Newtonian Fluid Research Articles

Superimposed squeeze and rotational flows of Newtonian and power-law fluids a)Dedicated to Nicolás M. Páez-Flor, Ph.D. In memoriam (1983–2023).

This study theoretically predicted the response of superimposed squeeze and rotational flows (SSRF) of fluids with different viscous behaviors (i.e., Newtonian, shear-thinning, and shear-thickening fluids). The theoretical predictions were verified using the plate-plate geometry for the SSRF measurements with the Newtonian and power-law fluids. In all the cases, the squeeze force increased as the gap decreased, but the response was very different for each rheological behavior. The variation in the squeeze force with the gap was not affected by the superimposed rotational shear stress value, owing to the nondependency of the viscosity on the shear for Newtonian fluids. However, for the power-law fluids, the squeeze force variation with the gap value was based on the value of the superimposed shear stress value. The decrease and increase in the viscosity with the shear stress for the shear-thinning and shear-thickening fluids, respectively, resulted in opposite trends of the squeeze force with the gap value variation. For the shear-thinning fluids, the squeeze force for each gap value decreased with increasing superimposed rotational shear stress. The opposite trend was observed for the shear-thickening fluid. In the absence of wall slip, the theoretical predictions well agreed with the experimental results.

Dynamics of heat transfer in complex fluid systems: Comparative analysis of Jeffrey, Williamson and Maxwell fluids with chemical reactions and mixed convection

This study addresses the complex dynamics of heat transfer in magnetohydrodynamic (MHD) systems involving Jeffrey, Williamson, Maxwell, and Newtonian fluids, focusing on how chemical reactions, activation energy, porosity, and mixed convection impact fluid behavior. The problem is critical due to the significant influence these factors have on industrial processes and applications involving non-Newtonian fluids. The developed a mathematical model represented by partial differential equations (PDEs), which were solved using similarity transformations and the fourth order Runge-Kutta (R-K) method combined with shooting technique, with MATLAB software facilitating the solution process. The results reveal that variations in magnetic field strength, porosity, and buoyancy force significantly affect fluid velocities, while radiation, Brownian motion, and thermophoresis alter temperature profiles. Furthermore, chemical reaction rates, Schmidt number, relaxation constant, and activation energy influence fluid concentrations. Key findings include that increasing porosity and magnetic field strength generally decreases fluid velocity, while higher radiation and Prandtl numbers reduce temperature. Chemical reactions and activation energy decrease fluid concentrations, with non-Newtonian fluids showing more pronounced effects compared to Newtonian fluids. The novelty of this work lies in its comprehensive analysis of multiple interacting parameters and their combined effects on heat transfer in MHD systems, providing insights that extend beyond previous studies in the literature. This research offers valuable implications for optimizing fluid dynamics in various industrial applications, including food processing, ink formulation, and friction reduction.

Super-resolution reconstruction of turbulence for Newtonian and viscoelastic fluids with a physical constraint

Super-resolution reconstruction (SR) of turbulent flow fields with high physical fidelity from low-resolution turbulence data is a novel and cost-effective way in a turbulence study. However, some naive image-to-image machine learning methods often produce nonphysical features inconsistent with the physical characteristics of turbulence. The present work proposes, respectively, convolutional neural network and generative adversarial network-based turbulence SR models using the kinetic energy spectra of turbulence flow as a physical constraint. The models have been validated in turbulence SR reconstruction for a Newtonian fluid under the flow condition of homogeneous isotropic turbulence at Reynolds number, Re=3140 and 4710 and viscoelastic fluid at the same Re numbers and Weisenberg number, Wi=0.796 and 1.194 (the elasticity number El=Wi/Re=0.000 254), respectively. The results show that with the energy spectra constraint (ESC), not only the nonphysical features occurred in the energy spectra of velocity field could be eliminated by the SR models, the errors of their reconstructed vorticity fields in comparison with the results of direct numerical simulation are also significantly smaller than those of the SR models without ESC. Therefore, incorporation of physical constraints is vital in preserving physical characteristics in SR of turbulent flow.

