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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]

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 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]

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]

• 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]

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]

The stability characteristics of a thin film of viscoelastic (Walters' B ′ model) fluid flowing down an inclined or vertical plane are analyzed under the combined influence of gravity and surface tension. A nonlinear free surface evolution equation is obtained by using the momentum-integral method. Normal mode technique and multiple scales method are used to obtain the results of linear and nonlinear stability analysis of this problem. The linear stability analysis gives the critical condition and critical wave number k c which include the viscoelastic parameter Γ , angle of inclination of the plane θ , Reynolds number R e and Weber number W e. The weakly nonlinear stability analysis that is based on the second Landau constant J 2 , reveals the condition for the existence of explosive unstable and supercritical stable zone along with the other two (unconditional stable and subcritical unstable) flow zones of this problem which is 3 (1 + 3 Γ) R e − 3 c o t θ − 4 R e W e k 2 = 0. It is found that all the four distinct flow zones of this problem exist in R e - k -, θ - k - and Γ - k -plane after the critical value of R e c , θ c and Γ c , respectively. A novel result of this analysis is that the film flow is stable (unstable) for a negative (positive) value of Γ irrespective of the values of R e and θ , as for example, a solution of polyisobutylene in cetane, compared with the viscous (Γ = 0) film flow case. Finally, we scrutinize the effect of Γ on the threshold amplitude and nonlinear wave speed by depicting some numerical examples in supercritical stable as well as subcritical unstable zone of this problem. • Momentum-integral method. • Linear stability analysis. • Weakly nonlinear stability analysis. • Various stability zones. • Threshold amplitudes and nonlinear wave speed. [ABSTRACT FROM AUTHOR]

• The effects of viscoelasticity on droplet formation are revealed. • The effects of fluid flow rate on droplet size and its distribution are investigated. • The role of fluid viscoelasticity on uniformity and stability of droplets is analyzed. • Prediction formula for the size of elastic droplets is constructed. The dynamics of viscoelastic droplets and the distribution of viscoelastic fluids in symmetrical parallelized microchannels are studied by using a high-speed camera. Typical parallel and slug flows are observed. The droplet formation process is divided into four stages, and the pinch-off point of the droplet moves downstream under high dispersed phase flow rates. When the flow rate ratio of the continuous phase to the dispersed phase is very low, the expanding stage disappears and the remaining three stages gradually lose clear boundaries, and the slug flow transforms into parallel flow. The influence of fluid elasticity is manifested in the appearance of unbreakable filaments when the droplet is pinched off, and the duration and maximum length of filaments are positively correlated with the fluid elasticity. Increasing the velocity of the dispersed phase appropriately, the homogeneity of droplet generation can be effectively enhanced. Finally, a prediction model of droplet size is established. [ABSTRACT FROM AUTHOR]

• SPH simulations of non-isothermal viscoelastic injection molding process are conducted. • The case of a 2D C-shaped cavity is analyzed for a wide range of parameters. • The case of a 3D door handle is simulated, and the results are visualized. • The results are helpful in gaining a better understanding of the molding process. In the present work, we focus on developing the smoothed particle hydrodynamics (SPH) method for simulation of non-isothermal viscoelastic free surface flows with application to the injection molding process. Specifically, the viscoelastic fluid is governed by the eXtended Pom-Pom (XPP) constitutive equation. The temperature-dependent viscosity and relaxation time are modeled using the Arrhenius relation. The governing equations are discretized by an improved SPH scheme, as presented by Xu and Yu, Appl. Math. Model. 73 (2019) pp. 715–731. We first verify the validity of the SPH method by solving the isothermal/non-isothermal Poiseuille flow of an XPP fluid and comparing the SPH solutions with the analytical solutions or finite volume method solutions. Then, we extend the method to 2D non-isothermal viscoelastic injection molding process of a C-shaped cavity. Some relevant physical information such as temperature, pressure, velocity, flow-induced stresses during the molding process are displayed. The convergence of the method is examined with several different particle sizes. The effects of the Péclet number, Reynolds number, Weissenberg number, viscous ratio, and XPP parameters, on the evolutions of the temperature and flow-induced stresses are analyzed in details. Results for 3D non-isothermal viscoelastic injection molding process of a door handle are lastly presented. [ABSTRACT FROM AUTHOR]

• The viscoelastic characteristics of fluid and traffic flow are mined, and traffic flow is regarded as viscoelastic fluid. • Based on the good effect of fractional calculus in viscoelastic fluid, the fractional calculus is introduced into traffic flow modelling. • According to the time-varying and grey characteristics of traffic flow, a time-varying fractional grey Riccati traffic flow model is established by choosing conformable fractional derivative. • The performance of the new model in multi-scenario traffic flow prediction shows its great advantages. Existing traffic flow models are insufficient to excavated the characteristics of fluids and are usually a constant coefficient differential model. They cannot reflect the characteristics of a traffic flow system changing with time, resulting in their poor adaptability. Firstly, the viscoelastic traffic flow model is simplified. The fractional viscoelastic traffic flow model is established in combination with modelling principle of the Bass model and successful application of fractional calculus in viscoelastic fluid. Conformable fractional derivative and the fractional grey model are then introduced to establish a fractional grey viscoelastic traffic flow model that can reflect time-varying characteristics. Finally, the new model is compared with traditional statistical models in terms of model efficiency and stability and is applied to the modelling of traffic flow and traffic congestion level in multiple scenarios. The modelling results are compared with six other models. Results show that the new model has better stability and modelling effect. [ABSTRACT FROM AUTHOR]

We study the linear stability of the Poiseuille flow of a viscoelastic upper convected Maxwell fluid in which the rheological parameters depend on the concentration of particles suspended in the fluid (dense suspension with negligible diffusion). After determining the basic flow and basic concentration profile we consider a temporal three dimensional perturbation in the form of a stream-wise and span-wise wave. We derive the linearized perturbed equation and prove the validity of Squire's theorem, extending the result of Tlapa and Bernstein (1970) in which the theorem was proved for constant rheological parameters. We discuss the relation between the Weissenberg and the Reynolds numbers. We finally study the 2D eigenvalue problem for the case of constant coefficients and for non-constant coefficients with low Weissenberg number. We solve the problem numerically by means of a spectral collocation method and we plot the marginal stability curves discussing how stability depends on the fluid rheology. • We study linear stability of a viscoelastic suspension. • Rheology depends on particles concentration. • We prove Squire's theorem • We solve the generalized Orr–Sommerfeld equation. • We plot the marginal stability curves. [ABSTRACT FROM AUTHOR]

