non-Newtonian Media Research Articles

Flow field analysis and flow prediction of pressure reducing valves in power-law media

A robust hydraulic system is necessary for industrial gluing equipment in order to transfer and regulate a variety of chemical fluid media. Certain operational conditions call for a certain flow output. In hydraulic systems, pressure reduction valves are frequently employed to regulate flow and pressure output. In order to analyze the flow of high viscosity special media inside the valve body, a colloidal medium that complies with the power-law constitutive law and a novel type of pressure-reducing valve appropriate for high viscosity fluids were chosen as the research objects in this study. First, the valve channel's flow performance and flow field characteristics were researched with a combination of simulation and experiments. Then the impact of pressure differences, opening, and temperature variations on flow rate was investigated. The proposed flow prediction formulas can be used to forecast the flow rate in engineering applications accurately which is verified by the comparison of the numerical and experimental results. Lastly, an analysis was done on the pressure reducing valve's capacity to regulate pressure under various operating circumstances. The research can offer a specific reference for the analysis of flow field characteristics inside valves in high viscosity media and the design of pressure-reducing valve bodies in non-Newtonian media. Furthermore, the research results can help determine whether the pressure reducing valve's operating condition is normal.

Film drainage and critical velocity of fluid particles in power-law fluids

This work studies the collision of fluid particles (bubbles or droplets) in non-Newtonian media whose viscosity obeys the power-law model, by analyzing the behavior of the drainage of the film between the particles. The model considers a time-dependent collision velocity governed by a force balance over each particle, which renders the estimation of both coalescence and rebound possible and as a result the critical velocity separating the two regimes. Results indicate that the shear-thinning behavior of the continuous medium favors coalescence, whereas shear-thickening films promote rebound. The critical velocity increases with decreasing power-law index and follows an exponential trend with the equivalent particle size for a given value of the power-law index. The exponent showing the dependency of the critical velocity on the equivalent particle size changes linearly with the power-law index within the investigated parameter range. Both the drainage behavior and the critical velocity are shown to be affected only negligibly by the selection of the drag force closure, i.e., whether they are proposed by considering Newtonian or non-Newtonian media.

Моделирование гидродинамики, теплообмена и процесса усреднения гранулированных сред в пневматическом циркуляционном аппарате

The mathematical modeling of hydrodynamics, heat transfer, and averaging of a highly concentrated granular medium in the working area of a vertical pneumatic circulation apparatus is performed. The hydrodynamics of a dense layer of the granular medium is described by a non-Newtonian model with partial slip conditions on solid walls. Such a representation of the granular medium dynamics allows one to approve theoretical calculations with available experimental data for a steady flow in a flat channel. The numerical applicability of the partial slip condition for a non-Newtonian fluid is confirmed by the analytical dependences obtained by the authors for a steady flow in a circular tube and a flat channel, which are transformed into the known analytical formulas under no-slip conditions for a non-Newtonian medium. On the basis of the proposed model, the heat exchange intensity is analyzed when setting the constant heat flux density or the constant temperature on the annular shelves in the apparatus. The intensity of the granular mixture averaging in the bunker with the introduction of additional annular shelves is studied, and the efficiency of granular mixture mixing during rotation is considered. A method for analyzing the mixing of a granular medium in dynamics in each local area of the apparatus is proposed, which is based on the determination of the inhomogeneity coefficient. The results of this study can be used when developing powder technology devices for drying, mixing, dosing, and transport.

Расчет коэффициента местного сопротивления при изотермическом течении неньютоновской несжимаемой жидкости в цилиндрическом канале с внезапным сужением

The engineering calculation and construction of the extrusion tool in the form of cylindrical forming channels with sudden narrowing is associated with the determination of the coefficient of resistance of sudden narrowing and local pressure losses. The available theoretical and experimental data on the values of the resistance coefficient of sudden narrowing are contradictory, approximate in nature and, in some cases, do not take into account the rheological properties of the liquid. Their use to calculate local pressure losses under laminar flow conditions leads to significant errors. To eliminate the indicated problems, a mathematical statement of the problem of isothermal stationary laminar flow of non-Newtonian non-compressible fluid in an axisymmetric channel with sudden narrowing was formulated. The mathematical model of flow in spatial formulation is formalized in the form of equations for preserving momentum and mass. As a rheological model, the Carreau model is taken, taking into account the presence of finite viscosity values at marginal shear rates. The numerical solution of the problem was performed by the finite element method using the Comsol MultiphysicsTM CFD modeling package. As a result of the solution, the picture of the current of the non-Newtonian medium was restored in the form of the distribution of current lines, kinematic and dynamic flow parameters. The impact of Reynolds number on change of geometric characteristics of flow structure, kinematic and dynamic flow parameters was evaluated. Values of local resistance coefficient and pressure losses for overcoming sudden narrowing for selected flow modes are calculated. The results of computational experiments are summarized in the form of a criterion ratio for calculating the coefficient of local resistances depending on the Reynolds number.

