Viscoelastic Properties Of Fluids Research Articles

Heat and mass transfer analysis in flow of Walter's B nanofluid: A numerical study of dual solutions

AbstractThis study investigates the behavior of Walter's liquid B fluid over a biaxially stretching/shrinking surface for Homann stagnation point flow, focusing on the rheological properties that are crucial for understanding physical phenomena in engineering and industrial processes. The problem is modeled using Buongiorno's model in the presence of a permeable surface subject to heat generation/absorption, Ohmic heating, and chemical reactions influenced by Arrhenius activation energy. The governing partial differential equations are solved numerically using an appropriate similarity transformation, and the results are graphically analyzed via MATLAB's bvp5c solver. The study highlights the importance of characterizing the intricate properties of viscoelastic fluids, with potential applications in biomedical engineering and materials science. The findings reveal the coexistence of two distinct flow regimes and dual solutions are obtained. It is noted that the activation energy parameter is shown to enhance mass distribution in both solutions, while chemical reactions accelerate reactant conversion but reduce mass distribution. Additionally, an increase in viscoelasticity shifts the fluid's behavior towards elasticity, creating greater resistance to shear deformation and reducing both velocity profiles.

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.

Propulsion of a chiral swimmer in viscoelastic fluids

Microswimmers often use chirality to generate translational movement from rotation motion, exhibiting distinct behaviors in complex fluids compared to simple Newtonian fluids. However, the underlying mechanism remains incompletely understood. In this study, we elucidate the precise mechanisms underlying the distinct behaviors of microswimmers in Newtonian and non-Newtonian fluids. We show that the enhanced speed of chiral swimmers is attributed to the Weissenberg effect induced by normal stress differences resulting from chiral flows. Additionally, we identify swimmer-specific normal stress differences in a viscoelastic fluid and demonstrate that swimming speed varies depending on whether the swimmer acts as a pusher or a puller. Moreover, we investigate the hydrodynamic interactions between a pair of chiral squirmers. When the squirmers are aligned parallel (perpendicular) to their swimming axis, they tend to separate (approach). These findings deepen our comprehension of the rheological properties of viscoelastic fluids containing microswimmers, promising advancements in various applications. Published by the American Physical Society 2024

Insights into metachronal propulsion's influence on Ellis fluid flow across tri‐layers amid dynamic thermal transport: Theoretical study

AbstractCilia‐based therapies are emerging for treating ciliopathies, such as inhalable drugs to propel mucus out of the lungs of patients with cystic fibrosis. This has motivated scientists and researchers to investigate cilia motion mechanics and viscoelastic fluid properties for biomedical engineering applications and disease treatments. In line with the diverse biological implications, this study focuses on the mass and heat transfer flow of tri‐layered non‐Newtonian fluids propelled by ciliary beating in a cylindrical tube. The fluid remains incompressible, with distinct layers that do not mix. The study considers the impact of mass and heat transfer in three distinct regimes, ensuring continuity at the interfaces. Mathematical modeling incorporating the lubrication approximation, small Reynolds number, and long wavelength approximation is employed for simplification. The resulting differential equations, along with boundary conditions, yield accurate solutions for temperature, velocity, and concentration fields in the three fluid layers and are discussed graphically. Key findings demonstrate that velocity and temperature fields are most pronounced in the inner fluid layer (PCL), while the concentration profile is most prominent in the outer layers (ACL), with moderate behavior in the central region. The implications of this research extend to diverse fields, including mucus clearance from the respiratory tract, microfluidics, esophageal transport, biofluid mechanics, and other areas of physiology. The insights gained from this study have promising applications in developing new treatments and biomedical engineering solutions.

