Behavior Of Viscoelastic Fluids Research Articles

Viscosity model based on Giesekus equation

Abstract This work presents a viscosity model based on the Giesekus equation. The model is shown to be more flexible than the Cross and Carreau models in representing the shear-thinning behavior of viscoelastic fluids. It has been investigated that the influence of the model parameters on the viscosity showed that the mobility parameter α plays a distinctive role in adjusting the inflection shape of the viscosity curve. The results show that the new model is able to accurately capture the shear-thinning behavior of polystyrene data, while the Cross and Carreau models tend to underestimate and overestimate the viscosity at the inflection point, respectively. It has been also shown that the Yasuda-type modification is also applicable to the proposed model. Moreover, the viscosity model has been applied to simultaneously fitting a polymeric liquid system and a particulate slurry system. The new viscosity model is a promising tool for modeling the shear-thinning behavior of viscoelastic fluids in a wide range of applications.

Role of squeezing phenomenon in the reactive dynamics of Jeffrey fluid

AbstractThis study sheds light on the complex dynamics of squeezing flow in Jeffrey fluids and highlights the significance of considering Cattaneo‐Christov heat flux and reactive Species. To simplify the mathematical formulation and facilitate numerical analysis, a similarity transformation is utilized to transform the governing partial differential equations into a collection of interconnected ordinary differential equations (ODEs). The transformed ODEs are subsequently resolved utilizing bvp4c technique. The application of the bvp4c technique enables accurate numerical analysis, offering valuable insights into the behavior of viscoelastic fluids under squeezing conditions with thermal effects and chemical reactions. Through numerical simulations, the temperature distribution, flow characteristics, and reaction kinetics within the Jeffrey fluid under squeezing conditions are examined.

Stability of Viscoelastic Solutions: BrijL4 and Sodium Cholate Mixtures with Metal Ions Across a Broad pH and Temperature Range.

The impact of pH, temperature, and metal ions on the rheological and interfacial properties of aqueous mixed surfactant solutions composed of anionic NaC (sodium cholate) and nonionic BrijL4 [polyoxyethylene (4) lauryl ether] surfactants has been investigated. The various compound systems were analyzed, considering variations in each selected factor. The results highlight the unique characteristics of the BrijL4/NaC mixture, suggesting its potential as a viable alternative to other existing surfactants. The synergistic effect between BrijL4 and NaC significantly reduces the critical micelle concentration (CMC) and improves the wetting properties on hydrophobic surfaces, surpassing those of single-component solutions. Additionally, sodium, calcium, and magnesium ions enhance surface wetting and decrease the CMC. Besides, the BrijL4/NaC solutions exhibit viscoelastic fluid behavior at higher surfactant concentrations. These viscoelastic BrijL4/NaC solutions demonstrate stability over various pH and temperature variations, exhibiting lower flow activation and scission energy values than those of other viscoelastic surfactant solutions. Notably, the BrijL4/NaC mixture has potential applications in gel-based foliar fertilizers and drug delivery systems. Furthermore, the rheological studies examine the impact of humic acid on the rheological properties of BrijL4/NaC mixture solutions, revealing that incorporating additional humic acids can achieve stable rheological properties.

A computational investigation of diffusivities and heat transfer in the flow of viscoelastic fluid through Darcy–Brinkman–Forchheimer medium

The main objective of this work is to examine the effects of non-linear thermal radiation and induced magnetic fields on the behavior of viscoelastic fluid as it flows through a porous material that does not follow Darcy’s law. Hence, the Darcy–Brinkman–Forchheimer model has been employed when formulating the momentum equation. The research postulates the presence of a chemical process involving two chemical species, A and B. The research utilizes the spectral relaxation method (SRM) for the numerical solution of the altered governing equations. The present algorithm is formulated and executed on computational software MATLAB. The findings demonstrate a high level of concurrence with previously known numerical outcomes in the context of a specific scenario. The findings of this research demonstrate that chemical species B functions as a catalyst in a horizontally subsurface environment. Consequently, the relationship between the homogeneous-heterogeneous scheme may be seen in the context of isothermal cubic autocatalytic events and first-order processes, respectively. The use of the heterogeneous reaction parameter offers significant benefits in reducing the concentration of the bulk fluid while increasing the concentration of the catalyst located on the subsurface. Moreover, the results indicate that the impacts of induced magnetic and viscoelastic factors on velocity and induced magnetic fields are similar in their outcomes but differ in their fundamental nature.

