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We investigate the cross-diffusion on MHD mixed convective thermo-solutal transport in viscoelastic fluid from a nonlinear stretching sheet. The novelty of the work is the analytical evaluation of the nonlinear stretching sheet in a porous medium with a variable magnetic parameter and radiative flux. Also, thermo-solutal transport of a mixed convective flow is analyzed with Dufour and Soret effects in the presence of the chemical reaction, heat source/sink. The governing PDEs are reduced into ODEs by similarity variables. ODEs were tackled analytically using the homotopy analysis method (HAM). The analysis is carried out up to the 15th order of approximation. HAM contains an h-curve, allowing a flexible method of controlling the series solution convergence area. Graphs and tables are plotted to analyze the influence of different parameters on the fluid. Rates of heat and mass flux are depicted using tables. Our results indicate that the increasing viscoelastic flow enhances the boundary layer, and the thermal boundary layer reduces as radiation enhances. The numerical demonstrations of the wall drag coefficient, Nusselt number and Sherwood number have been tabulated. The growing parameters are taken as 0. 5 ≤ M ≤ 2. 0 , 0. 1 ≤ Ri ≤ 0. 7 , 0. 3 ≤ K 0 ≤ 0. 9 , 0. 5 ≤ f w ≤ 2. 0 , 1 ≤ Rd ≤ 4 , 0. 3 ≤ Pr ≤ 0. 9 and 0. 5 ≤ K 2 ≤ 2. 0. [ABSTRACT FROM AUTHOR]

Much attention has been focused on viscoelastic microfluidics which can be widely used for the focusing and separation of particles/cells in continuous flows without any external force or energy. In this study, we demonstrate that microparticles can be separated by the elasto-inertial focusing and the concentration gradient of viscoelastic fluid in a microchannel with a rhombic cross-sectional shape. We have already presented a simple and robust fabrication method for microchannel with the rhombic cross-section, which was used for particle focusing in viscoelastic polyethylene oxide (PEO) solution. Using the fabricated microfluidic device, we observed the behavior of particles by size in viscoelastic fluids with various concentration gradients and presented their focusing and separation. Separation experiments were performed on 12, 5.0, and 2.1 µm particles, and the optimal separation conditions were sought according to flow rate, sample-to-sheath flow rate ratio, and PEO concentration gradient. [ABSTRACT FROM AUTHOR]

Roll coating is a popular method for applying a thin coating film to a continuous substrate, such as paper or foil. This study aims to investigate analytically the fluid flow through counter rotating rolls using a non-Newtonian model. The governing equation for the constitutive of the Oldroyd-B as a non-Newtonian fluid with momentum equation has been discovered. The nondimensionalizing of the fluid flow equations is done by using suitable dimensionless parameters. The equations are then simplified by using Lubrication Approximation Theory (LAT) to obtain the solution for various quantities. Analytical solutions for the velocity distribution, pressure and pressure gradients have been obtained by regular perturbation method. Numerical integration has been used to calculate separation point, coating thickness, separation force and power input of the fluid. The effect of involved parameter such as Weissenberg number We and viscosity on velocities, pressure gradient and pressure is presented in a variety of graphs and several other results are shown in tables. It has been observed that as the modified capillary number N C a 2 increases, the separation point moves toward the nip region, whereas the coating thickness declines. It has been witnessed that the We serves as the controlling parameter for flow rate, pressure distribution and power input, whereas for the coating thickness, the separation force increases, which are important for coating industries. [ABSTRACT FROM AUTHOR]

[Display omitted] Harnessing electrical energy from salinity gradients, particularly for powering micro and nanoscale devices, has become a focal point of recent research attention, due to its renewable and biocompatible nature. Much of the reported research in that direction revolves around optimizing the membrane architecture and the charge distribution to maximize the induced electric potential, with no particular emphasis on the fluid rheology. However, many of the modern miniature systems, typically the bio-inspired ones, concern fluids with complex rheological characteristics, where the results for Newtonian solvents may not trivially apply. Here, we hypothesize that the interplay between interfacial electro-mechanics and the fluid rheology can influence the effectiveness of salinity-gradient-modulated electrokinetics significantly – an aspect that has largely remained overlooked. Here we report the first experiments supplemented by a theoretical model that unveil how that the addition of polymers in a solvent modulates the salinity gradient – induced electric potential in a microfluidic channel. Our theoretical framework considers the simplified Phan-Thien Tanner (sPTT) constitutive model, which represents the viscoelastic characteristics of fluids. Experiments were conducted with combined pressure driven and salinity gradient driven flow through microchannel involving dilute solutions of polyethylene oxide (PEO) of different molecular weights and concentrations to successfully validate the theoretical approach. Our findings indicate that the induced electrical potential increased non-linearly with the saline concentration ratio across the microchannel, as compared traditional linear response. Our results demonstrate how the elasticity of fluid may enable realizing an optimal benefit to this effect, by arresting the viscous resistance and uplifting the elastic response via utilizing polymeric inclusions of high relaxation times. These results provide specific insights on preferential windows of augmenting the induced streaming potential by harnessing the viscoelastic nature of the solution and the imposed salt concentration, bearing critical implications in miniature energy harvesting and desalination technology. [ABSTRACT FROM AUTHOR]

In this paper, the impact of slip condition, radiation, constant heat and mass flux subjected to chemical reaction on an unsteady viscoelastic periodic flow is investigated. Further, the effect of an inclined magnetic field, heat source and diffusive thermodynamics of incompressible and electrically conductive fluid are also analyzed. The governing non-linear partial differential equations are solved by perturbation method. The final expressions for flow variables and their corresponding gradients at lower plate y = 0 are furnished. It is observed that the diffusive thermo effect Df improves the velocity and reduces skin friction for large values, an angle of inclination ψ and heat source parameter Q enhance velocity while the viscoelastic parameter decreases the same. Df and Q have opposite effects on temperature and subsides the heat transfer for enlarged values, and it is also noted that the effects of Re, Sc, and Kr increase the mass transfer as seen in the plotted graphs. Additionally, the effect of non-dimensional parameters Gr, Re, Pe, N and H on flow variables and their gradients at y = 0 are portrayed by graph’s and subsequently discussed in detail. [ABSTRACT FROM AUTHOR]