Improving the prediction of turbulent kinetic energy for drag reduction in turbulent viscoelastic pipe flow

Reducing turbulence in pipe flows using polymer additives is crucial for industrial applications like crude oil, water, and sewage transportation. While previous research has accurately predicted friction factor and velocity profiles, none has fully understood turbulent kinetic energy (TKE) behavior in such fluids. Authors are now focusing on exploring turbulence models to better understand the TKE behavior. In this research, we have introduced a model to improve the behavior of TKE in a modified generalized Newtonian fluid (GNF). The developed model aims to simulate the viscoelastic effects of fluids that result in drag reduction in turbulent pipe flow. The work is noteworthy as it integrates turbulence and viscoelastic components, offering a comprehensive understanding of the phenomenon. By incorporating the rheological properties of viscoelastic fluids and replacing the damping function with a non-Newtonian alternative proposed by Cruz and Pinho, the Launder–Sharma k–ε turbulence model is now suitable for simulating dilute non-Newtonian viscoelastic fluids. The viscoelastic aspect of the model employs the modified GNF model. The developed model has been subjected to simulations using the computational fluid dynamics software. The results obtained for fluid TKE demonstrate a significant improvement in comparison to our previous research and the findings of other researchers. Furthermore, the model's prediction for the Darcy friction factor has been enhanced, resulting in an average error of only 3.71% in this section. It is noteworthy that the model consistently maintains a high level of accuracy in predicting other essential flow parameters such as mean axial velocity and Reynolds stresses. The provided model advances our understanding of viscoelastic fluid behavior in turbulent pipe flow by applying the modified GNF model.

The bioengineering application of hyaluronic acid in tissue regeneration and repair

The multifaceted role of hyaluronic acid (HA) across diverse biomedical disciplines underscores its versatility in tissue regeneration and repair. HA hydrogels employ different crosslinking including chemical (chitosan, collagen), photo- initiation (riboflavin, LAP), enzymatic (HRP/H2O2), and physical interactions (hydrogen bonds, metal coordination). In biophysics and biochemistry, HA's signaling pathways, primarily through CD44 and RHAMM receptors, modulate cell behavior (cell migration; internalization of HA), inflammation, and wound healing. Particularly, smaller HA fragments stimulate inflammatory responses through toll-like receptors, impacting macrophages and cytokine expression. HA's implications in oncology highlight its involvement in tumor progression, metastasis, and treatment. Elevated HA in tumor stroma impacts apoptosis resistance and promotes tumor growth, presenting potential therapeutic targets to halt tumor progression. In orthopedics, HA's presence in synovial fluid aids in osteoarthritis management, as its supplementation alleviates pain, enhances synovial fluid's viscoelastic properties, and promotes cartilage integrity. In ophthalmology, HA's application in dry eye syndrome addresses symptoms by moisturizing the eyes, replenishing tear film deficiencies, and facilitating wound healing. Intravitreal injections and hydrogel-based systems offer versatile approaches for drug delivery and vitreous humor replacement. For skin regeneration and wound healing, HA hydrogel dressings exhibit exceptional properties by promoting moist wound healing and facilitating tissue repair. Integration of advanced regenerative tools like stem cells and solubilized amnion membranes into HA-based systems accelerates wound closure and tissue recovery. Overall, HA's unique properties and interactions render it a promising candidate across diverse biomedical domains, showcasing immense potentials in tissue regeneration and therapeutic interventions. Nevertheless, many detailed cellular and molecular mechanisms of HA and its applications remain unexplored and warrant further investigation.

On designing a wavy sinusoidal micromixer for efficient mixing of viscoelastic fluids harnessing elastic instability and elastic turbulence phenomena

Effective mixing in microscale systems encounters difficulties due to the inherently low Reynolds numbers. This investigation delves into harnessing elastic instability and elastic turbulence phenomena to improve the mixing performance of viscoelastic fluids within a wavy sinusoidal micromixer with variable cross-sectional areas. Previous experiments demonstrated enhanced mixing efficiency, while our numerical simulations indicate that this enhancement is true up to a certain Weissenberg number. Beyond this threshold, a further increase in the Weissenberg number results in diminished mixing efficiency. Moreover, we observe that mixing efficiency increases with the Deborah number, albeit with an exponential increase in pressure drop. Conversely, mixing efficiency also increases with the number of turns in the micromixer, albeit with a linear increase in pressure drop. Hence, selecting a wavy micromixer with more turns and a relatively lower Deborah number is advisable for achieving comparable efficiency with reduced pressure drop. Additionally, the shear-thinning properties of viscoelastic fluids impede mixing efficiency by suppressing elastic instability and elastic turbulence phenomena. In conclusion, this study provides valuable insights for designing optimal wavy micromixers that effectively mix viscoelastic fluids by utilizing elastic instability and elastic turbulence phenomena.