Longitudinal wave propagation in an elastic cylinder embedded in a viscoelastic fluid

Abstract A novel analytical investigation of longitudinal wave propagation in an elastic cylinder embedded in a viscoelastic fluid is proposed. The Maxwell model is used to describe the viscoelastic fluid behavior. With appropriate boundary conditions, a complex dispersion equation of longitudinal wave has been established. The aim of this paper is to study the effect of the fluid rheological properties on the longitudinal wave characteristics (attenuation and velocity). It is shown that the attenuation is the sum of a viscous and non viscous component. The viscosity induced attenuation is predominant at low frequencies. On the other hand, the effect of the liquid amount and elastic cylinder radius on the attenuation and velocity are studied. A critical normalized liquid thickness is highlighted. Beyond this critical value, the influence of the outer boundary condition can be neglected. At last, among other interesting phenomena, it is highlighted that if the Deborah number increases, the attenuation decreases. This variation characterize a stiffening of the viscoelastic medium. In addition, the obtained results show that the viscosity measurement should be performed at low frequencies using small elastic cylinder radius. Accordingly, these investigations are novel and can be applied in geophysics, food industry, medicine, non-destructive testing of materials, design and development of fluid sensors.

Induced-charge electroosmosis flow of viscoelastic fluids under different voltage arrangements

Efficient mixing of chemical analysis reagents with laboratory samples at a microscale is a key issue in numerous biomedical and chemical analyses but hardly to implement due to the limited of the low diffusivity in laminar flow. Induced-charge electroosmosis flow, as an innovative mixing method, has been proved to be effective and simple in rapid mixing attributes to its mechanism of vortex generation. This work aims to propose a new strategy for chaotic induced-charge electroosmosis flow based on different voltage arrangements to improve the mixing of viscoelastic fluids. The Phan–Thien–Tanner constitutive model is applied to characterize the flow behavior of viscoelastic fluid in a microfluidic preparation mixer. The direct numerical simulation method is used to solve the fully coupled Navier–Stokes and Poisson–Nernst–Planck equations for a polarizable cylinder in a two-dimensional cavity filled with electrolyte solution. The impact of Weissenberg number (Wi), Debye parameter, voltage strength on the velocity, net charge density, and potential profiles is investigated. The simulation results indicate that a greater Wi leads to the decrease in the maximum velocity, and a large voltage strength can heighten the net charge density and potential, thus improve the peak velocity. Moreover, the classical theoretical prediction that the maximum velocity is proportional to the square of the applied voltage has been authenticated.

Flow and heat transfer in Phan-Thien–Tanner viscoelastic fluid around a rotating hot cylinder in a square enclosure

Flow and heat transfer problems in non-Newtonian fluids are considerably more complicated compared to Newtonian fluids due to their non-linear behavior and complex properties. This paper numerically studied the flow and heat transfer of a viscoelastic fluid around a hot rotating cylinder in a square enclosure. The Phan-Thien–Tanner (PTT) model, one of the most accurate models available to describe the behavior of viscoelastic fluids, was used to obtain the constitutive equations of the viscoelastic fluid, which were then solved by using the finite-volume method with the Rheoheatfoam solver of the OpenFOAM software. The log-conformation approach was employed to avoid the divergence problem at high Weissenberg numbers. Simulations were conducted to investigate the effects of the Weissenberg number, Brinkman number, Reynolds number, and the ratio of the polymeric viscosity to total viscosity on the behavior of fluid flow and heat transfer. The results showed that increasing the Weissenberg number led to a higher shear thinning effect, which decreased the fluid's effective viscosity and viscous dissipation near the cylinder. As a result, heat transfer from the cylinder increased, and the frictional torque applied to the cylinder decreased. However, the shear thinning effect was negligible when the Weissenberg number exceeded 100. Furthermore, the tangential normal stress significantly increased as the Weissenberg number increased up to one. However, with further increases in the Weissenberg number, the tangential normal stress reduced, eventually reaching close to zero at high Weissenberg numbers.

