Inelastic Fluids Research Articles

Heat Transfer and Entropy Generation in Vibrational Flow: Newtonian vs. Inelastic Non-Newtonian Fluid

A computational method is employed to solve heat transfer and entropy generation within a circular pipe. The thermal boundary condition assumes a constant wall temperature, while viscosity is taken to be dependent on temperature. A power-law type shear-thinning fluid is utilized in the analysis, with sinusoidal vibration applied horizontally perpendicular to the flow direction. Temperature distributions across the pipe are illustrated. Additionally, the entropy generation rate over the entire fluid volume under vibration was examined, comparing the results between steady flow and vibrational flow for both types of fluids. It was found that radial mixing is more pronounced in non-Newtonian fluids as vibration increases the strain rate, which is higher for low Reynolds numbers. The research provides a quantitative analysis of heat transfer and entropy generation for both Newtonian and shear-thinning fluids at different Reynolds numbers. It was observed that the effectiveness of superimposed vibrational flow is limited, especially for low Reynolds numbers and flow behavior index characteristic of shear-thinning fluids.

Exploring integrated heat and mass transfer in von-Kármán dynamics involving Reiner-Rivlin fluid with regression models

The rotating disk system is widely used in several important applications, including turbomachinery design, mixing and stirring processes, centrifugal blood pumps development, optimizing electronic component, cooling efficiency, and various others. Moreover, regression models offer comprehensive and reliable prediction for important parameters in flows developed by revolving disks. This article presents similarity solutions for coupled heat and mass transfer with viscous dissipation in an inelastic non-Newtonian fluid flow across a permeable revolving disk. The inclusion of diffusion terms due to Dufour and Soret effects establishes coupling between energy and concentration equations. Temperature and concentrations at disk surface are supposed to vary quadratically along the radial direction. The impacts of MHD, heat source/sink dynamics and Joule heating effects on thermal boundary layer are also scrutinized. MATLAB's bvp5c tool, based on collocation scheme, generates numerical results. Homotopy analysis method, a widely accepted analytical solution procedure, is then applied to produce the series solution. Selection of the optimal auxiliary parameter values featured in the series solution is also included. The impact of Reiner-Rivlin fluid assumption on the torque required by the disk is assessed. Furthermore, linear and quadratic regression models are developed for the skin friction factors, Nusselt number and Sherwood number.

How Fluid Pseudoplasticity and Elasticity Affect Propeller Flows in Biogas Fermenters

AbstractMixing in biogas fermenters is complex due to the non‐Newtonian rheology of biogenic substrates, which exhibit both pseudoplasticity and elasticity. It is yet unclear how these non‐Newtonian properties affect propeller flows and the mixing behavior in fermenters. Therefore, propeller flows in Newtonian as well as shear‐thinning inelastic and elastic fluids are compared numerically and validated against particle image velocity (PIV) data. Elastic normal stresses lead to an increase of pumping rates in the laminar regime and a suppression of the formation of a propeller jet in the transitional regime. Thus, flow rates are severely overestimated by the inelastic, shear‐thinning model in this regime. The results indicate that elasticity is critical for an accurate modeling of flows of biogenic substrates.

Viscoelastic flow instabilities for enhanced heat transfer in battery pack cooling

Effective thermal management plays a critical role in ensuring peak performance for heavy-duty electric vehicle battery packs and high-performance electronics. To address the need for effective heat dissipation, liquid coolants are employed, which exhibit higher heat transfer performance compared to traditional air-cooled systems. However, the associated increased viscosity of such liquid coolants and constricted flow path lead to reduced mixing, thereby deteriorating the thermal performance of the system. Here, we explore the potential of utilizing viscoelastic liquid coolants for enhancing heat transfer from the heated walls of a constricted flow path with obstacles, modeling features of battery coolant channels. At low-Reynolds number regime, viscoelastic fluids exhibit instabilities which can disrupt the thermal boundary layer and enhance fluid mixing in the domain, thereby facilitating wall heat transfer. We employed computational fluid dynamics simulations, validated with experimental observations, to explore the effect of the flow geometry, Weissenberg number, solvent viscosity ratio, polymer extensibility, and Reynolds number on thermal performance. Our study indicates that the heat transfer is enhanced with flow instabilities in viscoelastic fluids, which can be generated exclusively in the flow channel with obstacles by increasing the Weissenberg number, reducing the solvent viscosity ratio, increasing the polymer extensibility, and increasing the Reynolds number. The enhancement in the heat transfer can exclusively be attributed to the elastic properties of the fluid in contrast to the inelastic shear-thinning fluids exhibiting no instability. The insights from the study can play an important role in the development of advanced, high-efficiency battery cooling systems, combining surface engineering and synthesis of optimized heat transfer liquids.

