Flow Of Viscoelastic Fluid Research Articles

Viscoelastic fluid flow in microporous media

This paper describes an experimental investigation of the flow of flexible polymer solutions through a distinctive micro-porous structure (typical pore sizes of 500 microns) with the primary focus on the interaction of the viscoelasticity of the working fluid with the micro-porous structure. In particular, we relate the bulk flow properties to measurable rheological parameters, demonstrating that a key parameter in estimating the pressure drop through the porous media (for a variety of polymer types, concentrations, solvents, molecular weights, and states of degradation) is the extensional relaxation time (or, more correctly, a characteristic time for extensional stress growth). A Weissenberg number (Wi) is calculated as a product of this extensional relaxation time and the nominal shear rate in the flow. Results, suitably normalised with Newtonian pressure-drop data, show a critical Wi of roughly 0.01 where all working fluids in two different pore structures reveal the onset of elastic dominance over viscous forces as the flowrate increases. Such a low critical value of Wi is due to the estimate of a nominal shear rate based on pore size, which severely underestimates the maximum shear rates within the complex pore structure. Significant deviation from the universal behaviour is observed for high concentrations of the polyacrylamide, which is thought to be a result of shear-thinning for these systems. Systematic degradation of the polyethylene oxide solutions caused an exponential decay in elasticity, which is reflected in the pressure-drop measurements. These imply that, although the flow through porous media is known to be a complex combination of both shear and extensional flow, the extensional effects are of primary importance in this context (or that transient stretching in the media is well represented by this relaxation time) of viscoelasticity. The findings highlight the significance of the transient extensional flow through the neck regions between the pores of the media, which are regions of contraction/expansion.

Numerical simulation of non-isothermal viscoelastic fluid flows using a VMS stabilized finite element formulation

The effect of temperature in viscoelastic fluid flows is studied applying a stabilized finite element formulation based on both a standard and a log-conformation reformulation (LCR), and the Variational Multiscale (VMS) method as stabilization technique. The log-conformation reformulation turns out to be crucial to solve the cases with a high Weissenberg number. Regarding temperature coupling, a two-way coupling strategy is employed: on the one hand, the dependence of viscoelastic fluid parameters on temperature is established, together with the addition of a new term to the energy equation which takes into account the stress work. The formulations and the iterative algorithms are validated in the well-known flow past a cylinder benchmark. Besides, the extension 1:3 case is studied, in which several scenarios are explored varying the values of the main dimensionless numbers that characterize the problem to see how the flow pattern and temperature distribution change along the channel. • A new formulation for solution of thermally coupled viscoelastic flows is presented. • The new formulation is based on the Variational Multiscale Method. • Both a standard and a logarithmic conformation reformulation approach are presented. • The behavior of the proposed methodology is tested in several numerical examples.

Fluid structure-interaction in a deformable microchannel conveying a viscoelastic fluid

We theoretically analyze the interaction between a viscoelastic fluid flow, whose constitutive equation is the simplified Phan–Thien–Tanner model, and a deformable slender shallow microchannel. The microchannel top wall displacement is analyzed considering two cases: a) as a thin plate, using the Kirchhoff–Love theory, and b) as a thick plate, based on the Reissner–Mindlin theory. The mathematical model is nondimensionalized, and dimensionless parameters related to problem physics arise that control the fluid–structure interaction. The governing equations that describe the hydrodynamic field are simplified using the lubrication theory, and the displacement of the top wall is analyzed for each plate theory, relating the hydrodynamic pressure and the volumetric flow rate. These equations are implicit in the pressure and are solved numerically. The effect of dimensionless parameters on the pressure drop-volumetric flow rate relationship is analyzed, showing that for a viscoelastic fluid flowing through deformable channels, the volumetric flow rate is higher than the case of a Newtonian fluid under the same pressure. Our results are compared against those published in the specialized literature, showing an excellent agreement.