Carbomer/arginine intelligent viscoelastic fluid with adjustable CO2-responsive viscosity

Environmentally responsive intelligent viscoelastic fluids have been used in many fields in recent years. The rheological behavior of different intelligent viscoelastic fluids can be changed by different stimulation methods. Among them, CO2, as a non-toxic green and abundant stimulus method, has attracted much attention. Therefore, CO2-responsive intelligent viscoelastic fluids have been continuously reported, in which viscoelastic fluids with CO2-responsive viscosity increase have been more reported, while those with CO2-responsive viscosity decrease have been less reported. Herein, carbomer (CBM), as a pH-responsive polymer with potential CO2-responsiveness, is applied to CO2-responsive viscosity decreasing viscoelastic fluids. CBM and arginine (Arg) formed a new CO2-responsive viscoelastic fluid, which achieved a significant decrease in viscosity after CO2-response. Firstly, by comparing the effects of NaOH and Arg on the rheological behavior of CBM solution, it is demonstrated that Arg can extend the viscosity variation range of CBM solution before and after CO2-response, and Arg can switch between “physical crosslinking agent” and “viscosity reducing agent”, and it is verified from the microscopic perspective. Then, the effects of Arg concentration and CBM concentration on the CO2-responsiveness and rheological behavior of CBM/Arg viscoelastic fluid were investigated. The multiple reversible CO2-responsive viscosity of CBM/Arg viscoelastic fluid was verified. Finally, the viscoelastic variations of CBM/Arg viscoelastic fluid before and after the response were investigated by dynamic rheology.

Numerical study on radiative MHD flow of viscoelastic fluids with distributed-order and variable-order space fractional operators

The magnetohydrodynamic (MHD) flow has been concerned widely for its widespread adoption in the field of astrophysics, electronics and many other industries over the years. The purpose of this article is to introduce the variable and distributed order space fractional models to characterize the MHD flow and heat transfer of heterogeneous viscoelastic fluids in a parallel plates. Based on the central difference approximation of Riesz space fractional derivative, the Crank–Nicolson difference scheme for the governing equations is established, and the effectiveness of the algorithm is verified by two numerical examples. We examine the effects of fractional-order model parameters on the velocity and temperature, our investigation indicates that for the constant fractional model, the larger the fractional order parameter, the smaller the velocity and temperature. The variable space fractional method can be used to describe dynamic behavior with time and space dependence, while the distributed space fractional model can describe various phenomena in which the number of differential orders varies over a certain range, characterizing their complex processes over space, and it is also more suitable for simulating the fluid flow and thermal behavior of complex viscoelastic magnetic fluid.

Flow-switching and mixing phenomena in electroosmotic flows of viscoelastic fluids

The present study uses numerical simulations and experiments to investigate the electroosmotic flows of viscoelastic fluids through a microchannel containing a cylindrical obstacle. As the electric field strength gradually increases, the flow dynamics within this microfluidic setup becomes chaotic and fluctuating. Notably, numerical simulations reveal a flow-switching phenomenon in viscoelastic fluids when the applied electric field strength exceeds a critical value, which is absent in simple Newtonian fluids under identical conditions. Corresponding experiments confirm these observations. Additionally, this study demonstrates the successful mixing of two viscoelastic fluids using the flow-switching phenomenon within the present microfluidic setup. To gain insight into the dynamics of coherent flow structures arising from the flow-switching phenomenon and their impact on the mixing process, data-driven dynamic mode decomposition (DMD) analysis is employed. Importantly, the DMD analysis uncovers the presence of upstream elastic instability, which is not discernible through traditional velocity or concentration field plots. Overall, this study aims to advance our understanding of the electrokinetic flow behavior of viscoelastic fluids in complex systems like porous media. Furthermore, it proposes a relatively simple and fabricable microfluidic technique for efficiently mixing viscoelastic fluids.