This study examines the gravitational instability of a finitely conducting magnetized viscoelastic fluid, under the influence of radiation pressure within the framework of a generalized hydrodynamic fluid model. The general dispersion relation, valid for strongly and weakly coupled fluids under kinetic and hydrodynamic limits respectively, is derived using normal mode analysis for a transverse wave propagation mode. The obtained Jeans instability criteria, in terms of critical Jeans wavenumbers under both limits, are modified by the presence of radiative effects, viscoelastic compressional speed, and Alfvén wave velocity. The findings highlight that viscoelastic compressional speed and radiative pressure slow the Jeans instability's growth rate, exerting a stabilizing effect on the initiation of gravitational collapse. The present investigation provides valuable insights into the role of radiative mechanisms in the gravitational collapse within the strongly coupled region of molecular cloud clumps. [ABSTRACT FROM AUTHOR]

An exact similarity solution is worked out for fluid motion in the vicinity of a cylindrical surface in an electrically conducting viscoelastic fluid obeying the Jeffrey model. Cylindrical surface expands axially with linear velocity and has a prescribed surface temperature. The present analysis focuses on the partial slip assumption which gives rise to a nonlinear case Robin-type (mixed) boundary condition in axial velocity. In contrast to a previously published study (J. Mech., vol 31, pp. 69–78, 2015) which only reported local similarity solutions in no-slip case, the present work provides an exact similarity analysis by defining a quadratic surface temperature. The effects of the magnetic field and Joule heating on the momentum and thermal transport phenomena are also scrutinized. A numerical routine is used to solve the equation accurately for a wide range of fluid parameters, including ranges that could not be handled by previous approximate analytical methods that were limited to the no-slip limit. The influences of viscoelasticity and partial slip on the flow behavior are investigated, and the coefficient of skin friction for a Jeffrey fluid is calculated. Obtained results are consistent with the previously published works under special situations. The case of flat surface, which can be obtained as a limiting case of the model, is not even explored in the past. [ABSTRACT FROM AUTHOR]

This article is concerned with the boundary layer formations over a deforming plane heated surface in a viscoelastic fluid having temperature-dependent physical properties. Viscoelastic fluid obeys a well-accepted Jeffrey fluid model that characterizes both relaxation and retardation times phenomena. Mathematical modeling is performed by considering exponential variations in viscosity, thermal conductivity, relaxation time, and retardation time with temperature. Transport equations are formulated under the aforesaid assumption and are solved for self-similar solutions using a numerical scheme. Solutions are utilized to generate streamlines and isotherms in both Newtonian and viscoelastic fluids. The momentum and thermal layers are specifically scrutinized for various controlling parameters. Illustrative results are included reflecting the consequences of variable physical properties on the induced viscoelastic fluid motion and accompanying heat transfer. In addition, skin friction factor for Jeffrey fluid with variable properties is evaluated and described. [ABSTRACT FROM AUTHOR]

The combined heat and mass transfer, the so-called thermosolutal convective problem, has become an attractive field of research in many diversified areas. In this paper, for the first time, oscillatory flow analysis has been carried out for triple diffusive viscoelastic fluid flow in a porous medium. A comprehensive model is developed for the modified Darcy–Brinkman–Oldroyd-B fluid, porous medium, Boussinesq approximation, heat and mass transfer across a finite temperature and concentration difference in the chemical potential of two salts. Triple diffusive viscoelastic fluid flows through porous media have grown significantly as this situation occurs in more than a few applications such as improved oil recovery filtration, liquid complex molding, solidification of liquid crystals, cooling of metallic plate in a bath, exotic lubricants and colloidal solutions, polymer processing, chemical and bioengineering industries, among others. The governing coupled nonlinear partial differential equations with boundary constraints represent the modeled flow problem. In addition, these equations are converted into non-dimensional form by employing suitable non-dimensionalizing quantities. The impacts of the pertinent parameters and related dimensionless numbers on the dimensionless velocity, temperature, concentrations, shear stress, heat and mass transfer are examined for both suction and injection cases. It has been found that when the injection level on the heated plate is increased, the shear rate increases for each channel plate. Furthermore, we recognized that the viscoelastic parameters exhibit an opposite kind of behavior on the velocity, temperature, and concentrations fields. [ABSTRACT FROM AUTHOR]

Bacteria exhibit swimming behavior through the rotation of helical flagellar filaments, a common mode of propulsion for artificial micro-swimmers as well. However, most studies have focused on helical filaments with a uniform radius, leaving limited research on filaments with nonuniform radii. This paper presents a simulation of the hydrodynamics of a rotating helical filament with a nonuniform radius. The degree of nonuniformity is characterized by a radius ratio, β. Using the OpenFOAM platform, a simulation module for non-Newtonian Stokes flow was developed and integrated. The kinematics of the filament were predefined by fixing either the pitch or the helical angle, in addition to the helical radius. Thrust acting on the filament were analyzed with regards to the helical radius ratio, rotation speed, and fluid viscoelasticity. Certain modifications were made to apply the resistive force theory (RFT) to filaments with nonuniform helical radii. Results revealed that when the pitch was fixed, the thrust of the helix varied non-monotonically with the radius ratio, with excessive ratios leading to increased resistance. In contrast, helices with fixed helical angles exhibited an increasing thrust with a higher radius ratio. The thrust was greater in Newtonian fluids compared to non-Newtonian fluids, and the propulsion of the helix was influenced by the Deborah number. As the Deborah number approached zero, the thrust of viscoelastic swimming speed approached that of viscous swimming speed. For small, β (, β =1 and 4), the ratio of the thrust in viscoelastic fluid to the thrust in viscous fluid was always less than unity. At, β = 9, elasticity hindered propulsion at low De (De<1.5), while the opposite was observed at high De (De>1.5). A new approach was proposed to evaluate the impact of viscoelasticity on the helix, it was expected that the new calculation method can reduce the computational effort effectively. [ABSTRACT FROM AUTHOR]