On the use of sinusoidal vibrations for disaggregating clusters of non-settling inertial particles immersed in yield-stress fluids

The effect of sinusoidal vibration is numerically investigated on the dynamical behavior of a cluster of 50 identical non-Brownian circular solid particles randomly distributed in a circular envelope. The cluster is immersed in a finite vessel filled with an inelastic viscoplastic fluid obeying the Casson model. The solid particles are modeled using the improved smoothed-profile method (iSPM) whereas the flow of the continuous phase is modeled using the lattice Boltzmann method (LBM). An in-house LBM-iSPM code, modified for Casson fluid, is used to study the effect of sinusoidal vibration on disaggregating the cluster. We have deliberately ignored the gravitational term in the equations of motion so that the sole effect of vibration on the cluster response can better be investigated. Numerical results suggest that vibration can disaggregate the cluster with its efficiency depending on the fluid's yield stress. For any given yield stress, vibration can disperse the cluster provided the frequency and/or amplitude of the forced oscillation are larger than a threshold. The secondary flow formed in the channel during the transient phase is shown to be the main cause of the cluster's fluid-mediated dispersion. It is shown that the system reaches equilibrium when the secondary flow is vanished through dissipation. Vibration is predicted to become more effective in disaggregating clusters the larger the size of the particles or the smaller their number density.

On the use of time-dependent fluids for delaying onset of transition to turbulence in the flat plate boundary-layer flow: A passive control of flow

Inelastic time-dependent fluids display continuous and reversible changes in viscosity when subjected to a constant shear-rate. These alterations arise from the gradual modification of the material’s microstructure due to shear-induced effects, known as shear rejuvenation. When this process generates smaller structural units, it is termed thixotropy; conversely, if it produces larger units, it is labeled anti-thixotropy. Aging is another characteristic of such fluids, denoting the capacity of the material to regain its original structure in the absence of shear, thus reversing the initial time-dependent change. This phenomenon often results from thermally activated Brownian motion prompting the reorganization of the material’s microconstituents. Consequently, attractive forces between these components can instigate the reconstruction of a network-like structure within the material. This study centers on investigating how variations in fluid microstructure impact the onset of transition to turbulence in a flat plate boundary-layer flow. Specifically, the focus is on cases where larger structural units emerge during the breakdown process (anti-thixotropy). To represent such fluids, the Quemada model, an inelastic structural-kinetic model, is employed. This model effectively captures thixotropy and anti-thixotropy by appropriately configuring model parameters. The analysis begins with obtaining a local similarity solution for the generalized Blasius equation, representing the base flow. Subsequently, the stability of this flow is assessed using linear temporal stability theory. This involves introducing infinitesimally-small normal-mode perturbations to the base flow, yielding the generalized Orr–Sommerfeld equation. Solving this equation using the spectral method provides insights into stability. Results from this study indicate that for low Deborah numbers, the shear-thickening behavior prevails, causing destabilization. In contrast, higher Deborah numbers lead to stability. This implies that anti-thixotropy effectively delays the onset of transition to turbulence and could hold practical applications for flow control.

Inelastic Solution for Power Law Fluid with Taylor Galerkin-Pressure Correction Finite Element Method: Axisymmetric Contraction Flows

In this study we examine the flow of inelastic fluids with various shear properties in axisymmetric contractions with various contraction ratios are selected as 4:1, 6:1 and 8:1 with both rounded-corner and sharp. Particular attention is paid to the effect of shear thickening and shear thinning upon the solution behavior. Power-law inelastic model is employed coupling with the conservation of momentum equation and continuity equation. The numerical simulation of such fluid is performed by using the Taylor Galerkin pressure correction (T-G/P-C) finite element algorithm. The effects of geometry structure and many factors such as Reynolds number (Re) and the parameters of power law model are presented in this study. Particularly, in this study we are focused on the influence of these factors on the solution components and the level of convergence. This research was a comparative study between sharp and rounded-corner contraction geometries with a ratio of 4:1, and to another comparative study among sharp contraction geometries with ratios of 4:1, 6:1, and 8:1. The practical implications of this study focused on vortex length and the impact of varying the parameters of the power law model and the Reynolds number (Re) on it for 4:1 contraction flow. The study dealt with the effect of different geometries on the rates of convergence of velocity and pressure as well as the characteristics of axial velocity and pressure on the axis of symmetry.