Effect of jet-cooking on rheological properties of navy bean flour suspensions

Navy beans are a gluten-free pulse containing great heathy sources for human beings. In this work, we compared the rheological properties of untreated navy bean flour suspensions (UNBFS) and jet-cooked navy bean flour suspensions (JCNBFS). Jet-cooking is a direct-contact heating process employing high-temperature and high-pressure steam for producing food and beverage products. We found that the linear rheological properties of 8% (wt.%) UNBFS exhibited viscoelastic fluid behavior; while 10% (wt.%) UNBFS displayed viscoelastic fluid/solid cross-over behavior; but 12% (wt.%) UNBFS displayed weak viscoelastic solid behavior. Unlike UNBFS, all three (8%, 10%, and 12%) (wt.%) jet-cooked navy bean flour suspensions (JCNBFS) displayed linear rheological properties having viscoelastic solid gel-like behaviors. The rheological properties of JCNBFS were strongly dependent on the concentration of the suspensions. The non-linear viscoelastic properties of the three suspensions of UNBFS exhibited similar viscosity shear thinning behavior. The degree of shear thinning was slightly reduced both at very low and high shear rates. The non-linear rheological properties of the three suspensions of JCNBFS also displayed shear thinning behaviors. The viscosity curves of the JCNBFS were much steeper than those of the UNBFS. This demonstrates that JCNBFS possessed greater shear thinning capacity than UNBFS. Both linear and non-linear rheological property studies for UNBFS and JCNBFS revealed that jet-cooking processing alters the molecular structures of navy bean flours’ starch and proteins, which would influence the navy bean flour suspensions’ properties. The results of this work will be useful to develop new food products from navy beans.

Characterization of electrohydrodynamic drop-on-demand injection of viscoelastic fluids in pulsed voltage

Electrohydrodynamic drop-on-demand (DOD) injection in pulsed voltage is a very promising technique for fabricating nanostructures. However, it is still a challenge to achieve stable, high-precision, high-frequency DOD injection due to the lack of clarity on the mechanism of viscoelastic fluid injection. In this paper, a dimensionless parameter study based on the volume of fluid (VOF) method is used to systematically study the kinetic behavior of viscoelastic fluids in pulsed voltages. Four independent dimensionless parameters of voltage duration τ* pulse, electric Bond number BoE, electric Reynolds number ReE, and the ratio of charge relaxation time to fluid relaxation time δ are proposed to determine the operational phase diagrams in the dimensionless plane for the no jet mode, cone-jet mode, dripping mode, and reaching the substrate mode. The result shows that the voltage duration is negatively correlated with both the electric Bond number and the electric Reynolds number at the critical injection. The critical injection condition occurs over a wide range of voltage durations when the electric Reynolds number is <10. Cone-jet occurs in the region of δ < 1, with a jet frequency exceeding 2 kHz at its highest and the droplet diameter reaches 1/12 of the initial droplet diameter. Furthermore, the ability to print micron-scale patterns with precision in cone-jet mode fully demonstrates the promise of viscoelastic fluids in pulsed voltage for applications in micro/nano fabrication.

Experimental study of the rheology of cellulose nanocrystals-enhanced C22-tailed zwitterionic wormlike micelles

Nano-materials enhanced zwitterionic surfactants fracturing fluids with greatly improved rheological properties are extensively employed in foam fracturing to stimulate unconventional gas/oil reservoirs. In this study, a novel worm-like micelles (WLMs) system composed of erucyl dimethyl amidopropyl betaine (EDAB, C22), alkyl polyglucoside (APG) and cellulose nanocrystals (CNC) is proposed. A series of rheology and dynamic light scattering tests were conducted to determine the optimal concentration, and the influence of various factors, including temperature, pH, and inorganic salts, on the viscoelasticity and structural morphology of WLMs systems were also analyzed. The results show that a 0.3 wt% EDAB/APG/CNC system exhibits optimal viscosity and viscoelastic fluid behavior. The increase of temperature accelerates the breaking rate of WLMs, resulting in a decrease in viscosity, but its shear viscosity can still maintain 87.42 mPa·s at 90 °C and is an order of magnitude greater than that of other systems. The change of pH can disturb the equilibrium state under the electrostatic interaction of EDAB and CNC, and the negative ions in EDAB and CNC molecules are easily protonated in acid medium, resulting in a lower viscosity than alkaline medium and much lower than neutral medium. The viscosity of the EDAB/APG/CNC system increases first and then decreases with the increase of inorganic salt concentration, and reaches a peak at 2.5 wt%. Proppant critical settling velocity tests show that the CNC improves the proppant-carrying capacity of the EDAB/APG/CNC system with favourable critical settling velocity. The CNC enhanced C22-tailed EDAB system provides a basis for optimizing foaming fracturing in unconventional reservoirs.