In this paper, a novel analytical approach based on nonlocal strain gradient theory is proposed to investigate small-scale effects on the radial vibration of isotropic spherical nanoparticles interacting with a viscoelastic fluid. The viscoelastic fluid is assumed to be compressible and takes into account both compressional and shear relaxation processes. The frequency equation is derived by imposing the fluid-nanosphere interface continuity conditions. To demonstrate the validity and accuracy of the approach, a comparison is made with the literature results in some particular cases, which shows a good agreement. Numerical examples are finally conducted to reveal the significance of small-scale effects in the radial vibrations, which need to be included in the nonlocal strain gradient model of submerged spherical nanoparticles. It is found that the vibration behavior greatly depends on the nanosphere size, nonlocal parameter, strain gradient parameter and glycerol-water mixture. Particularly, the small-scale effects play a very pronounced role when the spherical gold nanoparticle radius is smaller than 3 nm. Thus, the obtained frequency equation is very useful to interpret the experimental measurements of vibrational characteristics of nanospheres submerged in a viscoelastic fluid. [ABSTRACT FROM AUTHOR]

The Saffman‐Taylor instability of polymeric fluids flooding through saturated heterogeneous porous media is studied numerically. The displacement of a Newtonian fluid by a viscoelastic liquid is examined using a Hartley transformation and a fourth‐order Adams‐Bashforth technique. The flow is assumed to be miscible, and the Carreau‐Yasuda equation is used to model the shear‐thinning viscometric functions. The effects of different rheological properties and domain parameters on flow instability are studied in detail. It is found that a channeling regime is possible as the main difference between displacements through homogeneous and heterogeneous media. [ABSTRACT FROM AUTHOR]

The injection of a fluid into another fluid causes a spatiotemporal pattern along the injection front. Viscous fingering is a well-known example when the replaced material is a viscous fluid. Notably, most fluids are, in reality, viscoelastic, i.e., they behave as an elastic solid over short timescales. For this reason, it is important to study the situation when the replaced fluid is viscoelastic. In this study, we observed a dynamics of fluids when an incompressible organic liquid was injected into an oleophilic Hele-Shaw cell filled with an aqueous viscoelastic fluid made of a wormlike micellar solution. We found extensive tip splitting of the injection front, which led to thin fingers with a characteristic size comparable to four times the cell thickness. We examined the material properties and suggest that the thin fingering pattern observed in our system is due to the delamination of viscoelastic fluid from the bottom substrate surface. Our result shows that the effect of interfacial energy in the existing solid layer should be considered in the injection process. [ABSTRACT FROM AUTHOR]

Log-Conformation Representation (LCR) method effectively enhances the stability of viscoelastic fluid flow driven by a cavity at high Wi numbers. However, its stability is relatively poor under low viscosity ratio conditions. In this study, three momentum equation stabilization algorithms (Both-Sides-Diffusion, Discrete Elastic Viscous Split Stress-Vorticity, and velocity–stress coupling) were tested and compared in OpenFOAM to assess their stabilizing effects on the LCR method under low viscosity ratio conditions. The evaluation was based on changes in average kinetic energy and the maximum critical time step. The results indicate that the different momentum equation stabilization algorithms improve the numerical oscillations observed in the numerical simulation of low viscosity ratio cavity-driven flow to varying extents. This enables a reduction in the viscosity ratio that can be stably simulated by 0.03 to 0.15. Furthermore, these cases using the momentum equation stabilization algorithms require time steps that are 33% to 100% shorter than those of the original cases. This demonstrates the promoting effect of the additional diffusion term in the momentum equation on stability under low viscosity ratio conditions. The combination of LCR and velocity–stress coupling was used to analyze the impact of viscosity ratios on velocity, logarithmic conformation tensor, and average kinetic energy. As the viscosity ratio decreases, the contribution of fluid elasticity increases, resulting in more pronounced variations in velocity and stress. However, the viscosity ratio has little effect on the stress boundary layer at the top cover and corners. Under conditions with the same Wi number, the average kinetic energy decreases as the viscosity ratio decreases until stability is achieved. [ABSTRACT FROM AUTHOR]

The oscillating flow of the viscoelastic fluid‐saturated porous layer has been useful in many areas, including the petroleum, chemical, and bioengineering industries. It is studied using the modified Darcy‐Oldroyd‐B model in this article. The exact solution is obtained utilizing a simpler and more reasonable method. According to this velocity solution, the time‐velocity profile of one kind of viscoelastic fluid is analyzed. From the analysis, it was found that the flow behaves like the Newton fluid when the oscillating frequency is low, and the flow reversal occurs when the oscillating frequency is high. Further, velocity, temperature, shear stress, and the rate of heat transfer are exponential solutions that are obtained and analyzed for different values of known physical parameters. Finally, we recognize that the relaxation and retardation parameters in this model act in the opposite manner. [ABSTRACT FROM AUTHOR]

We have exploited the Oldroyd-B model to explain the appearance of stationary and oscillatory convection in a viscoelastic magnetic fluid saturating a porous horizontal layer heated from below. The analytical expressions of the Rayleigh number corresponding to each convection are determined as a function of dimensionless parameters. We note that the appearance of steady convection does not depend on the viscoelastic properties of the fluid. Using numerical simulations, we analysed the stabilising effect of each dimensionless parameter on the evolution of the convection and on the size of the convection cells formed. We note that in the oscillatory convection case, the values of the Darcy number, the parameter characterising the permeability of the medium, are low compared to those of stationary convection. The behaviour of the critical frequency for oscillatory convection is studied. The possibility of co-dimension-2 bifurcation is discussed and the boundary between the oscillatory and stationary convections is found. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel, simple and accurate analytical study based on nonlocal elasticity theory to forecast small-scale effects on the radial vibration of anisotropic gold nanospheres submerged in viscoelastic fluid (VEF). Eringen's model is used to determine the motion equation for anisotropic nanospheres, with the fluid assumed to be viscoelastic and compressible. The frequency equation is derived by imposing the fluid-nanosphere interface continuity conditions. A comparison with the literature results is conducted to demonstrate the validity and correctness of this analysis, which indicates a very good agreement. The importance of small-scale effects in the radial vibration, which need to be included in the nonlocal elasticity model of submerged nanospheres, is eventually revealed by numerical examples. It is discovered that the nanosphere size, nonlocal parameter, and glycerol–water mixture have a significant impact on the vibration behaviors. Our results show that the small scale is crucial for the radial vibration of gold nanoparticles when the gold nanosphere is smaller than 5. 5 nm. Thus, the resulting frequency equation is very useful to interpret experimental measurements of the vibration characteristics of submerged gold nanospheres in VEF. [ABSTRACT FROM AUTHOR]