Fluid–structure interaction in engineering based on its applications: A plenary and up-to-date review

The present study reviews the relevant research done on the fluid–structure interaction (FSI) in channels and vessels. The cases of FSI in channels with elastic plates, channels with variable geometry, flow airfoils, blood vessels, and heart valves are presented, using data from credible research articles. The review is carried out with a focus on the performance of the FSI method in solving engineering problems in channels, reporting its findings such as the effect of power-law exponent, the Nusselt number in different parts of a fluid, lift, and drag for a rigid cylinder and a plate in Newtonian fluids, the formation of eddy current, and the distribution of velocity and pressure in a fluid and on walls. The review is instrumental for researchers, engineers, and academics in providing comprehensive insight into methodologies and applications of fluid–structure interaction.

A new higher-order super compact finite difference scheme to study three-dimensional non-Newtonian flows

This work introduces a new higher-order accurate super compact (HOSC) finite difference scheme for solving complex unsteady three-dimensional (3D) non-Newtonian fluid flow problems. As per the author's knowledge, the proposed scheme is the first ever developed higher-order compact finite difference scheme to solve 3D non-Newtonian flow problems. The proposed scheme is fourth-order accurate in space and second-order accurate in time, utilizing only seven adjacent grid points at the (n+1)th time level for the finite difference discretization. A time-marching methodology is employed with pressure calculated via a pressure-correction strategy based on the modified artificial compressibility method. Using the power-law viscosity model, we tackle the benchmark problem of a 3D lid-driven cavity, systematically analyzing the varied rheological behavior of shear-thinning (n = 0.5), shear-thickening (n = 1.5), and Newtonian (n = 1.0) fluids across different Reynolds numbers (Re=1,50,100,200). Both Newtonian and non-Newtonian results are carefully investigated in terms of streamlines, velocity variation, pressure distributions, and viscosity contours, and the computed results are validated with the existing benchmark results. The findings demonstrate excellent agreement with the existing results. It is found that for shear-thinning fluid (n = 0.5), u velocity is higher near the top moving wall than the case of Newtonian (n = 1.0) and shear-thickening fluid (n = 1.5) for all Re values. This extensive analysis, using the new HOSC scheme, not only increases our understanding of non-Newtonian fluid behavior but also provides a robust foundation for future research and practical applications.

Revealing the dynamics of stagnant rings of third-grade fluid film with heat transfer in the presence of surface tension

In many engineering applications, including coating and lubrication operations, analyzing the temperature behavior of thin film flows on a vertically upward-moving tube is crucial to improving predictive models. This paper examines a steady third-grade fluid film flow with a surface tension gradient on a vertical tube. The mechanisms responsible for the fluid motion are upward tube motion, gravity, and surface tension gradient. This analysis focuses on heat transfer and stagnant ring dynamics. The formulated highly nonlinear ordinary differential equations are solved using the Adomian decomposition method. The conditions for stagnant rings and uniform film thickness are attained and discussed. The inverse capillary number C, Stokes number St, Deborah number De, and Brinkman number Br emerged as flow control parameters. The temperature of the fluid film rises with an increase in the C, St, De, and Br, whereas it decreases with an increase in thermal diffusion rate. The radius of stagnant rings tends to shrink by the increase in C, St, and De. When the value of De is high, third-grade fluid behaves like solids; only free drainage happens with smaller radius stagnant rings and high temperatures. A comparison between Newtonian and third-grade fluids regarding surface tension, velocity, temperature, stationary rings, and fluid film thickness is also provided.

An improved two phases-two points SPH model for submerged landslide

This research proposes an improved two phases-two points SPH model designed to simulate interactions between water and soil, particularly suitable for scenarios such as submerged landslides. This model treats water as a weakly compressible Newtonian fluid and soil as a cohesive-frictional material following an elastoplastic constitutive law, utilizing two layers of SPH particles to separately represent these two phases. An adaptive drag force formula is proposed that automatically switches between linear and nonlinear seepage modes based on the motion state of the porewater. Additionally, to improve the precision and stability of the model, a modified solid boundary condition and a method for calculating soil volume fraction are proposed, along with an SPH discretization formula that incorporates the effects of the volume fraction in a more effective way. The reliability of the improved two phases-two points SPH model is initially verified through two cases: a dry granular landslide and a submerged soil mass subjected to gravitational loading. Then, the effectiveness of the proposed improvement methods is further tested and validated through three submerged landslide cases with different grain diameters, demonstrating the applicability of the current model in simulating submerged landslides and its superiority in accuracy and stability compared to previous models.