• Analytical modeling of Love waves propagation in viscoelastic waveg-uide loaded with complex fluids is proposed. • Complex dispersion equation is established in order to quantitatively analyze the Love wave behavior. • Complex dispersion equation reveals a very good agreement with those in the literature in some particular cases. • Obtained results are fundamental and can be very useful in the design and optimization of Love wave fluid sensors. Love waves propagation in a viscoelastic waveguide loaded on its surface with viscoelastic fluids of finite thickness is investigated in this paper. The Maxwell and Kelvin-Voigt constitutive equations are employed in order to describe the fluid viscoelasticity. By solving the equations of motion in the different media (viscoelastic fluid, viscoelastic waveguide and elastic substrate) and imposing the suitable boundary conditions, an accurate and simple generalized complex dispersion equation is established for Love waves. Subsequently, a comparison is made with the published complex dispersion equations in the literature in some particular cases, and a very good agreement is showed. A detailed study was conducted by varying key parameters such as operating frequency, waveguide thickness and fluid thickness. The waveguide surface was subjected to various glycerol concentrations, with a wide range of dynamic viscosity, representing both Newtonian and viscoelastic behaviors. Theoretical analysis shows that to reasonably predict the characteristics responses of Love waves, the Maxwell fluid is more appropriate for low glycerol concentration and, the Kelvin-Voigt fluid is more suitable for high glycerol concentration and at high frequency. Results also evaluated the influence of layer thickness on the dispersion curves. The obtained results can be very useful in the design and optimization of Love wave fluid sensors. [ABSTRACT FROM AUTHOR]

This paper examines the unsteady two-dimensional boundary layer heat and mass transfer features of viscoelastic fluid flow near the neighborhood of forward and rare stagnation points. The heated circular cylinder is immersed in a viscoelastic fluid and the forward and rare stagnation points occurs near downward and upward directions of the cylinder respectively. The velocity near the surface of the cylinder is assumed to be zero and at very large distance from cylinder a uniform free stream velocity is spontaneously started in vertical direction. A non-similar transformation reduces the set of partial differential equations into non-similar partial differential equations. The transformed non-linear partial differential system is solved by using Keller box method. This technique shows well-behaved solutions for the steady-state (large time) and transient (small time) flows near the boundary layer region. Moreover, the body force present in this phenomena is in the form of convection which gives assisting (greater than zero) and opposing flows (less than zero). Parameters like the viscoelastic parameter, the convection parameter and the stagnation point parameter (forward and rare stagnation points) are found to control the flow field. Moreover, the Schmidt and the Prandtl numbers are used to control the concentration and temperature distributions. Features of several parameters on the non-dimensional concentration, temperature, local Nusselt and Sherwood numbers are viewed through graphs (2-d and 3-d) and tables. Contour images are plotted in order to visualize the three dimensional surface into two dimensional plane. [ABSTRACT FROM AUTHOR]

The evaluation of nanoparticle dispersion within viscoelastic fluids upon impact on hydrophobic and hydrophilic surfaces is conducted using the Euler-Lagrangian technique. The volume-of-fluid approach is employed in conjunction with the Lagrangian method to model the transport of nanoparticles in a three-phase system (particles-air-viscoelastic fluid). The assessment of nanoparticle dispersion was conducted over a range of Péclet numbers and contact angles (θ = 30 ° and 120 °) in three-dimensional (3D) space using the mean square displacement method. The findings suggest that the dispersion of nanoparticles is mainly influenced by normal stress. During droplet impact, nanoparticles exhibit non-Fickian superdiffusive behaviour due to the viscoelastic fluid's non-Gaussian distribution of velocity and stresses (normal and shear) fields. The wettability of the fluid with solid surfaces substantially affected the dispersion of nanoparticles in the viscoelastic fluid. [Display omitted] • Volume-of-fluid-Lagrangian method for simulating the transport of nanoparticles in viscoelastic fluid. • Normal stress governs the transport of nanoparticles upon droplet impact. • Nanoparticles exhibiting non-Fickian superdiffusion. [ABSTRACT FROM AUTHOR]

• Semi-analytical solutions for the laminar concentric core annular flow of Newtonian fluid-FENE-P fluid in inclined and horizontal pipes are obtained. • The FENE-P model in the fully developed steady laminar flow is used. • The shear-thinning effect of viscoelastic fluid has a significant effect on two-phase flow characteristics. • When the annulus fluid has the shear-thinning effect, the slip ratio can be less than 2. • The FENE-P viscoelastic fluid can transform the hydraulic characteristic curve in the multi-valued region into a single-valued curve to eliminate Ledinegg instability. Water-lubricated transportation of viscous oil is an important application of core annular flow (CAF), which significantly reduces friction pressure drop and saves pump power. However, the core oil floats up due to the density difference of oil and water, causing instability and even destruction of CAF, which restricts the application and development of the drag reduction technology. The viscoelastic fluid in the annular can inhibit the tendency of the core oil to float up and enhance the stability of the CAF. Nevertheless, theoretical studies related to the viscoelastic fluid CAF are currently missing. To make up for the lack of theoretical research, the solutions of laminar concentric viscous oil-viscoelastic fluid CAF in horizontal and inclined pipes are obtained in this work, and the annular fluid is regarded as viscoelastic fluid conforming to the FENE-P model. Based on the Navier–Stokes equation and FENE-P model, a non-dimensional CAF model is established, and the Newton–Raphson method is used to solve the model. The rheological behavior of annular fluid and the effects of viscoelastic fluid rheology and viscosity ratio on various CAF flow characteristics, including holdup, pressure gradient, slip ratio, and Ledinegg instability, are investigated. The results indicate that the shear-thinning effect of viscoelastic fluid has a significant effect on water holdup and expands the multi-solution region. Different from Newtonian fluid, when the annulus fluid is viscoelastic, the slip ratio can be less than 2. The most significant property is that the shear-thinning effect can transform the hydraulic characteristic curve in the multi-valued region into a single-valued curve, which helps to eliminate Ledinegg instability. [ABSTRACT FROM AUTHOR]

In this paper, the interaction between two initially circular in-line bubbles during their rise in a viscoelastic liquid under gravity is numerically simulated by weakly compressible smoothed particle hydrodynamics (WC-SPH). The background fluid is assumed to obey Oldroyd-B rheological model and the surface tension between two phases is evaluated by continuum surface tension (CST) method. First, it is shown that the obtained results for two benchmark problems, including two rising bubbles in a Newtonian fluid and a single rising bubble in a viscoelastic fluid, are in good agreement with previously published results. Then, together ascending of two unequal in-line bubbles in an Oldroyd-B viscoelastic liquid is simulated. Two different configurations are considered for the position of larger bubble and the center-of-mass of the bubbles and its velocity are presented for each case. Also, the differences of velocity and stress distributions in the background liquid are evaluated for two configurations. Based on the obtained results, it could be said that when the larger bubble is placed above the smaller one, merging does not occurred and the upper bubble has a dual cusped trailing edge. In addition, the effects of Deborah number, polymer concentration, density and viscosity ratios, Reynolds number, and Bond number are investigated on rising bubbles. To the best of authors' knowledge, it is the first time the simultaneous rising of two bubbles in Oldroyd-B fluids is investigated. • Two in-line bubbles rising in an Oldroyd-B liquid were simulated by WC-SPH. • When the larger bubble is placed lower, it rises faster and merging occurs. • When the smaller bubble is placed lower, the larger one has a dual cusped edge. • The maximum of the primary stress difference were compared for two configurations. • Rising bubbles are dramatically affected by De number and polymer concentration. [ABSTRACT FROM AUTHOR]