This article is devoted to the investigation of the weak solvability to the initial boundary value problem, which describes the viscoelastic fluid motion with memory. The memory of the fluid is considered not at a constant position of the fluid particle (as in most papers on this topic), but along the trajectory of the fluid particle (which is more physical). This leads to the appearance of an unknown function z, which is the trajectory of fluid particles and is determined by the velocity v of a fluid particle. However, in this case, the velocity v belongs to L 2 (0 , T ; V 1) , which does not allow the use of the classical Cauchy Problem solution. Therefore, we use the theory of regular Lagrangian flows to correctly determine the trajectory of the particle. This paper establishes the existence of weak solutions to the considered problem. For this purpose, the topological approximation approach to the study of mathematical hydrodynamics problems, constructed by Prof. V. G. Zvyagin, is used. [ABSTRACT FROM AUTHOR]

The existence of weak solutions of the initial-boundary value problem for the equations of motion of a viscoelastic fluid with memory along trajectories of a nonsmooth velocity field and with an inhomogeneous boundary condition is proved. The study relies on Galerkin-type approximations of the original problem followed by passage to the limit based on a priori estimates. The theory of regular Lagrangian flows is used to examine the behavior of trajectories of a nonsmooth velocity field. [ABSTRACT FROM AUTHOR]

In this study, we investigated the particle separation phenomenon in a microchannel with a T-shaped cross-section, a unique design detailed in our previous study. Utilizing a co-flow system within this T-shaped microchannel, we examined two types of flow configuration: one where a Newtonian fluid served as the inner fluid and a viscoelastic fluid as the outer fluid (Newtonian/viscoelastic), and another where both the inner and outer fluids were Newtonian fluids (Newtonian/Newtonian). We introduced a mixture of three differently sized particles into the microchannel through the outer fluid and observed that the co-flow of Newtonian/viscoelastic fluids effectively separated particles based on their size compared with Newtonian/Newtonian fluids. In this context, we evaluated and compared the particle separation efficiency, recovery rate, and enrichment factor across both co-flow configurations. The Newtonian/viscoelastic co-flow system demonstrated a superior efficiency and recovery ratio when compared with the Newtonian/Newtonian system. Additionally, we assessed the influence of the flow rate ratio between the inner and outer fluids on particle separation within each co-flow system. Our results indicated that increasing the flow rate ratio enhanced the separation efficiency, particularly in the Newtonian/viscoelastic co-flow configuration. Consequently, this study substantiates the potential of utilizing a Newtonian/viscoelastic co-flow system in a T-shaped straight microchannel for the simultaneous separation of three differently sized particles. [ABSTRACT FROM AUTHOR]

Copyright of Acta Scientiarum Naturalium Universitatis Sunyatseni / Zhongshan Daxue Xuebao is the property of Sun-Yat-Sen University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Medium exchange of particles/cells to a clean buffer with a low background is essential for biological, chemical, and clinical research, which has been conventionally conducted using centrifugation. However, owing to critical limitations, such as possible cell loss and physical stimulation of cells, microfluidic techniques have been adopted for medium exchange. This study demonstrates a continuous on-chip washing process in a co-flow system using viscoelastic and Newtonian fluids. The co-flow system was constructed by adding a small amount of biocompatible polymer (xanthan gum, XG) to a sample containing particles or cells and introducing Newtonian fluids as sheath flows. Polymer concentration-dependent and particle size-dependent lateral migration of particles in the co-flow system were examined, and then the optimal concentration and the critical particle size for medium exchange were determined at the fixed total flow rate of 100 μL/min. For clinical applications, the continuous on-chip washing of white blood cells (WBCs) in lysed blood samples was demonstrated, and the washing performance was evaluated using a scanning spectrophotometer. [ABSTRACT FROM AUTHOR]

Copyright of Polymer Materials Science & Engineering is the property of Sichuan University, Polymer Research Institute and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Present article aims at developing similarity solutions for heat transportation in swirling flow of viscoelastic fluid (obeying Jeffrey model) generated by an infinite porous rotating surface. The resulting thermal energy equation comprising frictional heating and Ohmic dissipation terms is mainly focused. Relevant equations simplified under boundary layer approximations have been solved analytically by a powerful homotopy based analytical scheme, while numerical solutions are constructed by a reliable MATLAB solver bvp4c. For homotopy based series solutions, total squared residual of the system is evaluated, and it is found to decline for increasing order of approximations. Both applied methods are shown to be in compliance with each other for wide range of viscoelastic fluid parameters. Computed solutions are utilized to understand the combined influence of viscoelasticity and viscous dissipation on heat transport phenomena associated with the Von-Kármán configuration. Subtle fluid dynamics entities such as resisting torque and Nusselt number are computed and elaborated. Results predict that the torque required by the disk drastically reduces when viscoelastic fluid assumption is applied. However, cooling rate of the disk in Newtonian fluid is better than that in viscoelastic fluid. Present results are found in agreement with that of the previous studies in a limiting situation. [ABSTRACT FROM AUTHOR]

This paper focuses on the spectral analysis of equations that describe the oscillations of a heavy pendulum partially filled with a homogeneous incompressible viscoelastic fluid. The constitutive equation of the fluid follows the simpler Oldroyd model. By examining the eigenvalues of the linear operator that describes the dynamics of the coupled system, it was demonstrated that under appropriate assumptions the equilibrium configuration remains stable in the linear approximation. Moreover, when the viscosity coefficient is sufficiently large the spectrum comprises three branches of eigenvalues with potential cluster points at 0 , β and ∞ where β represents the viscoelastic parameter of the fluid. These three branches of eigenvalues correspond to frequencies associated with various types of waves. This paper focuses on the spectral analysis of equations that describe the oscillations of a heavy pendulum partially filled with a homogeneous incompressible viscoelastic fluid. The constitutive equation of the fluid follows the simpler Oldroyd model. By examining the eigenvalues of the linear operator that describes the dynamics of the coupled system, it was demonstrated that under appropriate assumptions the equilibrium configuration remains stable in the linear approximation. Moreover, when the viscosity coefficient is sufficiently large the spectrum comprises three branches of eigenvalues with potential cluster points at , and where represents the viscoelastic parameter of the fluid. These three branches of eigenvalues correspond to frequencies associated with various types of waves. [ABSTRACT FROM AUTHOR]