Minimum Fluidization Velocity and Expansion Behavior of Spherical Particle Beds Fluidized with Inelastic and Viscoelastic Fluids

Minimum Fluidization Velocity and Expansion Behavior of Spherical Particle Beds Fluidized with Inelastic and Viscoelastic Fluids

Comparative study of the accuracy of friction factor correlations developed for flow of inelastic yield power-law fluids in pipes

An extensive review of the friction factor correlations used for pressure loss prediction of yield power-law (YPL) fluid flow in pipes has been conducted, and the results are summarized in this paper.A comparative study was also conducted to determine the predictive performances of various laminar and turbulent friction factor models developed for YPL fluid flow in pipes. Model predictions of frictional pressure losses were validated by comparing them with the experimentally measured pressure drop data obtained from the flow of several YPL fluids in pipes.Investigations were further extended to determine the impact of the variation of YPL fluid rheological characteristics (resulting from using different rheological characterization methods) on the pressure drop predictions.A wide range of generalized Reynolds numbers (i.e., 20 to 9000, as defined by the API-RP:13D) in a pipe flow configuration was considered in the analyses. The yield stress of the test fluids (determined by using the nonlinear curve fitting technique recommended by the API RP:13D) varied from 0.10 to 0.95 Pa.The results indicated that Hanks and Ricks' model predicted the pressure drop of YPL fluid flow in pipes better than any other models, both in laminar and turbulent flow regimes, matching the experimental data within a ±10% error range.Variations of the YPL model parameters (resulting from using different rheological characterization methods) significantly impacted the pressure drop predictions. Using YPL model parameters obtained from the non-iterative dual power law (DPL) approximation method (as recommended by API-RP:13D) and Hanks and Ricks' model yielded the most accurate pressure drop predictions for the pipe flow of YPL fluids.

Flow modeling for conveying sections in a co-rotating twin-screw extruder based on energy dissipation rate for continuous mixing of lithium-ion battery slurries

In the present work, we propose a new modeling scheme for flows of non-Newtonian fluids in the fully filled narrow-pitched conveying section in a co-rotating twin screw extruder, emphasizing the application to viscoplastic lithium-ion battery slurries for electrode manufacturing. A predictive tool for the relationship between flow rate, screw speed, and pressure build-up was presented for flows with a general class of inelastic non-Newtonian fluids. By introducing the effective viscosity and effective shear rate based on the energy dissipation rate, we showed that the conventional relationship between throughput number and pressure number for various non-Newtonian fluids collapse into a single master curve of a Newtonian fluid, from which the predictive relationship between flow rate, screw speed, and pressure build-up was established. The method was validated numerically with power-law fluids, a Carreau fluid, and a Herschel-Bulkley fluid (anode slurries) for a narrow-pitched conveying element module.

Immiscible viscous fingering in time-dependent fluids: A linear stability analysis

When a less viscous fluid displaces a more viscous fluid, the interface between the two fluids becomes unstable. The instability exhibits itself as a large number of fingers of the displacing fluid penetrating the displaced fluid. This phenomenon is called viscous fingering or Saffman–Taylor instability, and plays a key role in oil industry, among others. The present study aims at investigating the immiscible viscous fingering of inelastic time-dependent fluids (i.e., fluids for which viscosity varies with time even at a fixed shear rate) in a homogeneous saturated porous medium. To represent such fluids, in the present work, use is made of the Quemada model. As an inelastic structural-kinetic rheological model, it can capture both thixotropy and anti-thixotropy through proper setting of model parameters. The model incorporates a natural time, which, in dimensionless form, is represented by a nominal Deborah number. Using this rheological model, the generalized Darcy’s law is derived, which is used to derive the basic flow. The interfacial instability is investigated by using the linear temporal stability analysis; that is, infinitesimally-small, normal-mode perturbations are introduced to the basic flow and their evolution in time is monitored. Using the Young–Laplace equation, the generalized dispersion relation is derived, which is solved numerically. The results show that the thixotropy and anti-thixotropy stabilize the Newtonian/time-dependent and time-dependent/Newtonian displacements, respectively. On the other hand, the Newtonian/time-dependent and time-dependent/Newtonian displacements are destabilized by the anti-thixotropy and thixotropy, respectively.

