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Non-Newtonian liquids are characterized by stress and velocity-dependent dynamical response. In elasticity, and in particular, in the field of phononics, reciprocity in the equations acts against obtaining a directional response for passive media. Active stimuli-responsive materials have been conceived to overcome it. Significantly, Milton and Willis have shown theoretically in 2007 that quasi-rigid bodies containing masses at resonance can display a very rich dynamical behavior, hence opening a route toward the design of non-reciprocal and non-Newtonian metamaterials. In this paper, we design a solid structure that displays unidirectional shock resistance, thus going beyond Newton’s second law in analogy to non-Newtonian fluids. We design the mechanical metamaterial with finite element analysis and fabricate it using three-dimensional printing at the centimetric scale (with fused deposition modeling) and at the micrometric scale (with two-photon lithography). The non-Newtonian elastic response is measured via dynamical velocity-dependent experiments. Reversing the direction of the impact, we further highlight the intrinsic non-reciprocal response. In this work, authors demonstrate a model for non-reciprocal and non-Newtonian mechanical metamaterials by combining the concept of local resonances and fixing boundaries. Via computational models and impact experiments they show that stiffness substantially changes as a function of the loading velocity.

The main objective of this investigation to examine the momentum and thermal transportation of rotating dusty micropolar fluid flux with suspension of conducting dust particles across the stretched sheet. The novelty of the flow model is the exploration of the significance of boosting the volume concentration of dust particles in fluid dynamics. The governing PDEs of the problem for both phase models are transmuted into nonlinear coupled non-dimensional ODEs by utilizing suitable similarity modifications. The bvp4c technique was utilized in MATLAB script to acquire a graphical representation of the experimental results. This study illustrates the analysis of repercussions of pertinent parameters on non-Newtonian fluid and the dusty phase of fluid. By improving the volume concentration of dust particles and rotating parameters, the axial velocity for both phases depreciates, whereas temperature and transverse velocity for both phases have the opposite behavior. The micro-rotation distribution rises with higher contributions of rotating and material parameters, whereas it decreases against larger inputs of volume concentration of dust particles. The growing strength of the dust volume fraction (ϕd) caused the coefficient of skin friction to decrease along the x direction, and the skin friction coefficient is raised along the y direction.

Purpose The purpose of this study is to investigate heat transfer and electrokinetic non-Newtonian flow in a rectangular microchannel in the developed and transient states. Design/methodology/approach The Carreau–Yasuda model was considered to capture the non-Newtonian behavior of the fluid. The dimensionless forms of governing equations, including the continuity equation for the Carreau–Yasuda fluid, are numerically solved by considering the volumetric force term of electric current (DC). Findings The impact of pertinent parameters such as electrokinetic diameter (R), Brinkman number and Peclet number is examined graphically. It is observed that for increasing R, the bulk velocity decreases. The velocity of the bulk fluid reaches from the minimum to the maximum state across the microchannel over time. At the electrokinetic diameter of 400, the maximum velocity was obtained. Temperature graphs are plotted with changes in the various Brinkman number (0.1 < Br < 0.7) at different times, and local Nusselt are compared against changes in the Peclet number (0.1 < ℘e < 0.5). The results of this study show that by increasing the Brinkman number from 0.25 to 0.7, the temperature along the microchannel doubles. It was observed that increasing the Peclet number from 0.3 to 0.5 leads to 200% increment of the Nusselt number along the microchannel in some areas along the microchannel. The maximum temperature occurs at Brinkman number of 0.7 and the maximum value of the local Nusselt number is related to Peclet number 0.5. Over time in the transient mode, the Nusselt number also decreases along the microchannel. By the increasing of time, the temperature increases at given value of Brinkman, which is insignificant at Brinkman number of 0.1. The simulation results have been verified by Newtonian and non-Newtonian flows with adequate accuracy. Originality/value This study contributes to discovering the effects of transient flow of electroosmotic flow for non-Newtonian Carreau–Yasuda fluid and transient heat transfer through rectangular microchannel. To the authors’ knowledge, the said investigation is yet not available in existing literature.

