Journal of Non-Newtonian Fluid Mechanics最新文献

We analyze the fully developed Couette–Poiseuille flows of ferrofluids between two parallel flat walls subject to three types of time-varying magnetic fields. In these scenarios, ferrofluids exhibit diverse non-Newtonian characteristics such as distinct flow velocity distribution, apparent viscosity and shear stress compared to ordinary Couette–Poiseuille flows. The influence of spin viscosity is explored first through the solution of the governing equations with zero and non-zero spin viscosities. It shows that although the value of the spin viscosity is very small, its inviscid limit would have great influence over the velocity and spin velocity distributions. The assumption of zero spin viscosity leads to an exaggerated non-Newtonian behavior induced by time-varying magnetic fields in the ferrofluid Couette–Poiseuille flows. Then the solutions of equations with non-zero spin viscosity are utilized to delve into non-Newtonian behaviors of ferrofluid Couette–Poiseuille flow under the application of the three time-varying magnetic fields. The results indicate that negative rotational viscosity will occur if the dimensionless frequency lies in the range 1–10, which is a distinguishing feature compared with Newtonian flows. At this point, non-Newtonian flow induced by magnetic field arises, although this effect is very tiny. Within the same frequency range, reversed tangential stress appears in strong uniform alternating magnetic fields. The minimum negative rotational viscosity may arrive at up to 20 % of the intrinsic viscosity in the rotating magnetic field when the magnetization relaxation time is 4 ms.

The present experimental investigation combines the bulk flow properties of polymer solutions and measurable rheological parameters as they flow through a distinctive micro-porous structure, with micro-PIV (micro-particle image velocimetry) to measure the velocity distribution and velocity fluctuations within individual pores of a novel porous glass structure. To investigate the effects of fluid elasticity at pore scale, aqueous solutions of a polyacrylamide (PAA) & polyethylene oxide (PEO) in the concentration range of 50–200 ppm, which were characterized in both shear and extensional flows using shear and capillary break-up extensional rheometers (CaBER) respectively, were used as working fluids. The velocity field measurement includes the velocity magnitude and fluctuation intensity in several different pores within the porous material across a Weissenberg number $Wi$ range of approximately 0.01 to 1 for each of the test fluids. The global averaged fluctuation intensity increases with $Wi$ but the critical value, which indicates the onset of significant unsteadiness (i.e. well above noise floor/Newtonian baseline) within the flow at pore scale gives an approximately constant value of $Wi\approx$0.4, which is almost 40 times higher than the value that is observed in the pressure-drop measurements for the data to rise above the Newtonian base line. We therefore postulate that the enhanced pressure-drop behaviour of the bulk flow may not be due to local velocity fluctuations within the pores but due to mean flow effects, at least over a significant portion of the data (up to $Wi\approx$0.4).

Ken Walters was one of the most prominent rheologists of recent times. He brought his mathematical training to rheology and pioneered analysis of many common test procedures. In order to do this he contributed to the formation of nonlinear constitutive equations for viscoelastic fluids and he was an early exponent of computational studies in rheology. He also applied his skills in fruitful collaborations with industry - notably the oil and china clay industries. He was born in Swansea, South Wales, in 1934 and he remained a devoted Welshman despite travelling widely. His academic studies in Swansea with James Oldroyd led to the PhD degree in 1959. In 1960, after a stint in the U.S.A., he was appointed as a Lecturer at Aberystwyth, and he remained there until his death in 2022. He built a very strong research team at Aberystwyth which became a dominant factor in the rheological scene in the United Kingdom.

He was a keen promoter of rheology and he assisted in the organisation of many conferences and meetings. He was the founding Editor of the Journal of Non-Newtonian Fluid Mechanics (JNNFM). He authored or co-authored four well-known books on rheology plus several tracts of a religious nature - Ken was always a devoted Christian. He was also a very able sportsman especially at cricket and golf. He is survived by his wife Mary, three children and seven grandchildren.

