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Abstract Non-Newtonian fluid mechanics and computational rheology widely exploit elastic dumbbell models such as Oldroyd-B and FENE-P for a continuum description of viscoelastic fluid flows. However, these constitutive equations fail to accurately capture some characteristics of realistic polymers, such as the steady extension in simple shear and extensional flows, thus questioning the ability of continuum-level modeling to predict the hydrodynamic behavior of viscoelastic fluids in more complex flows. Here, we present seven elastic dumbbell models, which include different microstructurally inspired terms, i.e., (i) the finite polymer extensibility, (ii) the conformation-dependent friction coefficient, and (iii) the conformation-dependent non-affine deformation. We provide the expressions for the steady dumbbell extension in shear and extensional flows and the corresponding viscosities for various elastic dumbbell models incorporating different microscopic features. We show the necessity of including these microscopic features in a constitutive equation to reproduce the experimentally observed polymer extension in shear and extensional flows, highlighting their potential significance in accurately modeling viscoelastic channel flow with mixed kinematics. 

Physical Review . Polynyas—persistent regions of open water within polar sea ice—play a critical role in polar ocean-atmosphere interactions. We combine theoretical modeling and numerical simulations to investigate the dynamics and thermodynamics of wind-driven, latent-heat-generated polynya formation adjacent to straight and curved coastlines. Under the assumption of negligible ice internal pressure, we propose a one-dimensional, continuum, mass- and momentum-conserving theory characterizing the offshore distribution of ice velocity and the spatiotemporal evolution of ice concentration. Finite-element simulations incorporating realistic sea-ice rheology validate the theoretical predictions, demonstrating strong agreement in steady-state polynya widths and ice dynamics. These results align qualitatively with observational climate data. Furthermore, we generalize the framework to two dimensions, enabling quantitative predictions of leeward polynya formation around a model circular island. The proposed theoretical framework advances mechanistic understanding of polynya formation and provides a foundation for improving their representation in climate models. 

Single-chain nanoparticles (SCNPs) formviaintramolecular folding and cross-linking of polymers. We examine how dimensionless design parameters dictate SCNP morphology, highlighting the influence of shear flow. 

The Weissenberg effect, or rod-climbing phenomenon, occurs in non-Newtonian fluids where the fluid interface ascends along a rotating rod. Despite its prominence, theoretical insights into this phenomenon remain limited. In earlier work, Joseph & Fosdick (1973,Arch. Rat. Mech. Anal.vol. 49, pp. 321–380) employed domain perturbation methods for second-order fluids to determine the equilibrium interface height by expanding solutions based on the rotation speed. In this work, we investigate the time-dependent interface height through asymptotic analysis with dimensionless variables and equations using the Giesekus model. We begin by neglecting inertia to focus on the interaction between gravity, viscoelasticity and surface tension. In the small-deformation scenario, the governing equations indicate the presence of a boundary layer in time, where the interface rises rapidly over a short time scale before gradually approaching a steady state. By employing a stretched time variable, we derive the transient velocity field and corresponding interface shape on this short time scale, and recover the steady-state shape on a longer time scale. In contrast to the work of Joseph and Fosdick, which used the method of successive approximations to determine the steady shape of the interface, we explicitly derive the interface shape for both steady and transient cases. Subsequently, we reintroduce small but finite inertial effects to investigate their interaction with viscoelasticity, and propose a criterion for determining the conditions under which rod climbing occurs. Through numerical computations, we obtain the transient interface shapes, highlighting the interplay between time-dependent viscoelastic and inertial effects. 