In this article, we investigate an optimal control problem for the coupled system of partial differential equations describing the steady-state flow of a corotational-type Oldroyd fluid through a bounded 3D (or 2D) domain. The control function is included in Dirichlet boundary conditions for the velocity field; in other words, we consider a model of inflow–outflow control. The main result is a theorem that states sufficient conditions for the solvability of the corresponding optimization problem in the set of admissible weak solutions. Namely, we establish the existence of a weak solution that minimizes the cost functional under given constraints on controls and states. [ABSTRACT FROM AUTHOR]

The viscoelastic materials are a famous subclass of non-Newtonian fluids that present novel applications in various industrial processes. The most famous applications of viscoelastic fluid are observed in polymer processing. A major activity of the polymer processing industry is the production of thermoplastic polymer sheets and films. However, due to distinct rheology, a complete understanding of such materials is quite necessary for the polymer process. This continuation presents the rheological features of viscoelastic fluid with heat transfer phenomenon near the oblique stagnation point flow. The induced flow is accounted via stretched cylinder. The heat transfer analysis is also taken in the presence of non-linear heat flux. The problem is formulated using cylindrical coordinates in terms of non-linear coupled partial differential equations. Similarity transformation and normalized variables are used to convert the governing system into a set of ordinary differential equations. Due to the highly nonlinear model, the analytical solution of the system seems to be impossible therefore the approximate solution is obtained using the numerically stable and convergent finite difference method known as the Keller Box scheme. The simulated data via numerical algorithm is verified after comparing with already published investigations. The streamlines for the flow problem are presented. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The VOF method was used to numerically study the upward motion of a single bubble in viscoelastic fluid, and the Oldroyd-B model was applied to describe the fluid viscoelastic property. At low Weissenberg numbers (Wi≤1), the effects of the viscous force, the relaxation time, the surface tension and the viscosity ratio on the rising motion of the bubble were studied. The results show that, under relatively large viscous and elastic forces (such as Ga=2, Wi≥0.5 and β=0.2), the bubble exhibits the phenomenon of "a pointed rear end", and this phenomenon intensifies with the increase of the elasticity and the decrease of the surface tension. Otherwise, under a relatively weak elasticity (such as Wi=0.1), the phenomenon of "a pointed rear end" disappears, and the bubble bears a hat-like shape. For a large surface tension (such as Eo=1), the bubble bears a longitudinally elongated ellipse-like shape without distinct tail features. The effect of the surface tension on the bubble in viscoelastic fluid is like that in viscous fluid. The bubble has 2 types of rising motions, namely, "continuous acceleration" to a stable velocity and "acceleration-deceleration-reacceleration" to a stable velocity, and the bubble rising velocity in viscoelastic fluid is higher than that in pure viscous fluid. The elastic stress around the bubble is influenced by the viscosity and the relaxation time of the fluid, and with the decrease of the fluid viscosity or/and the increase of the relaxation time, the incidence of the elastic stress becomes wide. [ABSTRACT FROM AUTHOR]

This paper deals with the effect of thermo-diffusion on unsteady MHD oscillatory flow of viscoelastic fluid in an asymmetric wavy channel when a magnetic field and heat source are applied externally. The need for this study derives from the fact that most industrial fluids exhibit viscoelastic behavior. The dimensionless equations governing the fluid flow properties with respect to the boundary conditions are solved analytically and exact solutions obtained. Increasing values of viscoelastic parameter. Hartmann number and chemical reaction parameter reduce the fluid velocity profile. while the radiation parameter. thermo-diffusion effect and influence of the heat source enhance the fluid flow. The in fluence of flow parameters on velocity, temperature. and concentration profiles. skin friction coefficient. heat and mass transfer rate is discussed and graphically depicted. The values of skin friction coefficient and mass transfer rate for various physical parameters are tabulated. Finally. the findings of the current study have been compared to those of earlier studies. The comparison is seen to bear a good agreement. [ABSTRACT FROM AUTHOR]

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Analysis of a time‐independent magnetohydrodynamic viscoelastic fluid flow in a deformable inclined porous layer with first‐order chemical reaction has been investigated. Walters' fluid model has been used to study viscoelastic fluid. The walls are suctioned/injected at a constant rate. The expression representing the solution for solid displacement, fluid velocity, temperature, and concentration distribution is obtained. The effect of applicable parameters on solid displacement, fluid velocity, temperature, and concentration are discussed graphically, while skin friction, heat transfer, and mass transfer are revealed in a tabular structure. It is noticed that solid displacement, fluid velocity, and temperature profiles decrease when the viscoelastic parameter increase. Solid displacement enhances and the velocity of the fluid reduces owing to the influence of increasing drag parameter, whereas the reverse effect is seen for the volume fraction parameter. Nusselt number at the walls shows the opposite behavior for the viscoelastic parameter and Eckert number. Sherwood number at the walls shows opposite behavior for Reynolds number, Schmidt number, and radiation parameter. Also, the entropy generation number rises as a result of the influence of viscoelasticity and Eckert number. [ABSTRACT FROM AUTHOR]

The purpose of the current investigation is to analyze the influence of thermal diffusion on magnetohydrodynamic viscoelastic fluid flow with concurrent heat and mass transfer near an oscillating porous plate in a slip flow Regime under the influence of a uniform transverse magnetic field. The uniqueness of the present study is to examine the effects of viscoelastic property (Walters B' model) on the flow and heat transfer phenomena when a transverse magnetic field and time‐dependent fluctuating suction at the boundary surface are present in a porous medium with a uniform porous matrix. A regular perturbation technique is used to solve the governing equations for small elastic parameters. Graphical representations are used to show how different parameters affect skin friction, temperature, concentration, and velocity. It is observed that concentration distribution as well as the coefficient of friction is enhanced due to the thermal diffusion effect. It is noticed that the visco‐elastic parameters reduce the velocity of the fluid. In addition, chemical reactions and suction factors cause the flow field's temperature to drop. Furthermore, the fluid concentration drops under the chemical reaction effect. [ABSTRACT FROM AUTHOR]

