Newtonian Fluid Research Articles (Page 1)

Embedded 3D printing (EM3D) enables freeform patterning of soft materials by extruding ink into a yield-stress supporting matrix. While prior studies have focused on viscoplastic or shear-thinning inks, printing Newtonian fluids─such as silicone oil and liquid metal─remains challenging due to (i) matrix yielding induced by needle motion and (ii) Rayleigh-Plateau (RP) instability driven by interfacial tension. In this study, we investigate the EM3D of Newtonian inks with extremely low surface tension (silicone oil) and extremely high surface tension (Galinstan liquid metal), embedded in an elasto-viscoplastic Laponite matrix. Flow visualization with particle image velocimetry reveals that matrix yielding around the needle scales with (γ̇c/γ̇Y )1/3, where γ̇c = U/d is the characteristic shear rate and γ̇Y = 2πfγY is the yield threshold derived from amplitude sweep rheology. We demonstrate that printing orthogonal to a straight-needle aggravates matrix yielding and compromises print fidelity. To resolve this issue, we propose a bent-needle geometry, which reduces the yielded region and improves filament stability by minimizing stress propagation along the needle path. To address RP instability, we derive a theoretical stability criterion that balances interfacial tension Γ and yields stress τY, given by τY ∝ Γ/d. This prediction is experimentally validated using Newtonian inks with distinct interfacial tensions (35 mN/m for silicone oil and 345 mN/m for Galinstan). Our findings provide a unified design framework for Newtonian-ink EM3D, incorporating both rheological and geometric strategies to overcome flow-induced instability. This work expands the accessible material space for EM3D by providing fundamental insights into fluid-matrix interactions, offering practical guidelines for reliable printing of Newtonian inks in soft electronics and bioprinting applications.

Current analytical theories of recirculating flow in single-screw extruders consider only cross-channel flow in channels of infinite width with only one exception. Proper analysis of recirculating flow requires inclusion of normal velocities and the effect of finite channel width. More broadly, this paper presents an analytical description of lid-driven cavity flow—one of the most frequently studied flows in fluid dynamics. Expressions for velocities and flow rates for Newtonian fluids are obtained that satisfy the balance equations. These expressions have been compared to results of numerical analyses with good agreement. Flow rates and velocities are displayed with 3D surface plots and contour plots. These plots provide better insight into the flow behavior than 2D graphs. We have analyzed flow in slit channels with width much greater than the height (W>>H) and flow in a square channel (W=H). The vortex center (stagnation point) in a slit channel is located at normal coordinate ψ=2/3. The vortex center in a square channel is located at ψ=0.76. These analytical results allow for the development of better analytical models for melt temperature distribution, mixing, and devolatilization in single-screw extruders.

In the current work, we estimate the flow of helices of the unsteady fractionalized second grade fluid with MHD effect between uniaxial annular cylinders. The analytical outcomes are evaluated for the rotational and longitudinal velocity and the shear stress because of fluid circulation and translating between two infinite coaxial circular cylinders, which are turning their axis. Hardly anyone did this before and applied most modern non-integer Atangana Baleanu Caputo fractional time derivatives on the governing equation of second grade fluid with some natural effects. The outcomes are determined by using some integral transforms such as Laplace and finite Hankel transforms. The acquired outcomes exhibited in integral and series forms with newly defined special $\textbf{M}^{a,b}_{c}(\kappa,t)$ function. The outcome that fulfills both the governing equation and all designated account conditions. Additionally, the respective outcome for Newtonian fluid for the same movement is acquired in limited cases. The impact of material parameter $\alpha$ and kinematic viscosity of the $\alpha$ is also discussed. Last, we examined the behavior of distinct parameters on fluid movement along with graphically analogizing second grade and Newtonian fluids.