Wall effect on cluster particle's settling terminal velocity and drag coefficient in Newtonian and non-Newtonian fluid medium

The experimental investigation of the wall effect on the cluster particle settling in the Newtonian and non-Newtonian fluid medium is carried out in three different diameter flow channels. The cluster usually forms during the sedimentation of particles in a fluid medium, so it becomes necessary to study the behavior of the cluster particles. Different cluster particles are considered depending on the number of spheres (N) attached to the cluster and the cluster's shape. The present experiment covers the following range of conditions: 0.05 ≤ deq/D ≤ 0.24, 2 ≤ N ≤ 7, 0.64 ≤ n ≤ 1, and 0.14 ≤ K ≤ 1.81. The results reveal that the terminal velocity varies with the blockage ratio (deq/D), N, and cluster shape. For a particular deq/D ratio and the same N, the terminal velocity of polyhedron particles is high compared to the planar and chain shape particles. The blockage ratio and the Reynolds number affect the wall factor of the cluster particles. However, from the experiment, it is observed that the wall effect also depends on the orientation of the particles. The impact of the wall on the cluster particle is high in Newtonian fluid when compared to cluster particles in non-Newtonian fluid. The present work additionally investigates the influence of drag on cluster particles in the presence and absence of the wall effect. The numerical relationships are developed to predict experimental results in Newtonian and non-Newtonian fluid mediums.

Investigation of a non-Newtonian MR fluid flow between parallel plates by developed CFD code for different numerical schemes

Magnetorheological (MR) fluids are composed of a solution of micron-sized magnetizable particles dispersed in a carrier fluid, typically oil. Thus, the MR fluids are classified as smart fluids by showing variable apparent viscosity under a precisely controllable external magnetic field. This feature of the MR fluids gave the possibility to use them in the MR dampers to control variational damping forces. In this work, an MR damper on relatively small scales is considered to investigate the MR fluid flow behavior through the piston annuli where the magnetic field exists. This work mainly focuses on the numerical solutions of the flow variables in a magnetically excited non-Newtonian flow medium by comparing analytical results for various Reynolds numbers. The Herschel–Bulkley (HB) viscous model is used for the non-Newtonian characteristic of the MR fluid. For the numerical modeling of the HB viscous model, the regularized approaches are used to avoid numerical errors. However, contrary to the actual HB model, the regularized models can be incapable to give true apparent viscous values at very low shear rates depending on the regularization parameters. Thus, the present study aims to give a better understanding of choosing the optimal regularization parameters for the studied flow conditions. The second part of the study discusses the numerical discretization schemes aiming to present their performances while changing the Reynolds number between 0.002 and 1. In this manner, a Computational Fluid Mechanics (CFD) solver has been developed for two-dimensional geometries which are meshed with structured grids by using six different discretization schemes including two of the most known total variation diminishing (TVD) schemes. For simplicity of the problem, a two-dimensional parallel plates geometry and a constant magnitude of the magnetic field intensity along the piston annuli are assumed. The study also summarizes the CFD technique by evaluating the physical meaning of the flow field variables.

On Thermal Boundary Layer in a Viscous Non-Newtonian Medium

An existence and uniqueness theorem for a classical solution to the system of equations describing thermal boundary layers in viscous media with the Ladyzhenskaya rheological law is generalized.

Experimental and numerical investigations of thermal and flow characteristics of a shear-thinning non-Newtonian fluid in a differentially heated cavity

The thermal and flow characteristics of carboxymethyl cellulose (CMC) were investigated by experimental and numerical means, in order to assess the shear-thinning behaviour of a non-Newtonian fluid inside a differentially heated square cavity. A novel particle image velocimetry technique was used to analyse natural convective flow in a non-Newtonian fluid. The square cavity was filled with an aqueous solution of CMC, which exhibits non-Newtonian shear-thinning behaviour. The present study carried out a comparative analysis of several different numerical models, including the Power-law model, the Cross model, and the Carreau model, with the aim of producing a model that can be used to approximate viscosity distributions for non-Newtonian fluids. Three Rayleigh numbers were considered, Ra=1.22 × 104, 2.29 × 104, and 3.33 × 104. The patterns and magnitudes of velocity obtained from the experimental and numerical analyses were in close agreement in the proximity of the cavity walls and at the core of the natural convective flow. For CMC, the mean Nusselt number (Nu) showed a direct correlation with Ra. The outcomes provide some confidence in terms of their use as benchmark data for the simulation of a non-Newtonian fluid medium. For the first time, the proposed system was applied to non-Newtonian shear-thinning (pseudoplastic) flow, and quantities such as the distribution of mean Nu along the hot wall and the velocity field were determined concurrently for different Rayleigh numbers. Of the three alternative models, the Carreau model is the most effective, and is capable of predicting the thermal and flow performances within the thermal system described here with precision.

