non-Newtonian Flow Research Articles

A Prabhakar fractional approach with generalized fourier law for thermal activity of non-newtonian second-grade type fluid flow: a fractional approach

In this work, we studied the unsteady and incompressible flow of second-grade MHD fluid moving on a vertical oscillating plate, which is passing under the possessions of an applied inclined magnetic field. The non-dimensional governed equations are turned into a fractional model using the most advanced and effective fractional definition, Prabhakar fractional derivative, which is frequently based on generalized Fourier's and Fick's laws. The resultant system is handled using integral transform, i.e. the Laplace transformation (LT) scheme, and some numerical methods are also applied for the Laplace inverse. The graphical and numerical representation of all parameters is also deliberated to analyze the physical behavior of the effects of significant parameters. As a result, it concluded that the impact of the second-grade fluid constraint slowed down the momentum profile of the moving fluid. Furthermore, in comparing the velocity field attained by our applied fractional scheme with existing literature, the overlapping of both curves with each other indicates the validity of our attained results of momentum profile. Additionally, the overlapping of both numerical scheme curves for the Laplace inverse also verifies the study's findings.

An implicit conformation tensor decoupling approach for viscoelastic flow simulation within the monolithic projection framework

The highly nonlinear nature of the system governing equations makes it difficult to simulate viscoelastic flows efficiently. In this paper, an implicit decoupling approach is proposed for the viscoelastic flow simulation with a monolithic projection method. The decoupling approach can be derived from the approximate block factorization at the matrix level, which has been successfully applied into the Newtonian flow simulations. In our work, we extend this approach to decouple the pressure, conformation tensor and velocity from the viscoelastic flow system sequentially. Firstly, the pressure-conformation tensor-velocity decoupling is realized by a two-step approximate factorization. By combining the conformation tensor and velocity together at the first-step factorization, the original efficient pressure Poisson solver for the Newtonian flow simulation can be directly adopted in the present framework for non-Newtonian flow simulation. Secondly, the conformation tensor components are further decoupled from each other by the present component-decoupling approach. Then all quantities, including pressure, conformation tensor and velocity, can be resolved without iteration. Additionally, the accuracy corrector is proposed to access the prior scheme limiter-estimation problem introduced by the implicit high-resolution scheme. We numerically demonstrate that all quantities preserve the second-order accuracy in time and space as expected by the theoretical splitting errors. Finally, several different types of canonical benchmark flow examples are conducted to validate the present solver, including laminar flow, turbulent drag-reducing flow and the rotation of a spherical particle immersed in a sheared viscoelastic fluid.

Simulation of Pressure-Driven and Channel-Based Microfluidics on Different Abstract Levels: A Case Study.

A microfluidic device, or a Lab-on-a-Chip (LoC), performs lab operations on the microscale through the manipulation of fluids. The design and fabrication of such devices usually is a tedious process, and auxiliary tools, such as simulators, can alleviate the necessary effort for the design process. Simulations of fluids exist in various forms and can be categorized according to how well they represent the underlying physics, into so-called abstraction levels. In this work, we consider simulation approaches in 1D, which are based on analytical solutions of simplified problems, and approaches in 2D and 3D, for which we use two different Computational Fluid Dynamics (CFD) methods—namely, the Finite Volume Method (FVM) and the Lattice-Boltzmann Method (LBM). All these methods come with their pros and cons with respect to accuracy and required compute time, but unfortunately, most designers and researchers are not aware of the trade-off that can be made within the broad spectrum of available simulation approaches for microfluidics and end up choosing a simulation approach arbitrarily. We provide an overview of different simulation approaches as well as a case study of their performance to aid designers and researchers in their choice. To this end, we consider three representative use cases of pressure-driven and channel-based microfluidic devices (namely the non-Newtonian flow in a channel, the mixing of two fluids in a channel, and the behavior of droplets in channels). The considerations and evaluations raise the awareness and provide several insights for what simulation approaches can be utilized today when designing corresponding devices (and for what they cannot be utilized yet).