In this study, we propose a novel method to fabricate suspended polymer microfibers with the principle of liquid bridge in the range of 25–180 μm in thickness and centimeter range in length by stretching viscoelastic fluid, employing a commercial fused deposition modeling (FDM) 3D printer and a PLA (polylactic acid) 3D printing filament. Highly uniform thickness of microfibers (CV < 5%) is also achievable in various sizes by our proposed method in ranges of 25–30 μm and 75–130 μm. For the thickness control and the uniformity of the thickness, we investigate three main printing control factors (filament extrusion volume, printing speed, and gaps between printing nozzle and printing bed) through experiment. The observation from the experiment concludes that the filament extrusion volume is the most dominant factor to rule the thickness of the suspended polymer microfiber, and the printing speed is the following determinant factor. The uniformity of the thickness is maintained with a lower extrusion volume and a higher printing speed, and it is concluded that such a printing setting makes microfibers thinner due to smaller viscoelastic internal compressing force along the microfiber. Additionally, we analyze a relation of the three printing parameters to estimate the thickness of the microfiber by FDM 3D printing. [ABSTRACT FROM AUTHOR]

This paper examines the steady-state three dimensional momentum and internal energy change in rotating viscoelastic fluid flow along with convective boundary conditions. In most of the literature, the thermophysical properties of the fluid are assumed to be constant. But current analysis fills this gap by taking viscosity, conductivity and diffusivity to be temperature dependent. In order to create a chemical reaction in a system activation energy is added. Velocity of the fluid over an exponential three dimensional surface is varied exponentially while a Casson fluid model is assumed for temperature dependent viscosity. A similarity transformation diminishes the Navier-Stokes partial differential equations into ordinary differential equations and then solved numerically using Bvp4c for the velocity, temperature and concentration distributions. Moreover, drag forces, heat and mass transfer rates near the surface are calculated numerically in tabular form. Outcomes are discussed for parameters appearing in dimensionless system like rotating parameter, the viscoelastic parameter, Eckert number, Prandtl number, temperature distinction parameter, Schmidt number, thermal and concentration Biot numbers and variable viscosity, conductivity and diffusivity parameters. We found that the minimum force required to initiate the fluid motion increases with an increment in local rotation parameter Ω. An accretion in Ω exhibits curiously oscillatory pattern in velocity profile. Casson fluid β and viscosity parameter θ r has adverse influence on temperature profile. The fitted rate n and temperature difference parameter δ have conflicting influence on concentration profile. Activation energy E and Eckert number Ec causes increment in the behavior of temperature profile. In addition, numerical data of previous papers are matched with current data. [ABSTRACT FROM AUTHOR]

In immiscible liquid–liquid Newtonian flow through a porous medium, one phase often becomes trapped in corners or narrow regions by capillary forces as blobs (e.g. oil ganglia) deep within the matrix, whilst the second flow exhibits a steady and laminar flow (e.g. of water) that has negligible influence on the trapped liquid–liquid interfaces. However, recent microfluidic experiments have shown the situation radically changes when using a viscoelastic liquid, which is capable of exhibiting pore-scale unsteady flow that can deform such interfaces. Here, a computational model is developed which allows us to capture the forces that cause this behaviour and provide a framework for future investigations of this system. In this paper, the forces on trapped interfaces are investigated for the first time. Notably, when the viscoelastic flow becomes unsteady the forces on the trapped interfaces not only fluctuate but also become amplified, thus supporting experimental findings showing they can be used to free such interfaces. At Weissenberg values of 1.5 and above the fluctuations become important and the mean values of the forces on the interfaces decrease as the fluctuations grow. [ABSTRACT FROM AUTHOR]

Improvement in thermal and electric conductivity is the basic requirement of many nano-electrochemical systems. These systems in material science, energy management, and chemical processing can be efficiently handled with the presence of carbon nanotubes in the base fluid. Basically nanofluid is used to act as coolant with enhanced thermal conductivity in equipment such as radiators, heat exchangers, and electronic systems. Transfer of heat in nanofluids has been discussed by many researchers with ordinary derivative but here we have considered fractional derivatives to achieve more control on heat transfer. Here in this communication, we have discussed two-directional viscoelastic fluid flow with suspended carbon nanotubes. SWCNTs as well as MWCNTs are considered as nanoparticles in the base fluid. In order to achieve control of the flow and heat transfer, flow problem is modeled with Caputo fractional derivatives α , β along with fractional momentum and thermal relaxation times λ α and λ 1 β. In the electrically conducting flow regime, electric and magnetic fields are perpendicular to each other and Ohmic heating is appropriately handled in energy equation via Ohm's law. Governing fractional PDEs are nonlinear in nature and solved numerically with finite-difference discretization along with L 1 algorithm. Simulated results of velocity and temperature are noted for both the SWCNTs and MWCNTs. Velocity and temperature profiles for MWCNTs remained at a higher level when compared to SWCNTs for all the values of physical parameters. The presence of fractional derivatives, SWCNTs and MWCNTs made the results valuable that can be used to efficiently handle similar thermal management problems in engineering such as to achieve thermal control in the vehicle engines, refrigerators, grinders, boilers, chillers, and heat exchangers. • Unsteady two directional nanofluid flow with CNTs is constructed. • Control on flow is achieved via fractional derivatives and relaxation times. • Ohmic heating is maintained with the presence of uniform electric field. • Skin friction and Nusselt number are calculated for pertinent parameters. • Finite difference algorithm is used for solution of governing equations. [ABSTRACT FROM AUTHOR]

