Viscoelastic Fluid Model Research Articles

Electro-osmotic flow instability of viscoelastic fluids in a nanochannel

The study of the complex rheological properties of viscoelastic fluids in nanochannels will facilitate the application of nanofluidics in biomedical and other fields. However, the flow of viscoelastic fluids in nanochannels has significant instabilities, and numerical simulation failures are prone to occur at high Weissenberg numbers (Wi). In this study, the simplified Phan-Thien-Tanner viscoelastic fluid model is solved using the log-conformation tensor approach, and the effects of rheological parameters of the viscoelastic fluid, such as the Weissenberg number (Wi), extensibility parameter (ε), and viscosity ratio (β), on the flow characteristics and flow instability within the nanochannel are investigated. The results indicate that the variation of rheological parameters of viscoelastic fluids has a significant effect on the flow state and flow instability of fluids in nanochannels. When the rheological parameters are in a specific range, the flow velocity and outlet current in the nanochannel exhibit relatively regular periodic fluctuations. As the flow transitions from an up-and-down moving single-vortex state to a symmetric double-vortex state, the average velocity of the central axis in the nanochannel is increased by about 15%. Furthermore, when Wi increases from 150 to 400, the length and height of the vortex increase by 50% and 100%, respectively.

Evolution of local relaxed states and the modeling of viscoelastic fluids

We introduce a class of continuum mechanical models aimed at describing the behavior of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant material parameters is able to qualitatively reproduce a number of experimental observations in both simple shear and extensional flows, including linear viscoelastic properties, the rate dependence of steady-state material functions, the stress overshoot in incipient shear flows, and the difference in shear and extensional rheological curves. Furthermore, by allowing the relaxation time of the model to depend on the total strain, we can reproduce some experimental observations of the non-attainability of steady flows in uniaxial extension and link this to a concept of polymeric jamming or effective solidification. Remarkably, this modeling framework helps in understanding the interplay between different mechanisms that may compete in determining the rheology of non-Newtonian materials.

Numerical simulation of a partially ionized Oldroyd-B nanofluid flow driven by two homocentric rotating disks with motile microorganisms

Nanofluids are assumed to be an excellent source of enhanced heat transfer with advanced thermophysical characteristics. Nanofluids are the backbone of the heating and cooling in the industrial processes. This research delves into the dynamics of a partially ionized Oldroyd-B nanofluid flowing between stretchable rotating disks. The study investigates heat transfer mechanisms incorporating a modified Fourier law and convective heat conditions. The viscoelastic fluid model presented here allows for the examination of relaxation and retardation times. Furthermore, the heat and mass transport of the Oldroyd-B nanofluid is characterized using a Buongiorno model, which considers thermophoresis and Brownian diffusion effects. Additionally, the study explores the impact of gyrotactic microorganisms in nanofluids, potentially enhancing environmental management strategies. The governing equations transform into dimensionless forms using Von Karman similarity variables. Numerical investigation of the anticipated model is conducted using the bvp4c scheme in MATLAB. The variation of different parameters in the dimensionless equations is illustrated through graphs and in tabulated format. The results indicate that increasing thermophoresis and Lewis numbers lead to a decrease in fluid concentration. Moreover, the temperature of the fluid rises at the lower disk and declines at the upper disk relative to the Biot number. The proposed model is validated through comparison with closely related published work.

Local well-posedness of a viscoelastic fluid model for reactive polymers

In this paper, we study the Cauchy problem of the two-species incompressible viscoelastic fluid of Oldroyd-B system, which involving a reaction effect between two species of polymers. We prove the local existence with initial data in [Formula: see text] in a classical solution framework, and then provide a blow-up criteria. We concentrate on the a priori estimate, by using the energy method. In particular, the variant system in a general formulation is also studied, and the corresponding local well-posedness is established.

Vortex merging in strongly coupled dusty plasmas using a visco-elastic fluid model

This work is a numerical study of the two-dimensional merging phenomena between two Lamb–Oseen co-rotating vortices in a viscoelastic fluid. We use a generalized hydrodynamics fluid model to study vortex merging in a strongly coupled dusty plasma medium, which exhibits characteristics similar to a viscoelastic fluid. Several aspects influencing the merging phenomena are considered: the aspect ratio (core size/separation distance), the relative circulation strengths of each vortex, and the coupling strength of the medium. Unlike classical hydrodynamic fluids, we find that for viscoelastic fluids, shear waves facilitate the merging events even for widely separated vortices. The merging process is accelerated in media with higher coupling strengths and the resultant vortex shape decays more quickly as well. It is also found that varying either the vortex scale or the vortex circulation strength can result in a similar merging process, where a smaller (larger) vortex acts like a vortex with weaker (stronger) circulation. Finally, we show that a Poynting-like conservation theorem is satisfied for the examined merging processes.

