The world of medicinal therapies has been historically, and remains to be, dominated by the use of elegant organic molecular structures. Now, a novel medical treatment is emerging based on CeO₂ nano-crystals that are discrete clusters of a few hundred atoms. This development is generating a great deal of exciting and promising research activity, as evidenced by this Special Issue of Biomolecules. In this paper, we provide both a steady-state and time-dependent mathematical description of a sequence of reactions: superoxide generation, superoxide dismutase, and hydrogen peroxide catalase and ceria regeneration. This sequence describes the reactive oxygen species (ROS); superoxide, O₂^–, molecular oxygen, O₂, hydroxide ion OH^– and hydrogen peroxide, H₂O₂, interacting with the Ce^3+, and Ce⁴⁺ surface cations of nanoparticle ceria, CeO₂. Particular emphasis is placed on the predicted time-dependent role of the Ce³⁺/Ce⁴⁺ ratio within the crystal. The net reaction is succinctly described as: H₂O₂ + 2O₂^– + 2H⁺ → 2H₂O + 2O₂. The chemical equations and mathematical treatment appears to align well with several critical in vivo observations such as; direct and specific superoxide dismutase (SOD), ROS control, catalytic regeneration, ceria self-regulation and self-limiting behavior. However, in contrast to experimental observations, the model predicts that the 4+ ceric ion state is the key SOD agent. Future work is suggested based on these calculations.

Fluid dynamic simulations using the FENE-P model of polymer physics are compared to those of an incompressible Newtonian fluid base case in order to understand the role of elasticity in the formation of vortices in a 90° bend narrow channel. The analysis bridges the flow behavior of a purely elastic fluid and that of a Newtonian fluid. We evaluated how four dimensionless numbers—Reynolds number (Re), Weissenberg number (Wi), viscosity ratio (β), and elasticity number (El)—affect the formation of vortices. It is shown that increasing Re and Wi, or lowering β will cause vortices to grow in size. Two phase space diagrams, β vs. El and β vs. Re, were created to show the range of values where inertial and elastic vortices form. Both diagrams have three zones. Depending on the polymer viscosity ratio and the elasticity number, the vortices form either upstream of the bend (elasticity driven) or form downstream of the bend (inertia driven), are suppressed. Our predictions are in good agreement with previous experimental and numerical works.

We develop a rheological model to approximate the nonlinear rheology of wormlike micelles using two constitutive models to represent a structural transition at high shear rates. The model is intended to describe the behavior of semidilute wormlike micellar solutions over a wide range of shear rates whose parameters can be determined mainly from small-amplitude equilibrium measurements. Length evolution equations are incorporated into reactive Rolie-Poly entangled-polymer rheology and dilute reactive-rod rheology, with a kinetic exchange between the two models. Although the micelle length is remarkably reduced during flow, surprisingly, we propose that they are not shortened by stress-enhanced breakage, which remains thermally driven. Instead, we hypothesize that stretching energy introduces a linear potential that decreases the rate of recombination and reduces the mean micelle length. This stress-hindered recombination approach accurately describes transient stress-growth upon start-up shear flow, and it predicts a transition of shear viscosity and alignment response observed at high shear rates. The proposed mechanism applies only when self-recombination occurs frequently. The effect of varying the relative rate of self-recombination on the rheology of wormlike micelles at high shear rates is yet to be explored.

The pressure-driven flow of a macroscale network model, which was derived from mescoscale network considerations and was developed to describe wormlike micellar mixtures, the Vasquez, Cook, McKinley (VCM) model [Vasquez et al., J. Non-Newtonian Fluid Mech. 144, 122–139 (2007)], is investigated in a periodically varying, converging/diverging channel. The VCM model consists of a coupled system of nonlinear partial differential equations describing two elastically active breaking and reforming micellar species. Previous analysis of the VCM model has shown that it captures both purely shear and purely extensional flow behaviors of wormlike micellar solutions. In this paper, the combined effects of shear and extension are probed by simulating the flow in a converging/diverging channel. Using domain perturbation analysis, the model equations are perturbed about the straight channel geometry thereby describing the flow through the perturbed, wavy wall geometry. The resulting first order perturbed system of (linear) partial differential equations is solved numerically using the overlapping Schwarz alternating domain decomposition method. The analysis shows that even in this simple perturbation, the VCM model is capable of capturing signatures of experimental flow behaviors of wormlike micelles through converging geometries. These signatures include the deviation from Newtonian fore-aft symmetry as well as a nonmonotonic relationship between the first normal stress difference and the extension rate along the centerline.

Applications often expose wormlike micelle solutions to a very wide range of shear and temperature conditions. The two-species model presented in Part I [Salipante et al., J. Rheol. 68 (2024)] describes the nonlinear rheology over a wide range of shear rates. Here, we compare the model predictions to measurements using a combination of microcapillary and rotational rheology to measure the viscosity of surfactant solutions across seven decades of shear rate and five decades of viscosity. The effect of temperature is studied between 20 and 60 °C for different surfactant concentrations. Model parameters are determined from both small-amplitude shear measurements and fitting to the nonlinear data. Under shear stress, the model predicts due to hindered combination kinetics that the average micelle length decreases from several micrometers to a few hundred nanometers. At sufficiently high stress, the micelle shear rheology exhibits a transition from entangled wormlike behavior to a dilute rod rheology in agreement with the model. Transient stress-growth measurements exhibit a large overshoot, which is rather well predicted by the model with hindered combination rate. Microcapillary flow birefringence also is adequately predicted by the model, confirming the accuracy of its predicted micelle lengths and exhibiting a marked change in stress-optic response at the transition between entangled polymers and dilute rods. The relaxation of retardance after flow cessation follows model predictions that include micelle-micelle interactions, which are sensitive to the rotational diffusivity and length. These methods can be applied broadly to explore relationships between composition and performance.