Thermal diffusivity of inclined magnetized Cross fluid with temperature dependent thermal conductivity: Spectral Relaxation scheme

Understanding and controlling the thermal transport phenomena are crucial in numerous applications. The current research emphasizes thermal diffusivity of an inclined magnetized Cross fluid with temperature-dependent thermal conductivity with a computational iterative spectral relaxation scheme. Cross mathematical model is employed to characterizes non-Newtonian behavior and to uncover viscoelastic properties of fluid. Flow is incorporated under temperature thermal influence and external inclined magnetic strength is considered for thermal variations. Various prominent factors, including cross index, magnetic field, inclination angle, temperature-dependent thermal conductivity are analyzed on the fluid's thermal diffusivity. The flow governing PDEs are converted into system of ODEs by using suitable transformation. Spectral relaxation computation scheme is then used for controlling the new set equations. SRM algorithm controlling subsystems is built through MATLAB. Numerical results are illustrated by MATLAB graphs. Physical quantities such as Sherwood numbers, Nusselt and skin friction coefficient are visually taken place through statistical graphs with two cases of imposed magnetic field. The results of this investigation shed light on how non-Newtonian fluids behave when exposed to temperature changes and magnetic fields and useful in understanding and leverage these effects for specific applications.

Electrokinetic ion transport of viscoelastic fluids in a pH-regulated nanochannel

The objects of nanofluidics-based biological detection are usually viscoelastic fluids, and the rheological properties of viscoelastic fluids can have complex effects on electroosmotic flow and electrokinetic ion transport in nanochannels. However, researchers have mainly focused on Newtonian fluids. In this study, numerical simulations were performed on the electrokinetic ion transport of viscoelastic fluids in a pH-regulated nanochannel. The Oldroyd-B model is used to describe the behavior of the polyacrylamide (PAM) solution, and the Poisson-Nernst-Planck model is used to describe the potential and ion concentration in the electrolyte solution. Compared with the Newtonian fluid, at pH = 8, the PAM solution of cp = 500 ppm has a larger region of low ion concentration in front of the nanochannel entrance and has a larger region of high ion concentration behind the nanochannel exit. When the pH is increased to 8, the surface charge density |σw| increases sharply, which is about 5 times of that at pH = 6. At pH = 8, cKCl = 20 mM, and cp = 500 ppm, two distinct vortices appear behind the nanochannel exit, and rotate in opposite directions.

Effect of elasticity on the induced charge electro-osmotic mixing of viscoelastic fluids in a micromixer with a conductive cylinder

Mixing of reagents in microfluidics is critical, and currently, the focus is on Newtonian fluids, but these reagents are often viscoelastic fluids. In this study, a micromixer containing a conductive cylinder is proposed based on the principle of induced charge electro-osmosis (ICEO). The Oldroyd-B constitutive model was chosen to characterize the flow properties of viscoelastic fluids, and the Poisson–Boltzmann model was used to describe the ion distribution in the electrolyte. The impact of the elasticity number (El) of viscoelastic fluids on the mixing efficiency, velocity, and vortex in the micromixer was studied. The results show that the mixing efficiency is only 55.41% when El = 0 (Newtonian fluid), and the mixing efficiency reaches 99.08% when El = 50. As El increases from 0 to 50, the cross-sectional average velocity at 50 μm from the micromixer exit decreases from 160 to 26.1 μm/s. Furthermore, the vortices around the conductive plate generated by the ICEO phenomenon begin to fluctuate at El = 7.