The present analysis mathematically investigates the thermohaline convection problem in viscoelastic fluid layer saturating porous media by utilizing the modified Boussinesq approximation. By performing linear stability analysis, the Darcy–Rayleigh numbers for stationary and oscillatory modes of convection are derived. The effects of different parameters describing the problem are studied numerically. In nonlinear stability analysis, the heat and mass transfer rates in the form of Nusselt and Sherwood numbers, respectively, are obtained for oscillatory convection using the derived Ginzburg–Landau equation. From the results, it is observed that overstability is the preferred mode of instability in linear stability. It is found that in linear double‐diffusive convection problems, the stress relaxation imparts a destabilizing effect whereas the strain retardation time, the coefficient of specific heat variation due to temperature, and the concentration gradient have a stabilizing effect on the system's stability. The numerical values of heat and mass transfer rates varied with the coefficient of specific heat showing that the heat transport decreases while the mass transport increases. Also, the stress relaxation time, the concentration gradient, and the gravity modulation's amplitude increase while the strain retardation time decreases the heat and mass transfer rates. The wavelength of oscillations remains unaltered with the variation of specific heat variation due to temperature. The modulation frequency does not affect the heat/mass transfer rate; though, the wavelength of oscillations decreases with increasing frequency. [ABSTRACT FROM AUTHOR]

The interface of viscous-Rivlin-Ericksen fluids is analyzed through the linear theory of stability analysis when mass and heat is transferring across the interface. The Rivlin-Ericksen fluid lies in the upper region while the lower region of the interface contains viscous fluid. The gravitational acceleration destabilizes the top-heavy arrangement and interface instability is governed by Rayleigh-Taylor instability. The two-dimensional interface is considered, and the viscous potential flow theory is employed to establish the relationship between perturbation's growth and wave number. This relationship is analyzed, and the perturbation's growth is plotted for various flow parameters. A marginal stability condition is obtained, and it is given in terms of heat transport coefficient Λ and wave number. The marginal stability criterion is analyzed using the well-known Newton-Raphson method. The heat and mass transfer phenomenon drives the unstable interface toward stability. It is pointed out that the viscoelastic coefficient λo influences the interface to be stable while the thickness of the viscoelastic fluid makes the interface unstable. Atwood numbers and Weber numbers show destabilizing behavior. [ABSTRACT FROM AUTHOR]

This work derives an approximate solution of the laminar viscoelastic fluid flow through a parallel flat plate microchannel, driven by electroosmotic and external pressure forces. In contrast to other works published in the past, in the present analysis, the fluid's rheology obeys the generalized Phan–Thien–Tanner model that has been proposed recently, which uses the Mittag-Leffler function instead of linear or exponential functions of the trace for the stress tensor. The hydrodynamic analysis considers a non-linear Navier slip law at the wall that follows a power-law behavior on the shear stress. For the electric potential in the electric double layer, the Debye–Hückel approximation was used, and it is assumed that the wall's zeta potentials are symmetric. The solution obtained in this work depends on several dimensionless parameters that allow controlling the flow: ɛ W i 2 characterizes the fluid's viscoelasticity, the electrokinetic parameter κ ̄ , the dimensionless slip coefficient L ̄ , the slip-power exponent m , and the ratio between pressure and electroosmotic forces, G. Besides, the influence of two parameters of the Mittag-Leffler function, α and β , notably affects the flow's characteristics. Our results evidence the important consequences of considering the generalized Phan–Thien–Tanner model and the slippage effect on the flow field compared to that described by the Phan–Thien–Tanner model. • Electroosmotic/pressure-driven flow of a viscoelastic fluid is studied. • The generalized Phan–Thien–Tanner model is considered as the rheological model. • The Nonlinear Navier slip was used as boundary condition. • Mittag-Leffler function parameters influence notably on the fluid flow. • Slip coefficients at the wall may increase up to two orders the volumetric flow rate. [ABSTRACT FROM AUTHOR]

The steady‐state laminar nonisothermal, incompressible viscoelastic fluid flows with the Jeffrey model between two counterrotating (same direction) rolls are studied analytically. The Jeffrey model is reduced to the Newtonian model after some appropriate modifications. The new dimensionless governing equations are acquired through suitable nondimensional values. The lubrication approximation theory is employed for the simplification of emerging equations. The exact expressions for pressure gradient, velocity, temperature, and flow rate are accomplished whereas some quantities of interest such as pressure, coating thickness, power transmitted by rolls to the fluid, and roll separation force are computed numerically by using a numerical method. The influence of emerging parameters such as the ratio of relaxation time to the retardation time λ1 ${\lambda }_{1}$, magnetohydrodynamic (MHD) parameter M $M$ and Brinkman number Br $Br$ on velocity profile, temperature profile, pressure gradient, pressure distribution, coating thickness, power input, and force of roll separation are presented numerically in a tabular way and specific outcomes are demonstrated graphically. The MHD acts as a regulatory parameter for various quantities of important interest, such as velocity, coating thickness, and temperature. It is worth noting that the coating thickness decreases as modified capillaries number is increased. [ABSTRACT FROM AUTHOR]

We construct weak solutions to the 3D hypoviscous incompressible elastodynamics with finite kinetic energy which was unknown in literatures. Our result holds for fractional hypoviscosity (− Δ) θ , where 0 ≤ θ < 1. The proof consists of a convex integration scheme with new building blocks of 2D intermittency and suitable temporal correctors, which are motivated by the inherent geometric structure of the viscoelastic equations. [ABSTRACT FROM AUTHOR]

The two-dimensional laminar boundary layer flow of viscoelastic fluid over a moving/static wedge, in the porous matrix, subjected to a uniformly applied magnetic field is studied to investigate the interplay of viscoelastic fluid and moving wedge. The viscoelastic fluid in the boundary layer is modelled using Walters' liquid B fluid which describes the gradually fading memory. The wedge is allowed to move in the same/or opposite direction to that of mainstream flow, and the fluid flow vertically through the wedge is also taken into account. The resultant governing equation, obtained with the help of appropriate similarity transformations, is analysed numerically using the Keller-box method. The general features of the investigated physical solutions are the continuation of a Newtonian fluid, the effect of Walters' liquid B fluid and the pressure gradient to enhance the velocity and decrease the thickness of the boundary layer. Analysis of the boundary layer flow of viscoelastic fluid along with the magnetic field and porous medium unveils single and double solution structures. We noticed an additional solution in the boundary layer for the same set of parameters. Naturally, there exists a critical point beyond which even a single solution does not exist. As the combination of magnetic and permeability parameters is increased, both solutions coalesce into one, thereby yielding a single solution to the model. The linear stability analysis is also performed on the dual solutions, and it reveals that the first solution is always practically realizable. Further, when the velocity ratio parameter is taken sufficiently large, the present model reduces to the flow situation in which the boundary layer forms due to a stretching sheet in a still fluid, and the corresponding equation is solved using an exponentially decaying series solution. Both results are shown to be compared well with each other and existing results in the literature. The interesting flow phenomena are discussed in detail. [ABSTRACT FROM AUTHOR]