Peristaltic Flow of Viscoelastic Giesekus Fluid through Concentric Annuli with Heat Transfer

The flow of non-Newtonian Giesekus fluid through a peristaltic annulus is presented. The interaction between the flow velocity and the heat transfer distributions is obtained due to the viscous dissipation in the energy equation. Due to the slow motion of the Giesekus fluid (Polymer solution), the small value of the Reynolds number is assumed. A modified longwave approximation, due to a series of the wavenumber, is applied to determine the zero as well as the first order distributions for the stress components, the velocity, and temperature. Also, the pressure rise, the radial position of the zero shear rates, and the rate of the heat flux are obtained numerically. The rheological properties of the non-Newtonian Giesekus fluid are discussed due to the mobility parameter and the time relaxation parameter. The graphical results illustrate that the mobility parameter and the time relaxation parameter enhance the flow. Meanwhile, the flow increases due to the peristaltic motion. According to the viscous dissipation effect, the temperature rises with the time relaxation parameter. Also, the contours of the streamlines are presented and the results illustrate that the trapping bolus disappears for the fluids with small-time relaxation and for the flow through a fixed channel without the peristalsis.

Giesekus fluid flow past a sphere in a pipe

A numerical simulation of a viscoelastic fluid flow past a sphere in a round pipe is carried out. The four mode Giesekus model is taken as a rheological model. By the example of a polymer melt flow, the features of the flow around a sphere in comparison with the flow around a cylinder are revealed. Velocity and stress profiles for polymer melt and polymer solution fluid flow around a sphere at the same Weissenberg numbers are analyzed.

The Caputo–Fabrizio (CF) and Atangana–Baleanu in Caputo sense (ABC) fractional time‐derivative approach on transient free convection flow between two vertical parallel plates: A semi‐analytical solution

AbstractA comparative analysis on semi‐analytical solution of transient free convection flow of fractional Maxwell viscoelastic fluid between two vertical parallel plates has been investigated by employing the Caputo–Fabrizio (CF) and Atangana–Baleanus in Caputo sense (ABC) fractional time derivative. The semi‐analytical solutions for dimensionless temperature, velocity, skin friction, and mass flux are obtained using both approach (CF and ABC) and solution presented in the Laplace domain. The Riemann sum approximation was used to invert all solutions from the Laplace domain to the time domain. The influence of pertinent parameters on dimensionless temperature and velocity for both CF and ABC approach are presented graphically and in tabular form and thereafter discussed. The significant result obtained from this study is that both temperature and velocity in CF and ABC increase as the time and relaxation time parameter increases, while temperature and velocity via CF and ABC model decrease when the fractional parameter increases. It is also significant to note that, temperature, velocity, skin friction, and mass flux have a higher value in the CF model than the ABC model.

Numerical Modelling of Multicellular Spheroid Compression: Viscoelastic Fluid vs. Viscoelastic Solid

Parallel-plate compression of multicellular spheroids (MCSs) is a promising and popular technique to quantify the viscoelastic properties of living tissues. This work presents two different approaches to the simulation of the MCS compression based on viscoelastic solid and viscoelastic fluid models. The first one is the standard linear solid model implemented in ABAQUS/CAE. The second one is the new model for 3D viscoelastic free surface fluid flow, which combines the Oldroyd-B incompressible fluid model and the incompressible neo-Hookean solid model via incorporation of an additional elastic tensor and a dynamic equation for it. The simulation results indicate that either approach can be applied to model the MCS compression with reasonable accuracy. Future application of the viscoelastic free surface fluid model is the MCSs fusion highly-demanded in bioprinting.

A Hierarchical Grid Solver for Simulation of Flows of Complex Fluids.

Tree-based grids bring the advantage of using fast Cartesian discretizations, such as finite differences, and the flexibility and accuracy of local mesh refinement. The main challenge is how to adapt the discretization stencil near the interfaces between grid elements of different sizes, which is usually solved by local high-order geometrical interpolations. Most methods usually avoid this by limiting the mesh configuration (usually to graded quadtree/octree grids), reducing the number of cases to be treated locally. In this work, we employ a moving least squares meshless interpolation technique, allowing for more complex mesh configurations, still keeping the overall order of accuracy. This technique was implemented in the HiG-Flow code to simulate Newtonian, generalized Newtonian and viscoelastic fluids flows. Numerical tests and application to viscoelastic fluid flow simulations were performed to illustrate the flexibility and robustness of this new approach.

