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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.

In this paper we consider the initial–boundary value problem describing the motion of weakly concentrated aqueous polymer solutions. The model involves the regularized Jaumann’s derivative in the rheological relation. Also this model is considered with non-linear viscosity. On the basis of the topological approximation approach to the study of hydrodynamics problems the existence of weak solutions is proved. Also we consider an optimal feedback control problem for this initial–boundary value problem. The existence of an optimal solution minimizing a given performance functional is proved.

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]

Purpose: The main theme of this paper is the effect of viscous dissipation Darcy–Forchheimer flow and heat transfer augmentation of a viscoelastic fluid over an incessant moving needle. Design/methodology/approach: The governing partial differential equations of the current problem are diminished into a set of ordinary differential equations using requisite similarity transformations. Energy equation is extended by using Cattaneo–Christov heat flux model with variable thermal conductivity. By applying boundary layer approximation system of equations is framed. Findings: Convective condition is also introduced in this analysis. Obtained set of similarity equations are then solved with the help of efficient numerical method four–fifth-order RKF-45. Originality/value: The outcomes of various pertinent parameters on the velocity, temperature distributions are analysed by using portraits. [ABSTRACT FROM AUTHOR]

This work deals with the numerical solutions of viscoelastic fluid flow, this solutions coresponding to unsteady unidirectional flow of Oldryod fluids. Numerical solution is based on finite lifference method using implicit Crank-Nicolson scheme for the velocity, and improved Euler method or the stress tensor. The numerical results of plane Couette flow and plane Poiseuille flow obtainedy this method are presented and compared with the steady solution when time t is large enough. [ABSTRACT FROM AUTHOR]

This paper consists of a mathematical analysis of MHD free convective flow of viscoelastic fluid through a porous regime in an inclined channel. The flow system is permeated by a uniform moving magnetic field with strong magnetic intensity to produce Hall and ion-slip effects. The flow governing equations are obtained from the suitable field and constitutive equations and solved analytically. To accentuate the consequences of various flow controlling parameters to the nature of the flow, numerical results are discussed in assistance with graphs and tables. An important fact noted from the study that Hall current generates the flow in the direction perpendicular to the main flow while ion-slip current reduces the flow in the direction perpendicular to the main flow. It is also seen that the moving magnetic field produces less rigidity in the flow in comparison to the stationary magnetic field. [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]

A new fractional finite volume method is developed for the mixed convection boundary layer flow and heat transfer of viscoelastic fluid over a flat plate. The spatial fractional derivative of the Riemann–Liouville type is employed in the constitutive relation and modified Fourier's law respectively. Nonlinear and coupled boundary layer governing equations are formulated with non-uniform boundary conditions. The discretized scheme combined with the shifted Grünwald–Letnikov formula is proved to be conditionally stable, further the convergence and accuracy of the numerical solutions are presented. Results demonstrate that space fractional derivative parameters have strong effects on the velocity and temperature distributions. Moreover, the viscoelastic fluid with spatial fractional derivative performs stress relaxation with distance from the intersections of velocity profiles. [ABSTRACT FROM AUTHOR]

In this paper, the steady magnetohydrodynamic mixed convection flow of a viscoelastic fluid over a magnetized vertical surface embedded in a uniform porous material with rotation is considered. The Hall and induced magnetic field effects are also considered in this investigation. The regular perturbation technique is used to find the solutions of flow governing equations. To analyze the consequences of flow'influencing parameters to the flow variables, numerical computation has been performed and the results are illustrated in graphical and tabular forms. It is interesting to note that magnetic diffusion leads to the increase of the fluid flow. It brings a decrement in the induced magnetic field in the vicinity of the magnetized vertical surface. [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]

The idea of fractional derivatives is applied to several problems of viscoelastic fluid. However, most of these problems (fluid problems), were studied analytically using different integral transform techniques, as most of these problems are linear. The idea of the above fractional derivatives is rarely applied to fluid problems governed by nonlinear partial differential equations. Most importantly, in the nonlinear problems, either the fractional models are developed by artificial replacement of the classical derivatives with fractional derivatives or simple classical problems (without developing the fractional model even using artificial replacement) are solved. These problems were mostly solved for steady-state fluid problems. In the present article, studied unsteady nonlinear non- Newtonian fluid problem (Cattaneo-Friedrich Maxwell (CFM) model) and the fractional model are developed starting from the fractional constitutive equations to the fractional governing equations; in other words, the artificial replacement of the classical derivatives with fractional derivatives is not done, but in details, the fractional problem is modeled from the fractional constitutive equations. More exactly two-dimensional magnetic resistive flow in a porous medium of fractional Maxwell fluid (FMF) over an inclined plate with variable velocity and the temperature is studied. The Caputo time-fractional derivative model (CFM) is used in the governing equations. The proposed model is numerically solved via finite difference method (FDM) along with L1-scheme for discretization. The numerical results are presented in various figures. These results indicated that the fractional parameters significantly affect the temperature and velocity fields. It is noticed that the temperature field increased with an increase in the fractional parameter. Whereas, the effect of fractional parameters is opposite on the velocity field the plate. Moreover, the velocity field retarded with strengthening in the magnetic parameter due to enhancement in Lorentz force. However, this effect reverses in the case of the temperature profile. [ABSTRACT FROM AUTHOR]

