non-Newtonian Fluid Mechanics Research Articles

On more insightful dimensionless numbers for computational viscoelastic rheology

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 (λ) and the nominal total viscosity (η) instead of their effective counterparts when defining the Reynolds number (Re), the Weissenberg number (Wi) and the ratio of solvent to total viscosities (β) (β 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 β 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 β) 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.

Exploring the interaction of viscosity and nipple design on feeding performance in an infant pig model.

Infant feeding behaviors are modulated via sensorimotor feedback, such that sensory perturbations can significantly impact performance. Properties of the nipple and milk (e.g., nipple hole size and viscosity) are critical sources of sensory information. However, the direct effects of varying milk and nipple properties on infant motor output and the subsequent changes in feeding performance are poorly understood. In this study, we use an infant pig model to explore the interaction between nipple hole size and milk viscosity. Using high-speed videofluoroscopy and electromyography, we measured key performance metrics including sucks per swallow and suck duration, then synchronized these data with the onset and offset of activity of jaw opening and closing muscles. The combination of a small nipple hole and thick milk resulted in negative effects on both suck and swallow performance, with reduced feeding efficiency compared to the other treatments. It also appears that this combination of viscosity and hole size disrupts the coordination between correlates of tongue and jaw movements. We did not see a difference in feeding efficiency between viscosities when infants fed on the large-hole nipple, which may be the result of non-Newtonian fluid mechanics. Our results emphasize the importance of considering both fluid and nipple properties when considering alterations to an infant's feeding system.

Significance of Darcy–Forchheimer law and magnetic field on the comparison of Williamson–Casson fluid subject to an exponential stretching sheet

Non-Newtonian fluid mechanics is becoming more and more relevant as time marches on due to the increasing number of fluids encountered in everyday life that exhibit non-Newtonian behavior. It is our intention to cover the multitude of aspects of non-Newtonian fluid mechanics: The effects of magnetohydrodynamic (MHD) laminar boundary layer flow with heat and concentration transfers are considered in the case of Darcy–Forchheimer Williamson–Casson fluids installed over an exponentially extending sheet. There has been an examination and comparison of the effects of momentum fields, thermal radiation, Joule heating, suction/ injection, and compound responses. By using a suitable closeness change, the boundary conditions (BCs) and partial differential equations (PDEs) are reduced to dimensionless structures. The following set of ordinary differential equations (ODEs) and associated BCs are to be clarified using the bvp4c technique. The investigation’s findings indicate that boundary layer thicknesses for velocity, temperature, and concentration normally decline as we get farther from the sheet’s edge, and it is discovered that the Williamson–Casson parameter interferes with velocity profiles. Graphs are developed for Darcy–Forchheimer [Formula: see text], magnetic parameter M, Lewis number Le, radiation parameter [Formula: see text], porosity parameter [Formula: see text], and Eckert number [Formula: see text]. The numeric values of [Formula: see text] and [Formula: see text] are validated with available data and found to be in excellent agreement.

Editorial: Celebrating the contributions of Professor Guieppe Marrucci to rheology and non-Newtonian fluid mechanics

Direct numerical simulations (DNS) of generalized Newtonian fluids in a rectangular channel at a friction velocity of 180 are performed using OpenFOAM. The simulations are performed for a Newtonian fluid, a power-law fluid, and a Herschel-Bulkley (HB) fluid. Two-point correlations of the streamwise velocity reveal that a significant increase in the computational domain size is required to avoid statistical correlation due to the shear-thinning and yield stress. The analogous Kolmogorov scale shows that the dissipative structures may be orders of magnitude larger with these two non-Newtonian behaviors. This is demonstrated to be linked to the significant increase in the viscosity. The mean streamwise velocity field integrates to a larger bulk velocity with increased shear-thinning as compared with the Newtonian fluid flow. The addition of the yield stress does the same with respect to the power-law fluid flow. The difference in the velocity profiles is more pronounced in the outer layer. It, however, is observed that the rheology does not play a significant role in the outer layer for the mean streamwise velocity. It is shown that an HB fluid flow does not necessarily show an increase in the fluctuating streamwise velocity with respect to a power-law fluid flow. It is also shown that low power index and high Hedstrom number lead to strong turbulence anisotropy due to the weakening of turbulence. The turbulent kinetic energy (TKE) budget reveals that the studied non-Newtonian behavior mainly affects the inner layer of the flow. The yield stress is also seen to show small variations in the TKE budget in the outer layer. This is attributed to the weakening turbulence as a result of the increased viscosity near the center. It is also demonstrated that the studied HB fluid flow results can be successfully reproduced by under-resolved DNS.