STABILIZED NUMERICAL METHODS FOR THE TWO KINDS OF PROBLEMS OF INCOMPRESSIBLE FLUID FLOWS

A mixed finite element method (MFEM) stabilized for the two kinds of problems related to the incompressible fluid flow is demonstrated. In the first kind, the Newtonian fluid flow is illustrated with the MFEM and considered discontinuous scheme. Initially, the model equations are considered nonlinear and un-stabilize. The model equations are solved for linear terms with the special technique first and then the model equation with the extra added term is utilized later to stabilize the model equations. A steady-state viscoelastic Oseen fluid flow model with Oldroyd-B type formulations was demonstrated in the second kind of problem with SUPG method. The nonlinear problems are linearized through the Oseen scheme. Numerical results for both the model equations are given and compared. The SUPG method is found more suitable and active.

On viscoelastic fluid in a vertical porous media channel with Soret and Dufour effects

The time and spatial fractional constitutive models are employed to examine the flow, heat and mass transfer of a viscoelastic fluid flowing in a vertical porous media square channel accompanied by Soret and Dufour effects. The fractional modified Fourier’s law and Fick’s model are utilized to characterize the heat and mass transfer. The finite difference algorithm is used to calculate the governing equations. The numerical technique is validated and can be extended to solve similar problems. Results indicate that the enlargement of fractional derivative in momentum equation heightens the flow resistance between liquid molecules, while the increase of fractional derivative in temperature and concentration equations weakens the heat and mass transfer.

Statistical properties of two-dimensional elastic turbulence.

We numerically investigate the spatial and temporal statistical properties of a dilute polymer solution in the elastic turbulence regime, i.e., in the chaotic flow state occurring at vanishing Reynolds and high Weissenberg numbers. We aim at elucidating the relations between measurements of flow properties performed in the spatial domain with the ones taken in the temporal domain, which is a key point for the interpretation of experimental results on elastic turbulence and to discuss the validity of Taylor's hypothesis. To this end, we carry out extensive direct numerical simulations of the two-dimensional Kolmogorov flow of an Oldroyd-B viscoelastic fluid. Static pointlike numerical probes are placed at different locations in the flow, particularly at the extrema of mean flow amplitude. The results in the fully developed elastic turbulence regime reveal large velocity fluctuations, as compared to the mean flow, leading to a partial breakdown of Taylor's frozen-field hypothesis. While second-order statistics, probed by spectra and structure functions, display consistent scaling behaviors in the spatial and temporal domains, the third-order statistics highlight robust differences. In particular the temporal analysis fails to capture the skewness of streamwise longitudinal velocity increments. Finally, we assess both the degree of statistical inhomogeneity and isotropy of the flow turbulent fluctuations as a function of scale. While the system is only weakly nonhomogenous in the cross-stream direction, it is found to be highly anisotropic at all scales.

Analytical and numerical study for oscillatory flow of viscoelastic fluid in a tube with isosceles right triangular cross section

Abstract A theoretical investigation is carried out to analyze the oscillatory flow of second-grade fluid under the periodic pressure gradient in a long tube of isosceles right triangular cross section in the present study. The analytical expressions for the velocity profile and phase difference are obtained. The numerical solutions are calculated by using the finite difference method with Crank–Nicolson (C–N) scheme. In comparison with the Newtonian fluid (λ = 0), the effects of retardation time, Deborah number and Womersley number on the velocity profile and phase difference are discussed numerically and graphically. For smaller Womersley number, the behavior of second-grade fluid is dominated by viscosity. For larger Womersley number α = 20, the flow becomes more difficult to be generated under periodic pressure gradient with increasing retardation time. Furthermore, the analytical expressions of the mean velocity amplitude and phase difference are given explicitly for discussing.