The study of turbulent flow in polygonal ducts holds significant relevance across industries, drawing the attention of fluid dynamicists over many decades. Despite substantial research on square and triangular ducts, the fluid dynamic correspondence with total sides ( m ) and flow behaviour indices ( n ) across the larger rheological spectrum of pseudoplastic, Newtonian, and dilatant fluids remains underexplored. To address the literature gap, we numerically model the rheological turbulent flow in straight ducts with regular polygonal cross-sections, offering unified insights and advancing understanding of geometric and rheological influences in internal flows. We analyse the nature of secondary flow originating inside the polygonal ducts, characterised by oppositely directed vorticity zones and curvature in in-plane streamlines. Results show that the secondary velocity magnitudes peak at approximately 1% of the bulk velocity near corners and decay downstream, influenced by both m and n . Dilatant fluids exhibit higher secondary velocities near the inlet but faster spatial decay. The near-wall strain rate distributions indicate higher strain rates in dilatant fluids and thickened viscous sublayers in pseudoplastic fluids. However, the net boundary-layer-thickness at the fully-developed state is predominantly influenced by the flow behaviour index rather than duct geometry, with shear-thickening fluids exhibiting nearly 10% thicker layers than shear-thinning fluids under identical Reynolds numbers. The three-dimensional illustrations bring out the influences of m and n on quasi-streamwise vortices, with increased three-dimensionality sustained in shear-thickening flows. Notably, vortex persistence drops by nearly 88% when m increases from 3 to 10, highlighting the reduced role of corner-induced secondary flows as the cross-section approaches circularity. We propose new correlations to predict the entry length, centreline-to-bulk velocity ratios, and friction factors of the fluid flow with reasonable accuracy (10%–16%). The findings and proposed correlations contribute to efficient duct design, paving the way for future studies in complex geometries and advanced fluid systems.

Deformable microchannels emulate a key characteristic of soft biological systems and flexible engineering devices: the flow-induced deformation of the conduit due to slow viscous flow within. Elucidating the two-way coupling between oscillatory flow and deformation of a three-dimensional (3-D) rectangular channel is crucial for designing lab-on-a-chip and organ-on-a-chip microsystems and eventually understanding flow–structure instabilities that can enhance mixing and transport. To this end, we determine the axial variations of the primary flow, pressure and deformation for Newtonian fluids in the canonical geometry of a slender (long) and shallow (wide) 3-D rectangular channel with a deformable top wall under the assumption of weak compliance and without restriction on the oscillation frequency (i.e. on the Womersley number). Unlike rigid conduits, the pressure distribution is not linear with the axial coordinate. To validate this prediction, we design a polydimethylsiloxane-based experimental platform with a speaker-based flow-generation apparatus and a pressure acquisition system with multiple ports along the axial length of the channel. The experimental measurements show good agreement with the predicted pressure profiles across a wide range of the key dimensionless quantities: the Womersley number, the compliance number and the elastoviscous number. Finally, we explore how the nonlinear flow–deformation coupling leads to self-induced streaming (rectification of the oscillatory flow). Following Zhang and Rallabandi ( J. Fluid Mech. , vol. 996, 2024, p. A16), we develop a theory for the cycle-averaged pressure based on the primary problem’s solution, and we validate the predictions for the axial distribution of the streaming pressure against the experimental measurements.

ABSTRACT The Jeffery–Hamel flow, a classic benchmark in fluid dynamics, describes the motion of an incompressible viscous fluid within convergent or divergent channels. Although extensively studied for Newtonian fluids, the dynamics of such flows in channels with stretching or shrinking walls, especially for couple‐stress fluids, remain largely unexplored. In this study, we pioneer the use of artificial neural networks (ANNs) to solve a fifth‐order nonlinear differential equation arising from the two‐dimensional Jeffery–Hamel flow of couple‐stress fluids within stretching/shrinking channels, addressing a complex, nonlinear fluid dynamics problem. By capturing microstructural effects and the unique rheology of couple‐stress fluids, our approach enables high‐accuracy solutions for complex flow behaviour influenced by wall deformation. We focus exclusively on fluid flow behaviour, analysing the influence of key parameters such as Reynolds number, magnetic parameter, channel angle, stretching parameter, and couple stress parameter on velocity distribution and flow structure. Our results reveal new flow topologies and response patterns that are unattainable with traditional analytical or numerical methods. The proposed ANN‐based methodology bridges significant gaps in the literature and provides a powerful tool for modelling biological, industrial, and microfluidic flows in adaptive geometries. This work advances the understanding of the dynamics of Jeffery–Hamel flow in couple‐stress fluids within magnetically influenced stretching/shrinking channels, demonstrating unprecedented microstructural interactions absent in prior Newtonian or non‐Newtonian studies, and unveiling the effectiveness of intelligent methods for solving problems in computational fluid mechanics.