Rational understanding of viscoelastic drop impact dynamics on porous surfaces considering rheological properties

Understanding of viscoelastic drop impact on porous solid surfaces emerges as the essential physics for broad industrial and biological systems. However, there have been few studies concerning the post-drop impact transition considering rheological properties and dynamics. Here, we report the post-impact dynamics of viscoelastic drops on porous mesh surfaces using experimental and theoretical analyses. Five concentrations of highly viscous polymer solutions with shear-thinning and viscoelastic characteristics exhibit different rheological properties (viscosity, storage, loss moduli, etc.). These changes in the rheological features result in four distinguishable impact dynamics on two-dimensional mesh surfaces. Viscoelastic drops that exhibit viscoelastic solid properties (storage modulus > loss modulus) resulted in combined elastic solid-like motions and viscous fluid-like motions depending on the impact velocity and anti-penetration effects (such as capillary pressure and yield stress). Meanwhile, decreases in the viscoelastic fluid properties resulted in monotonous viscosity-dominant behaviors. A pressure-balance equation was proposed to theoretically predict the filament column penetration length of viscoelastic solid drops. The theoretical results correlated with the experimentally measured values until necking occurred in the filament column. We believe that this study on viscoelastic drop impact dynamics can shed light on future applications that involve various mechanical behaviors of non-Newtonian fluid drops, such as 3D printing, coating, bio-fluid treatments, and polymeric solutions.

A generalized model for field assessment of particle settling velocity in a viscoelastic fluid

The accurate prediction of particle settling velocity in viscoelastic fluids is important for the design, analysis, and optimization of various oil-field operations including hole cleaning and cuttings transport in oil and gas well drilling, proppant transport in hydraulic fracturing operations. An experimental study was, therefore, conducted to investigate the effect of fluid viscoelastic properties on the particle settling velocity. The main objectives of the study were to understand the factors that influence the particle settling velocity in shear-thinning viscoelastic fluids and develop a generalized model for the field assessment of particle settling velocity in shear-thinning viscoelastic fluids.We prepared ten different fluids, which were divided into two groups based on their shear viscosity values. In each group, five fluids were having similar shear viscosity and variable elasticity values. Nineteen different spherical particles were used to conduct particle settling experiments with a density range from 2700 kg/m3 to 6000 kg/m3 and a diameter range from 1 mm to 4 mm. Rheological characterizations of the fluids have been conducted by using funnel viscometer, API Rotational viscometer, controlled shear rate, and amplitude sweep test measurements. The fluid elasticity was quantified by using the concept of energy dissipation, which is determined by using standard field measurements of the apparent viscosity (AV) and the funnel viscosity.Finally, based on the experimental results and theory of the particle settling in non-Newtonian fluids, we proposed a model that can be used for predicting particle settling velocity in shear thinning viscoelastic fluids. The statistical analyses have shown that the root means square error and mean absolute percentage error of model predictions were 0.0032 m/s and 4.1%, respectively.

Tangential Shear Stress in Oscillatory Flow of a Viscoelastic Incompressible Fluid in a Plane Channel

The problems of oscillatory flow of a viscoelastic incompressible fluid in a plane channel are solved for a given harmonic oscillation of the fluid flow rate. The transfer function (amplitude–phase frequency response) is determined. Using this function, the effect of the acceleration oscillation frequency and the relaxation properties of fluid on the ratio of the tangential shear stress on channel wall to the velocity averaged over the channel cross-section (cross-sectional velocity) is determined. It is shown that the viscoelastic properties of fluid, as well as its acceleration, are the limiting factors for using the quasi-stationary approach. The found formulas for determining the transfer function for viscoelastic fluid flow in the case of non-stationary stream make it possible to determine the dissipations of mechanical energy in a non-stationary flow of the medium which are of importance for calculation of the control of hydraulic and pneumatic systems.

Interfacial and rheological investigation of enhanced oil recovery agents derived from Spirulina biomass