A continuum model for the elongation and orientation of Von Willebrand factor with applications in arterial flow

The blood protein Von Willebrand factor (VWF) is critical in facilitating arterial thrombosis. At pathologically high shear rates, the protein unfolds and binds to the arterial wall, enabling the rapid deposition of platelets from the blood. We present a novel continuum model for VWF dynamics in flow based on a modified viscoelastic fluid model that incorporates a single constitutive relation to describe the propensity of VWF to unfold as a function of the scalar shear rate. Using experimental data of VWF unfolding in pure shear flow, we fix the parameters for VWF’s unfolding propensity and the maximum VWF length, so that the protein is half unfolded at a shear rate of approximately 5000s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$5000\\,\ ext {s}^{-1}$$\\end{document}. We then use the theoretical model to predict VWF’s behaviour in two complex flows where experimental data are challenging to obtain: pure elongational flow and stenotic arterial flow. In pure elongational flow, our model predicts that VWF is 50% unfolded at approximately 2000s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2000\\,\ ext {s}^{-1}$$\\end{document}, matching the established hypothesis that VWF unfolds at lower shear rates in elongational flow than in shear flow. We demonstrate the sensitivity of this elongational flow prediction to the value of maximum VWF length used in the model, which varies significantly across experimental studies, predicting that VWF can unfold between 2000and3200s-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2000\ ext { and }3200\\,\ ext {s}^{-1}$$\\end{document} depending on the selected value. Finally, we examine VWF dynamics in a range of idealised arterial stenoses, predicting the relative extension of VWF in elongational flow structures in the centre of the artery compared to high shear regions near the arterial walls.

Parametric simulations of fractal-fractional non-linear viscoelastic fluid model with finite difference scheme

Fractal-fractional derivatives are more general than the fractional derivative and classical derivative in terms of order. Fractal-fractional derivative is used in those models where the classical continuum hypothesis theory fails. More precisely, these derivative operators are used where the surface or space is discontinuous, e.g., porous medium. Fractal-fractional derivative is considered advance tool to analyze the fluid dynamic model more than fractional and classical model. Given the extensive applicability of fractal-fractional derivatives, the current analysis focuses on investigating the behavior of a non-linear Walter’s-B fluid model under the influence of time-varying temperature and concentration During the simulation process, we have also taken into account the effects of first-order chemical reactions, Soret numbers, thermal radiation, Joule heating, and viscous dissipation of energy. A magnetic field with a strength of B0 was applied to the left plate in the transverse direction. The classical mathematical model was first developed using relative constitutive equations and later generalized with the fractal-fractional derivative operator. Numerical solutions to the generalized model have been obtained using the finite difference method. Various graphs are drawn from the obtained numerical solutions to study the influence of physical parameters on the rheology of Walter’s-B fluid. It has been observed that by varying the fractional and fractal order of the generalized model, one can easily derive fractal, fractional, and classical models.

Parameter estimation on polymer solutions with fractional viscoelastic model

The rheological properties of polymer solutions are extremely complex and it leads to a specific power-law behavior in response to creep experiments, which can not be better characterized by the classical viscoelastic constitutive models. The renowned viscoelastic fluid models with fractional derivatives have shown astonishing advantages in characterizing the broad relaxation process of the multiple materials with power-law response behavior. In this paper, we use the fractional Maxwell constitutive model to simulate the power-law responses for several polymer solutions through experimental measuring, and better fitting results than classical models can be found.

Note on the start-up of Couette flow for viscoelastic fluids

This paper is concerned with the numerical modeling of viscoelastic fluids in non-steady shear motions. Time-dependent solutions for three-constant differential models are obtained at the start-up of the planar Couette flows. The influences of (i) the Reynolds number, (ii) the value of κ− material parameter (the ratio between the retardation time and relaxation time), and (iii) the initial condition for the normal stress on the velocity and stresses distributions in the gap are investigated using the numerical solutions obtained with Mathematica software. The focus of the study is the analysis of the Jaumann model (characterized by the corotational derivative) in transitory simple shear rheological tests, as a function of initial conditions for stresses. The steady solutions, corroborated with the non-monotonicity of the steady flow curve, confirm the kink presence in the steady velocity distributions and the formation of shear bandings at Re ≥ 1. The analyses of the strain- and stress-controlled simulations performed at different initial and boundary conditions offer possible explanations of some spurious data recorded in shear measurements of complex viscoelastic fluids. The findings have important consequences for performing transient shear experiments; specifically, it is demonstrated that reproducibility and correlations between the tests require the control of initial normal stresses in the sample.