Professor E. Mitsoulis's contributions to rheology and computational non-Newtonian fluid mechanics

Professor E. Mitsoulis's contributions to rheology and computational non-Newtonian fluid mechanics

Application of a maritime CFD code to a benchmark problem for non-Newtonian fluids: the flow around a sphere

The ship’s resistance and manoeuvrability in shallow waters can be adversely influenced by the presence of fluid mud layers on the seabed of ports and waterways. Fluid mud exhibits a complex non-Newtonian rheology that is often described using the Herschel–Bulkley model. The latter has been recently implemented in a maritime finite-volume CFD code to study the manoeuvrability of ships in the presence of muddy seabeds. In this paper, we explore the accuracy and robustness of the CFD code in simulating the flow of Herschel–Bulkley fluids, including power-law, Bingham and Newtonian fluids as particular cases. As a stepping stone towards the final maritime applications, the study is carried out on a classic benchmark problem in non-Newtonian fluid mechanics: the laminar flow around a sphere. The aim is to test the performance of the non-Newtonian solver before applying it to the more complex scenarios. Present results could also be used as reference data for future testing. Flow simulations are carried out at low Reynolds numbers in order to compare our results with an extensive collection of data from the literature. Results agree both qualitatively and quantitatively with literature. Difficulties in the convergence of the iterative solver emerged when simulating Bingham and Herschel–Bulkley flows. A simple change in the interpolation of the apparent viscosity has mitigated such difficulties. The results of this work, combined with our previous code verification exercises, suggest that the non-Newtonian solver works as intended and it can be thus employed on more complex applications.

Assessment of polymer feedback coupling approaches in simulation of viscoelastic fluids using the lattice Boltzmann method

The lattice Boltzmann method (LBM) has emerged as a popular approach to simulate complex non-Newtonian fluid mechanics problems, such as those involving viscoelastic fluids. In these cases, the LBM solver often requires modelling additional non-linear and non-ideal hydrodynamic contributions to the flow resulting from the addition of polymer molecules. These additional contributions, commonly referred to as the polymer feedback, are either incorporated directly in the Boltzmann stress (pressure method) or alternatively in the momentum field as a forcing contribution (forcing method). The choice of coupling approach has in previous works been strongly speculated to impact the numerical accuracy and stability of LBM solvers for viscoelastic fluids, however no formal comparison has been conducted. In this work, we compare the two popular polymer feedback coupling approaches, as well as the various schemes commonly used in the forcing method, namely, the explicit forcing (EF) scheme (He et al., 1998), the Guo et al. scheme (Guo et al., 2002), and the exact-difference-method (EDM) (Kupershtokh et al., 2009). First, through a theoretical comparison in recovering the macroscopic equations, we show that both the EF and Guo et al. forcing schemes retain the exact hydrodynamic representation up to second-order, whereas the EDM scheme includes additional lattice error terms. Similarly, the pressure method retains additional unphysical terms, which are known to violate Galilean invariance. Through numerical tests, involving the steady and time-dependent Poiseuille flow cases, as well as the four-roll mill problem under both steady and transient regimes, it is shown that the forcing method has enhanced numerical accuracy and stability at varying elastic effects. Alternatively, owing to the violation of Galilean invariance, the pressure method proved to be unstable even for moderate elastic effects. The obtained results are useful in determining the optimal polymer feedback coupling approach when simulating viscoelastic fluids using LBM, as well as further testing the generality of previous LBM findings on non-ideal coupling approaches for viscoelastic fluids.