Experimental viscosity monitoring in complex pipe systems for flows of drilling muds based on the energy dissipation rate

This study aimed to measure the viscosity of non-Newtonian fluids (xanthan gum solution and drilling muds) in-situ during complex pipe flows using pressure drop and flow rate data without sampling. This method of viscometry can be applied to various inelastic non-Newtonian fluids and pipe systems of general geometries, including shear-thinning fluids (such as xanthan gum) and viscoplastic fluids with yield stress (drilling mud), as long as the flow rate and pressure drop within the system can be measured in-situ. The method employs two flow numbers (energy dissipation rate coefficient and effective shear rate coefficient) that are mainly determined by the flow geometry, nearly independent of the rheological behavior of a fluid. The representative effective shear rate for a given system is determined by the effective shear rate coefficient and flow rate; and the relationship between effective viscosity and material viscosity was found to be identical. The method was validated with three different non-Newtonian fluids in three different lab-scale complex pipe systems, including a straight circular pipe with connectors, a pipe system with an intermediate branch, and a 3D pipe system with height and slope variations. The accuracy assessment of viscosity measurement and pressure drop prediction showed no more than an 18.7% error in all the cases. The in-situ viscosity measurement method presented in this study can be used for process monitoring and process quantification of non-Newtonian fluid flows in various types of pipe flows used in industrial processes.

Capillary imbibition of inelastic non-Newtonian fluids in an asymmetric flow assay

Inelastic non-Newtonian fluids are imbibed in a non-uniform conical-shaped microfluidic channel, discussed quantitatively using a theoretical model. We consider the Ostwald–de Waele power-law model to describe the rheology of the inelastic non-Newtonian fluids. Consistent with the reduced order model, the theoretical framework developed here accounts for the coupled effects of fluid rheology, flow configuration, and surface wettability to describe the transient progression of the filling length in the capillary under varied cases. Considering the simultaneously intervening interactions resulting due to rheological effect, geometrical modulation, and surface wetting condition during the imbibition phenomenon, we demonstrate the temporal advancement of the filling phase fluid length in the non-uniform capillary for a set of involving parameters pertinent to this analysis. Non-uniformity in the capillary cross-section gives rise to an alteration in the viscous force acting at the fluid–fluid–solid interface, which in turn, leads to a control over the temporal progression of fluid length, retaining a balance between the capillary and viscous forces. From the predicted relation between filing length and time of filling, we identify three distinct regimes of filling and establish the befitting scaling laws describing the imbibition phenomenon in the respective regimes.

Permeability and Mobility for Flows of Inelastic Non-Newtonian Fluids in Porous Media Based on the Energy Dissipation Rate

Permeability and Mobility for Flows of Inelastic Non-Newtonian Fluids in Porous Media Based on the Energy Dissipation Rate

Peeling of linearly elastic sheets using complex fluids at low Reynolds numbers

We investigate the transient, fluid–structure interaction (FSI) of a non-Newtonian fluid peeling two Hookean sheets at low Reynolds numbers ( R e ≪ 1 ). Two different non-Newtonian fluids are considered – a simplified Phan–Thien–Tanner (sPTT) model fluid, and an inelastic fluid with shear-thinning viscosity (generalized Newtonian fluid). In the limit of small gap between the sheets, we invoke a lubrication approximation and numerically solve for the gap height between the two sheets during the start-up of a pressure-controlled flow. What we observe is that for an impulse pressure applied to the sheet inlet, the peeling front moves diffusively ( x f ∼ t 1 / 2 ) towards the end of the sheet when the fluid is Newtonian. However, when one examines a complex fluid with shear-thinning, the propagation front moves sub-diffusively in time ( x f ∼ t α , α < 0 . 5 ), but ultimately reaches the end faster due to an order of magnitude larger prefactor for the propagation speed. We provide scaling analyses and similarity solutions to delineate several regimes of peeling based on the sheet elasticity, flow Weissenberg number (for sPTT fluid), and shear-thinning exponent (for generalized Newtonian fluids). To conclude, this study aims to afford to the experimentalist a system of knowledge to a priori delineate the peeling characteristics of a certain class of complex fluids. • Modeled fluid–structure interaction of a complex fluid peeling two Hookean sheets. • Examined two different fluid constitutive rheological models. • Developed simulations and similarity solutions for the peeling front during start-up. • Quantified peeling time effects due to shear thinning. • Peeling time for a shear-thinning fluid is smaller than a Newtonian fluid.