Theoretical and numerical investigation of the carreau fluid model during a non-isothermal roll coating process: A comparative study

BackgroundThe roll-coating process plays an important role in many industries for its practical applications, such as paint, PVC-coated fabrics and plastic industries. Roll coating is commonly used to put thin coating films over continuous substrates such as foils and papers. There are several roll-to-roll coating methods, including forward and roll over web. However, the reverse roll coating study of the non-Newtonian fluid model is presented in this paper. The constitutive equation for the viscoelastic Carreau fluid model as the non-Newtonian fluid is derived using the momentum and energy equations. To simplify the nonlinear systems of partial differential equations, appropriate non-dimensional parameters are employed to convert them into systems of ordinary differential equations. MethodBy taking the Weissenberg number as a small parameter, a series solution is obtained for considerable quantities like pressure gradient, axial velocity, flow rate, pressure distribution, and temperature distribution using the perturbation method. In contrast, the numeric outcome of some quantities of engineering interest, like flow rate, coating thickness, share stresses, and separation points, are calculated. Streamlines in 2D and 3D are also drawn to observe the flow pattern. To validate the solution, the problem is also solved numerically with the BVP Midrich method. The analysis of the results demonstrates a satisfactory agreement between the analytical and numerical solutions. ResultsThe graphical investigation examines the influence of different fluid parameters on velocity profile, shear stress, pressure profile, temperature profile, and pressure gradient. A comprehensive mechanism behind these outcomes is deliberated. It has been observed that velocity rises on increasing the Weissenberg number; however, velocity decreases in the case of the velocities ratio. Further, the Brickman number has a significant influence on the temperature profile and has increased with the increase in the Brickman number. Moreover, the separation point and coating thickness decrease with the velocities ratio increase. The results accuracy is checked against papers that have already been published. The comparison reveals good agreement; therefore, the resultant analytical model gives new ways to forecast film thickness and explain influence parameters. Hence, these factors may help in an efficient coating process and improve the substrate life.

Applying Super High Resolution Fluorescence Microscope and Advanced Smart Cloud Algorithm in Real-Time Quantitative Processing and Analysis of Electroconvection

In an electrochemical cell at high current densities, electroconvection plays a critical role in determining the morphology of electrodeposited metals. The resultant dendrite formation leads to risky battery performance failure. Over the past decades, though intensive theoretical analysis and experimental effort have been done, the detailed structure and dynamics of electroconvection remain unknown, because experimental observations lacked the resolution to expose the fundamental, hierarchical spatial structure of these flows, while the data processing algorithms were not fully established for large sample size. To address this shortcoming, we built an advanced optical electrochemical cell that fits in situ imaging with a super-resolution fluorescence microscope. By observing and recording real-time motions of electrolytes, electroconvection flows have been interrogated at unprecedented, high temporal and spatial resolution. As a complement to the visualization studies, a cloud-computing analysis algorithm was developed by combining a higher resolution Particle Image Velocimetry algorithm and a machine learning model to enable velocity distribution data over the entire optical field of view at nanoscale or microscale spatial resolution. Consequently, detailed velocity maps are obtained across the optical electrochemical cell, allowing us to quantitatively measure and analyze the initiation and evolution of the hierarchical microstructures inside the electroconvection in a unidirectional electric field. With these powerful tools, we further studied the effect of polymer viscoelasticity on electroconvection and electrodeposition. The addition of an ultrahigh molar mass polyethylene oxide to the electrolytes transforms the materials to a viscoelastic fluid state that changes the electroconvection dependence on time and voltage and induces a smooth electrodeposition on the metal anode by unique polymer rheological properties. Especially, the relaxation of long polymer chains in electrolyte provides a promising manner to prevent dendrite growth. We further analyzed these observations using direct numerical simulations for Newtonian and viscoelastic fluid models, and the quantitative analysis of experimental results indicates good consistency with simulation predictions.