Many subsurface engineering applications involve radial injection of non‐Newtonian fluids into fractured media, where the displacement efficiency of injected fluids profoundly impacts the injection performance. Despite its importance, how to enhance radial displacement efficiency of non‐Newtonian fluids in rough fractures remains rarely reported. Here, by conducting visualization experiments of shear‐thinning fluids radially displacing silicone oil in a rough fracture, we report a novel transition in displacement patterns from capillary fingering to compact displacement (CD) to viscous fingering with increasing injection rate, which differs from conventional expectations for Newtonian fluids. This transition induces a non‐monotonic variation in displacement efficiency, thereby enabling potential control of displacement performance. We further propose theoretical models to predict the transition and identify the optimal range of flow rate for maximizing displacement efficiency, with model predictions showing good agreement with experimental observations. This work provides guidance for predicting and enhancing displacement efficiency in engineering operations involving shear‐thinning fluids.

Non-Newtonian fluids are characterized by complex rheological behaviour that affects the hydrodynamic features, such as the flow rate–pressure drop relation. While flow rate–pressure drop measurements of such fluids are common in the literature, a comparison of experimental data with theory is rare, even for shear-thinning fluids at low Reynolds number, presumably due to the lack of analytical expressions for the flow rate–pressure drop relation covering the entire range of pressures and flow rates. Such a comparison, however, is of fundamental importance as it may provide insight into the adequacy of the constitutive model that was used and the values of the rheological parameters. In this work, we present a theoretical approach to calculating the flow rate–pressure drop relation of shear-thinning fluids in long, narrow channels that can be used for comparison with experimental measurements. We utilize the Carreau constitutive model and provide a semi-analytical expression for the flow rate–pressure drop relation. In particular, we derive three asymptotic solutions for small, intermediate and large values of the dimensionless pressures or flow rates, which agree with distinct limits previously known and allow us to approximate analytically the entire flow rate–pressure drop curve. We compare our semi-analytical and asymptotic results with the experimental measurements of Pipe et al. (Rheol. Acta, vol. 47, 2008, pp. 621–642) and find excellent agreement. Our results rationalize the change in the slope of the flow rate–pressure drop data, when reported in log–log coordinates, at high flow rates, which cannot be explained using a simple power-law model.

An in-situ measurement technique to determine the rheology of a fluid based on the experimentally measured velocity profile of a flow in a mini-channel is introduced. The velocity profiles of a Newtonian and different shear-thinning fluids along a rectangular channel were measured using shadowgraph particle image velocimetry (PIV). Deionized water and different concentrations of a polyacrylamide solution were used as Newtonian and shear-thinning fluids, respectively and were studied at different Reynolds numbers. The flow indices of the fluids were determined by comparing the experimental velocity profile measurements with developed theory that takes into account the non-Newtonian nature of the fluids rheology. The results indicated that the non-Newtonian behavior of the shear-thinning fluid intensified at lower Reynolds numbers and it behaved more as a Newtonian fluid as the Reynolds number increased. A comparison between the power law index determined from experimental monitoring of the velocity profile at different Reynolds numbers and measurements from a rheometer reflected good agreement. The results from the study validate the new approach of the rheology measurement of Newtonian and non-Newtonian flows through straight, rectangular cross-section channels. The proposed approach can be further utilized using other methods such as X-ray PIV to characterize the rheology of non-transparent fluids and in general, for all non-Newtonian fluids.

Electroosmotic flow (EOF) has been widely used in various biochemical microfluidic applications, many of which use viscoelastic non-Newtonian fluid. This study numerically investigates the EOF of viscoelastic fluid through a 10:1 constriction microfluidic channel connecting two reservoirs on either side. The flow is modelled by the Oldroyd-B (OB) model coupled with the Poisson–Boltzmann model. EOF of polyacrylamide (PAA) solution is studied as a function of the PAA concentration and the applied electric field. In contrast to steady EOF of Newtonian fluid, the EOF of PAA solution becomes unstable when the applied electric field (PAA concentration) exceeds a critical value for a fixed PAA concentration (electric field), and vortices form at the upstream of the constriction. EOF velocity of viscoelastic fluid becomes spatially and temporally dependent, and the velocity at the exit of the constriction microchannel is much higher than that at its entrance, which is in qualitative agreement with experimental observation from the literature. Under the same apparent viscosity, the time-averaged velocity of the viscoelastic fluid is lower than that of the Newtonian fluid.