On the similarities of the sPTT and FENE-P models for polymeric fluids

<h2>Abstract</h2> For many commonly used single mode viscoelastic constitutive equations of differential type, it is well known that they share many features. For example, in certain parameter limits the models due to Giesekus, Phan-Thien Tanner and FENE-type models approach the Oldroyd-B model. In this talk, I'll compare the response of the linear form of the simplified Phan-Thien Tanner model [due to Phan-Thien and Tanner, Journal of Non-Newtonian Fluid Mechanics, 2 (1977) 353–365] (the "sPTT") and the Finitely Extensible Nonlinear Elastic model that follows the Peterlin approximation [due to Bird et al., Journal of Non-Newtonian Fluid Mechanics, 7 (1980) 213–235] (the "FENE-P"). I'll show that for steady homogeneous flows such as steady simple shear flow or pure extension the response of both models is identical under certain conditions. For more general flows we show analytically that the results from the two models only formally approach each other when both the polymer concentration and Weissenberg number is small. We then use a numerical approach to investigate the response of the two models when the flow is "complex" under two different definitions: firstly, when the applied deformation field is homogenous in space but transient in time (so called "start-up" shear and planar extensional flow) and then for "complex" flows (through a range of geometries) which, although Eulerian steady, are unsteady in a Lagrangian sense. Under the limit that the flows remain Eulerian steady (so the Weissenberg number is typically small), we see once again a very close agreement between the FENE-P and sPTT models.

Editorial for special issue on “Oldroyd at 100: Celebrating the impact of J. G. Oldroyd on non-Newtonian fluid mechanics

Editorial for special issue on “Oldroyd at 100: Celebrating the impact of J. G. Oldroyd on non-Newtonian fluid mechanics

Response to “Comment on the paper “Wall effects for spherical particle in confined shear-thickening fluids, Shuai Tian, Journal of Non-Newtonian Fluid Mechanics 257(2018) 13–21″”

• The physical problem investigated in Rajasekhar and Kishore (2012) and Tian (2018) is explained. • Two models are employed to study falling particle problem in a bounded flow. • Boundary configuration with stationary particle and moving tube wall is proven to be appropriate for bounded flow. The present response is being written to clarify the issues raised in the above article.

Different Formulations to Solve the Giesekus Model for Flow between Two Parallel Plates

This work presents different formulations to obtain the solution for the Giesekus constitutive model for a flow between two parallel plates. The first one is the formulation based on work by Schleiniger, G; Weinacht, R.J., [Journal of Non-Newtonian Fluid Mechanics, 40, 79–102 (1991)]. The second formulation is based on the concept of changing the independent variable to obtain the solution of the fluid flow components in terms of this variable. This change allows the flow components to be obtained analytically, with the exception of the velocity profile, which is obtained using a high-order numerical integration method. The last formulation is based on the numerical simulation of the governing equations using high-order approximations. The results show that each formulation presented has advantages and disadvantages, and it was investigated different viscoelastic fluid flows by varying the dimensionless parameters, considering purely polymeric fluid flow, closer to purely polymeric fluid flow, solvent contribution on the mixture of fluid, and high Weissenberg numbers.

Building on Oldroyd’s viscoplastic legacy: Perspectives and new developments

The decade following the second world war heralded the publication of a collection of important papers on non-Newtonian fluid mechanics; Oldroyd’s work featured heavily in this collection. Not only did these articles establish important results, but Oldroyd’s style and methods set the scene for subsequent work in the area, exploiting mathematical analysis to formulate problems, establish results and guide further research. While Oldroyd’s name will forever be linked with the study of elastic fluids, the purpose of the present paper is to offer a modern perspective on a number of Oldroyd’s papers on viscoplastic fluids from 1947–1951 [1], [2], [3], [4], [5], [6], [7], [8]. Along the way, we sprinkle in a brief review of some of the subsequent developments stemming from Oldroyd’s advances, together with a few new results guided by his work. Following the approach of most of Oldroyd’s original papers, we focus on unidirectional flow down conduits. In an Appendix, we complement this discussion with a lubrication analysis, extending, clarifying and correcting the important original analysis of Walton and Bittleston (1991) [9]; although lubrication theory was not directly utilized by Oldroyd, the methodology aligns with his philosophy of using asymptotic and analytical approaches.

The Effect of Bubbles on Particle Migration in Non-Newtonian Fluids

The movement of the gas–liquid interface caused by the movement of the bubble position will have an impact on the starting conditions for particle migration. This article quantifies the influence of moving bubbles on the starting conditions of particle migration in non-Newtonian fluids, and it aims to better understand the influence of bubbles moving in non-Newtonian fluids on particle migration to achieve more effective control. First, the forces and moments acting on the particles are analyzed; then, fluid dynamics, non-Newtonian fluid mechanics, extended DLVO (Derjaguin Landau Verwey Overbeek theory), surface tension, and friction are applied on the combined effects of particle migration. Then, we reasonably predict the influence of gas–liquid interface movement on particle migration in non-Newtonian fluids. The theoretical results show that the movement of the gas–liquid interface in non-Newtonian fluids will increase the separation force acting on the particles, which will lead to particle migration. Second, we carry out the particle migration experiment of moving bubbles in non-Newtonian fluid. Experiments show that when the solid–liquid two-phase flow is originally stable, particle migration occurs after the bubble movement is added. This phenomenon shows that the non-Newtonian fluid with bubble motion has stronger particle migration ability. Although there are some errors, the experimental results basically support the theoretical data.