Investigating the Influence of Die Structure on the Transverse Uniformity of Slot Coating

Abstract Transverse uniformity is an important measurement of the coating quality for slot coating. In this paper, the influence of die structure on the transverse uniformity is investigated according to a fully 3D mathematical modelling and numerical simulations. In the modelling part, the coating liquid is regarded as generalized Newtonian fluid and the fluid flow inner the die head is governed by the 3D incompressible Navier-Stokes equations. In solving the model, an efficient fractional step finite element method is used. Four kinds of commonly used die structures are simulated and analysed. The results show that the die structure has great influence on the transverse uniformity. Generally, dies with double cavities can get better transverse uniformity that single cavity.

The role of temperature-dependent solubility in the stability of thermohaline convection within a Voigt-fluid layer

The study focuses on both linear and weakly nonlinear stability analyses of thermohaline convection within a Voigt-fluid layer, considering the effects of temperature-dependent solubility. Analytical methods are employed to derive conditions for the onset of both stationary and oscillatory convection. The linear stability analysis is performed using normal mode analysis to explore how various physical parameters influence the initiation of convection. Notably, unlike Newtonian fluids, the Navier-Stokes-Voigt fluid suppresses the typical quasiperiodic bifurcation from a steady state. To gain deeper insight into the onset of convection, a weakly nonlinear stability analysis is conducted using a modified perturbation method, leading to the Ginzburg-Landau equation. This reveals the potential for subcritical instability, a phenomenon not fully captured by linear analysis alone. Additionally, the study examines how different physical parameters affect convective heat and mass transfer, with findings that align with previous studies in specific limiting cases.

Immiscible non-Newtonian displacement flows in stationary and axially rotating pipes

We examine immiscible displacement flows in stationary and rotating pipes, at a fixed inclination angle in a density-unstable configuration, using a viscoplastic fluid to displace a less viscous Newtonian fluid. We employ non-intrusive experimental methods, such as camera imaging, planar laser-induced fluorescence (PLIF), and ultrasound Doppler velocimetry (UDV). We analyze the impact of key dimensionless numbers, including the imposed Reynolds numbers (Re, Re*), rotational Reynolds number (Rer), capillary number (Ca), and viscosity ratio (M), on flow patterns, regime classifications, regime transition boundaries, interfacial instabilities, and displacement efficiency. Our experiments demonstrate distinct immiscible displacement flow patterns in stationary and rotating pipes. In stationary pipes, heavier fluids slump underneath lighter ones, resulting in lift-head and wavy interface stratified flows, driven by gravity. Decreasing M slows the interface evolution and reduces its front velocity, while increasing Re* shortens the thin layer of the interface tail. In rotating pipes, the interplay between viscous, rotational, and capillary forces generates swirling slug flows with stable, elongated, and chaotic sub-regimes. Progressively, decreasing M leads to swirling dispersed droplet flow, swirling fragmented flow, and, eventually, swirling bulk flow. The interface dynamics, such as wave formations and velocity profiles, is influenced by rotational forces and inertial effects, with Fourier analysis showing the dependence of the interfacial front velocity's dominant frequency on Re and Rer. Finally, UDV measurements reveal the existence/absence of countercurrent flows in stationary/rotating pipes, while PLIF results provide further insight into droplet formation and concentration field behavior at the pipe center plane.

Flow field analysis of newtonian fluid flow induced by planetary and radial motion of drill string

Abstract At present, in the process of oil drilling, the drill string is an essential downhole drilling tool. It is immersed in the hole filled with drilling fluid for a long time, and it is driven by the rotation of the rotary table to drill down. In this process, the drill string will not only rotate around its axis but also may rotate around the axis of the hole and produce radial motion. It is important to study the flow law of Newtonian fluid flow induced by drill string movement, which can effectively reduce drilling accidents caused by drill string vortex and buckling, thus reducing economic losses. After research and analysis, the finite volume method, which has good applicability and obvious advantages, is used to discretize the established mathematical model, and the mathematical equation after discretization is obtained. By using MATLAB software, the flow field of Newtonian fluid induced by drill string rotation motion is analyzed, the axial velocity distribution diagram and tangential velocity distribution diagram are obtained, and the velocity flow diagram under different eccentricity conditions is drawn. It is found that secondary flow occurs only when the eccentricity reaches a certain distance requirement.

