The influence of geometric scale on the extensional rheology of viscoelastic fluids was systematically investigated using a liquid dripping method. Polyethylene oxide aqueous solutions were tested with seven nozzles of different outer diameters ranging from 0.23 mm to 2.77 mm. The temporal evolution of the filament diameter was analyzed to obtain the extensional relaxation time, extensional viscosity, and maximum Weissenberg number. To quantitatively evaluate the scale effect, a surface-area-to-volume ratio was introduced as a geometric parameter. The results show that as the nozzle diameter increases, both the extensional relaxation time and the maximum Weissenberg number gradually approach asymptotic values. This indicates that when the influence of scale effects is negligible, the measured rheological properties more accurately represent the intrinsic viscoelastic response of the fluid. These findings demonstrate that the geometric scale significantly affects the observed extensional behavior in filament thinning experiments. Furthermore, this study establishes a practical experimental guideline that recommends the use of sufficiently large nozzle diameters to minimize scale effects. The use of large nozzles enables reliable evaluation of the extensional viscosity of complex fluids and contributes to improving the accuracy of rheological measurements in complex flow systems.

We investigate extensional viscosity and polymer conformation in dilute polymer solutions under uniaxial extensional flow using dissipative particle dynamics simulations. At high extension rates, polymers are significantly stretched by extensional flows, and the extensional viscosity growth function exhibits strain hardening. To reveal their quantitative relation, we adopt an analysis method based on the Rouse-type model. We demonstrate that the extensional viscosity growth function is determined by the instantaneous gyration radii in the parallel and perpendicular directions to the extensional direction and their time derivatives. Our approach also provides a framework to describe the steady-state extensional viscosity of dilute polymer solutions for various chain lengths and concentrations in terms of the polymer gyration radius.

In this study, we investigated how symmetric and asymmetric slit geometries influenced the flow-induced structure of rod-like micellar solutions in abrupt contraction-expansion flows. Birefringence and stream-pathline measurements were conducted to clarify the relationship between micellar orientation, elastic stresses, and geometric confinement. The results showed that (i) the in-slit birefringence distribution systematically changes with geometry, exhibiting a strongly asymmetric pattern in asymmetric channels, (ii) the characteristic birefringence structure upstream of the slit is strongly affected by channel height, suggesting the contribution of out-of-plane strain, and (iii) the flow field is dominated by elastic effects under all conditions tested, as indicated by large Weissenberg numbers. Temperature variation substantially modified the micellar length and flexibility, leading to enhanced birefringence at low temperature and markedly reduced birefringence at high temperature, where the birefringence was confined inside the slit. These results demonstrated that geometry-dependent strain fields and the degree of spatial constraint jointly governed the formation of flow-induced structures in rod-like micellar solutions.

Our superposition rheometry is so called a parallel superposition method and was anticipated in the previous paper to be a significant method for the rheology of complex fluids. In this report, as to the analyzation after this method, it is found that the deformation of elastic component, λ, in a complex fluid is estimated by the Eq. 1. This equation is the addition of elastic and viscous forces and is fit to a three-component rheology model. Dividing value of the deformation by the shear rate, λ/͘γ, is the relaxation time of Maxwell model. The consistency of this relaxation time is confirmed by coincidence with those values by other methods, using an HEUR (C24-hydrophobically modified ethoxylated urethane) aqueous solution which is a Maxwell fluid with single relaxation. As the rigidity modulus and the deformation are measured separately, utilization and understanding of various rheological properties or behaviors related to the deformation are greatly expected to progress.

This study proposes a simple method for detecting ultrafine bubble (UFB) by utilizing bubble behavior near rough surfaces. UFB, with diameters less than 1 μm, are widely used in industrial applications, but their detection remains challenging due to their nanoscale size. In this work, a rough wall was placed in water containing UFB, and bubble generation and growth near the surface were observed under controlled flow conditions. The results revealed that bubble generation and growth depend on three factors: UFB presence, flow, and surface roughness. In UFB water, bubbles exhibited significant growth, whereas they shrank and disappeared in deionized water. Furthermore, initial gas cavities trapped in surface cavities acted as nucleation sites, and their removal by degassing suppressed bubble formation even in UFB water. Comparison with classical nucleation theory suggests that local pressure reduction and direct gas supply from UFB enable bubble growth below the theoretical critical radius. This approach provides a practical and low-cost method for evaluating UFB presence without specialized instruments.