The current study's simulation made use of COMSOL Multiphysics' CFD. Blood was used as the basic fluid in this simulation. Blood was considered to be a laminar, unstable, and incompressible Newtonian fluid, and its Newtonian nature is tolerable at high shear rates. The behavior of blood flow was investigated to ascertain the effects of temperature, velocity, and pressure through vascular stenosis. Gold (Au) and silver (Ag) nanoparticles were the two types utilized in this investigation. The mass, momentum, and energy equations were solved using the CFD method. A fine element size mesh was made using COMSOL. The analysis's conclusions show that the artery's velocity fluctuates over constrained sections, falling both before and after the stenotic zone and being higher in a diseased location. The heat transfer feature's upper and lower boundary temperatures were selected to be 24.85°C and 27.35°C, respectively. The nanoparticles affected the density, specific heat, dynamic viscosity, and thermal conductivity of blood. The use of gold and silver nanoparticles prevented overheating since they both have high thermal conductivity, which is essential for quickly dispersing heat. Nusselt number variations were also calculated, and the results show that the curve decreases inside the stenosis. At t = 0.7 s and 1 s, recirculation occurs right after the stenosed area, and it is possible to infer that the streamlines behave abnormally. These discoveries will have a significant impact on the treatment of stenosed arteries.

A study of Newtonian fluid flow through a homogeneous porous medium in a curved horizontal pipe using perturbation method

Saffman-Taylor fingering instabilities in shear-thinning fluids displacing Newtonian fluids

Droplets sliding down a partially wetted surface are a ubiquitous phenomenon in nature and everyday life. Despite its apparent simplicity, it hinders complex intricacies for theoretical and numerical descriptions matching the experimental observations, even for the simplest case of a drop sliding down a homogeneous surface. A key aspect to be considered is the distribution of contact angles along the droplet perimeter, which can be challenging to include in the theoretical/numerical analysis. The scenario can become more complex when considering geometrically or chemically patterned surfaces or complex fluids. Indeed, these aspects can provide strategies to passively control the droplet motion in terms of velocity or direction. This review gathers the state of the art of experimental, numerical, and theoretical research about droplets made of Newtonian and non-Newtonian fluids sliding down homogeneous, chemically heterogeneous, or geometrically patterned surfaces.

We demonstrate how magnetic nanoparticles, through field-induced chaining and the resulting non-Newtonian magnetorheological behavior, substantially modulate ion concentration polarization in converging microchannels. Rather than direct magnetic trapping, it is the altered fluid rheology under applied magnetic fields that governs the extent of depletion and enrichment.. A coupled Poisson-Nernst-Planck and Navier-Stokes model was extended with a Bingham-like constitutive law to capture non-Newtonian rheology. Simulations reveal that the electric force to viscous force parameter C1, inverse of bulk concentration parameter C2, MR coupling parameter C3 and transport parameter Pe jointly regulate enrichment. For Newtonian fluids, the enrichment factor (EF) saturates at EF ≈ 3, whereas MR fluids exhibit up to a 3-fold enhancement (EF ≈ 10) at high C3. Mesh refinement and enrichment-window sensitivity tests indicate numerical uncertainties of 5-7%. These results demonstrate how magnetic-field-tunable rheology can synergistically amplify ICP-based preconcentration, offering a strategy to design next-generation microfluidic enrichment platforms.

Dispersion is a common phenomenon in miscible displacement flows. In the primary cementing process displacement takes place in a narrow eccentric annulus. Both turbulent Taylor dispersion and laminar advective dispersion occur, depending on flow regime. Since dispersion can cause mixing and contamination close to the displacement front, it is essential to understand and quantify. The usual modelling approach is a form of Hele-Shaw model in which quantities are averaged across the narrow annular gap: a so-called two-dimensional narrow gap (2DGA) model. Zhang & Frigaard ( J. Fluid Mech ., vol. 947, 2022, A732), introduced a dispersive two-dimensional gap-averaged (D2DGA) model for displacement of two Newtonian fluids, by modifying the earlier 2DGA model. This brings a significant improvement in revealing physical phenomena observed experimentally and in three-dimensional computations, but is limited to Newtonian fluids. In this study we adapt the D2DGA model approach for two Herschel–Bulkley fluids. We first obtain weak velocity solutions using the augmented Lagrangian method, while keeping the same two-layer flow assumption as the Newtonian D2DGA model. These solutions are then used to define closure relationships that are needed to compute the dispersive two-dimensional flows. Results reveal that the modified version of the D2DGA model can now predict expected frontal behaviours for two Herschel–Bulkley fluids, revealing dispersion, frontal shock, spike and static wall layer solutions. We then explore the displacement behaviour in more detail by investigating the impact of rheological properties and buoyancy on the mobility of fluids in a planar frontal displacement flow and their vulnerability to fingering-type instabilities. As the underlying flows are dispersive, our analysis reveals three distinct behaviours: (i) stable, (ii) partial penetration of the dispersing front, and (iii) unstable regimes. We explore these regimes and how they are affected by the two fluid rheologies.