Experimental and theoretical study of the rheological properties of non-newtonian media (solutions of viscoelastic surfactants) under quasi-static and dynamic loading

Experimental and theoretical study of the rheological properties of non-newtonian media (solutions of viscoelastic surfactants) under quasi-static and dynamic loading

Towards the Determination of Machining Allowances and Surface Roughness of 3D-Printed Parts Subjected to Abrasive Flow Machining

Abrasive flow machining (AFM) is considered as one of the best-suited techniques for surface finishing of laser powder bed fused (LPBF) parts. In order to determine the AFM-related allowances to be applied during the design of LPBF parts, a numerical tool allowing to predict the material removal and the surface roughness of these parts as a function of the AFM conditions is developed. This numerical tool is based on the use of a simplified viscoelastic non-Newtonian medium flow model and calibrated using specially designed artifacts containing four planar surfaces with different surface roughnesses to account for the build orientation dependence of the surface finish of LPBF parts. The model calibration allows the determination of the abrasive medium-polished part slip coefficient, the fluid relaxation time and the abrading (Preston) coefficient, as well as of the surface roughness evolution as a function of the material removal. For model validation, LPBF parts printed from the same material as the calibration artifacts, but having a relatively complex tubular geometry, were polished using the same abrasive medium. The average discrepancy between the calculated and experimental material removal and surface roughness values did not exceed 25%, which is deemed acceptable for real-case applications. A practical application of the numerical tool developed was demonstrated using the predicted AFM allowances for the generation of a compensated computer-aided design (CAD) model of the part to be printed.

Modelling the hydrodynamics of a two-phase flow in the non-Newtonian fluid

The paper presents the results of modelling the flow of droplets in the flow of a non-Newtonian fluid. The task is solved in a nonstationary formulation. We determined the time of stabilization of the speed profile of the droplets and the length of the initial hydrodynamic sector. We compared the specified characteristics for the main flow of the non-Newtonian fluid and for the set of droplets in the flow. We show the coincidence of the lengths of the initial hydrodynamic sections determined by the stabilization of speeds for the droplets and the non-Newtonian medium.

High-efficiency nano polishing of steel materials

Abstract The application of a specific rheological polishing slurry is proposed first for high-efficiency machining of steel materials to achieve high-quality ultraprecision finished surfaces. The rheology of the polishing slurry was explored to show that the non-Newtonian medium with certain parameters of content components exhibits shear-thickening behavior. Then the new high-efficiency nano polishing approach is applied to process spherical surfaces of bearing steel. Several controllable parameters such as shear rheology, abrasive data, rotational speed, and processing time are experimentally investigated in this polishing process. A special finding is that the surface roughness and material removal rate can increase simultaneously when a small abrasive size is applied due to the thickening mechanism during the shearing flow of slurries. Excessive abrasives can decrease surface quality due to the uneven agglomeration of particles scratching the surface. Under optimized conditions, a high-accuracy spherical bearing steel surface with a roughness of 12.6 nm and roundness of 5.3 μm was achieved after a processing time of 2.5 h. Thus, a potential ultraprecision machining method for target materials is obtained in this study.

Coalescence of fluid particles with deformable interfaces in non-Newtonian media

The drainage of the non-Newtonian film between two approaching fluid particles are studied. The non-Newtonian continuous phase is a generalized Newtonian fluid that obeys the power-law model, and the deformable particle interfaces are allowed to have any degree of tangential mobility. The interaction is a gentle collision with a constant relative approach velocity. The film equations are simplified by using the lubrication theory in the thin film limit and combined with the boundary integral method. The effect of the non-Newtonian behavior on the film drainage and on the coalescence time is investigated through the power index. It is found that the non-Newtonian behavior significantly affects the number and type of the rims emerging at the interfaces. At a given approach velocity, when there are no rims or when the interfaces are fully mobile, the coalescence times for Newtonian and non-Newtonian fluids appear to be the same. Otherwise, the coalescence time increases with the power index, i.e., it is faster for shear-thinning fluids and slower for shear-thickening ones. This effect of the non-Newtonian behavior is found to amplify with the tangential mobility of the interfaces and the relative approach velocity.