Resolving Salt-Induced Agglomeration of Laponite Suspensions Using X-ray Photon Correlation Spectroscopy and Molecular Dynamics Simulations.

Linking the physics of the relaxation behavior of viscoelastic fluids as they form arrested gel states to the underlying chemical changes is essential for developing predictive controls on the properties of the suspensions. In this study, 3 wt.% laponite suspensions are studied as model systems to probe the influence of salt-induced relaxation behavior arising from the assembly of laponite nanodisks. X-ray Photon Correlation Spectroscopy (XPCS) measurements show that laponite suspensions prepared in the presence of 5 mM concentrations of CaCl2, MgCl2 and CsCl salts accelerate the formation of arrested gel states, with CaCl2 having a significant impact followed by CsCl and MgCl2 salts. The competing effects of ion size and charge on relaxation behavior are noted. For example, the relaxation times of laponite suspensions in the presence of Mg2+ ions are slower compared to Cs+ ions despite the higher charge, suggesting that cation size dominates in this scenario. The faster relaxation behavior of laponite suspensions in the presence of Ca2+ ions compared to Cs+ ions shows that a higher charge dominates the size of the ion. The trends in relaxation behavior are consistent with the cluster formation behavior of laponite suspensions and the electrostatic interactions predicted from MD simulations. Charge balance is achieved by the intercalation of the cations at the negatively charged surfaces of laponite suspensions. These studies show that the arrested gel state of laponite suspensions is accelerated in the presence of salts, with ion sizes and charges having a competing effect on relaxation behavior.

The role of relaxation and retardation phenomenon of Oldroyd-B fluid flow through Stehfest’s and Tzou’s algorithms

Abstract Delayed response (delay of the elasticity) and time needed for initial stress can lead to relaxation and retardation phenomenon; this is because of the consistent behavior of viscoelastic fluid on thermodynamic principles. In this context, the aim of this article is to investigate the unsteady, incompressible, and Oldroyd-B viscoelastic fluid under wall slip conditions to know the hidden aspects of relaxation and retardation. The motion of the liquid is assumed over a flat vertical plate which moves through an oscillating velocity. A fractional model is developed by using the modern definition of the non-singular kernel proposed by Caputo and Fabrizio. We have obtained a semi-analytical solution of the non-dimensional model by using the Laplace transformation that satisfies our imposed suitable boundary conditions. We have tackled the Laplace inverse by employing Stehfest’s and Tzou’s algorithms. The velocity is enhanced by decreasing the estimations of relaxation time λ as well as slip parameter, and the temperature is also increasing for a considerable measure of the fractional factor. The effects of different fractional and physical parameters are plotted using Mathcad software based on the relaxation and retardation phenomenon of Oldroyd-B viscoelastic fluid.

A hybrid lattice Boltzmann model for simulating viscoelastic instabilities

Low-Reynolds-number viscoelastic fluids exhibit a chaotic behaviour linked to the growth of elastic instabilities when the polymer molecules are stretched excessively. Despite offering various exciting benefits, the numerical difficulties associated with simulating this complex regime have left a lot still unexplored regarding the transition and onset of these low-Reynolds number viscoelastic instabilities. Recently, methods based on the lattice Boltzmann method (LBM) have emerged as a viable numerical tool for studying the behaviour of viscoelastic fluids largely due to the simplicity, adaptability, and intrinsic parallel features of LBM. However, extensive memory requirements and the inability to preserve numerical stability have restricted previous attempts from simulating viscoelastic instabilities. In this work, a hybrid lattice Boltzmann model is applied to simulate low-Reynolds number viscoelastic instabilities. In this approach, the hydrodynamic field is solved using a lattice Boltzmann model, whereas the polymer field is solved separately using a high-resolution finite difference scheme with the logarithmic Cholesky decomposition. The model is first validated for steady viscoelastic flows using the four-roll mill case, where the results are compared against the analytical solution and previous numerical studies. The model is then applied to simulate a chaotic low-Reynolds number viscoelastic instability by initialising a small perturbation to the isotropic polymer stress. The results at different Weissenberg numbers experience complex flow dynamics at sufficiently long time durations, which transition from quasi-periodic to periodic to aperiodic states with increasing elastic effects. The quasi-periodic regime was found to experience the fastest transition into the transient regime, with the transitioning time being delayed as the Weissenberg number increased. This work proves the capability of applying a coupled lattice Boltzmann method for exploring the complex flow behaviour of elastic instabilities, allowing the potential to explore more challenging and practical viscoelastic instability cases.