This study investigates viscoelastic fluid, which possesses both viscous and elastics properties, by employing a fractional derivative model to reveal the stress relaxation phenomenon with distance. The spatial-fractional derivative used in the momentum conservation equation is the Riemann–Liouville type derivative. Further, we use non-uniform boundary conditions subject to the boundary layer equations of the fluid flowing through a semi-infinite permeable flat surface. Owing to the fractional derivative model and non-uniform boundary conditions, this problem is complex. Thus, a finite difference scheme is applied after the coupled continuity equation and momentum equation are decoupled and linearized. The accuracy, convergence, and stability of the numerical method are presented. It is shown that non-uniform mass transfer through a permeable surface considerably affects the velocity boundary layer. By illustrating the physical interactions between the velocity fields in the boundary layer and the permeation mode in the surface, this paper predicts the velocity distributions with varying permeable surface, and also provides the possibility of changing the velocity fields by altering the permeable sheet. The results and numerical technique used in this study will help in the understanding of fractional calculus investigation in engineering. [ABSTRACT FROM AUTHOR]

We have investigated the non-axisymmetric Homann stagnation-point flow of a viscoelastic fluid over a rigid plate. In a recent paper Weidman (2012) has modified Homann's stagnation point flow and made it non-axisymmetric over a rigid plate. Now if the fluid is non-Newtonian a new family of asymmetric stagnation-point flows arises depending on the shear to strain-rate ratio γ (= b ∕ a) and the viscoelastic parameter k. Here a , b are the strain rate and shear rate of the stagnation-point flow. The governing momentum equations are solved numerically using fourth order Runge–Kutta method with shooting technique. The effect of the various parameters on the wall shear stress parameters, the dimensionless velocities, the displacement thicknesses and the velocity distributions are analysed. Numerical results of wall shear stress and displacement thicknesses are compared with their large value behaviours and those behaviours give a good agreement with the corresponding numerical solutions. [ABSTRACT FROM AUTHOR]

• Poiseuille flow of a Giesekus fluid with Newtonian solvent. • Analytical solution. • Limiting values of Deborah number related to mobility parameter. • Calculation of velocity and stress tensor components. • Discussion. A semi analytical solution is obtained here for the fully developed plane Poiseuille flow of a Giesekus fluid with a Newtonian solvent. The fluid behaviour is described using the Deborah number, the mobility factor and an appropriate ratio of fluid viscosity to total viscosity as parameters. The given solution shows that the velocity increases significantly with rising the polymer concentration, confirming that dilution of the solution produces the same effect as an increase in resistance. The analysis demonstrates that there are limiting values of Deborah number related to the mobility parameter. [ABSTRACT FROM AUTHOR]

The article focuses on the shear-thinning and viscoelastic constitutive modelling and numerical simulation of blood flow in a stenosed and bifurcating artery. Specifically, the shear-thinning and viscoelastic behaviour of blood are modelled and implemented via the Oldroyd-B and Generalized Oldroyd-B constitutive models. A robust and efficient general purpose numerical (and computational) methodology for the simulation of blood flow in a stenosed and bifurcating artery is also developed and implemented. The numerical algorithm is developed more generally to resolve the mathematical model equations arising out of the all-encompassing Generalized Giesekus constitutive model. This model reduces to the Generalized Oldroyd-B model and subsequently also to the standard Oldroyd-B model simply by switching off certain material parameters. The inclusion of the Generalized Giesekus model must therefore be viewed in this context, to facilitate the development of an all encompassing general purpose numerical code. The blood flow modelling is otherwise done via the Oldroyd-B and Generalized Oldroyd-B constitutive models. The shear-thinning effects are implemented via the Cross model for shear-viscosity. The Generalized Oldroyd-B model results all illustrate that the velocity is directly proportional to the constriction caused by the stenosis. The higher the blockage from the constriction, the higher would the velocity spurt through the constriction. This velocity behaviour correspondingly enhances the wall shear-stresses as the constriction increases, caused by the presence of the stenosis. High wall shear-stresses greatly increase the possibility of rupture of the stenosis. This can lead to catastrophic consequences in the usual case where the stenosis is caused, say, by tumor growth. As demonstrated near the contraction of a standard 4:1 contraction flow geometry, dramatic fluid flow effects, which are attributable to the polymeric-stresses, specifically to the first normal stress difference, are observed in the vicinity of the constrictions resulting from the presence of the stenosis. Such effects, include, flow recirculation and reversal, vortex formation, and spurt phenomena. • The study explores blood flow simulations in stenosed and bifurcating arteries. • The blood is modelled as shear-thinning and viscoelastic using Oldroyd-B models. • Finite volume methods implemented on the OpenFOAM software platform are used. • The blood velocity is directly proportional to the stenosis constriction size. • The velocity and shear-stress behavior may lead to severe physiological effects. [ABSTRACT FROM AUTHOR]

• CS-FEM is applied to the numerical simulation of viscoelastic fluid flow for the first time. • The gradient smoothing for viscoelastic fluid flow is arbitrary within each smoothing cell. • Two smoothed CBS schemes are presented to solve the viscoelastic equations. • The cell-based smoothing procedure is used to evaluate the viscoelastic fluid drag. This paper generalizes the cell-based smoothed finite element method (CS-FEM) to viscoelastic fluid flows under the fractional-step umbrella. The characteristic-based split (CBS) scheme is employed to decouple the Navier–Stokes equations and the Oldroyd-B constitutive model. Moreover, the discrete elastic-viscous-split-stress (DEVSS) procedure and stabilized pressure gradient projection (SPGP) are introduced into a second-order CBS framework. The projections of velocity and pressure gradients therein combine to form the DEVSS-G/CBS(B)-SPGP algorithm that further stabilizes the discretized model. Both proposed schemes are suitable for use in CS-FEM because they accept equal low-order interpolations for primitive variables. The spatial discretization is based upon bilinear four-node quadrilateral elements where all gradient-related items are smoothed without any methodological difficulties. In particular, the cell-based smoothing concept enables accurate evaluation of viscoelastic fluid force. The developed methods are validated against previously published data for several benchmark problems. A satisfactory agreement exists between the present and earlier results. [ABSTRACT FROM AUTHOR]

• Dispersion in an electro-osmotic flow of a viscoelastic fluid through a porous-walled microchannel is modeled. • Continuity of solute species concentration and its flux is considered at microchannel-porous medium interface. • Dispersion is an increasing function of degree of fluid elasticity. • Dispersion exhibits a non-monotonic behavior against nondimensional Debye-Hückel parameter. An analytical expression for the dispersion coefficient in an electro-osmotic flow of a viscoelastic fluid (which obeys the simplified Phan-Thien-Tanner rheological model) through a porous-walled microchannel is theoretically developed. The decomposition technique in combination with the assumptions behind the Taylor-Aris theory of the solute species dispersion is used to derive the dispersion coefficient in a porous-walled microchannel. The microchannel-porous medium interaction via the exchange of the solute species between the two media is included in derivation of the dispersion coefficient in a porous-walled microchannel. In other words, the continuity of the solute species concentration and its flux is considered at the interface between the microchannel and the porous medium. The developed dispersion coefficient in a porous-walled microchannel is a function of three parameters, which characterize the Péclet number, the fluid elasticity, and the nondimensional Debye-Hückel parameter. The proposed model is also capable to deliver the dispersion coefficient in a nonporous-walled microchannel (where a no-flux boundary condition is considered at the walls), which is in agreement with the existing model in literature. [ABSTRACT FROM AUTHOR]