Predicting inkjet jetting behavior for viscoelastic inks using machine learning

Abstract Inkjet printing offers significant potential for additive manufacturing technology. However, predicting jetting behavior is challenging because the rheological properties of functional inks commonly used in the industry are overlooked in printability maps that rely on the Ohnesorge and Weber numbers. We present a machine learning-based predictive model for jetting behavior that incorporates the Deborah number, the Ohnesorge number, and the waveform parameters. Ten viscoelastic inks have been prepared and their storage modulus and loss modulus measured, showing good agreement with those obtained by the theoretical Maxwell model. With the relaxation time of the viscoelastic ink obtained by analyzing the Maxwell model equations, the Deborah number could be calculated. We collected a large data set of jetting behaviors of each ink with various waveforms using drop watching system. Three distinct machine learning models were employed to build predictive models. After comparing the prediction accuracy of the machine learning models, we found that multilayer perceptron showed outstanding prediction accuracy. The final predictive model exhibited remarkable accuracy for an unknown ink based on waveform parameters, and the correlation between jetting behavior and ink properties was reasonable. Finally, we developed a printability map characterized by the Ohnesorge and Deborah numbers through the proposed predictive model for viscoelastic fluids and the chosen industrial printhead.

Quantification of viscous and damage dissipation of bituminous binder and mastic using White-Metzner model

ABSTRACT Bituminous pavement layers are composite in nature, consisting of binder, filler, and aggregates. Understanding the mechanical behaviour of bituminous layers demands investigation of their different material scales, such as the binder, mastic, and mixture scales. While substantial investigation has been carried out on binder and mixture related to fatigue damage, not much research is carried out on mastic. Of the methods used to characterise fatigue damage, energy dissipation is widely used; however, it is complicated due to the presence of other modes of dissipation, such as viscous dissipation. In this study, an attempt is made to separate viscous dissipation and dissipation due to damage for both binder and mastic using a nonlinear viscoelastic fluid model. For this purpose, six types of materials were tested at temperatures of 20 ∘ C and 25 ∘ C, 10 Hz frequency, and five different strain levels spanning the linear and non-linear regimes, for 20,000 cycles. Material parameters for the non-linear White-Metzner model incorporated with the Williamson model were determined for an initial cycle and using these parameters, the viscous component of energy dissipation was determined. Dissipation due to damage was estimated by separating viscous dissipation from total dissipation at every 2000th cycle and based on the evolution of viscous and damage dissipation across cycles, three trends were observed. Based on the trends observed, the influence of strain amplitude, temperature and modifiers on the fatigue resistance of the materials was ascertained.

Flow instabilities of second-grade fluid over a stretching sheet

The work at hand studies thin-film flow instabilities in a non-Newtonian second-grade fluid moving over a stretching sheet. The analysis considers the free surface evolution equation of the thin second-grade viscoelastic fluid model based on the long-wave approximation method. We undertook a linear stability analysis using a normal mode approach and obtained expressions for the linear time growth rate, linear phase speed, and critical wavenumber, which illustrates the linear stability structure of the flow system. Furthermore, the multi-scale analysis of the fluid’s weakly non-linear stability characteristics reveals the presence of subcritical instability in the linear stability zone. The study shows that the varying flow parameters affect the threshold amplitude, which influences the stable and unstable zones in the subcritical region. The outcomes show a stabilizing effect spanning the range of non-dimensional parameters, such as the second-grade parameter ranging from 0 to 100 in values, the surface tension parameter ranging from 0 to 100 in values, and the modified Froude number from 0 to 100 in values.

Application of symmetry analysis to viscoelastic fluid model

In the present paper, we apply Lie symmetry to the Suliciu relaxation system governed by viscoelastic shallow fluid. Utilizing the local symmetries of the governing PDEs, we derive the one-dimensional optimal system of subalgebras and construct several new exact solutions through symmetry reduction. Further, we employ the direct multipliers method to the given model to extract new conservation laws. Furthermore, we establish potential systems and inverse potential systems (IPS) to classify the nonlocal symmetry of the governing system. In addition, we develop some non-trivial exact solutions of the given model using the nonlocal symmetries of IPS. Finally, we investigate the propagation and interaction of C1-wave and characteristic shock.

Dynamics of non-Newtonian synovial fluid through permeable membrane with periodic filtration

This research measures the flow of synovial fluid through permeable membrane. It is assumed in this study that the ultrafiltration of blood plasma is a continuous function and repeatedly forms the action to keep synovial fluid normal in the joints. The novelty of this research is to analyze the rheology of synovial fluid under the periodic filtration rate within the membrane. To estimate the pressure and shear stress which are essential for the flow of synovial fluid between the synovial joints, mathematical modeling has been made for the synovial fluid flow through permeable membrane by the laws of mass and momentum and viscoelastic LPTT fluid model. The LPTT fluid has the viscoelastic effects in the presence of relaxation time, therefore for synovial fluid the present fluid model represents the best rheological properties. To find the analytical results for the rheology of the synovial fluid, a method proposed by Langlois is used. This research concludes that the pressure difference and transverse velocity are high when the periodic filtration is cosine type whereas the shear stress on the wall is high for sine type of filtration.