Rheological modeling and simulation of semi-solid slurry based on experimental study

The rheological behavior of semi-solid slurry is systematically studied via three different testing modes under either shear stress or shear rate control mode. Then the non-Newtonian constitutive parameters, consistency coefficient k and power-law index n, are determined by using Power-Law (PL) and Herschel-Bulkley (HB) models. Results indicate that the viscosity curve from the shear stress control test is more suitable for the PL model fitting and numerical simulation. This investigation not only provides important insights into the rheological characteristics of slurry during semi-solid die casting but also offers a new modeling strategy for non-Newtonian fluid flow.

Modeling blood flow through the carotid bifurcation

Three-dimensional experimental model, combined with numerical simulations, finds noticeable differences among Newtonian and non-Newtonian flow regimes.

Numerical simulation of superparamagnetic nanoparticle motion in blood vessels for magnetic drug delivery.

A numerical model is developed for the motion of superparamagnetic nanoparticles in a non-Newtonian blood flow under the influence of a magnetic field. The rheological properties of blood are modeled by the Carreau flow and viscosity, and the stochastic effects of Brownian motion and red blood cell collisions are considered. The model is validated with existing data and good agreement with experimental results is shown. The effectiveness of magnetic drug delivery in various blood vessels is assessed and found to be most successful in arterioles and capillaries. A range of magnetic field strengths are modeled using equationsfor both a bar magnet and a point dipole: it is shown that the bar magnet is effective at capturing nanoparticles in limited cases, while the point dipole is highly effective across a range of conditions. A parameter study is conducted to show the effects of changing the dipole moment, the distance from the magnet to the blood vessel, and the initial release point of the nanoparticles. The distance from the magnet to the blood vessel is shown to play a significant role in determining nanoparticle capture rate. The optimal initial release position is found to be located within the tumor radius in capillaries and arterioles to prevent rapid diffusion to the edges of the blood vessel prior to arriving at the tumor and near the edge of the magnet when a bar magnet is used.

Nanoparticle transport within non-Newtonian fluid flow in porous media.

Control over dispersion of nanoparticles in polymer solutions through porous media is important for subsurface applications such as soil remediation and enhanced oil recovery. Dispersion is affected by the spatial heterogeneity of porous media, the non-Newtonian behavior of polymer solutions, and the Brownian motion of nanoparticles. Here, we use the Euler-Lagrangian method to simulate the flow of nanoparticles and inelastic non-Newtonian fluids (described by Meter model) in a range of porous media samples and injection rates. In one case, we use a fine mesh of more than 3 million mesh points to model nanoparticles transport in a sandstone sample. The results show that the velocity distribution of nanoparticles in the porous medium is non-Gaussian, which leads to the non-Fickian behavior of nanoparticles dispersion. Due to pore-space confinement, the long-time mean-square displacement of nanoparticles depends nonlinearly on time. Additionally, the gradient of shear stress in the pore space of the porous medium dictates the transport behavior of nanoparticles in the porous medium. Furthermore, the Brownian motion of nanoparticles increases the dispersion of nanoparticles along the longitudinal and transverse direction.

Fluid structure interaction versus rigid-wall approach in the study of the symptomatic stenosed carotid artery: Importance of wall compliance and resilience of loose connective tissue.