• New class of exact stationary solutions of the Maxwell viscoelastic equations is given. • Example of a nonsingular solution is presented. • Exact solutions for α = − 1 , 0 , 1 of the Johnson-Segalman model were derived. Stationary two-dimensional flow near a free critical point of an incompressible viscoelastic Maxwell medium with upper, lower, and corotational convective derivatives in the rheological constitutive law is considered. Analysis of the analytical unstationary solution found earlier (S. V. Meleshko, N. P. Moshkin, and V. V. Pukhnachev, On exact analytical solutions of equations of Maxwell incompressible viscoelastic medium. Int. J. Non-Lin. Mech. , 105:152–157, 2018) provides a new class of stationary solutions. The solutions found comprise both already known as well as substantially new solutions. Nonsingular solutions of the stress tensor at the critical point and bounded at infinity are constructed. Exact analytical formulae for the stress tensor with the Weissenberg number W i = 1 / 2 are obtained. [ABSTRACT FROM AUTHOR]

Highlights • A novel theoretical approach has been developed to predict surface Love wave behavior, propagating in elastic waveguide loaded on its surface with a viscoelastic fluid. • The waveguide surface was subjected to various glycerol concentrations, with a wide range of dynamic viscosity, representing both Newtonian and viscoelastic behaviors. • The dispersion curves of attenuation and phase velocity are investigated in order to evaluate their sensitivity. • The numerical solutions show that the attenuation and phase velocity of surface Love wave are strongly correlated with waveguide thickness and glycerol concentrations. • The obtained results are fundamental and can serve as benchmark solution in design of Love wave. Abstract A novel approach based on the exact theory has been developed to accurately predict the behavior of surface Love wave propagating in elastic waveguide loaded on its surface with a viscoelastic fluid. A detailed study was conducted by varying key parameters such as operating frequency, waveguide and substrate. The waveguide surface was subjected to various glycerol concentrations, with a wide range of dynamic viscosity, representing both Newtonian and viscoelastic behaviors. The dispersion curves of attenuation and phase velocity are investigated in function of the above parameters in order to evaluate their sensitivity. The numerical solutions show that the attenuation and phase velocity of surface Love wave are strongly correlated with waveguide thickness and glycerol concentrations. Results also highlighted the substrate thickness effect on the vibration characteristics of the Love wave. Moreover, the Love wave triggers a viscoelastic response in water–glycerol mixtures similar to that of literature. The obtained results are fundamental and can serve as benchmark solution in design of Love wave sensors. [ABSTRACT FROM AUTHOR]

Abstract In this study, rising and deformation of a single bubble in a viscoelastic fluid obeying the Giesekus model are numerically simulated by a modified version of weakly compressible smoothed particle hydrodynamics (WC-SPH). It is shown that the developed algorithm is robust enough to simulate two-phase flow with large density and viscosity ratios (up to 1000 and 100, respectively) not only in Newtonian cases but also in viscoelastic ones. After quantitative and qualitative verification of the developed code against previously published results, it is applied for simulating the rising bubble in the Giesekus fluid as a realistic model for polymeric solutions. Several simulations are performed to investigate the effects of mobility factor (0 ≤ α ≤ 1), polymer concentration (2.5 ≤ c l ≤ 20), relaxation time (1.14 ≤ De ≤ 114), density ratio (10 ≤ ρ l ∕ ρ b ≤ 1000) as well as domain width (6.6 ≤ W/D 0 ≤ 16.6). It is found that in contrast to relaxation and polymer concentration parameters which have dramatic effects on the rising bubble, the mobility factor has no significant effect on the rising bubble in high viscous polymeric solution. Also, the cusp trailing edge is postponed by decreasing the domain width. [ABSTRACT FROM AUTHOR]

Highlights • A new viscoelastic immersed boundary multiphase flow solver is developed. • The formulation comprises the log-conformation tensor. • The sedimentation, rotation and cross-stream migration of a sphere are studied. • The shear induced particle alignment in wall-bounded fluids is studied. • The open-source computational libraries CFDEMcoupling and OpenFOAM are employed. Abstract This study reports the development of a direct simulation code for solid spheres moving through viscoelastic fluids with a range of different rheological behaviors. The numerical algorithm was implemented on an open-source finite-volume solver coupled with an immersed boundary method, and is able to perform fully-resolved simulations, wherein all flow scales associated with the particle motion are resolved. The formulation employed exploits the log-conformation tensor to avoid high Weissenberg number issues when calculating the polymeric extra stress. A number of benchmark flows were simulated using this method, to assess the accuracy of the newly-developed solver. First, the sedimentation of a sphere in a bounded domain surrounded by either Newtonian or viscoelastic fluid was computed, and the numerical results were verified by comparison with experimental and computational data from the literature. Additionally, the spatial and temporal accuracies of the algorithm were evaluated, and different transient and advection discretization schemes were investigated. Second, the rotation of a sphere in a homogeneous shear flow was studied, and again the numerical results obtained were compared to those from the literature. Good agreement is obtained for the variation in the particle rotation rate as a function of Weissenberg number, using both the newly implemented algorithm and an alternative fixed-mesh approach. Finally, the cross-stream migration of a neutrally buoyant sphere in a steady Poiseuille flow, consisting of either a Newtonian or viscoelastic suspending fluid was investigated. For the Newtonian fluid good agreement was obtained for the particle equilibrium position when compared to the well known Segré–Silberberg effect, and for the viscoelastic fluid the effect of the retardation ratio on the final particle equilibrium position was studied. Additionally, the newly-developed solver capabilities were tested to study the shear-induced particle alignment in wall-bounded Newtonian and viscoelastic fluids. The role of the fluid rheology and finite gap size on both the rate and approach pathways of the solid particles is illustrated. [ABSTRACT FROM AUTHOR]