The natural habitats of microorganisms in the human microbiome, ocean and soil ecosystems are full of colloids and macromolecules. Such environments exhibit non-Newtonian flow properties, drastically affecting the locomotion of microorganisms 1 – 5 . Although the low-Reynolds-number hydrodynamics of swimming flagellated bacteria in simple Newtonian fluids has been well developed 6 – 9 , our understanding of bacterial motility in complex non-Newtonian fluids is less mature 10 , 11 . Even after six decades of research, fundamental questions about the nature and origin of bacterial motility enhancement in polymer solutions are still under debate 12 – 23 . Here we show that flagellated bacteria in dilute colloidal suspensions display quantitatively similar motile behaviours to those in dilute polymer solutions, in particular a universal particle-size-dependent motility enhancement up to 80% accompanied by a strong suppression of bacterial wobbling 18 , 24 . By virtue of the hard-sphere nature of colloids, whose size and volume fraction we vary across experiments, our results shed light on the long-standing controversy over bacterial motility enhancement in complex fluids and suggest that polymer dynamics may not be essential for capturing the phenomenon 12 – 23 . A physical model that incorporates the colloidal nature of complex fluids quantitatively explains bacterial wobbling dynamics and mobility enhancement in both colloidal and polymeric fluids. Our findings contribute to the understanding of motile behaviours of bacteria in complex fluids, which are relevant for a wide range of microbiological processes 25 and for engineering bacterial swimming in complex environments 26 , 27 . Bacteria swimming in colloidal suspensions are shown to behave similarly to those in polymer solutions revealing a mechanism for motile behaviour in complex fluids.

We propose a novel approach for non-Newtonian viscoelastic steady flows based on a decomposition of the rate-of-deformation tensor which here, in a simplified version, leads to an anisotropic generalised Newtonian fluid-like model with separated treatment of kinematics pertaining to shear and extensional flows. Care is taken to assure that the approach is objective and does not introduce spurious effects due to dependence on a specific reference frame. This is done by separating the rate-of-deformation tensor into shear and elongational components, with the local scalar shear and elongation rates being the second invariant of each tensor separately, and by modifying the method used to separate the rate-of-deformation tensor so that it becomes independent of superimposed rigid rotations, thus satisfying the principle of material indifference. We assess the model with two test cases: planar contraction flow, often employed to evaluate numerical methods or constitutive equations and for which experimentally observed corner vortex enhancement and pressure drop increase are seldom found in numerical simulations; and flow past confined or unconfined cylinders, for which experiments indicate a drag increase due to elasticity and most predictions give a drag decrease. With our anisotropic model, incorporating additional elongational-flow-related terms, large vortices and accentuated pressure drop coefficients can be predicted for the contraction problem and enhanced drag coefficient for the cylinder problems. This is the first work where problems of non-Newtonian fluid mechanics are solved numerically with separation of strain rate into shear and elongational components.

Mammalian spermatozoa in organisms with internal fertilization are required to swim in the cervical and oviductal mucus, whose rheological properties differ substantially from those of water. Moreover, on the way to the oviduct, a change in sperm motility called hyperactivation may occur. In the present study, we focused on the motion characteristics of hyperactivated bovine sperm and investigated the effect of the surrounding fluid on motility. We prepared two kinds of polyacrylamide with high-viscosity non-Newtonian fluid properties, similar to the actual cervical and oviductal mucus. Using semen from Japanese cattle, we evaluated curvilinear velocity (VCL), straight-line velocity (VSL), and average path velocity (VAP). Additionally, we estimated linearity (LIN), straightness (STR), and wobble (WOB) as sperm motility parameters for several surrounding fluids. We successfully induced hyperactivation of bovine sperm in high-viscosity non-Newtonian fluid. Hyperactivation resulted in an increase in VCL and a decrease in VSL. In the high-viscosity non-Newtonian fluid, the hyperactivated sperm moved in a zig-zag pattern with regularity, different from the movement observed in a diluted solution. The increase in WOB in the non-Newtonian fluid suggests that hyperactivated sperm efficiently progress along the groove that exists on the oviductal mucus wall. These results improve our understanding of the motility of bovine sperm when they undergo hyperactivation in the actual cervical and oviductal mucus.