Deriving constitutive models (CMs) from numerical data has been an attractive approach as a systematic CM building method. One recent study is Rheo-SINDy, which extended the sparse identification of nonlinear dynamics (SINDy) method to rheology. Although the Rheo-SINDy framework discovered an approximate CM from numerical data under shear flow, its versatility has not been investigated. To clarify its applicability to other types of flows, this study applied Rheo-SINDy to numerically generated data under extensional flow conditions. As baseline tests for extensional flow, we considered two problems: (i) whether the Rheo-SINDy framework can reproduce the famous Giesekus model from data generated by that model, and (ii) whether it can derive an approximate CM from data generated by a dumbbell model with a finite extensible nonlinear elastic (FENE) spring. For problem (i), we confirmed that Rheo-SINDy can identify the exact expression of the Giesekus model under extensional flow. For problem (ii), the Rheo-SINDy framework discovered a relatively simple expression of the approximate CM by manually designing the library matrix based on rheological knowledge. The identified approximate CM can reasonably predict extensional rheological properties of the FENE dumbbell model, including an extrapolation region. These findings demonstrate the fundamental validity of using Rheo-SINDy under extensional flow.

We investigated the linear viscoelastic behavior of poly(1-ethyl-3-vinylimidazolium bis(trifluoromethanesulfonyl)imide) (PC₂-TFSI) while varying its molecular weight to clarify the molecular origin of the unusual zero-shear viscosity scaling, η₀ ∝ M^1.7, reported in earlier studies for unentangled poly(ionic liquid)s. PC₂-TFSI exhibited a broadening of linear viscoelastic spectra in the vicinity of glass transition zone, similar to the shape of spectra observed for other alkyl-substituted vinylimidazolium-based poly(ionic liquid)s. Therefore, we attributed this broadening to cooperative local motions, such as sub-Rouse motion, caused by enhanced intra-chain interactions. By decomposing the complex modulus of PC₂-TFSI into three components, the glassy, sub-Rouse, and Rouse components, through the modified stress-optical rule, we found that the relaxation time of the sub-Rouse mode increased as the molecular weight of PC₂-TFSI increased. Moreover, the limiting viscosity associated with the sub-Rouse mode followed the scaling of η_lim ∝ M^1.1. Since polymer chain relaxation occurs in a hierarchical manner, the obtained scaling exponent for the sub-Rouse mode can account for the gap between the theoretical prediction of η₀ ∝ M^1.0 and the experimentally observed scaling of zero-shear viscosity of η₀ ∝ M^1.7. The molecular-weight dependence of local motions is unexpected, but we hypothesize that it arises from the enhancement of the solvent-like behavior of dissociated counterions as the PIL molecular weight increases.

Understanding how reversible interactions influence polymer dynamics is essential for designing advanced functional materials. Host–guest complexes represent a versatile class of reversible interactions owing to their molecular selectivity and tunable bonding strength. Although host–guest complexes have been widely utilized as reversible cross-links in aqueous polymer systems, their role in bulk polymers remains unclear, mainly because direct experimental observation of complex formation in the solid state is challenging. This study addresses whether host–guest complexes can function as effective reversible cross-links in polymers and how they influence chain dynamics. Herein, polymers incorporating host–guest complexes exhibited characteristic changes in linear viscoelasticity that are quantitatively described by the sticky reptation model. The plateau modulus (G_N) gradually decreased, while the terminal relaxation time (τ_d) increased with increasing host–guest content. The G_N values are well explained by considering both entanglement dilution and reinforcement by reversible cross-links. The prolonged τd indicates suppressed chain reptation due to reversible topological constraints. Furthermore, the effective association probability (p) and bonding lifetime (τ_s) were extracted through model-based analysis, providing indirect yet quantitative evidence of reversible complex formation in polymers. These findings establish rheological analysis for probing supramolecular interactions in polymers and highlight host–guest complexes as tunable modifiers of polymer dynamics.