Abstract Experiments were conducted to elucidate the effect of fluid elasticity on the motion of single spherical and cylindrical particles in viscoelastic fluids. Aqueous solutions of polyacrylamide in the concentration range of 0.35–0.6% wt./vol. were used as test fluids. The phenomenon of drag enhancement was observed. The maximum drag enhancement occurred at a Weissenberg number (Wi) of 60, beyond which the inertial effects dominate over the viscoelastic effects. In order to signify the relative importance of fluid elasticity and inertia, the results in terms of drag enhancement are represented as a function of elasticity number (E = Wi/Re). The drag enhancement exhibited asymptotic behavior with variation in elasticity number which depicts the dominance of elastic and inertial forces over each other. Based on the observed experimental data, a correlation used to predict drag for the particles falling in viscoelastic fluids has been proposed by incorporating the fluid elasticity and inertia in terms of corrective elasticity number function f(E). Experiments were also conducted to investigate the effect of fluid elasticity on the orientation of cylindrical particles settling in Newtonian, non Newtonian inelastic and viscoelastic fluids. It is found that the tilt angle (with vertical, α), characterizing the orientation of cylinders, decreases with fluid elasticity. However, the reverse behavior is observed with similar particles settling in inelastic fluid with increase in Reynolds number, whereas tilt angle remains constant in Newtonian fluid. Further, an attempt has been made to generate a correlation used to predict the tilt angle as a function of elasticity number and aspect ratio. Graphical abstract Unlabelled Image Highlights • Drag enhancement exhibited an asymptotic behavior with elasticity number, E = Wi/Re. • The maximum drag enhancement occurs at a Weissenberg number (Wi) of 60. • Use of Holzer and Sommerfeld (Holzer and Sommerfeld, 2008 [ 24 ]) correlation is extended for viscoelastic fluids. • Settling characteristics of solid cylinders in viscoelastic fluids are reported. • A correlation used to predict tilt angle as a function of E and L/d is proposed. [ABSTRACT FROM AUTHOR]

Highlights • Drag is measured for suspension of particles in Viscoelastic (VEF) and Newtonian (NF) fluid. • Phase-velocity and particle-concentration is determined using Refractive-Index-Matched PIV. • Particles migrate towards the core and particle-induced stress is higher for VEF than NF. • Fluid Reynolds shear stress decreases for increasing particle concentration. Abstract We experimentally investigate the influence of finite-size spherical particles in turbulent flows of a Newtonian and a drag reducing viscoelastic fluid at varying particle volume fractions and fixed Reynolds number. Experiments are performed in a square duct at a Reynolds number Re 2 H of nearly 1.1 × 104, Weissenberg number Wi for single phase flow is between 1 and 2 and results in a drag-reduction of 43% compared to a Newtonian flow (at the same Re 2 H). Particles are almost neutrally-buoyant hydrogel spheres having a density ratio of 1.0035 ± 0.0003 and a duct height 2 H to particle diameter d p ratio of around 10. We measure flow statistics for four different volume fractions ϕ namely 5, 10, 15 and 20% by using refractive-index-matched Particle Image Velocimetry (PIV). For both Newtonian Fluid (NF) and Visceolastic Fluid (VEF), the drag monotonically increases with ϕ. For NF, the magnitude of drag increase due to particle addition can be reasonably estimated using a concentration dependent effective viscosity for volume fractions below 10%. The drag increase is, however, underestimated at higher ϕ. For VEF, the absolute value of drag is lower than NF but, its rate of increase with ϕ is higher. Similar to particles in a NF, particles in VEF tend to migrate towards the center of the duct and form a layer of high concentration at the wall. Interestingly, relatively higher migration towards the center and lower migration towards the walls is observed for VEF. The primary Reynolds shear stress reduces with increasing ϕ throughout the duct height for both types of fluid. [ABSTRACT FROM AUTHOR]

Abstract Developing proper turbulence models in order to predict flow characteristics of viscoelastic drag-reducing fluids has become as a considerable portion of non-Newtonian flows researches. In this numerical study, three different low-Reynolds-number k- ε models namely, Launder–Sharma, Lam–Bremhorst and Malin are used based on the adopted viscoelastic turbulence closure of Cruz et al. (2004). Simulation results for friction factor, mean axial velocity, turbulent kinetic energy and Reynolds shear stress are obtained for three aqueous polymer solutions (0.3% carboxymethyl cellulose, 0.2% xanthan gum and 0.2% polyacrylamide) and validated against the corresponding experimental data. While a good agreement exists for the bulk parameters like drag reduction (DR) or, equivalently, the friction factor, some discrepancies are observed in other simulation results of turbulence characteristics, in particular for situations with higher DR levels. The Malin's model which accounts for the shear-thinning property of the polymeric solutions, leads to the closest results for carboxymethyl cellulose and xanthan gum cases, while for polyacrylamide with the lowest power index n , the friction factor is larger than other simulation results and an increasing difference from the experimental data is observed. Highlights • Viscoelastic turbulent pipe flows of three aqueous polymer solutions are simulated. • Performances of different low-Reynolds-number k- ε models are examined. • The shear-thinning property is exerted in the Newtonian turbulence models. • Comparison of the results is made by validating against the experimental data. • Choosing the proper turbulence model for different power index values is suggested. [ABSTRACT FROM AUTHOR]

Highlights • Complex local flow around a tiny bubble surface under pressure-oscillating field. • 2D flow birefringence profile captured by the latest high-speed polarization camera. • A negative wake generated cyclically at the tail of bubble due to rapid deformation. Abstract The motion of a tiny air bubble in an aqueous solution of cetyl trimethyl ammonium bromide and sodium salicylate (CTAB/NaSal), which forms wormlike micelles, was observed using a high-speed polarization camera. Complex local flow is observed around the bubble surface because the bubble shape deforms repeatedly at 100 Hz. The camera can be used to measure the retardation distribution, which is related to the stress field around the bubble. Different retardation and orientation angle distributions were observed during the contraction and expansion phases. In the contraction phase, a strong retardation distribution appears at the tail of the cusped bubble. The occurrence of uniaxial elongation deformation is considered to be due to the negative wake because they are closely correlated. In contrast, a weak retardation distribution spreads at the upper side of the bubble during the expansion phase, where biaxial extensional deformation occurs due to expansion of the bubble surface. These significant changes in strong elastic stress distributions, which correspond to the orientation angle profiles, can result in increase of bubble rising velocities. [ABSTRACT FROM AUTHOR]

Abstract Fractional MHD viscoelastic fluid flow has been discussed in this study. Two dimensional and two directional unsteady flow field is more critically analyzed via non-integer time derivatives. Three memory parameters are incorporated to explore the viscoelastic characteristics of the model. Variations in concentration occurred due to homogeneous-heterogeneous reactions in the flow domain. Change in concentrations consequently leads to one of the lasting chemical species. Heterogeneous reactions are observed at the boundary while homogeneous reactions are seen in the flowing region. We consider different orders of diffusion coefficients of chemical reacting species to tackle the wider class of physical and chemical processes. Governing equations are nonlinear in nature. Hence a recently established finite difference technique along with " L 1 algorithm" is used for discretization and solution of governing fractional partial differential equations. Presence of chemical reactions in flow process made the simulations valuable for chemical industry. Highlights • Unsteady two dimensional fractional flow is constructed. • Chemical species are considered with unequal diffusivities. • Average Sherwood numbers are plotted for pertinent parameters. • Finite difference algorithm is used for solution of governing equations. [ABSTRACT FROM AUTHOR]