This paper studies the combined effects of radiation and galactic cosmic ray pressures on the gravitational instability of magnetized and rotating viscoelastic fluids. The dispersion relations are derived using the normal mode analysis and discussed in the hydrodynamic (weakly coupled fluid) and kinetic (strongly coupled fluid) limits. These dispersion relations are analyzed separately for transverse and longitudinal wave propagation modes. Jeans instability criteria are obtained for kinetic and hydrodynamic limits for both modes of wave propagation, and it is found that the critical Jeans wavenumbers in each case are modified due to the presence of viscoelastic effects, radiation and cosmic rays pressures, and Alfvên wave velocity. It is also observed that the radiation pressure, cosmic ray pressure and viscoelastic parameters suppress the growth rate and thus have stabilizing effects on the Jeans instability. However, cosmic ray diffusion has a destabilizing effect on the onset of gravitational instability. The effects of various parameters on the growth rate of instability are calculated numerically and the outcomes are depicted graphically. The results of the present analysis shall be helpful in understanding the impact of cosmic rays and radiative mechanisms on the gravitational collapse in the viscoelastic region of molecular cloud clumps. • The effects of radiation and CR pressures on GI of viscoelastic fluid are studied. • Jeans wavenumber is modified due to both pressures in each mode of wave propagation. • Radiation pressure, CR pressure and viscoelasticity decrease the growth rate of GI. • Results shall be useful in analyzing CR and radiative mechanisms in molecular clouds. [ABSTRACT FROM AUTHOR]

The present study is aimed at inspecting magnetohydrodynamic (MHD) viscoelastic hybrid nanofluid flow over circular stretched cylinder. We consider here alumina and silver as nanoparticles with base fluid carboxymethyl cellulose solution. The effect of heat source, heat radiation, and activation energy are taken into account. Moreover, with small Reynolds number, the induced magnetic field has no noticeable effect. The leading dimensional equations are converted to dimension-free form by employing similarity transformations. The converted equations are calculated by using MATLAB bvp4c numerical method. Graphs and tables are used to analyze velocity, skin friction, temperature, heat-mass transport rate, and concentration for numerous physical factors. Observation reflects that viscoelastic and curvature parameters enhance velocity profile. Moreover, heat source enhances fluid temperature. It is clearly reflected that volume fraction parameter for alumina and silver enhances the heat transport’s rate. The mass transport’s rate reduces for Arrhenius energy parameter. The present work compares to prior work without considering the newly added effects and finds consistent findings. [ABSTRACT FROM AUTHOR]

• Mixed convection for a viscoelastic fluid within a square enclosure containing a rotating cylinder was numerically simulated. • The Phan-Thien-Tanner (PTT) model was used to describe the viscoelastic fluid behavior via the OpenFOAM software. • The numerical divergence at high Weissenberg numbers was addressed using a log-conformation approach. • Elevating the Weissenberg number reduced the frictional torque by 54 % and raised the Nusselt number from −1.33 to 3.32. • As the Weissenberg number increased from 1 to 100, there was a significant decline in the tangential normal stress. This paper for the first time conducted numerical simulations for the mixed convective flow and heat transfer with a viscoelastic fluid within a square enclosure containing a rotating cylinder. The flow regime was considered laminar, two-dimensional, and transient, and the Phan-Thien-Tanner (PTT) model, recognized as one of the most accurate nonlinear models for viscoelastic fluids, was used to describe the viscoelastic fluid behavior, mathematically. Solving nonlinear fluid equations, predicting the complex properties of viscoelastic fluids using the constitutive equation of the PTT model, and considering viscous dissipation were the challenges of this research. Additionally, the paper addressed the numerical divergence at high Weissenberg numbers using a log-conformation approach based on a logarithmic variable change in the polymer stress equation. The effects of the Richardson, Weissenberg, and Brinkman numbers and the ratio of polymeric viscosity to total viscosity on fluid flow and heat transfer were investigated by solving the nonlinear equations via the finite volume method. This was accomplished using the rheoHeatFoam solver within the OpenFOAM software. Local and average heat transfer characteristics around the rotating cylinder were fully studied. The results showed that elevating the Weissenberg number enhances the shear-thinning effect and diminishes the effective viscosity of the fluid by 63 %, resulting in a 54 % reduction in both the shear stress around the cylinder and the frictional torque applied to it, as well as a decrease in the viscous dissipation. Furthermore, increasing the Weissenberg number raised the Nusselt number from -1.33 to 3.32, signifying a complete reversal in the direction of heat transfer. However, the shear-thinning effect became negligible when the Weissenberg number exceeded 100. Moreover, the tangential normal stress significantly increased with an increase in the Weissenberg number up to one. However, as the Weissenberg number increased from 1 to 100, there was a significant decline in the tangential normal stress. Consequently, at very high Weissenberg numbers, the tangential normal stress approached zero, resembling a Newtonian fluid. [ABSTRACT FROM AUTHOR]

In this paper, we study two problems describing small motions of partially dissipative hydraulic systems. The first problem concerns small motions of a hydraulic system consisting of a viscoelastic fluid and a barotropic gas located above the fluid; the second concerns small motions of the hydraulic system "viscoelastic fluid–ideal fluid–ideal fluid" in an immovable vessel. Using the operator approach developed in previous works of the authors, we reduce both problems to the Cauchy problem for a differential-operator equation in a Hilbert space and prove a theorem on the solvability of the problem on an arbitrary finite time interval. [ABSTRACT FROM AUTHOR]