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.

Rheology and microstructure of zwitterionic-anionic surfactant for enhanced oil recovery

Surfactants have been widely used in enhanced oil recovery. The zwitterionic surfactant possesses a high critical micelle concentration, that its use requires an increased concentration and thus it is uneconomical. In this paper the use of erucic acid amidopropyl- betaine (EDAB, C22) and sodium alkyl sulfate (SDS) is proposed to construct a worm-like micelle with mass ratio of 1.5:1. The viscoelasticity and the structural morphology of worm-like micelle systems were studied using cryo-transmission electron microscopy, dynamic light scattering (DLS) and rheology. The results showed that EDAB/SDS with a mass concentration of 0.3% (0.18% EDAB + 0.12% SDS) exhibited viscoelastic fluid behavior when the pH value was 9.15 at 43 °C. The shear viscosity of the EDAB/SDS system is greater than that of the EDAB system. It shows that longer linear worm-like micelle and larger entangled three-dimensional network structure are formed in the EDAB/SDS system. The rheological properties EDAB/SDS system are affected by pH, temperature and inorganic salts. The viscoelasticity of the EDAB/SDS system increases first and then decreases with the increase of temperature and NaCl concentration. The electrostatic interaction between EDAB and SDS can be adjusted by changing the pH value to affect the aggregation behavior of worm-like micelle molecules. Worm-like micelles continue to grow longitudinally with the increase of pH value and form larger aggregate structures, which are manifested by an increase in viscosity.

Induced charge electroosmosis characteristics of viscoelastic fluid around a metal cylinder

The mixing of chemical analysis reagents at the microscale is critical. Most of the biological fluids and polymer solutions used in the field of biomedicine belong to the category of non-Newtonian fluids which have received limited attention in the research of induced charge electroosmosis (ICEO). In this study, the flow behavior of viscoelastic fluid described by the Oldroyd-B constitutive model in a microfluidic sample preparation mixer under different conditions is studied by numerical simulation. The nonlinear Poisson-Nernst-Planck equation which controls the distribution of potential and ion concentration is used and solved by the finite volume method. This paper analyses the influence of polar voltage, electrical double layer (EDL) thickness, and Weissenberg (Wi) number on the ICEO characteristics of viscoelastic fluid around a metal cylinder. The most obvious finding to emerge from this study is that the Wi number of polymer solutions has a significant impact on fluid velocity. Due to the shear thickening characteristics, the fluid flow rate will decrease as the Wi number increases, respectively, under various voltage conditions used. Similarly, the decrease of EDL thickness and the increase of applied voltage can result in the rise of the charge density close to the wall and the corresponding increase of the coulomb force, therefore resulting in the rise of fluid velocity. A linear relationship between ICEO velocity and electric field strength squared is observed in all the examined PAA solutions. The fluid velocity affects the relative movement between different streamlines which will cause the fluid micro-elements to deform, stretch, and fold, and then increase the interface area between the fluids to be mixed, thereby increasing the mixing effect. This research might explore services for the detection of viscoelastic fluids such as biological fluids and develop high-performance microfluidic preparation mixers for viscoelastic fluids.

Bifurcation analysis for a flow of viscoelastic fluid due to peristaltic activity

In this article, bifurcation analysis is performed to study the qualitative nature of stagnation points and various flow regions for a peristaltic transport of viscoelastic fluid through an axisymmetric tube. The rheological behavior of viscoelastic fluid is characterized by the simplified Phan–Than–Tanner fluid model. An analytic solution in a wave frame is obtained subject to the low Reynolds number and long wavelength approximations. The stagnation points and their bifurcations (critical conditions) are explored by developing a system of autonomous differential equations. The dynamical system theory is employed to examine the nature and bifurcations of obtained stagnation points. The ranges of various flow phenomena and their bifurcations are scrutinized graphically through global bifurcation diagrams. This analysis reveals that the bifurcation in the flow is manifested at large flow rate for high extensional parameter and Weissenberg number. Backward flow phenomenon enhances and trapping diminishes with an increase in the Weissenberg number. At the end, the results of present analysis are verified by making a comparison with the existing literature.