Highlights • Thermally fully developed flow in a two-layer dragging system is investigated. • The upper layer fluid is modeled by PTT fluid. • The bottom layer fluid is electrolyte solution affected by electromagnetic field. • The analytical expressions of velocity and temperature are derived. • The dependence of the entropy generation rate on related parameters is discussed. Abstract The entropy generation analysis is investigated in two-fluid dragging systems. The bottom layer fluid is considered as electrolyte solution affected by the applied magnetic field and the upper layer fluid is viewed as non-conducting viscoelastic Phan-Thien-Tanner (PTT) fluid. Under the combined influences of electric and magnetic fields, the upper layer non-conducting PTT fluid can be dragged by the bottom layer fluid due to the interfacial shear stress. Firstly, we obtain the analytical velocity expressions for both bottom layer and upper layer fluids under the unidirectional flow assumption. The bottom layer fluid velocity distribution shows a classical M-type velocity profile. The upper layer fluid flow can be viewed as the plate Couette flow or Couette-Poiseuille flow. Subsequently, the thermal transport characteristic and entropy generation analysis are discussed in the present two-fluid dragging system. The results show that magnetic field can enhance the local entropy generation rate, but viscoelastic physical parameter can restrain the local entropy generation rate. The present theoretical research can be used in the design of thermofluidic device. By manipulating the electric and magnetic fields strength and the ratio of fluid rheological properties, the fluid motion and heat transfer characteristics can be manoeuvred efficiently. [ABSTRACT FROM AUTHOR]

Highlights • DNS of rotating plane Couette flow of Giesekus viscoelastic fluid is performed at low Re. • Viscoelasticity leads to instability and pulsatile motion at moderate Weissenberg number. • Flow remains homogeneous in streamwise direction even at high Weissenberg number. • Roll-cell magnitude pulsates with a period on the order of cell-rotation turnover time. • Pulsation is due to a delay in the response of viscoelastic force to vortex development. Abstract For the clarification of the routes to elasto-inertial turbulence (EIT), it is essential to understand how viscoelasticity modulates coherent flow structures including the longitudinal vortices. We focused on a rotating plane Couette flow that provides two-dimensional (2D) roll cells for the steady laminar Newtonian-fluid case, and we investigated how the steady longitudinal vortices are modulated by viscoelasticity at different Weissenberg numbers. The viscoelasticity was found to induce an unsteady flow state where the 2D roll-cell structure was periodically enhanced and damped with a constant period, keeping the homogeneity in the streamwise direction. This pulsatile motion of the roll cell was caused by a time lag in the response of the viscoelastic force to the vortex development. Both the pulsation period and time lag were found to be scaled by the turnover time of cell rotation rather than by the relaxation time, despite the viscoelasticity-induced instability. We also discuss the counter torque on the roll cell and the net energy balance, considering their relevance to polymer drag reduction and EIT. [ABSTRACT FROM AUTHOR]

Highlights • The heat transfer flow of a Walters’ liquid B in a porous medium with Navier slip is investigated. • The physical problem is modelled into nonlinear PDE’s to ODE’s via similarity transformation. • The analytical solutions derived for velocity and temperature fields by Kummer’s function. • Temperature profiles are analyzed for two type of boundary heating processes namely PST and PHF. • The temperature distribution inside the stretching sheet is found to be controlled by Pr, N R and N I. Abstract This paper investigates the steady-state momentum and radiation heat transfer flow of a viscoelastic fluid in a porous media in the presence of a linear Navier slip boundary condition. The velocity of the fluid over the linear stretching sheet is varied linearly with the axial distance while a Walters’ liquid-B model is assumed for the viscosity. A similarity transformation reduces the Navier–Stokes equations to a set of partial differential equations that are converted into ordinary differential equations and solved analytically for the velocity. Moreover, heat is balanced between a temperature dependent heat source and radiation and leads to a differential equation with variable coefficients. The temperature equation is transformed to a confluent hypergeometric differential equation using the Rosseland approximation for the radiation and solved analytically. Results are discussed for two boundary conditions of the sheet, the prescribed surface temperature and the wall heat flux. Parameters like the Reynolds number, the viscoelastic parameter and the boundary slip parameter are found to determine the flow field. In addition, the Prandtl number, the radiation number, the wall temperature and the heat source/sink parameters are found to control the temperature distribution inside the stretching sheet. [ABSTRACT FROM AUTHOR]

• CO 2 can reversibly change rheological properties of aqueous solutions. • CO 2 -responsiveness of carbomer is reported for the first time. • Arginine, as a kind of biomolecule, also has CO 2 -responsive groups. Environmentally responsive intelligent viscoelastic fluids have been used in many fields in recent years. The rheological behavior of different intelligent viscoelastic fluids can be changed by different stimulation methods. Among them, CO 2 , as a non-toxic green and abundant stimulus method, has attracted much attention. Therefore, CO 2 -responsive intelligent viscoelastic fluids have been continuously reported, in which viscoelastic fluids with CO 2 -responsive viscosity increase have been more reported, while those with CO 2 -responsive viscosity decrease have been less reported. Herein, carbomer (CBM), as a pH-responsive polymer with potential CO 2 -responsiveness, is applied to CO 2 -responsive viscosity decreasing viscoelastic fluids. CBM and arginine (Arg) formed a new CO 2 -responsive viscoelastic fluid, which achieved a significant decrease in viscosity after CO 2 -response. Firstly, by comparing the effects of NaOH and Arg on the rheological behavior of CBM solution, it is demonstrated that Arg can extend the viscosity variation range of CBM solution before and after CO 2 -response, and Arg can switch between "physical crosslinking agent" and "viscosity reducing agent", and it is verified from the microscopic perspective. Then, the effects of Arg concentration and CBM concentration on the CO 2 -responsiveness and rheological behavior of CBM/Arg viscoelastic fluid were investigated. The multiple reversible CO 2 -responsive viscosity of CBM/Arg viscoelastic fluid was verified. Finally, the viscoelastic variations of CBM/Arg viscoelastic fluid before and after the response were investigated by dynamic rheology. [ABSTRACT FROM AUTHOR]