Impact of flexible walls of curved channel on biological flow of Reiner-Rivlin fluid

In this study, the Reiner-Rivlin fluid model is opted for examination as the complex dynamical fluid and is flowing on account of the waves travelling on the walls of flexible curved channel. The governing equations are solved analytically up to the first order to analyse the velocity profiles. As the governing equation is highly nonlinear, so the problem is solved by regular perturbation technique about small wave number. After the implication of regular perturbation, the second order Cauchy Euler ordinary differential equations are obtained for both the systems. A detailed analysis is conducted on the effects of diverse factors, such as the rheological properties of fluid, the curvature radius of the channel, the wave amplitude and the wall properties. The velocity of the fluid enhanced by increasing wall properties parameters, wave number, Reynolds number and the amplitude ratio parameter. It is also observed that the Reiner-Rivlin fluid flows slowly as compare to the Newtonian fluid, this type of findings can be helpful for the understanding of many physiological processes, like blood flow and food swallowing. This study enlightens the interaction between the curved nature of the channel and Reiner-Rivlin fluid flow in peristalsis that can be a great contribution for the designing of biomedical devices. Such types of problems have great significance in many physiological processes and engineering applications like microfluidic devices and drug delivery systems.

Nonlinear parametric models of viscoelastic fluid flows.

Reduced-order models (ROMs) have been widely adopted in fluid mechanics, particularly in the context of Newtonian fluid flows. These models offer the ability to predict complex dynamics, such as instabilities and oscillations, at a considerably reduced computational cost. In contrast, the reduced-order modelling of non-Newtonian viscoelastic fluid flows remains relatively unexplored. This work leverages the sparse identification of nonlinear dynamics (SINDy) algorithm to develop interpretable ROMs for viscoelastic flows. In particular, we explore a benchmark oscillatory viscoelastic flow on the four-roll mill geometry using the classical Oldroyd-B fluid. This flow exemplifies many canonical challenges associated with non-Newtonian flows, including transitions, asymmetries, instabilities, and bifurcations arising from the interplay of viscous and elastic forces, all of which require expensive computations in order to resolve the fast timescales and long transients characteristic of such flows. First, we demonstrate the effectiveness of our data-driven surrogate model to predict the transient evolution and accurately reconstruct the spatial flow field for fixed flow parameters. We then develop a fully parametric, nonlinear model capable of capturing the dynamic variations as a function of the Weissenberg number. While the training data are predominantly concentrated on a limit cycle regime for moderate , we show that the parametrized model can be used to extrapolate, accurately predicting the dominant dynamics in the case of high Weissenberg numbers. The proposed methodology represents an initial step in applying machine learning and reduced-order modelling techniques to viscoelastic flows.

Double-diffusive convection in flow of Carreau fluid with variable density inside converging and diverging channels of rectilinear walls

In this article, the effects of double-diffusive convection have been seen on the flow of Carreau fluid of variable density, maintained inside straight and converging (diverging) channels. Note that the channel walls exhibit variable porosity and undergo stretching or shrinking at non-uniform velocities. In the flow domain, we have taken into account the convective transport of both heat and species mass concentrations. The pseudo-similarity solutions of previous investigation for such type flows are not used here; however, a new set of similarity transformations has been formed, which reduced the governing system (PDEs) into an exact set of ordinary differential equations (ODEs), whereas the longstanding issues of semi-similarity solutions have been successfully resolved in this particular case and in general for all situations of Carreau fluid flow. In a nutshell, a unified mathematical approach has been devised in this paper. We strictly emphasized the simulation of flow of Carreau fluid and double diffusive convection in flow inside a channel with multiple dynamical behaviours and structures (both Jeffery Hammel and Poissuielle flow types) of walls. The boundary layer approximation and stream function assumptions have not been used in the study's execution. The shear thinning and shear thickening features of Carreau fluids with variable density cause them to exhibit lower axial velocity in the centre of a horizontal channel than Newtonian fluids due to variable wall configurations and complex flow conditions. By enhancing buoyancy driven convection, which promotes effective heat dispersion, increasing the solutal and thermal Grashof numbers (GrS=GrT>0) lowers the temperature field. It has been found that in channel with diverging walls (a1=2.0), increasing the modified Reynolds numbers (σ1,σ2>0) increases concentration profiles, i.e. ϕ(η), while decreasing them in channel with rectilinear walls (a1=0.0).