Brownian motion and thermophoresis effects on MHD flow of viscoelastic fluid over stretching/shrinking sheet in the presence of thermal radiation and chemical reaction

AbstractThe study covers the robust viscoelastic fluid stream across a stretchable surface. The analysis is conducted taking into account Brownian movement, chemical reactions, and thermophoresis. The dominant partial differential equations become regular differential equations. The method used to solve nonlinear systems is homotopy analysis. The solutions are graphically designed to illustrate the impact on speed, temperature, and concentration profiles of different parameters. The Mathematica code contains a graphical representation of the effects of different variables on speed, temperature, and distribution profiles. It is seen that, Fluid speed decreases with increases in K and M. From graphical representation, the friction of the skin on increasing K is seen to decrease. Sherwood number improves and Nusselt reduces with an increase in Nb. It is also mentioned.

Modeling and analysis of double fractional order Jeffreys viscoelastic fluids flow

In this paper, the rheological properties of welan gum solutions with mass fractions of 2%, 3% and 4% are measured using an Anton paar MCR 302 rheometer. It is found that the liquids fit the five-parameter Jeffreys model of double fractional order with corresponding rheological parameters. The behaviors of these fluids over linear stretching surface are studied based on the experimental results. We find that, compared with the Newtonian fluid, there exists an inflection on viscoelastic fluid velocity curve, which separated velocity curve into two parts with different concave-convexity. For the interval from inflection to external boundary, which similar to Newtonian fluid, the viscosity plays a major role, while for the interval from stretching surface to inflection, the elasticity plays a major role. At the inflection, the velocity gradient curve arrives its extreme. It is also found that, as viscoelastic solutions mass fractions decrease, the thickness boundary layer becomes thinner and the elasticity effect is weakened. Those results reveal the complex physical mechanism of viscoelastic fluid film flow and provide a theoretical basis for relevant engineering design.

Low Reynolds Number Pulsatile Flow of a Viscoelastic Fluid Through a Channel: Effects of Fluid Rheology and Pulsation Parameters

Abstract As the first endeavor, we have analyzed the pulsatile flow of Oldroyd-B viscoelastic fluid where the combined effects of fluid elasticity and pulsation parameters on the flow characteristics are numerically studied at a low Reynolds number. Computations are performed using a finite volume-based open-source solver OpenFOAM™ by appending the log-conformation tensor approach to stabilize the numerical solution at high Deborah number. Significant flow velocity enhancement is achieved by increasing the viscoelastic behavior of the fluid. High-velocity gradient zones and high polymeric stress regions are observed near the channel wall. The magnitude of axial velocity attenuates with increasing pulsation amplitude or pulsation frequency, and the extent of this attenuation is highly dependent on the Deborah number or the retardation ratio. This work finds application in the transport of polymeric solutions, extrusion, and injection molding of polymer melts in several process industries.

Role of elasto-inertial turbulence in viscoelastic drag-reducing turbulence

Two kinds of nonlinearities coexist in viscoelastic fluid flows, i.e., inertia and elasticity, which can engender different types of chaotic states including inertial turbulence (IT), drag-reducing turbulence (DRT), elastic turbulence, and elasto-inertial turbulence (EIT). The state of maximum drag reduction (MDR), the ultimate state of DRT of viscoelastic fluids, is recently regarded as EIT. This Letter quantitatively demonstrates the role of IT and EIT in drag-reducing turbulent flows passing through the parallel plane channels via the contributions of Reynolds shear stress and the nonlinear part of elastic shear stress to flow drag. The nature of DRT is reexamined under a wide range of flow conditions covering a series of flow regimes from the onset of DR to MDR with the Oldroyd-B model. We argue that EIT-related dynamics appears in DRT long before settling to MDR state and competitively coexists with IT in both spatial and temporal domains at moderate and high Reynolds number (Re). More specifically, under a low DR condition, EIT first emerges close to the channel walls. With the increase in elasticity, low-drag EIT gradually replaces a high-drag IT from channel walls to center, resulting in a drastic decrease in flow drag comparing with IT. When EIT dynamics dominates the whole channel, MDR phenomenon occurs. Our findings provide evidence that DRT phenomenon is the result of IT and EIT interaction.