• The two-dimensional viscoelastic fluid flow toward a stretching sheet is inspected. • Stagnation point flow of a viscoelastic micropolar fluid is studied. • Mixed convection flow of a viscoelastic micropolar fluid towards a stretchable sheet. • Concentration and thermal stratification boundary conditions and activation energy are studied. • Fourier and Fick's law effects are analyzed for the viscoelastic micropolar fluid. This analysis describes the stagnation point and mixed convection flow of a viscoelastic micropolar fluid into a porous medium towards a stretchable sheet and magnetic field. Concentration and thermal stratification boundary conditions and activation energy are studied. For the flow of heat and mass transportation, Fourier and Fick's law is also accommodated into account. Suitable similarity variables are utilized to attain the dimensionless form of the governed equations. These dimensionless equations have been resolved numerically with the help of BVP4C approach. The velocity profile is reduced with the stronger estimations of ε and M. The coefficient of skin friction has an increasing effect by improving values of K , β , M , and ∊. The velocity sketch has the opposite behavior for ∊ and β t. Stronger estimations of β and δ e lead to the decay of the temperature profile. The angular velocity of the fluid upsurges due to the stronger values of K. [ABSTRACT FROM AUTHOR]

Ion-selective properties are widely used in desalination, energy storage in batteries, electroplating, etc. This paper presents a direct numerical simulation of electroconvective flow (ECF) in electrolyte solutions on a perfectly selective membrane surface (PSMS), considering fluid viscoelasticity and Joule heating. Different polymer elasticities on PSMS mass transfer are investigated in detail, including the instantaneous evolution, morphology structure, ion transport mechanism, and global assessment. The results reveal that polymer electrolytes promote the formation of small vortices (low flux) and merge into a reduced number of large vortex structures (high flux). The crown and spike morphology of charge density and the mushroom-like morphology of salt concentration tend to be cloudier in the polymer electrolytes, with a marked decrease in injection height compared to that of Newtonian fluid. The streaks of strong polymer stretching reduce fluctuations with increased interface impedance in the extended space charge layer (ESCL), described by the first normal stress difference (N1) and the local Weissenberg number (Wi l). The cumulative distribution function (CDF) and power spectral density (PSD) are characterized by an effective enhancement of the system stability, reducing the ion mass transfer and reaching a maximum of 45 %. The relevant results also facilitate an improved understanding of the complex nature of polymeric fluids in electroosmotic flow. [Display omitted] [ABSTRACT FROM AUTHOR]

We study the motion of vitreous humour in a deforming eyeball. From the mechanical and computational perspective this is a task to solve a fluid-structure interaction problem between a complex viscoelastic fluid (vitreous humour) and a nonlinear elastic solid (sclera and lens). We propose a numerical methodology capable of handling the fluid-structure interaction problem, and we demonstrate its applicability via solving the corresponding governing equations in a realistic geometrical setting and for realistic parameter values. It is shown that the choice of the rheological model for the vitreous humour has a negligible influence on the overall flow pattern in the domain of interest, whilst it has a significant impact on the mechanical stress distribution in the domain of interest. [ABSTRACT FROM AUTHOR]

Unsteady two-dimensional flows of incompressible viscoelastic Maxwell medium with upper, low and corotational convective derivatives in the rheological constitutive law are considered. A class of partially invariant solutions is analyzed. Using transition to Lagrangian coordinates, an exact solution of the problem of unsteady flow near free-stagnation point was constructed. For the model with Johnson–Segalman convected derivative and special linear dependence of the vertical component of velocity, the general solutions were derived. [ABSTRACT FROM AUTHOR]

Highlights • Interactions between viscoelastic fluid and rigid disks or ellipsoids are addressed. • A method for the direct simulation of viscoelastic suspensions is proposed. • The numerical method is built upon a fictitious domain approach. • The fluid-structure issue is solved with a splitting scheme and penalty methods. • Numerical results are presented for both dilute and dense regimes. Abstract In this paper, we present a numerical method which performs the direct simulation of 2D viscoelastic suspensions. Objectives. Interactions between viscoelastic fluids of Oldroyd type, including inertial effects, and a large number of rigid disks or ellipsoids are addressed. Method. The numerical method is built upon a fictitious domain approach which consists in defining the fluid-structure problem over the whole domain (fluid+solid), see e.g. [1]. In the Newtonian case [2, 3], the resulting variational formulation, although classical, uses non-standard functional spaces which include the rigidity constraints. From the numerical point of view, these constraints can be addressed by penalty methods, leading to the possible use of standard finite elements solvers with fixed structured meshes. We show how this approach can be adapted to viscoelastic fluids of Oldroyd type. Results. Two types of configurations are investigated in dilute and dense regimes: sedimentation of circular particles and shear flows with ellipsoidal particles. [ABSTRACT FROM AUTHOR]

We investigate the influence of viscous dissipation on the convective heat transfer and entropy generation characteristics for the Poiseuille flow of a viscoelastic fluid in an asymmetrically heated slit microchannel. We use the simplified Phan –Thein –Tanner constitutive equations to describe the rheology of the fluid. Considering hydrodynamic slip at fluid–solid interface, we analytically solve the transport equations to obtain the velocity and temperature fields inside the flow domain, which are further used to evaluate the Nusselt number and the thermodynamic irreversibility generation rate. The results show that the present thermo-fluidic transport process is strongly influenced by the governing dimensionless parameters viz. , the Brinkman number, heat flux ratio, viscoelastic group and slip coefficient. Finally, this study reveals that the Brinkman number and viscoelastic parameter have reverse effects on the Nusselt number and entropy generation rate as compared to the slip coefficient. [ABSTRACT FROM AUTHOR]

Purely-elastic flow instabilities have been extensively investigated in pressure-driven systems, but little attention has been paid to electrically-driven systems. This work attempts to fill this gap by investigating the electroosmotic flow of viscoelastic fluids in cross-slot and flow-focusing micro-devices, with a special focus on the onset of elastic instabilities. Relying on the visualization of dye patterns, the onset of electro-elastic instabilities for dilute and semi-dilute polyacrylamide solutions was observed at a low bulk Weissenberg number, O (10 −2 ), through a direct transition from a steady symmetric flow to a time-dependent asymmetric flow. Time-series analysis of the dye interface patterns revealed a broad range of excitation frequencies with a power-law decay. The elastic instabilities observed seem not to improve significantly the mixing efficiency, contrarily to what has been previously reported for unstable pressure-driven flows. Numerical simulations of the electroosmotic flows were also carried out with a finite-volume method, showing that the observed electro-elastic instabilities can be predicted numerically. Both the experimental and numerical results suggest that the large stresses developed inside the electric double layer, coupled with the streamline curvature around the geometry corners, play a fundamental role in the onset and in the dynamics of the observed electro-elastic instabilities. However, further research is needed to clarify the mechanism of electro-elastic instabilities, and, in general, to improve our understanding of the complex behavior of polymeric fluids in electroosmotic flows. [ABSTRACT FROM AUTHOR]