The dimensionless group quantifying viscosity change due to viscous heating has been known throughout the past century as the Nahme number, the Griffith number, the Nahme–Griffith number, and even misleadingly the Brinkman number. Until the time of this writing, there has been no published biographical record of Rudolf Nahme or Richard Griffith and no clear tracing of their namesake dimensionless groups through the literature. Here, we review these dimensionless groups, tell the stories of three key contributors—Rudolf Nahme, Richard Griffith, and Arthur Hagg—, and follow the development of the naming conventions to the present day. This review synthesizes an updated understanding of these numbers, including the distinction between stress and velocity forms, alternative measures of the temperature sensitivity of viscosity, and clarification of model-agnostic versus model-specific descriptions for thermorheological behavior.
Orthogonal superposition rheology is a powerful technique for probing the viscoelastic properties of complex materials under flow. However, its accuracy is heavily dependent on the precise calibration of four calibration parameters: the instrument’s transducer mass M, friction coefficient ζ, stiffness coefficient K, and geometry end-effects captured through the end-factor c⊥. This work demonstrates that the standard, decoupled calibration procedure, which utilizes static weights and Newtonian standards, can result in negative stiffness coefficients and nonminimum phase behavior, which are not representative for the experimental conditions when characterizing complex materials. The standard calibration also fails to account for the mathematical coupling between the friction coefficient and the orthogonal end-factor. In this paper, we demonstrate that, by exploiting the frequency-dependency of the moduli of a viscoelastic material, here different aqueous poly(ethylene)oxide solutions, the calibration offsets for the transducer mass, friction coefficient, and stiffness coefficient can be determined independently, together with the corresponding true orthogonal end-factor. Furthermore, the presence of the sample avoids the unstable behavior that occurs during the standard calibration methods. Validation of this novel calibration procedure across multiple rheometers with a polyisobutylene-CALTRAN solution shows that the proposed method performs equally to or better than traditional calibrations, particularly at high frequencies where instrument inertia dominates. This viscoelastic calibration procedure ensures a physically consistent calibration for the characterization of complex fluids.
Dripping-onto-substrate (DoS) rheometry is a well-established method for measuring the extensional rheology of low-viscosity liquids. However, clear guidelines on the capabilities and limitations of the technique are lacking. In the present work, we define operational limits for measuring a transient extensional viscosity directly from observations of the rate of filament thinning, as well as model-based bounds on calculating a viscosity eta and extensional relaxation time tau E of a liquid using DoS. Dilute solutions of polyethylene oxide and polyacrylamide are used to probe the lower limit of measurable tau E, demonstrating that values as low as 0.1 ms can be resolved, provided (a) the intrinsic Deborah number (based on the ratio of the relaxation time and the Rayleigh breakup time scale) is De >= O ( 0.1 ) and (b) an instrumental constraint related to spatial and temporal resolution is satisfied. This instrumental constraint is quantified through a new metric we define as the filament capture rate, a "figure of merit" (expressed in s(-1)) that can be used to quantify the number of data points within the elastocapillary regime that are available for extraction of tau(E). Finally, model-agnostic bounds for reliable measurements of the transient extensional viscosity eta(+)(E) using DoS rheometry are derived. These bounds prescribe experimental limitations due to inertia, gravity, and measurement resolution (spatial and temporal) that can assist rheologists in the design and interpretation of extensional viscosity measurements using DoS. Collectively, these results provide a quantitative roadmap for reliable DoS rheometry and affirm its use for measuring the transient extensional viscosity of liquid-like materials.
The mechanism underlying the deterioration of the aircraft tire-runway friction coefficient under conditions of water accumulation and runway contamination at high-altitude airports remains unclear. Existing research has primarily focused on low-altitude, normal-pressure environments, making it difficult to explain how changes in the tire-water film-runway contact state under low-pressure conditions affect friction performance. Based on field tests and smoothed particle hydrodynamics-finite element method fluid-structure interaction numerical simulations, this paper establishes a friction coefficient analysis model for water-contaminated runways in high-altitude, low-pressure environments, extending the simulation altitude range of 0-5000 m. The model's predicted friction coefficients showed 96.42% agreement with field test results, validating the model's reliability for evaluating macroscopic friction performance. The results show that as altitude increases, the corrected tire pressure rises from 1.2500 to 1.2973 MPa, while the runway friction coefficient decreases from 0.382 to 0.238, representing a total decrease of approximately 37.7%. The friction coefficient's deterioration exhibits a distinct inflection point near 2438 m: below this altitude, it decays slowly in a nearly linear manner; above it, the deterioration transitions to a nonlinear, accelerated decline. This transition primarily stems from the coupled changes in tire contact deformation, effective contact area, and dynamic water separation effects at the interface under low-pressure conditions. Based on the above results, this paper establishes an empirical model of the friction coefficient for water-contaminated runways, with elevation as the core variable, providing a quantitative basis for evaluating runway friction performance and making operational safety decisions at high-altitude airports.
Flow of nondilute elongated particle suspensions produces complex microstructure and rheology due to coupling of single-particle orientations with anisotropic interparticle interactions. Current theories to describe this coupling are lacking except in the cases of asymptotically large aspect ratios. We address this gap through a combined experimental and theoretical study of the flow-induced microstructure and rheology of semidilute cellulose nanocrystal dispersions. We show that current theories for nondilute rodlike Brownian dispersions significantly underpredict the viscosity and degree of shear thinning for these fluids, and that these differences are likely due to flow-induced changes in the radial distribution of interparticle separations (or its Fourier equivalent, the structure factor) for particles with a finite aspect ratio. We, therefore, develop and apply a scattering analysis that isolates contributions due to the anisotropic interparticle structure from those due to single-particle orientation through an extended form of the random phase approximation (RPA), allowing estimation of a mean-field parameter describing the strength of interparticle interactions due to flow. The analysis is validated and applied to rheoscattering measurements in steady-state simple shear flow and in complex, Lagrangian unsteady deformation histories. Ultimately, we distinguish two regimes of behavior-one in which the flow-induced microstructure can be accurately predicted using interactions observed at equilibrium, and another in which the mean-field interaction strength is modified by flow. We, thus, propose that the extended RPA model could be used as a widely applicable tool to infer and model nonequilibrium structures and interactions of anisotropic materials from scattering measurements in flow and other orienting fields.