A number of commercial fluids, including synthetic automotive oils, food and consumer products containing polymer additives exhibit weakly rate-thickening responses in the final stages of capillarity-driven thinning, where a large accumulated strain and high extensional strain rate alter the thinning dynamics of the slender liquid filament. Consequently, measurements of capillarity-driven thinning dynamics typically feature two distinct regions at the early and late stages of the filament breakup process, each dominated by distinct mechanisms. These features have been incorporated in a simple Inelastic Rate-Thickening (IRT) model with linear and quadratic contributions to the constitutive stress–strain rate relationship, in which the apparent extensional viscosity slowly thickens at high strain rates. We numerically compute the thinning dynamics of the IRT model assuming an axially-slender axisymmetric filament and no fluid inertia. The computational results motivate a similarity transformation and we obtain a new self-similar solution in which the second-order stress is balanced by capillarity. The new asymptotic solution leads to a self-similar filament shape that is more slender than the Newtonian counterpart and, close to singularity, results in a quadratic dependence of the mid-point radius of the filament with time to breakup. A new and distinct asymptotic geometric correction factor, $X\approx 0.5827$ is derived and we show that a more accurate value of the true extensional viscosity in a rate-thickening fluid can be recovered from an interpolated time-varying geometric correction factor based on the magnitudes of different stress components. Finally, we propose a statistically data-driven protocol to select the best-fit constitutive model using a parameter-free information criterion. This enables us to more accurately quantify the extensional rheological behavior of complex rate-thickening viscoelastic fluids using capillarity-driven thinning dynamics.

Abrupt contraction flows involving viscoelastic fluids represent a longstanding computational challenge within the field of non-Newtonian fluid mechanics. Despite the apparent simplicity of the geometry, these flows have given rise to intricate discussions in the study of viscoelastic phenomena. This study aims to re-examine the numerical solutions for flows through abrupt contractions, offering a fresh interpretation through the lens of reformulated dimensionless numbers. These numbers are designed to consider the characteristic shear rate of the problem, providing a more comprehensive understanding of the underlying dynamics.

When investigating models with intermediate levels of complexity, such as the Giesekus and Phan-Thien-Tanner constitutive equations, the usual comparison with the corresponding Oldroyd-B model becomes inadequate because it tends to rely on the nominal relaxation time ($\lambda$) and the nominal total viscosity ($\eta$) instead of their effective counterparts when defining the Reynolds number ($Re$), the Weissenberg number ($Wi$) and the ratio of solvent to total viscosities ($\beta$) ($\beta$ plays a role only in rheological models involving a solvent contribution). If these dimensionless numbers are tailored to account for the characteristic shear rate specific to the problem under investigation, the choice of the corresponding Oldroyd-B flow, at the adequate values of $Re$, $Wi$, and $\beta$ allows for significantly better quantification of the correct effects of nonlinear viscoelasticity of the original model.

We show the conventional approach tends to overemphasize the role of the nonlinear parameter in nonlinear constitutive equations, like the Giesekus and PTT models, when examining standard abrupt contraction flow outputs such as the Couette correction and vortex size. This overestimation occurs because the conventional method does not allow the Reynolds and Weissenberg numbers (and possibly $\beta$) to carry the portion of the nonlinear effect that can potentially be captured by the linear Oldroyd-B model through the use of characteristic shear rate-based values. We believe the present approach provides a better perspective of the role played by the nonlinear parameter and its extension to more general flows is also discussed.

This work aims to introduce a groundbreaking approach by directly computing the Fokker–Planck equation, providing a mesoscopic scale orientation indicator based on the 2D-probability density function (PDF) of the fibers’ orientation state. Unlike conventional methods that rely on pre-averaged quantities and closure approximations, our method offers enhanced accuracy and information preservation. The model’s enhanced accuracy can be served as a foundational tool for future studies, enabling the development of comprehensive models describing the fluid-flow coupling problem with precision. Consequently, this advancement facilitates the simulation of real-case scenarios, such as the dynamic motion of fibers during the injection phase of molten thermoplastics within a mold cavity. The novelty of this work lies in its application of the Streamline-Upwind/Petrov–Galerkin (SUPG) finite element method, on both orientation and physical spaces. Our model shows the potential to improve the understanding and prediction of fiber behavior in industrial applications, offering valuable insights into process optimization and design. Implemented within a finite element framework, a comprehensive investigation is conducted into the effects of mesh refinement, time scheme, and time stepping on the computational modeling of the PDF evolution, aiming to strike an optimal balance between model precision and computational efficiency. The validation tests were conducted for the case of simple shear flow to examine the influence of the interaction coefficient $C_I$ and the fiber shape factor $\lambda$ on the resolution of the probability distribution function. The numerical results demonstrate the evolution of fiber orientation over time under Poiseuille flow conditions.

In this short Editorial to support the Commemorative Special Issue in honour of our founding Editor, Professor Ken Walters FRS, we draw together a series of informal “reflections” from current (and previous) Editors of the Journal, together with a number of his key collaborators.