A study on mixed electro-osmotic/pressure-driven microchannel flows of a generalised Phan-Thien–Tanner fluid

This work presents new semi-analytical solutions for the combined fully developed electro-osmotic pressure-driven flow in microchannels of viscoelastic fluids, described by the generalised Phan-Thien–Tanner model (gPTT) recently proposed by Ferras et al. (Journal of Non-Newtonian Fluid Mechanics, 269:88–99, 2019). This generalised version of the PTT model presents a new function for the trace of the stress tensor—the Mittag–Leffler function—where one or two new fitting constants are considered in order to obtain additional fitting flexibility. The semi-analytical solution is obtained under sufficiently weak electric potential that allows the Debye–Huckel approximation for the electrokinetic fields and for thin electric double layers. Based on the solution, the effects of the various relevant dimensionless numbers are assessed and discussed, such as the influence of $$\varepsilon Wi^2$$ , of the parameters $$\alpha $$ and $$\beta $$ of the gPTT model, and also of $${\bar{\kappa }}$$ , the dimensionless Debye–Huckel parameter. We conclude that the new model characteristics enhance the effects of both $$\varepsilon Wi^2$$ and $${\bar{\kappa }}$$ on the velocity distribution across the microchannels. The effects of a high zeta potential and of the finite size of ions are also studied numerically.

Comment on the paper “Wall effects for spherical particle in confined shear-thickening fluids, Shuai Tian, Journal of Non-Newtonian Fluid Mechanics 257(2018) 13–21”

Comment on the paper “Wall effects for spherical particle in confined shear-thickening fluids, Shuai Tian, Journal of Non-Newtonian Fluid Mechanics 257(2018) 13–21”

A hybrid analytical algorithm for thin film flow problem occurring in non-Newtonian fluid mechanics

In this work, we investigate thin film flow of a third grade fluid down a inclined plane. The solution of a nonlinear boundary value problem (BVP) is derived by using an effective well organized computational scheme namely homotopy perturbation Elzaki transform method. Furthermore, this model is also resolved by Elzaki decomposition technique. The outcomes achieved by these two approaches are consistent with each other and because of that this technique may be regarded as an optional and effective scheme for determining results of linear and nonlinear BVP. Moreover, the homotopy perturbation Elzaki transform method leads over the Elzaki decomposition method since the nonlinear problems are solved without utilization of Adomian polynomials.

Corrigendum to "Local similarity solution for steady laminar planar jet flow of viscoelastic FENE-P fluids" [Journal of Non-Newtonian Fluid Mechanics 279 (2020) 104265

Corrigendum to "Local similarity solution for steady laminar planar jet flow of viscoelastic FENE-P fluids" [Journal of Non-Newtonian Fluid Mechanics 279 (2020) 104265

Papers from the 2019 Institute of Non-Newtonian Fluid Mechanics Meeting in Lake Vyrnwy, Wales

Papers from the 2019 Institute of Non-Newtonian Fluid Mechanics Meeting in Lake Vyrnwy, Wales

Two Efficient Computational Algorithms to Solve the Nonlinear Singular Lane-Emden Equations

In this paper, two efficient computational algorithms based on Rational and Exponential Bessel (RB and EB) functions are compared to solve several well-known classes of nonlinear Lane-Emden type models. The problems, which are define in some models of non-Newtonian fluid mechanics and mathematical physics, are nonlinear ordinary differential equations of second-order over the semi-infinite interval and have a singularity at x = 0. The nonlinear Lane-Emden equations are converted to a sequence of linear differential equations by utilizing the quasilinearization method (QLM), and then these linear equations are solved by RB and EB collocation methods. Afterwards, the obtained results are compared with the solution of other methods to demonstrate the efficiency and applicability of the proposed methods.

Recent Advances in Mechanics of Non-Newtonian Fluids

Flow of non-Newtonian (non-linear) fluids occurs not only in nature, for example, mud slides and avalanches, but also in many industrial processes involving chemicals (polymers), biological materials (blood), food (honey, ketchup, yogurt), pharmaceutical and personal care items (shampoo, creams), etc [...]