The process of heat transfer that involves non-Newtonian fluids in porous regions has attracted considerable attention due to its practical application. A mathematical model is proposed for monitoring fluid flow properties and heat transmission in order to optimize the final output. Thus, this attempt aims to demonstrate the behavior of fluid flow in porous regions, using the Brinkman viscoelastic model for combined convective transport over a sphere embedded in porous medium. The governing partial differential equations (PDEs) of the proposed model are transformed into a set of less complex equations by applying the non-dimensional variables and non-similarity transformation, before they are numerically solved via the Keller-Box method (KBM) with the help of MATLAB software. In order to validate the model for the present issue, numerical values from current and earlier reports are compared in a particular case. The studied parameters such as combined convection, Brinkman and viscoelastic are analyzed to obtain the velocity and temperature distribution. Graphs are used to illustrate the variation in local skin friction and the Nusselt number. The results of this study showcase that when the viscoelastic and Brinkman parameters are enlarged, the fluid velocity drops and the temperature increases, while the combined convection parameter reacts in an opposite manner. Additionally, as the Brinkman and combined convection parameters are increased, the physical magnitudes of skin friction and Nusselt number are increased across the sphere. Of all the parameters reported in this study, the viscoelastic parameter could delay the separation of boundary layers, while the Brinkman and combined convection parameters show no effect on the flow separation. The results obtained can be used as a foundation for other complex boundary layer issues, particularly in the engineering field. The findings also can help researchers to gain a better understanding of heat transfer analysis and fluid flow properties. [ABSTRACT FROM AUTHOR]

In this study, an analysis of the rotating flow of viscoelastic Oldroyd-B fluid along with porous medium featuring the Soret–Dufour effects is explored. The heat transport mechanism is discussed with the involvement of thermal radiation and heat source/sink. Additionally, the thermophoresis of particle deposition and chemical reaction are taken into the concentration equation in order to investigate the mass transportation in the liquid. To formulate the non-linear ordinary differential equations, the von Karman similarity approach is used in the system of partial differential equations and then integrated numerically by the bvp midrich scheme in Maple programming. Results are provided by graphical framework and tabular form. A quick parametric survey is carried out concerning flow field, thermal, and solutal distributions through graph representation. The curves show that increasing the values of the retardation time parameter decreases the radial velocity while increasing the angular velocity. Additionally, when the relaxation time parameter becomes powerful, the magnitude of the velocity curves decreases considerably in the radial and axial directions. The presence of a radiation parameter indicates that the fluid will absorb a greater amount of heat, which is equivalent to a higher temperature. Further, an increase in the stretching parameter leads to a reduction in the temperature components. [ABSTRACT FROM AUTHOR]

Droplet breakup in microconstrictions is an important phenomenon in industrial applications. This work aimed to investigate the droplet breakup in the square microchannel with a short square constriction to generate the slug flow, which drew little attention before. Mechanism analysis indicated that this breakup process included the shear‐force‐dominated, squeezing‐force‐dominated, and pinch‐off stages. Nonuniform daughter droplets were generated in the constriction with their interface restricted in the horizontal and perpendicular directions by the microchannel walls. The average relative deviation of the daughter droplet size was <30%, much lower than that for the breakup with the daughter droplet restricted only in one direction. An empirical equation with a deviation of <20% was provided to show the dependence of the daughter droplet size on the operation conditions. The comparison results suggested that the different restriction effects of microchannel wall on daughter droplets led to the different breakup mechanisms in different constrictions. [ABSTRACT FROM AUTHOR]

Here, an investigation of MHD Couette flow of a chemically reacting viscoelastic fluid past a deformable porous layer with entropy generation using Walters liquid model has been considered. A binary, homogeneous, and isotropic mixture of fluid and solid phases in the porous medium is considered. The impact of heat source parameter and Soret effect are taken into account. The governing equations are solved analytically to obtain the expressions for solid displacement, fluid velocity, temperature, and concentration. The impact of relevant parameters on the flow system, temperature, concentration, mass transfer flux, entropy generation number, and Bejan number are discussed graphically. It is observed that solid displacement enhances due to the growth of drag and viscoelastic parameter, while it reduces due to rising volume fraction parameter. Fluid velocity rises when the volume fraction parameter increases. Rising Brinkmann number enhances the temperature, while Brinkmann number and Soret number reduces the species concentration. The irreversibility of heat transfer dominates the flow near the channel plates, while the effect of fluid friction irreversibility can be observed within the channel centerline region. [ABSTRACT FROM AUTHOR]

This paper reports the manipulation of elastic instability of the viscoelastic fluid in a rhombus cross microchannel (RCM) structure. The bistable instability and unsteady instability of the flow is firstly demonstrated in a standard cross microchannel (SCM) for reference. We then keep the bi-stable instability over a much wider injection rate range in the RCM, which is attributed to the stabilizing effect of the rhombus structure. A semi-bistable instability was also established in the RCM at a high enough injection rate. In addition, the unsteady elastic instability is realized in the RCM through an asymmetric injection rate condition. [ABSTRACT FROM AUTHOR]

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. • A non-monotonic trend is present in the mixing of viscoelastic fluids in a wavy micromixer. • A more feasible way to increase the mixing to increase the number of turns than decrease the wavelength. • Shear-thinning properties of viscoelastic fluids have a tendency to suppress the mixing efficiency. [ABSTRACT FROM AUTHOR]

Few simulations currently explore the dynamics of microswimmers swimming through viscoelastic environments. In this study, we employ a direct-forcing fictitious domain method to investigate the collective behavior of spherical squirmers within viscoelastic fluids at low Reynolds numbers. Our findings reveal clear differences between pusher and puller swimmers: puller swimmers exhibit a tendency to aggregate into clusters, particularly noticeable in suspensions with high concentrations, which increases the average speed of the swimmers. Through an analysis of the cluster-size distribution function, we observe the larger-scale clusters of puller swimmers with increasing concentration. Moreover, the presence of fluid elasticity significantly reduces both the average swimming speed of squirmers and the fluid's kinetic energy. • The collective dynamics of squirmers in viscoelastic fluids are analyzed by using fictitious domain method. • Large-scale clusters are observed only in highly concentrated puller suspensions. • The clustering of puller squirmers enhances their swimming speed. • Fluid elasticity reduces the average swimming speed of squirmers and fluid kinetic energy. [ABSTRACT FROM AUTHOR]