Motion and deformation of migrating compound droplets in shear-thinning fluids in a microcapillary tube

The deformation dynamics of a moving compound droplet inside a microcapillary tube is investigated in Newtonian and non-Newtonian ambient fluids. The numerical method used is a ternary phase-field model to determine the temporal evolution and the subsequent hydrodynamics of compound droplets traveling inside a microcapillary tube. By solving the axisymmetric momentum equations, the compound droplet movement is identified by tracing the spatiotemporal evolution of a pair of two deformable interfaces. Results indicate that the rheological properties of the continuous phase significantly influence the compound droplet characteristics. The position of the center of the mass of both inner and outer drops along the tube axis increases linearly in a Newtonian ambient fluid while it is nonlinear in a non-Newtonian medium, and the deviation from the linear behavior increases as the concentration of the polymer solution increases. These distinct behaviors occur after a particular normalized time (t*, which is normalized with R/Uavg in which R is the radius of the tube and Uavg is the average inlet velocity) during the early stages of droplet formation (t*∼1). The migration of the compound drop inside a Newtonian fluid approaches a relatively constant velocity after a specific time of the initial movement. Conversely, the movement velocity of both drops increases gradually until the pinch-off moment in non-Newtonian fluids, which means that a moving compound drop has an accelerative motion in all stages of movement in non-Newtonian fluids. The findings presented here are essential for employing compound droplets in droplet microfluidic systems for biological applications.

Non-Newtonian effect on heat transfer and entropy generation of natural convection nanofluid flow inside a vertical wavy porous cavity

A numerical study on heat transfer and entropy generation in natural convection of non-Newtonian nanofluid flow has been explored within a differentially heated two-dimensional wavy porous cavity. In the present study, copper (Cu)–water nanofluid is considered for the investigation where the specific behavior of Cu nanoparticles in water is considered to behave as non-Newtonian based on previously established experimental results. The power-law model and the Brinkman-extended Darcy model has been used to characterize the non-Newtonian porous medium. The governing equations of the flow are solved using the finite volume method with the collocated grid arrangement. Numerical results are presented through streamlines, isotherms, local Nusselt number and entropy generation rate to study the effects of a range of Darcy number (Da), volume fractions (ϕ) of nanofluids, Rayleigh numbers (Ra), and the power-law index (n). Results show that the rate of heat transfer from the wavy wall to the medium becomes enhanced by decreasing the power-law index but increasing the volume fraction of nanoparticles. Increase of porosity level and buoyancy forces of the medium augments flow strength and results in a thinner boundary layer within the cavity. At negligible porosity level of the enclosure, effect of volume fraction of nanoparticles over thermal conductivity of the nanofluids is imperceptible. Interestingly, when the Darcy–Rayleigh number Ra^*gg 10, the power-law effect becomes more significant than the volume fraction effect in the augmentation of the convective heat transfer process. The local entropy generation is highly dominated by heat transfer irreversibility within the porous enclosure for all conditions of the flow medium. The particular wavy shape of the cavity strongly influences the heat transfer flow pattern and local entropy generation. Interestingly, contour graphs of local entropy generation and local Bejan number show a rotationally symmetric pattern of order two about the center of the wavy cavity.

Modeling the onset of thermosolutal convective instability in a non-Newtonian nanofluid-saturated porous medium layer

The onset of double-diffusive (thermosolutal) convection in horizontal porous layer saturated with an incompressible couple stress nanofluid saturated is studied with thermal conductivity and viscosity dependent on the nanoparticle volume fraction. To represent the momentum equation for porous media, a modified Darcy-Maxwell nanofluid model incorporating the effects of Brownian motion and thermophoresis has been used. The thermal energy equation includes regular diffusion and cross diffusion (Soret thermo-diffusion and Dufour diffuso-thermal) terms. A linear stability analysis depends on the normal mode technique and the onset criterion for stationary and oscillatory convection is derived analytically. The nonlinear theory based on the representation of the Fourier series method is applied to capture the behavior of heat and mass transfer. It is found that the couple stress parameter enhances the stability of the system in both the stationary and oscillatory convection modes. The viscosity ratio and conductivity ratio both enhance heat and mass transfer. Transient Nusselt number is found to be oscillatory when time is small. However, when time becomes very large, all the three transient Nusselt number values approach to their steady state values.