The purpose of this paper is to demonstrate the importance of a compliant wall approach in modeling of non‐Newtonian and non‐physiological blood flows. A case study of a stenosed and symptomatic carotid bifurcation was considered to show the influence of the wall‐resilience assumption on the flow parameters obtained with numerical simulations. Patient‐specific data concerning the geometry and flow conditions were collected and used to carry out two‐way coupled fluid structure interaction simulations of the pulsatile blood flow through carotid artery. The wall compliance was considered separately as related to the wall‐elasticity and as associated with the reaction of the loose connective tissue surrounding the carotid bifurcation. The obtained hemodynamic parameters were compared to those which were found in rigid‐wall simulations. The difference between the results obtained for rigid‐wall and compliant‐wall approaches for the peak‐systolic area‐averaged wall shear stress achieved 35%, whereas the difference between the time‐averaged local vorticity and shear strain reached, respectively, 42% and 43%. The influence of the highly resilient wall on the monitored hemodynamic parameters was significant even if time‐averaged values are compared, which suggests that these metrics are considerably overestimated if the wall compliance is not considered. Moreover, the findings show that the mechanical response of the loose connective tissue cannot be neglected in blood flow simulations. Additionally, this study indicates that stiffening of the arterial wall due to atherosclerosis significantly rises hemodynamic parameters. This explains the therapeutic benefits of surgical removal of plaque lesions formed in the carotid bifurcation (endarterectomy).

Pulsatile flow of thixotropic blood in artery under external body acceleration

This work presents a numerical technique for simulating non-Newtonian blood flow in human’s arteries driven by an oscillating pressure gradient. The blood is considered as a thixotropic fluid and its structural properties are considered to obey Moore’s thixotropic model as a constitutive equation. The equations of motion are simplified considering the flow laminar, axisymmetric and the fluid incompressible. A numerical solution is presented using finite difference method in order to compute the velocity field and wall shear stress distribution. The numerical results obtained have been validated with the analytical solution available in the literature. Furthermore, the effect of the structural properties, the average of the pressure gradient and the external acceleration on the velocity and wall shear stress distribution is investigated. These results reveal the influence of the different parameters studied on the pipe flow response of the thixotropic fluid.

Open-source finite volume solvers for multiphase (n-phase) flows involving either Newtonian or non-Newtonian complex fluids

Two new control volume solvers multiFluidInterFoam and rheoMultiFluidInterFoam are presented for the simulation of Newtonian and non-Newtonian n-phase flows (n≥2), respectively, fully accounting for interfacial tension and contact-angle effects for each phase. The multiFluidInterFoam solver modifies certain crucial aspects of the regular multiphaseInterFoam solver provided by OpenFOAM for Newtonian flows, improving its efficiency and robustness, but most importantly improving considerably its accuracy for surface tension driven flows. The new solver uses the volume-of-fluid (VOF) method based on the MULES method and artificial interface compression for the interface capturing, in combination with a suitable continuum surface force model; i.e. the interfacial tension coefficient decomposition method is employed to treat pairings of interfacial tension between the phases. VOF smoothing is also implemented by applying a Laplacian filter on the distribution of volume fractions, and the SIMPLEC algorithm is employed for the velocity–pressure coupling. The above algorithm has also been extended with the development of the rheoMultiFluidInterFoam solver which is capable of fully taking into account complex non-Newtonian effects (e.g. yield stress, viscoelasticity, etc.) of the involved liquids. To this end, the developed solver incorporates the RheoTool toolbox (Pimenta and Alves, 2017), utilizing a wealth of constitutive equations suitable for modeling different types of fluids with complex rheology. Our solvers are tested for both the implementation of the surface tension and of the constitutive equations in a wide range of different flow setups, considering typical benchmark two-phase and three-phase flows, such as the cases of dam break with an obstacle, spreading of a floating lens, a levitating drop, and a bubble rising in an ambient fluid; flows involving Newtonian, viscoplastic and viscoelastic liquids have been considered. Comparisons against analytical solutions or previously published numerical data are performed clearly demonstrating the capability of the new solvers to efficiently and accurately simulate interfacial tension dominated three-phase flows (and n-phase flows in general) for both simple and complex liquids.