Abstract This study investigates fully developed, steady, laminar forced convective heat transfer in Couette–Poiseuille flow of power‐law fluids between heated parallel plates, relevant to dynamic wall heat exchangers, microfluidic devices, and polymer processing. The analysis examines the influence of the flow rate ratio between the shear‐driven (Couette) and total imposed flow on heat transfer for Newtonian and power‐law fluids, with variations in power‐law index , upper plate velocity , and Brinkman number ( or ) including viscous dissipation. A semi‐analytical velocity profile is derived, while the temperature distribution and Nusselt number are obtained analytically. These solutions provide insights into flow and heat transfer mechanisms, allow quick evaluation without extensive computations, and serve as reliable references for validating numerical simulations. Results are validated against ANSYS Fluent simulations and literature data. Findings reveal an optimal shear‐driven component opposing the pressure‐driven flow that maximizes heat transfer for a moving insulated plate. For negligible viscous dissipation , shear‐thinning fluids enhance heat transfer under purely pressure‐driven flow, while shear‐thickening fluids reach a maximum Nusselt number comparable to Newtonian fluids but at lower shear‐driven motion, reducing energy demand. The novelty lies in identifying the optimal flow rate ratio between Couette and Poiseuille components in non‐Newtonian fluids, offering a framework to maximize heat transfer while minimizing energy input. The findings aid thermal management in systems with combined flow‐driving mechanisms, for example, dynamic wall heat exchangers.

This study examines the impact of the non-Darcy Forchheimer coefficient, Activation energy, chemical reaction, thermal radiation, and Brownian parameter on the flow of a viscous Newtonian fluid undergoing Brownian motion across a stretching sheet with a changing heat source or sink. The model equation accounts for ohmic heating effects as well as changes in fluid viscosity and thermal conductivity. By using pertinent dimensionless variables, the flow equations are transformed. Also, the transformed nonlinear equations are solved by the MATLAB-BVP4C method. Graphs and tables are used to examine the influence of the relevant parameters. Our key findings are that the Forchheimer parameter and variable viscosity parameter decline fluid velocity. Brownian parameter and thermophoresis improve fluid temperature and chemical reaction parameter declines fluid concentration.

In this paper, the effect of feedback control on the criterion for the onset of Darcy-Bénard convection[Formula: see text]in a horizontal Boussinesq Newtonian fluid is studied theoretically. The bounding isothermal lower and upper surfaces are considered to be rigid. The single term Galerkin method[Formula: see text]and the Maclaurin series expansion[Formula: see text]are combined with the Newton-Raphson method[Formula: see text]of three variables to perform a linear stability analysis[Formula: see text] in order to determine eigen value. To make a weakly nonlinear stability analysis[Formula: see text] of the system, a Vadasz Lorenz model[Formula: see text] is constructed. The model's various properties are discovered to be identical to those of the standard Lorenz model. The [Formula: see text] exhibits both dissipative and conservative characteristics and the bounded nature of its solution is demonstrated by the trapping region, which takes the form of an ellipsoid. The Hopf-Rayleigh number determined from the autonomous dynamical system predicts the onset of chaos. The influence of the controller gain parameter and the Biot number on the onset of convection has been analyzed. Results from the study reveal that the controller gain parameter stabilizes the system and further delays the onset of chaos. Overall, the study establishes that an increase in the Biot number promotes long-term periodic motion over chaotic behavior, while an increase in the controller gain parameter enlarges the trapping region, thereby contributing to improved system stability.

Abstract This study presents a numerical investigation of the dynamic response of a Newtonian fluid interface subjected to mixed oscillatory deformations. A slender cylindrical probe, floating horizontally at a water–air interface and partially submerged by capillary forces, is driven sinusoidally in the direction perpendicular to its axis. The interface exhibits shear, dilatational, and extensional viscosities, and the system is modeled using the finite volume method within the OpenFOAM framework. The governing equations are nondimensionalized and solved for a wide range of Marangoni numbers ( $$Ma \in [1, 10^5]$$ M a ∈ [ 1 , 10 5 ] ) and dilatational-to-shear viscosity ratios ( $$\Theta \in [1, 10^5]$$ Θ ∈ [ 1 , 10 5 ] ). The simulations enable the decomposition of the total interfacial force into its constituent components, revealing distinct regimes dominated by Marangoni, dilatational, or extensional stresses. The results demonstrate the feasibility of isolating these contributions under specific conditions, offering insights into the design and interpretation of interfacial rheometry experiments. The influence of geometric parameters and oscillation characteristics is also explored, confirming the robustness of the observed force dynamics.

