi.org/10.1122/8.0000337  

   Kammer, Christoph; Blackwell, Brendan; Arratia, Paulo E.; Ponte Castañeda, Pedro (May 2022, Journal of Rheology)

   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. 

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4. Microfluidic rheology of methylcellulose solutions in hyperbolic contractions and the effect of salt in shear and extensional flows

   https://doi.org/10.1039/d0sm00371a  

   Micklavzina, Benjamin L.; Metaxas, Athena E.; Dutcher, Cari S. (June 2020, Soft Matter)

   Methylcellulose solutions are known to form microfibrils at elevated temperatures or in the presence of salt. The fibrils have a significant impact on the solution's rheological properties. Here, the shear and extensional properties of methylcellulose solutions with added salt are measured using hyperbolic microfluidic channels, allowing for new characterization at lower molecular weights and higher shear and strain rates that are difficult to access by macroscale rheology studies. 1 and 2 wt% methylcellulose solutions with molecular weight of 150 kg mol −1 with NaCl content between 0 to 5 wt% have been characterized. All solutions were found to be shear thinning, with power law thinning behavior at shear rates above 100 s −1 . The addition of NaCl up to 5 wt% had only small effects on shear viscosity at the shear rates probed (100 s −1 and 10 000 s −1 ). Extensional viscosities as low as 0.02 Pa s were also measured. Unlike the results for shear viscosity, the addition of 5 wt% NaCl caused significant changes in extensional viscosity, increasing by up to 10 times, depending on extension rate. Additionally, all solutions tested showed apparent extensional thinning in the high strain rate regime (>100 s −1 ), which has not been reported in other studies of methylcellulose solutions. These findings may provide insight for those using methylcellulose solutions in process designs involving extensional flows over a wide range of strain rates. 

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5. Simulations of dynamically cross-linked actin networks: Morphology, rheology, and hydrodynamic interactions

   https://doi.org/10.1371/journal.pcbi.1009240  

   Maxian, Ondrej; Peláez, Raúl P.; Mogilner, Alex; Donev, Aleksandar (December 2021, PLOS Computational Biology)

   Merks, Roeland M.H. (Ed.)

   Cross-linked actin networks are the primary component of the cell cytoskeleton and have been the subject of numerous experimental and modeling studies. While these studies have demonstrated that the networks are viscoelastic materials, evolving from elastic solids on short timescales to viscous fluids on long ones, questions remain about the duration of each asymptotic regime, the role of the surrounding fluid, and the behavior of the networks on intermediate timescales. Here we perform detailed simulations of passively cross-linked non-Brownian actin networks to quantify the principal timescales involved in the elastoviscous behavior, study the role of nonlocal hydrodynamic interactions, and parameterize continuum models from discrete stochastic simulations. To do this, we extend our recent computational framework for semiflexible filament suspensions, which is based on nonlocal slender body theory, to actin networks with dynamic cross linkers and finite filament lifetime. We introduce a model where the cross linkers are elastic springs with sticky ends stochastically binding to and unbinding from the elastic filaments, which randomly turn over at a characteristic rate. We show that, depending on the parameters, the network evolves to a steady state morphology that is either an isotropic actin mesh or a mesh with embedded actin bundles. For different degrees of bundling, we numerically apply small-amplitude oscillatory shear deformation to extract three timescales from networks of hundreds of filaments and cross linkers. We analyze the dependence of these timescales, which range from the order of hundredths of a second to the actin turnover time of several seconds, on the dynamic nature of the links, solvent viscosity, and filament bending stiffness. We show that the network is mostly elastic on the short time scale, with the elasticity coming mainly from the cross links, and viscous on the long time scale, with the effective viscosity originating primarily from stretching and breaking of the cross links. We show that the influence of nonlocal hydrodynamic interactions depends on the network morphology: for homogeneous meshworks, nonlocal hydrodynamics gives only a small correction to the viscous behavior, but for bundled networks it both hinders the formation of bundles and significantly lowers the resistance to shear once bundles are formed. We use our results to construct three-timescale generalized Maxwell models of the networks. 

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