Artificial Neural Networking (ANN) Model for Convective Heat Transfer in Thermally Magnetized Multiple Flow Regimes with Temperature Stratification Effects

The convective heat transfer in non-Newtonian fluid flow in the presence of temperature stratification, heat generation, and heat absorption effects is debated by using artificial neural networking. The heat transfer rate is examined for the four different thermal flow regimes namely (I) thermal flow field towards a flat surface along with thermal radiations, (II) thermal flow field towards a flat surface without thermal radiations, (III) thermal flow field over a cylindrical surface with thermal radiations, and (IV) thermal flow field over a cylindrical surface without thermal radiations. For each regime, a Nusselt number is carried out to construct an artificial neural networking model. The model prediction performance is reported by using varied neuron numbers and input parameters, and the results are assessed. The ANN model is designed by using the Bayesian regularization training procedure, and a high-performing MLP network model is used. The data used in the creation of the MLP network was 80 percent for model training and 20 percent for testing. The graph shows the degree of agreement between the ANN model projected values and the goal values. We discovered that an artificial neural network model can provide high-efficiency forecasts for heat transfer rates having engineering standpoints. For both flat and cylindrical surfaces, the heat transfer normal to the surface reflects inciting nature towards the Prandtl number and heat absorption parameter, while the opposite is the case for the temperature stratification parameter and heat generation parameter. It is important to note that the magnitude of heat transfer is significantly larger for Flow Regime-IV in comparison with Flow Regimes-I, -II, and -III.

Non-smooth evolution of non-Newtonian flows influenced by thermal effects

Abstract Non-smooth evolution in thermo-viscoplastic flows is investigated. The nonlinear Norton–Hoff model coupled with the unsteady heat system govern the fluid motion. This contribution is an extension of the previous established works. The novelty of this paper is to supply a close scrutiny result of the spawned interface through the medium of the pervasive Schauder fixed point. Numerical results are exhibited to illustrate the effectiveness of the advocated approach.

Effect of Soil Type and Application of Ecological Fertilizer Composed of Ash from Biomass Combustion on Selected Physicochemical, Thermal, and Rheological Properties of Potato Starch.

The aim of the study was to assess the effect of soil type and the application of fertilizer composed of ashes from biomass combustion to potatoes on selected physicochemical, rheological, and thermal properties of potato starches isolated by using the laboratory method. Potatoes were grown in Haplic Luvisol (HL) and Gleyic Chernozem (GC) soil and fertilized with different doses of biomass combustion ash (D1–D6) with different mineral contents. The thermodynamic characteristics of gelatinization and retrogradation were identified by DSC. The analyses of rheological properties included the determination of the gelatinization characteristics by using the RVA method, flow curves, and assessment of the viscoelastic properties of starch gels. It was found that the starches tested contained from 24.7 to 29.7 g/100 g d.m. amylose, and the clarity of 1% starch pastes ranged from 59% to 68%. The gelatinization characteristics that were determined showed statistically significant differences between the starches analyzed in terms of the tested factors. The value of maximum viscosity and final viscosity varied, respectively, in the range of 2017–2404 mPa·s and 2811–3112 mPa·s, respectively. The samples of the potato starches studied showed a non-Newtonian flow, shear thinning, and the phenomenon of thixotropy. After cooling, the starch gels showed different viscoelastic properties, all of which were weak gels (tan δ = G″/G′ > 0.1).

A Casson nanofluid flow within the conical gap between rotating surfaces of a cone and a horizontal disc

The present study highlights the flow of an incompressible nanofluid following the non-Newtonian flow. The non-Newtonian fluid behavior is characterized by the Casson prototype. The flow occupies the conical gap between the rotating/stationary surfaces of the cone and the horizontal disc. Heat and mass transfer is also considered. The novelty of the proposed mathematical model is supplemented with the impacts of a uniform magnetic field imposed vertically upon the flow together with Ohmic dissipation and chemical reactions. The constitutive equations of the Casson fluid have been interpreted along with the cylindrical coordinates. The governing partial differential equations of momentum, energy, and concentration are converted into a set of nonlinear ordinary differential equations via appropriate similarity transformations. This scheme leads to a set of coupled nonlinear ordinary equations concerning velocity, temperature, and nanoparticles concentration distributions. These equations are analytically solved by means of the Homotopy perturbation method (HPM). The theoretical findings are presented in both graphical and tabular forms. The main objective of this study is to discuss the effects of the rotations of both cone and disc and the effects of the other parameters in the two cases of rotation alternatively. Additionally, the effect of the angle between the cone and the disk is one of our interesting points because of the importance of its effect in some engineering industry applications. The rotation parameters are found to have reduction effects on both the temperature and the radial velocity of the fluid, while they have an enhancing effect on the azimuthal velocity. The effects of other parameters with these rotations are found to be qualitatively the same as some earlier published studies. To validate the current mathematical model, a comparison with the previous scientific reports is made.