Transport of chemical species alongside magnetic pseudoplastic nanomaterial through a porous surface

Pseudoplastic fluids are non-Newtonian fluids with intriguing uses in current research and industry. Among many other extant models, the Sutterby fluid model is an essential viscoelastic fluid model that demonstrates shear thinning and shear thickening properties in high polymer aqueous solutions by manifesting viscous and elastic aspects during deformation. The magneto hydrodynamic effects of Sutterby nanofluid on porous elastic surfaces in the presence of chemical processes are examined in this theoretical study. By using similarity transformation, the mathematical model of a governed problem is converted into a collection of differential equations. A shooting strategy is used to solve these nonlinear coupled ordinary differential equations. The velocities, temperatures, and chemical species concentrations of fluids are graphically shown. Physical quantities of importance, such as local heat and mass flow, are visually represented using bar charts. Heat and mass transport, as well as chemical species concentration, decrease with Hartman number in both suction and injection. Chemical concentration of governed fluid rises for homogeneous reactions but drops for heterogeneous reactions. Temperature and concentration of fluid increases for thermophoresis parameter but decreases for Brownian motion parameter, also the effects of injection are much stronger and higher than suction.

A reliable analytic technique for the modified prototypical Kelvin–Voigt viscoelastic fluid model by means of the hyperbolic tangent function

Inspired by the extensive applicability of solitons in nonlinear optics, advanced telecommunication industry, trans-continental, and trans-oceanic systems, coupled with the copious functionality of viscoelastic models in highway engineering pavement theory, civil engineering, and solid mechanics, unique closed-form solutions have been obtained for a highly nonlinear model built on a highly nonlinear partial differential equation, which describes the dynamics of the incompressible viscoelastic Kelvin–Voigt fluid viz: the modified (1＋1) dimension Oskolkov equation. Abundant solitary and traveling wave solutions to the prototypical Kelvin–Voigt incompressible model have been elucidated and put forward by means of the hyperbolic tangent method using the tangent function as an ansatz on the transformed nonlinear ordinary differential equation, thus, depicted breather, cusp, rouge, compacton, and kink waveforms via graphical illustrations for arbitrary intervals x∈a1,a2, t∈b1,b2, a1,a2,b1,b2∈Z.This present research yields new traveling wave profiles and structures with holomorphic terms, precise with minimized computational work, capturing all solitonic features of the Kelvin–Voigt model, contrary to the existing results with cumbersome and longwinded solution profiles, thus, the present research novelty established. The dynamical analyses, the mathematical, and solution framework presented here will be of substantial benefit to the geosciences, ocean, plasma, and, material sciences, civil engineering, nanotechnology, signaling, and signal processing to effectively tackle and convey theoretical explorations on cogent equations arising in these afore-mentioned fields. Notably, the impact of the diffusive parameter Ω<0 on the incompressible model induces a significant translation of the solution profiles whilst the methodology of this study is unprecedented for the model with no existence in the literature.

Spectral Collocation Technique for Solving Two-Dimensional Multi-Term Time Fractional Viscoelastic Non-Newtonian Fluid Model

Applications of non-Newtonian fluids have been widespread across industries, accompanied by theoretical developments in engineering and mathematics. This paper studies a two-dimensional multi-term time fractional viscoelastic non-Newtonian fluid model by using two autonomous consecutive spectral collocation strategies. A modification of the spectral approach is implemented, leading to an algebraic system of equations able to obtain an approximate symmetric solution for the model. Numerical examples illustrate the effectiveness of the technique in terms of accuracy and convergence.

A Geometric Look at Momentum Flux and Stress in Fluid Mechanics

We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form-valued 2-forms, and their divergence as a covariant exterior derivative. We review the necessary tools of differential geometry and obtain the corresponding coordinate-free form of the equations of motion for a variety of inviscid fluid models—compressible and incompressible Euler equations, Lagrangian-averaged Euler-alpha equations, magnetohydrodynamics and shallow-water models—using a variational derivation which automatically yields a symmetric momentum flux. We also consider dissipative effects and discuss the geometric form of the Navier–Stokes equations for viscous fluids and of the Oldroyd-B model for visco-elastic fluids.