A theory of solutions of charged polyelectrolyte (PE) macromolecules, treating them as electric dipoles, is proposed. In a thin thread of PE solution sustained between two disks-whether wettable or nonwettable-these dipoles are reoriented by an axial electric field, aligning themselves with the field direction. This alignment causes significant axial elastic stresses and affects capillary self-thinning dynamics of the thread, slowing the process and potentially arresting it entirely, and even leading to oscillatory regimes. Accordingly, the evolution of the thread radius deviates significantly from the exponential decay characteristic of solutions of flexible polymer macromolecules and the linear decay characteristic of Newtonian fluids. At relatively high electric field strengths, in a thread where elastic stresses become dominant, an oscillatory regime emerges. Here, the cross-sectional radius not only decreases but also increases and oscillates in time-a behavior rooted in an ill-posedness of the problem reducing to the Laplace equation in case of strong electric fields. This indicates a manifestation of Hadamard instability. The theory is supported by experimental data acquired in this work.

The nonlinear monotone H 1 H^1 -energy stability of laminar flows in a layer between two parallel planes filled with a Navier–Stokes–Voigt fluid is studied. It is proved that the critical Reynolds numbers for monotone H 1 H^1 -energy stability for the Couette and Poiseuille flows of the zero-order Navier–Stokes–Voigt fluid are the same as those found by Orr for Newtonian fluids. However, the exponential decay coefficient depends on the Kelvin–Voigt parameter Λ \Lambda . Furthermore, a Squire theorem holds in the nonlinear case: the least stabilizing perturbations in H 1 H^1 -energy are the two-dimensional spanwise perturbations.

We study locomotion of a model crawler corresponding to a deforming upper boundary of finite length above a thin Newtonian fluid film whose viscosity varies spatially. We first derive a general locomotion velocity formula with fluid viscosity variations via the lubrication theory. For further analysis, the surface of the crawler is described by a combination of transverse and longitudinal traveling waves and we find that under a uniform viscosity a transverse wave results in a retrograde crawler, while a longitudinal wave leads to a direct crawler. We then analyze the time-averaged locomotion behaviors under two scenarios: (i) a sharp viscosity interface and (ii) a linear viscosity gradient. Using the asymptotic expansions of small surface deformations and the method of multiple timescale analysis, we derive an explicit form of the average velocity that captures nonlinear, accumulative interactions between the crawler and the spatially varying environment. (i) In the case of a viscosity interface, the time-averaged speed of the crawler is always slower than that in the uniform viscosity, for both the transverse and longitudinal wave cases. Notably, the speed reduction is most significant when the crawler's front enters a more viscous layer and the crawler's rear exits from the same layer. (ii) In the case of a viscosity gradient, the crawler's speed becomes slower for the transverse wave, while for the longitudinal wave, the locomotion speed does not change significantly. Our analysis illustrates the fundamental importance of interactions between a locomotor and its environment, and separating the timescale behind the locomotion.

Abstract This study investigates the stability of plane Poiseuille flow of an electrically conducting Casson fluid through a homogeneous porous medium under a uniform transverse magnetic field. The flow, driven by a pressure gradient between two flat plates, is analyzed for the effects of the Casson parameter (β), permeability (M), Hartmann number (Ha), and slip length (l), under both symmetric and asymmetric slip conditions. A generalized eigenvalue problem is solved numerically using the Chebyshev spectral collocation method to determine the onset of instability. Results show that increasing the slip length (l) enhances flow stability for the Casson fluid, while Newtonian flow remains relatively unaffected within specific ranges of β, M, Ha, and l. Eigenspectrum analysis reveals that initial instabilities appear as wall modes, which diminish as β decreases and M, Ha, and l increase. The neutral stability curves for various parameter values are extensions of the classical Tollmien-Schlichting instability in Newtonian fluids. An energy budget analysis identifies negative energy production from Reynolds stress as the key stabilizing factor. Meanwhile, viscous dissipation, porous medium effects, and magnetic field contribute positively to the energy balance, promoting stability throughout the flow.