Analysis of vortices in viscoelastic fluid flow through confined geometries at low Reynolds numbers

Understanding the behavior of viscoelastic (VE) fluids in confined geometries is crucial for applications in biologic systems, heat transfer devices, enhanced oil recovery, and many others. Here, we perform a systematic steady-state simulation of a VE fluid at low Reynolds numbers through a channel with successive smooth contractions and expansions. We analyze the hydrodynamic performance of the fluid with particular attention to vortex patterns that develop downstream of the contractions. We show that elastic vortices form at higher contraction ratios and that there are critical Weissenberg numbers (Wic) unique to each contraction ratio where the flow shifts from non-vortical to vortical. This Wic increases with an increasing contraction length. The coexistence of elongational-, shear-, and rotational-flow is essential for vortex development and evolution. We also analyzed the effect of the Deborah number (De) on the vortex pattern in a multiple contraction system and observed that the vortex area significantly depends on the distance between the contractions. We show that there are three distinctly different regions in De, in which the flow characteristics change in successive contractions. For high De, the flow in the downstream contraction is significantly affected by the upstream contraction. Our results have implications for the use of VE fluids with various VE properties in different types of porous media.

On the mechanisms of sheet-like extension structures formation and self-sustaining process in elasto-inertial turbulence

The elasto-inertial turbulence (EIT) of viscoelastic fluid is induced by the interaction between elastic instability and flow inertia. The recent discovery of the EIT regime enables new insights into the maximum drag reduction phenomenon of viscoelastic fluid flows and verifies the role of elastic instability in drag-reducing turbulence. In this study, the direct numerical simulation (DNS) of EIT is carried out by using the Oldroyd-B model for the first time. EIT simulations are conducted at a fixed Weissenberg number of 60 with a Reynolds number ranging from 1000 to 6000. Based on the DNS results, the Reynolds stress and elastic stress budgets are analyzed, and the formation of sheet-like structures of polymer extension is confirmed. It indicates that EIT has a complex energy picture. The self-sustaining nature of EIT not only involves the energy transformation from streamwise elastic energy (EE) into turbulent kinetic energy (TKE), but also relies on the energy transformation of wall-normal TKE into EE, which further induces energy absorption of elastic shear stress from the mean motion and the transformation of this energy into streamwise EE. Sheet-like structures reflect the polymer extension characteristics in the streamwise direction. Their formation comes from the wall-normal extension induced by turbulence perturbations, which further generates extra nonlinear elastic shear stress that absorbs energy from the mean motion and eventually forms sheet-like structures. In the self-sustaining cycle, fluid inertia lifts the sheet-like structures of polymer extension, further inducing flow instability.

A local in time existence and uniqueness result of an inverse problem for the Kelvin-Voigt fluids

In this paper, we consider an inverse problem for three dimensional viscoelastic fluid flow equations, which arises from the motion of Kelvin–Voigt fluids in bounded domains. This inverse problem aims to reconstruct the velocity and kernel of the memory term simultaneously, from the measurement described as an integral overdetermination condition. By using the contraction mapping principle in an appropriate space, a local in time existence and uniqueness result for the inverse problem of Kelvin–Voigt fluids are obtained. Furthermore, using similar arguments, a global in time existence and uniqueness result for an inverse problem for Oseen type equations are also achieved.

Analytical estimation of energy dissipations: Viscous, Joulian, and Darcy of viscoelastic fluid flow phenomena over a deformable surface

AbstractIn this paper, analytical estimation of energy dissipations, such as viscous, Joulian, and Darcy dissipation of viscoelastic flow phenomena over a deformable surface has been presented. This supplement to the study of many transport processes, which occur in nature, and various experimental setups that are driven or modified by the composition of the various flow characteristics and material or phase constitution. These processes are very important and have received considerable attention in the literature. The estimation of dissipative energy in the process of transport energy is an important phenomenon to investigate. The present analysis is carried out on steady MHD viscoelastic liquid due to deformable domains. Moreover, the impact of internal heat sources and prescribed thermal conditions, such as surface temperature and heat flux, are carefully studied. Analytical solutions to governing equations are obtained with the help of Kummer's function. The solutions are presented graphically as well as in tables to estimate the energy losses and their effects on transport processes, which serve as the salient features of the current analysis. The outcomes serve as a guideline due to the process of transport properties as per the design requirements. Looking into the current scenario, dissipative heat energies have several applications in industries and technological processes, such as electric heaters, fuses, food processing, and several others.