This study investigates interfacial and rheological properties of novel, Spirulina-based fluids developed for potential use in enhanced oil recovery (EOR) applications. The purpose of this investigation is to determine the driving mechanism(s) behind the EOR performance of these materials after a previous study concluded that the EOR fluids are a promising technology with up to 96% recovery of the original oil in place (OOIP). It was then hypothesized that the EOR mechanism arose from the interfacial energy effects and/or the rheological properties. In this study, Arthrospira platensis (Spirulina) biomass is modified by different denaturants (sodium hydroxide, citric acid, and urea) and tested for a wide range of interfacial and rheological properties. The interfacial properties include surface tension, interfacial tension with hydraulic oil, contact angle against silicon dioxide, and work of adhesion between the fluid and the silicon dioxide surface. The rheology focuses on determining fluid viscoelastic properties and flow behaviors. Additionally, this study compares and correlates the results amongst each other, which also includes pH, EOR performance, and denaturant concentration.The EOR performance of these fluids strongly correlates with the increased viscosity, reduced interfacial tension (IFT), and increased wettability in the EOR fluids. All of the investigated EOR solutions reduced the IFT. Most of the EOR solutions were found to be mostly shear-thinning with shear-thickening approximately in the 2,000–5,000 s−1 range. From the results, it is concluded that the performance of the different types of EOR fluids is based on different mechanisms. Sodium hydroxide-based fluids are driven by increased low-shear viscosity, reduced IFT, alkaline pH shift, and improved wettability. The citric acid-based fluids do not exhibit high viscosity values in the low shear range, which indicates that their EOR performance seems to be driven by reduced IFT, acidic pH shift, improved wettability, and increased fluid rigidity by the generation of crosslinks in the macromolecular structure. Urea-based fluids did not exhibit improved viscosity, which means that their modest EOR performance is likely driven by reduced IFT and improved wettability. While a shear-thickening rheology is often considered to be a mechanism for improving EOR, it is concluded that the shear-thickening effect is not a dominant mechanism for these fluids, especially since the highest performing EOR fluid (highest NaOH concentration) did not display shear thickening.

Lagrangian stretching reveals stress topology in viscoelastic flows

Viscoelastic flows are pervasive in a host of natural and industrial processes, where the emergence of nonlinear and time-dependent dynamics regulates flow resistance, energy consumption, and particulate dispersal. Polymeric stress induced by the advection and stretching of suspended polymers feeds back on the underlying fluid flow, which ultimately dictates the dynamics, instability, and transport properties of viscoelastic fluids. However, direct experimental quantification of the stress field is challenging, and a fundamental understanding of how Lagrangian flow structure regulates the distribution of polymeric stress is lacking. In this work, we show that the topology of the polymeric stress field precisely mirrors the Lagrangian stretching field, where the latter depends solely on flow kinematics. We develop a general analytical expression that directly relates the polymeric stress and stretching in weakly viscoelastic fluids for both nonlinear and unsteady flows, which is also extended to special cases characterized by strong kinematics. Furthermore, numerical simulations reveal a clear correlation between the stress and stretching field topologies for unstable viscoelastic flows across a broad range of geometries. Ultimately, our results establish a connection between the Eulerian stress field and the Lagrangian structure of viscoelastic flows. This work provides a simple framework to determine the topology of polymeric stress directly from readily measurable flow field data and lays the foundation for directly linking the polymeric stress to flow transport properties.

Numerical Study for the Performance of Viscoelastic Fluids on Displacing Oil Based on the Fractional-Order Maxwell Model.

In the study of polymer flooding, researchers usually ignore the genetic stress properties of viscoelastic fluids. In this paper, we investigate the process of viscoelastic fluid flooding the remaining oil in the dead end. This work uses the fractional-order Maxwell in the traditional momentum equation. Furthermore, a semi-analytic solution of the flow control equation for fractional-order viscoelastic fluids is derived, and the oil-repelling process of viscoelastic fluids is simulated by a secondary development of OpenFOAM. The results show that velocity fractional-order derivative α significantly affects polymer solution characteristics, and increasing the elasticity of the fluid can significantly improve the oil repelling efficiency. Compared to the Newtonian fluid flow model, the fractional order derivative a and relaxation time b in the two-parameter instanton equation can accurately characterize the degree of elasticity of the fluid. The smaller the a, the more elastic the fluid is and the higher the oil-repelling efficiency. The larger the b, the less elastic the fluid is and the lower the cancellation efficiency. Moreover, the disturbance of the polymer solution to the dead end is divided into two elastic perturbation areas. The stronger the elasticity of the polymer solution, the higher the peak value of the area in the dead end and the higher the final oil displacement efficiency.