Heat dissipation rate in a nonequilibrium viscoelastic medium

A living non-Newtonian matter like the cell cortex and tissues are driven out-of-equilibrium at multiple spatial and temporal scales. The stochastic dynamics of a particle embedded in such a medium are non-Markovian, given by a generalized Langevin equation. Due to the non-Markovian nature of the dynamics, the heat dissipation and the entropy production rate cannot be computed using the standard methods for Markovian processes. In this work, to calculate heat dissipation, we use an effective Markov description of the non-Markovian dynamics, which includes the degrees-of-freedom of the medium. Specifically, we calculate entropy production and heat dissipation rate for a spherical colloid in a non-Newtonian medium whose rheology is given by a Maxwell viscoelastic element in parallel with a viscous fluid element, connected to different temperature baths. This problem is nonequilibrium for two reasons: the medium is nonequilibrium due to different effective temperatures of the bath, and the particle is driven out-of-equilibrium by an external stochastic force. When the medium is nonequilibrium, the effective non-Markov dynamics of the particle may lead to a negative value of heat dissipation and entropy production rate. The positivity is restored when the medium’s degree-of-freedom is considered. When the medium is at equilibrium, and the only nonequilibrium component is the external driving, the correct dissipation is obtained from the effective description of the particle.

Accelerating flows of pseudo-plastic and dilatant non-newtonian fluids in straight pipelines

The accelerated flows of non-Newtonian fluids are studied, the viscosity-strength properties of which are described by the equation τ = kΥn. Dependencies are obtained for calculating the velocity field and the time it takes to reach the stationary flow for liquids with arbitrary rheological parameters. Keywords technical fluid, non-Newtonian medium, rheology, viscometer, model, acceleration flow, pipeline. a.kotesova@mail.ru

A Three-Dimensional Cell Culture Platform for Long Time-Scale Observations of Bio-Nano Interactions.

We know surprisingly little about the long-term outcomes for nanomaterials interacting with organisms. To date, most of what we know is derived from in vivo studies that limit the range of materials studied and the scope of advanced molecular biology tools applied. Long-term in vitro nanoparticle studies are hampered by a lack of suitable models, as standard cell culture techniques present several drawbacks, while technical limitations render current three-dimensional (3D) cellular spheroid models less suited. Now, by controlling the kinetic processes of cell assembly and division in a non-Newtonian culture medium, we engineer reproducible cell clusters of controlled size and phenotype, leading to a convenient and flexible long-term 3D culture that allows nanoparticle studies over many weeks in an in vitro setting. We present applications of this model for the assessment of intracellular polymeric and silica nanoparticle persistence and found that hydrocarbon-based polymeric nanoparticles undergo no apparent degradation over long time periods with no obvious biological impact, while amorphous silica nanoparticles degrade at different rates over several weeks, depending on their synthesis method.

Three-dimensional vibrations of multilayered hollow spheres submerged in a complex fluid

Fluid–structure interaction is fundamental to the characteristics of the induced flows due to the motion of structures in fluids and also is crucial to the performance of submerged structures. This paper presents a three-dimensional analytical study of the intrinsic free vibration of an elastic multilayered hollow sphere interacting with an exterior non-Newtonian fluid medium. The fluid is assumed to be characterized by a compressible linear viscoelastic model accounting for both the shear and compressional relaxation processes. For small-amplitude vibrations, the equations governing the viscoelastic fluid can be linearized, which are then solved by introducing appropriate potential functions. The solid is assumed to exhibit a particular material anisotropy, i.e. spherical isotropy, which includes material isotropy as a special case. The equations governing the anisotropic solid are solved in spherical coordinates using the state-space formalism, which finally establishes two separate transfer relations correlating the state vectors at the innermost surface with those at the outermost surface of the multilayered hollow sphere. By imposing the continuity conditions at the fluid–solid interface, two separate analytical characteristic equations are derived, which characterize two independent classes of vibration. Numerical examples are finally conducted to validate the theoretical derivation as well as to investigate the effects of various factors, including fluid viscosity and compressibility, fluid viscoelasticity, solid anisotropy and surface effect, as well as solid intrinsic damping, on the vibration characteristics of the submerged hollow sphere. Particularly, our theoretically predicted vibration frequencies and quality factors of gold nanospheres with intrinsic damping immersed in water agree exceptionally well with the available experimentally measured results. The reported analytical solution is truly and fully three-dimensional, covering from the purely radial breathing mode to the torsional mode to any general spheroidal mode as well as being applicable to various simpler situations, and hence can be a broad-spectrum benchmark in the study of fluid–structure interaction.