Settling behavior of spherical particles in eccentric annulus filled with viscous inelastic fluid

Hole cleaning is a complex process as there are many variables affecting cuttings removal (e.g. drilling fluid type, density, flow rate and rheological properties, cuttings size, drill pipe rotation speed). With the increasing number of drilling small diameter wells (e.g. coiled tubing drilling applications, ultra-deep wells drilled for exploitations of unconventional oil and gas resources), the wall resistance of the micro annulus also emerges as one of the most critical factors affecting the cuttings accumulation in wellbore. The eccentricity of drill pipes commonly observed during the drilling process of ultra-deep well and coiled tubing well makes the wall resistance effect on the cuttings transport even more prominent. Understanding the wall resistance effect on the particle settling behavior in eccentric annuli is, therefore, crucial for hydraulic design of efficient cuttings transport operations in these wells. In this study, a total of 196 sets of particle settling experiments were carried out to investigate the particle settling behavior in eccentric annuli filled with power-law fluids. The test matrix included the eccentricity ranges of 0–0.80, the dimensionless diameter ranges of 0.13–0.75 and the particle Reynolds number ranges of 0.09–32.34. A high-speed camera was used to record the particle settling process and determine the influences of the eccentricity, the dimensionless diameter, the fluid rheological properties, and the solid particle characteristics on the wall factor and the particle settling velocity. The functional relationship among the dimensionless diameter, the particle Reynolds number, and the wall factor was determined by using the method of controlling variables. An eccentric annulus wall factor model with average relative error of 5.16% was established. Moreover, by introducing Archimedes number, an explicit model of particle settling velocity in the eccentric annulus with average relative error of 10.17% was established. A sample calculation of particle settling velocity was provided to show the application of the explicit model. Results of this study can be used as a guideline by field engineers to improve hydraulic design of cuttings transport operations in concentric and eccentric annuli.

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.

A new mechanism of viscoelastic fluid for enhanced oil recovery: Viscoelastic oscillation

This report summarizes our recent experimental findings [Xie et al., Phys. Rev. Lett., 2022] and pore-scale simulation results [Xie et al., Phys. Rev. Fluids., 2020] on viscoelastic oscillation, which is a new observation of viscoelastic instability in the multiphase flow state. The viscoelastic oscillation causes trapping of droplets in contraction-expansion micro-channels regardless of the injection rate. Based on the force balance analysis on the viscous, capillary and elastic forces, the oscillation amplitude is found to linearly increase with viscoelasticity, and the trapped droplet size is determined by the elasto-capillary number. The oscillation also helps to extract droplets from their originally trapped positions such as dead-ends once a critical Deborah number is reached. These results successfully explain the phenomenon that the alternative injection of viscoelastic and inelastic fluids continually produces additional oil, indicating that the viscoelastic oscillation is a new important mechanism of viscoelastic fluid for enhanced oil recovery. Cited as: Xie, C., Xu, K., Qi, P., Xu, J., Balhoff, M. T. A new mechanism of viscoelastic fluid for enhanced oil recovery: Viscoelastic oscillation. Advances in Geo-Energy Research, 2022, 6(3): 267-268. https://doi.org/10.46690/ager.2022.03.10

Minimum principle for the flow of inelastic non-Newtonian fluids in macroscopic heterogeneous porous media

Non-Newtonian fluids are found in many applications related to porous or fractured media. At a macroscopic scale, inelastic non-Newtonian fluid obeys a nonlinear Darcy's equation. This paper show thats the solution of such a nonlinear equation in a heterogeneous permeability field obeys a minimum principle similar to the minimum dissipation principle of Stokes flow.

Laminar flow and pressure drop of complex fluids in a Sulzer SMX+TM static mixer

Static mixers are an effective model system for investigating the effect of fluid rheology on pressure losses in laminar flow. Viscoelastic pressure drop enhancement in real process fluids was investigated using experimental methods and computer simulations of a SMX+TM mixer. The results were compared against classical friction factor correlations for non-elastic fluids and literature correlation for elastic fluids (developed using aqueous polymers). CFD predictions of pressure losses for both inelastic and viscoelastic process fluids were consistent with the measurements. The literature correlation for viscoelastic fluids progressively overestimated the friction factor with increasing Reynolds number. The CFD results were analysed to discern the impact of the flow field on laminar mixing.