Chemical reaction and thermal radiation via Cattaneo-Christov double diffusion (CCDD) effects on squeezing non-Newtonian nanofluid flow between two - parallel vertical plates

Chemical reaction and thermal radiation via Cattaneo-Christov double diffusion (CCDD) effects on squeezing non-Newtonian nanofluid flow between two - parallel vertical plates

An axisymmetric flow analysis by means of tangent hyperbolic fluid with Cattaneo-Christov heat and mass flux model

In present analysis three dimensional steady, axisymmetric, incompressible, non-Newtonian tangent hyperbolic flow of nanofluid due to rotating disk is investigated. A rotating disc is a phenomena in which a disc rotates around an axis at a constant angular velocity and each point on the disc follows a circle's arc. The force necessary to move the disc to overcome frictional resistance is determined by the shear stress between the disc and the rotating fluid and the heat transfer is affected by the local flow field. The heat and mass transfer field is explored in the existence of chemical reaction and Cattaneo-Christov heat and mass flux model. By using similarities transformations, the supreme partial differential equations of the problem are turned into typical differential equations respectively. The determining differential equations are solved on MATLAB software by using bvp4c method that has been cracked through shooting technique. The deviation of velocity, temperature and mass profiles for different inputs of power-law index, Prandtl number, Brownian motion parameter, Schmidt number, thermophoretic parameter, heat and mass relaxation time parameters and chemical reaction parameter are displayed via graphs. The increment happens in radial velocity field whereas tangential and axial velocity fields reduces due to power index parameter n. The results show that for Cattaneo-Christov model, the temperature and concentration profiles exhibit reducing behaviour than that of Fourier's classical model. The concentration within fluid declined due to chemical reaction.

Reynolds number effect of the turbulent micropolar channel flow

The turbulent regime of non-Newtonian flows presents a particular interest as flow behavior is directly affected by the internal microstructure type of the fluid. Differences in the dispersed phase of a particle laden flow can either lead to drag reduction and turbulence attenuation or to drag and turbulence enhancement in polymer flows and dense suspensions, respectively. A general concept of non-Newtonian fluid flow may be considered in a continuous manner through the micropolar theory, recognizing the limitations that bound this theory. In recent articles [Sofiadis and Sarris, “Microrotation viscosity effect on turbulent micropolar fluid channel flow,” Phys. Fluids 33, 095126 (2021); Sofiadis and Sarris, “Turbulence intensity modulation by micropolar fluids,” Fluids 6, 195 (2021)], the micropolar viscosity effect of the turbulent channel flow under constant Reynolds number and its turbulent modulation were investigated. The present study focuses on the investigation of the turbulent micropolar regime as the Reynolds number increases in a channel flow. Findings support that the micropolar stress, which was found to assist turbulence enhancement in the present model, attenuates as Re increases. Effects on the friction behavior of the flow, as Reynolds number increases, become more important for cases of higher micropolar viscosity, where a reverse drag behavior is observed as compared to lower micropolar viscosity ones. Finally, turbulence intensification for these cases declines close to the wall in contrast to lower micropolar viscosity flows, which manage to sustain high turbulence and increase drag in the near-wall region along with Re.