A spherical capsule (radius$$R$$) is suspended in a viscous liquid (viscosity$$\mu$$) and exposed to a uniaxial extensional flow of strain rate$$E$$. The elasticity of the membrane surrounding the capsule is described by the Skalak constitutive law, expressed in terms of a surface shear modulus$$G$$and an area dilatation modulus$$K$$. Dimensional arguments imply that the slenderness$$\epsilon$$of the deformed capsule depends only upon$$K/G$$and the elastic capillary number$${Ca}=\mu R E/G$$. We address the coupled flow–deformation problem in the limit of strong flow,$${Ca}\gg 1$$, where large deformation allows for the use of approximation methods in the limit$$\epsilon \ll 1$$. The key conceptual challenge, encountered at the very formulation of the problem, is in describing the Lagrangian mapping from the spherical reference state in a manner compatible with hydrodynamic slender-body formulation. Scaling analysis reveals that$$\epsilon$$is proportional to$${Ca}^{-2/3}$$, with the hydrodynamic problem introducing a dependence of the proportionality prefactor upon$$\ln \epsilon$$. Going beyond scaling arguments, we employ asymptotic methods to obtain a reduced formulation, consisting of a differential equation governing a mapping field and an integral equation governing the axial tension distribution. The leading-order deformation is independent of the ratio$$K/G$$; in particular, we find the approximation$$\epsilon ^{2/3} {Ca}\approx 0.2753\ln (2/\epsilon ^2)$$for the relation between$$\epsilon$$and$$Ca$$. A scaling analysis for the neo-Hookean constitutive law reveals the impossibility of a steady slender shape, in agreement with existing numerical simulations. More generally, the present asymptotic paradigm allows us to rigorously discriminate between strain-softening and strain-hardening models. 

We analyse the steady viscoelastic fluid flow in slowly varying contracting channels of arbitrary shape and present a theory based on the lubrication approximation for calculating the flow rate–pressure drop relation at low and high Deborah ($$De$$) numbers. Unlike most prior theoretical studies leveraging the Oldroyd-B model, we describe the fluid viscoelasticity using a FENE-CR model and examine how the polymer chains’ finite extensibility impacts the pressure drop. We employ the low-Deborah-number lubrication analysis to provide analytical expressions for the pressure drop up to$$O(De^4)$$. We further consider the ultra-dilute limit and exploit a one-way coupling between the parabolic velocity and elastic stresses to calculate the pressure drop of the FENE-CR fluid for arbitrary values of the Deborah number. Such an approach allows us to elucidate elastic stress contributions governing the pressure drop variations and the effect of finite extensibility for all$$De$$. We validate our theoretical predictions with two-dimensional numerical simulations and find excellent agreement. We show that, at low Deborah numbers, the pressure drop of the FENE-CR fluid monotonically decreases with$$De$$, similar to the previous results for the Oldroyd-B and FENE-P fluids. However, at high Deborah numbers, in contrast to a linear decrease for the Oldroyd-B fluid, the pressure drop of the FENE-CR fluid exhibits a non-monotonic variation due to finite extensibility, first decreasing and then increasing with$$De$$. Nevertheless, even at sufficiently high Deborah numbers, the pressure drop of the FENE-CR fluid in the ultra-dilute and lubrication limits is lower than the corresponding Newtonian pressure drop. 

Lubrication theory is adapted to incorporate the large normal stresses that occur for order-one Deborah numbers,$$De$$, the ratio of the relaxation time to the residence time. Comparing with the pressure drop for a Newtonian viscous fluid with a viscosity equal to that of an Oldroyd-B fluid in steady simple shear, we find numerically a reduced pressure drop through a contraction and an increased pressure drop through an expansion, both changing linearly with$$De$$at high$$De$$. For a constriction, there is a smaller pressure drop that plateaus at high$$De$$. For a contraction, much of the change in pressure drop occurs in the stress relaxation in a long exit channel. An asymptotic analysis for high$$De$$, based on the idea that normal stresses are stretched by an accelerating flow in proportion to the square of the velocity, reveals that the large linear changes in pressure drop are due to higher normal stresses pulling the fluid through the narrowest gap. A secondary cause of the reduction is that the elastic shear stresses do not have time to build up to their steady-state equilibrium value while they accelerate through a contraction. We find for a contraction or expansion that the high$$De$$analysis works well for$$De>0.4$$.