Lattice Boltzmann simulations of unsteady Bingham fluid flows

Transient flows of viscoplastic fluids have very peculiar characteristics. The startup and cessation flows of viscoplastic materials have been subject to many theoretical and numerical investigations. The most challenging aspect of numerical solutions of viscoplastic fluids is the viscosity singularity during the transition from yielded to unyielded material. Hence, the proper representation of yield surfaces is the most critical aspect of numerical methods in viscoplastic fluid flow. In the present work, we use a lattice Boltzmann scheme to solve an ideal Bingham fluid’s startup and cessation flows. This numerical scheme advantage is that can represent infinite viscosity without noticeable numerical instabilities, producing yield surfaces with more accuracy and quality. Theoretical solutions for the startup flow are available in the literature. However, it is unclear which is more accurate and what their validity ranges are. Nonetheless, these solutions served as a reference for the present simulations. The overall aspect of the numerical solutions agreed with the theoretical models. The cessation flow of the Bingham fluid was also simulated. Unlike a Newtonian fluid, this type of flow is known to have a finite period until cessation. The simulations correctly reproduced this behavior. The transient yield surfaces matched very well with augmented Lagrangian solutions.

Slot coating of time-dependent structured materials: Effects of thixotropy on the flow dynamics and operating limits

Some of the most common liquid-like formulations rooted in the coating industry consist of rheologically complex structured materials such as inks, paints, and slurries. Yet, the impact of time-dependent structuring effects due to thixotropy on thin film coating applications remains elusive and still unclear. Here, we present a computational study of the effects of thixotropy on slot coating of time-dependent structured materials. By coupling a recent fluidity-based constitutive model for thixotropic materials with a well-established finite element/elliptic mesh generation method for free surface flows, we assess the role of thixotropy by comparing the predictions from the thixotropic model with those from a simple Generalized Newtonian Fluid model that uses the same flow curve for the material steady-state equilibrium viscosity. We find that thixotropy can indeed have a major impact on slot coating applications, potentially bringing strong implications not only to the flow dynamics but also to the operating limits of the process. In conclusion, the results and discussions we present in this study underscore the importance of accounting for thixotropy to genuinely model and fundamentally understand the behavior of time-dependent structured materials with complex rheology in processing flows like those ubiquitous across the broad fields of coating science and engineering.

Synthesis, Properties, and Biocompatibility of 4-Carboxyphenyboronic Acid-Modified Gelatin-Methacryloyl: A Hydrogel for Retinal Surgeries.

The current surgical adjunctive for vitreoretinal surgeries fails to provide an adequate 3D structure for cellular regeneration. A one-pot synthesis of gelatin-methacryloyl (GelMA) followed by modification with 4-carboxyphenylboronic acid (4-CPBA) was performed to fabricate 4-CPBA-modified GelMA (4CPBA@GelMA), a gelatin-based hydrogel. 4CPBA@GelMA was photo-cross-linked by 405 nm violet light and examined using nuclear magnetic resonance (NMR), Fourier-transform infrared spectrometry (FTIR), scanning electron microscopy (SEM), and rheometry. In vitro biocompatibility was examined by Müller cell proliferation assays exposed to 4CPBA@GelMA and violet light. In vivo retinal biocompatibility was evaluated by electroretinography of rat eyes that were exposed to intravitreally injected and photo-cross-linked 4CPBA@GelMA at days 3, 7, 14, and 28 post-injection. Following electroretinography, histology and immunohistochemistry were performed on the retinas. The NMR results indicated amidation of GelMA by 4-CPBA, and FTIR confirmed the presence of the CPBA ring in 4CPBA@GelMA samples. SEM revealed that 4CPBA@GelMA had significantly larger pores than GelMA (56.9 ± 9.5 vs 35.1 ± 2.8 μm; P < 0.001). Rheological findings showed that, unlike GelMA and gelatin, 4CPBA@GelMA has Newtonian fluid properties at room temperature. Exposure to 4CPBA@GelMA did not significantly affect Müller cell viability in a proliferation assay; moreover, electroretinography findings indicated normal waveforms and implicit times, and histology and immunohistochemistry examinations revealed no significant changes. In this study, we established the high retinal compatibility of 4CPBA@GelMA. The low viscosity of 4CPBA@GelMA is ideal for injection via small-gauge needles, and the larger pore size and three-dimensional network both potentiate cellular migration and growth. These features made 4CPBA@GelMA a candidate for vitreoretinal surgical adjunctive that might promote retinal regeneration.