Portable Quartz Crystal Resonator Sensor for Characterising the Gelation Kinetics and Viscoelastic Properties of Hydrogels

Hydrogel biomaterials have found use in various biomedical applications partly due to their biocompatibility and tuneable viscoelastic properties. The ideal rheological properties of hydrogels depend highly on the application and should be considered early in the design process. Rheometry is the most common method to study the viscoelastic properties of hydrogels. However, rheometers occupy much space and are costly instruments. On the other hand, quartz crystal resonators (QCRs) are devices that can be used as low-cost, small, and accurate sensors to measure the viscoelastic properties of fluids. For this reason, we explore the capabilities of a low-cost and compact QCR sensor to sense and characterise the gelation process of hydrogels while using a low sample amount and by sensing two different crosslink reactions: covalent bonds and divalent ions. The gelation of covalently crosslinked mucin hydrogels and physically crosslinked alginate hydrogels could be monitored using the sensor, clearly distinguishing the effect of several parameters affecting the viscoelastic properties of hydrogels, including crosslinking chemistry, polymer concentrations, and crosslinker concentrations. QCR sensors offer an economical and portable alternative method to characterise changes in a hydrogel material's viscous properties to contribute to this type of material design, thus providing a novel approach.

Publisher's Note: “A novel general modeling of the viscoelastic properties of fluids: Application to mechanical relaxation and low frequency oscillation measurements of liquid water” [Phys. Fluids 34, 043109 (2022)

Publisher's Note: “A novel general modeling of the viscoelastic properties of fluids: Application to mechanical relaxation and low frequency oscillation measurements of liquid water” [Phys. Fluids <b>34</b>, 043109 (2022)

A novel general modeling of the viscoelastic properties of fluids: Application to mechanical relaxation and low frequency oscillation measurements of liquid water

The aim of this paper is to calculate the time dependence of the mean position (and orientation) of a fluid particle when a fluid system at thermodynamic equilibrium is submitted to a mechanical action. The starting point of this novel theoretical approach is the introduction of a mechanical energy functional. Then using the notions of inertial modes and action temperature, and assuming a mechanical energy equipartition principle per mode, the model predicts the existence of a dynamic phase transition where the rheological behavior of the medium evolves from a solid-like to a liquid-like regime when the mechanical action is increased. The well-known Newtonian behavior is recovered as the limiting case. The present modeling is applied to the analysis of recent liquid water viscoelastic data pointing out a prevalent elastic behavior in confined geometry. It is demonstrated that the model makes it possible to understand these data in a coherent and unified way with the transport properties (viscosity and self-diffusion coefficient). It is concluded that any finite volume of fluid at rest possesses a static shear elasticity and should therefore be considered as a solid-like medium.

Acoustic streaming in Maxwell fluids generated by standing waves in two-dimensional microchannels

In this work, a semianalytic solution for the acoustic streaming phenomenon, generated by standing waves in Maxwell fluids through a two-dimensional microchannel (resonator), is derived. The mathematical model is non-dimensionalized and several dimensionless parameters that characterize the phenomenon arise: the ratio between the oscillation amplitude of the resonator and the half-wavelength ( $\eta =2A/\lambda _{a}$ ); the product of the fluid relaxation time times the angular frequency known as the Deborah number ( $De=\lambda _{1}\omega$ ); the aspect ratio between the microchannel height and the wavelength ( $\epsilon =2 H_{0}/\lambda _{a}$ ); and the ratio between half the height of the microchannel and the thickness of the viscous boundary layer ( $\alpha =H_{0}/\delta _{\nu }$ ). In the limit when $\eta \ll 1$ , we obtain the hydrodynamic behaviour of the system using a regular perturbation method. In the present work, we show that the acoustic streaming speed is proportional to $\alpha ^{2.65}De^{1.9}$ , and the acoustic pressure varies as $\alpha ^{6/5}De^{1/2}$ . Also, we have found that the growth of inner vortex is due to convective terms in the Maxwell rheological equation. Furthermore, the velocity antinodes show a high dependency on the Deborah number, highlighting the fluid's viscoelastic properties and the appearance of resonance points. Due to the limitations of perturbation methods, we will only analyse narrow microchannels.