Drainage of power-law fluids from fractured or porous finite domains

We develop a sharp-interface model that captures the coupled effect of spatial heterogeneity and fluid rheology on one-dimensional Newtonian and non-Newtonian buoyancy-driven flow spreading in fractured and porous media over a horizontal impermeable bed. We study the flow in three different geometries: (i) a constant uniform aperture, (ii) an aperture variable along the vertical axis, i.e. perpendicular to the direction of propagation and (iii) an aperture variable along the horizontal axis, i.e. parallel to the direction of propagation. The non-Newtonian rheology is described by the power-law equation of rheological index n and the aperture variation in both directions by a positive number r . The self-similar solutions of the flow obtained at late times allow the transformation of the nonlinear PDEs governing the spreading into nonlinear ODEs. The current shape is affected by the interplay between the rheological index and the spatial variability of the aperture. The residual liquid mass that remains in the fracture at any given time is computed from the current profiles, obtaining a negative power-law behavior in the time of exponent dependent on n and r . In addition, sensitivity analysis is performed to highlight the impact of the model parameters on the current profile and residual mass. The dimensionless analysis outcomes are compared to two real examples of flow within a uniform and a wedge-shaped aperture along the flow direction. The numerical results of the examples confirm that the proposed model can successfully capture the propagation of the gravity current, its profile, and drainage flow rate. • Drainage of one-dimensional non-Newtonian gravity-driven currents from an edge of a fractured finite domain is investigated. • Late-time similarity solutions are derived for different geometrical variations of fracture aperture. • The analogy between Hele-Shaw non-Newtonian flow in fractures and porous media flow is discussed. • Two realistic case studies illustrating the applicability of our results are extensively discussed.

A comparison of Newtonian and non-Newtonian pulsatile blood rheology in carotid bifurcation through fluid–solid interaction hemodynamic assessment based on experimental data

Endothelial cells play a crucial role in the arterial homeostasis. In addition to physiological risk factors, abnormal levels of hemodynamic parameters induced by the pulsatile flow contribute to atherosclerotic plaque formation and development. In this study, we used an experimental setup to study the hemodynamics of Newtonian and non-Newtonian blood flow on a deformable model of human carotid bifurcation. The flow/pressure pulses of the experimental model were fed into a fluid–structure interaction numerical model, and respective hemodynamic parameters were obtained and compared between the two flow regimes. Results revealed noticeable differences among the two flow regimes when the pulsatile nature of blood flow and pressure were considered, with more distinct differences near junction sites. Velocity profiles of the non-Newtonian model were more flattened with higher back flow during the diastole. The shear stress waves as well as shear-dependent parameters, such as oscillatory shear index, relative residence time, and vorticity, as well as wall stress and strain, also indicated significant differences among the two models. Regardless of flow regime, results showed a good agreement with clinical outcomes in human carotid bifurcation, especially the carotid sinus. Near the bifurcation, marked fluctuations of shear stress are evident. Around the junction site, wall pulsation experienced variations up to five times of the normal pulse span. The quantified hemodynamic parameters obtained from proposed accurate model of carotid bifurcation may help to achieve technological solutions to adjust the out of biological ranges of these parameters, and avoid atheroma formation or treat the diseased artery.

Theoretical study of non-Newtonian micropolar nanofluid flow over an exponentially stretching surface with free stream velocity

The computational analysis of the second-order micropolar stagnation point flow of nanofluid over an exponentially permeable stretching sheet is considered. The freestream velocity with the thermal slip effects is taken into account in this analysis. This model is developed on the basis of flow assumptions and reduced into partial differential equations before applying the boundary layer approximations. The governing equations as a mathematical model are simplified with the help of suitable transformations. The differential system is further solved by using the bvp4c. Both graphs and tables are used to report observations. The skin friction and Nusselt number are reported for both weak and strong concentrations. The magnitude of skin friction is noticed greater for strong concentration in comparison with weak concentration. Subject to couple stress, the values of skin friction are relatively high for the case of weak concentration in comparison with strong concentration. Micropolar profile admit the direct relation toward micropolar parameter and micro-gyration parameter. Both Sherwood number and Nusselt number admits higher values for strong concentration as compared to weak concentration.