Poiseuille Flow of the Suspension of Gold Nanoparticles in Second-grade Fluid: Analytical Solutions

The Poiseuille flows have been extensively restricted to Newtonian fluids through a channel, and the significance of such flows has spanned several industries, from chemical industries to engineering applications. The restriction to Newtonian flows has impacted the further advancement in the study of Poiseuille flow and as a result, studies on Poiseuille flows have been neglected for decades. In this study, the Poiseuille flow of the second-grade nanofluid fluid is considered. The base fluid is the viscoelastic Second-grade fluid, a fluid that is both shear-thinning and shear-thickening under different conditions and whose applications can be found in polymer processing and cosmetic production. This study invokes the general assumptions of Poiseuille flow, which reduces the governing equations to ordinary differential equations. The results from simulating the model show that the velocity drops as both the second-grade fluid parameter and the volume fraction increase. The flow rate increases with increasing channel width.

Heat and mass transfer in tri‐layer ependymal ciliary transport with diverse viscosity

AbstractSpecialized cilia known as ependymal cilia help the cerebrospinal fluid, which is important for nutrient delivery and waste elimination, to circulate in the brain. Many species rely on cilia and flagella for fluid movement and motility. Cilia and flagella, for instance, produce propulsive forces that allow unicellular creatures like Paramecium and Euglena to move through their surroundings. Ciliary transport plays a role in the flow of egg cells, or oocytes, via the fallopian tubes in the female reproductive system. The transfer of the egg towards the uterus is facilitated by the synchronized wave‐like motion produced by the cilia lining the fallopian tubes. Like this, ciliary transport in men aids in the passage of sperm cells via the epididymis. Many scientists and researchers are studying the mechanics of cilia motion and the properties of the viscoelastic fluid layer to develop new treatments and applications in biomedical engineering and for some diseases. Motivated by a wide range of biological applications, the objective of this study is to investigate the heat and mass transfer flow of tri‐layered Newtonian fluids flowing with the help of ciliary beating in a Cartesian coordinate. The fluid is incompressible, and fluid layers are not intermixed. The fluid flow with heat and mass transfer is first modelled in wave and then transmuted into fixed. Solutions for temperature profile, velocity distribution, stresses and concentration distribution are obtained. The influence of incipient parameters is displayed with graphs and plotted with the computational software MATHEMATICA 13.0 in the results section. The key findings obtained from graphs show that the maximum magnitude for temperature and velocity is achieved in the middle layer of fluid whereas in the outer layer concentration profile is maximum. It is predicted that this approach will make an essential contribution to the progress and enhancement of various types of drug delivery systems in the biomedical industry and biomechanics.

Spatially and temporally high-order dynamic nonlinear variational multiscale methods for generalized Newtonian flows

Non-Newtonian fluids are of interest in industrial sectors, biological problems and other natural phenomena. This work proposes rheologically-dependent, spatially and temporally high-order non-residual stabilized finite element formulations. The accuracy of the methods is assessed by tackling highly-convective time-dependent power-law flows. The spatial approximation uses Lagrangian finite elements up to fourth order. The temporal integration is done via backward differentiation formulas of order one, two and three. A key aspect of our work is using a non-residual orthogonal variational multiscale (VMS) formulation to stabilize dominant convection and to allow equal-order interpolation of velocity and pressure. Our VMS method uses dynamic nonlinear subscales, which have not been tested so far for generalized Newtonian fluids. In this work, the use of high-order temporal discretizations for the subscale components is systematically evaluated. Numerical experiments consider the flow over a confined cylinder for Reynolds numbers between 40 and 400 and power-law indices between 0.4 and 1.8. Numerical testing demonstrates the method to be stable in all combinations of spatial and temporal orders. Our results show that using high-order spatial discretizations more accurately approximates boundary layers and viscosity fields. Moreover, higher temporal orders allow using larger time steps while still capturing highly dynamic behaviors with better resolution in frequency spectra.