The viscoelastic nature of blood flow through 25% size of stenosis is investigated numerically using Comsol-Multiphysics 5.4. The flow geometry of the stenosed artery is modeled by asymmetric 2D channel with a rigid wall. Blood is characterized as a mixture of Newtonian and viscoelastic fluid. The coupled nonlinear Navier–Stokes equation and the Oldroyd-B models equations are solved numerically in General PDE solver. The governing equations are discretized using the finite element method for the two-dimensional flow to estimate the velocity and pressure distribution. The effect of the velocity field, pressure distribution, and wall shear stress is reported for the Newtonian model and the viscoelastic Oldroyd-B model. The deviation of fluid behavior from the Newtonian fluids is compared to the practical blood behavior. The effects of Weissenberg number (Wi) over velocity field and wall shear stress have tested for moderate Reynolds numbers. The Oldroyd-B model showed quite reliable blood behavior when compared to existing literature values. [ABSTRACT FROM AUTHOR]

This paper presents a numerical comparison of viscoelastic shear-thinning fluid flow using a generalized Oldroyd-B model and Johnson–Segalman model under various settings. Results for the standard shear-thinning generalization of Oldroyd-B model are used as a reference for comparison with those obtained for the same flow cases using Johnson–Segalman model that has specific adjustment of convected derivative to assure shear-thinning behavior. The modeling strategy is first briefly described, pointing out the main differences between the generalized Oldroyd-B model (using the Cross model for shear-thinning viscosity) and the Johnson–Segalman model operating in shear-thinning regime. Then, both models are used for blood flow simulation in an idealized stenosed axisymmetric vessel under different flow rates for various model parameters. The simulations are performed using an in-house numerical code based on finite-volume discretization. The obtained results are mutually compared and discussed in detail, focusing on the qualitative assessment of the most distinct flow field differences. It is shown that despite all models sharing the same asymptotic viscosities, the behavior of the Johnson–Segalman model can be (depending on flow regime) quite different from the predictions of the generalized Oldroyd-B model.

Recently, studies on particle behavior under Newtonian and non-Newtonian fluids in microchannel have attracted considerable attention because particles and cells of interest can be manipulated and separated from biological samples without any external force. In this paper, two kinds of microchannels with non-rectangular cross-section were fabricated using basic MEMS processes (photolithography, reactive ion etching and anisotropy wet etching), plasma bonding and self-alignment between two PDMS structures. They were used to achieve the experiments for inertial and elasto-inertial particle focusing under Newtonian and non-Newtonian fluids. The particle behavior was compared and investigated for different flow rates and particle size in the microchannel with rhombic and equilateral hexagonal cross section. We also investigated the influence of Newtonian fluid and viscoelastic fluid on particle migration in both microchannels through the numerical simulation. The experimental results showed the multi-line particle focusing in Newtonian fluid over a wide range of flow rates, but the single-line particle focusing was formed in the centerline under non-Newtonian fluid. The tighter particle focusing appeared under non-Newtonian fluid in the microchannel with equilateral hexagonal cross-section than in the microchannel with rhombic cross section because of the effect of an obtuse angle. It revealed that particles suspended in the channel are likely to drift toward a channel center due to a negative net elasto-inertial force throughout the cross-sectional area. Simulation results support the present experimental observation that the viscoelastic fluid in the microchannel with rhombic and equilateral hexagonal cross-section significantly influences on the particle migration toward the channel center owing to coupled effect of inertia and elasticity.

Abstract We investigate the stability of Rayleigh–Taylor (RT) problem of the stratified incompressible viscoelastic fluids under the rotation and the gravity in a horizontal periodic domain, in which the rotation axis is parallel to the direction of gravity, the two fluids are immiscible, and the heavier fluid lies on the lighter one. We establish a stability condition for the RT problem. Moreover, we prove that, under the stability condition, the RT problem enjoys a unique strong solution, which exponentially decays with respect to time. In addition, we note that the stability condition is independent of rotation angular velocity, and the rotation has no destabilizing effect.

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]

The thermal convection of a Jeffreys fluid subjected to a plane Poiseuille flow in a fluid-porous system composed of a fluid layer and a porous layer is studied in the paper. A linear stability analysis and a Chebyshev τ-QZ algorithm are employed to solve the thermal mixed convection. Unlike the case in a single layer, the neutral curves of the two-layer system may be bi-modal in the proper depth ratio of the two layers. We find that the longitudinal rolls (LRs) only depend on the depth ratio. With the existence of the shear flow, the effects of the depth ratio, the Reynolds number, the Prandtl number, the stress relaxation, and strain retardation times on the transverse rolls (TRs) are also studied. Additionally, the thermal instability of the viscoelastic fluid is found to be more unstable than that of the Newtonian fluid in a two-layer system. In contrast to the case for Newtonian fluids, the TRs rather than the LRs may be the preferred mode for the viscoelastic fluids in some cases. [ABSTRACT FROM AUTHOR]

We performed direct numerical simulations of a turbulent channel flow in viscoelastic fluids to assess various spatial scaling methods and to find a scaling method that can visualise the spatial features regardless of fluid properties. The Giesekus and Oldroyd-B models were used as constitutive equations to model the viscoelastic fluids alongside a Newtonian fluid. The initial scaling method that can consider local viscosity variations demonstrated an increase in the size of the velocity streaks and a decrease in the number of quasi-streamwise vortices, with no change in the observed spatial features of the turbulence structures. After scaling using the ratio of the wall friction coefficients, we observed typical spatial features of the principal turbulence structures that coincided with those of the Newtonian fluid. The results indicate that the characteristics peculiar to the turbulent flow of viscoelastic fluids can be predicted in a manner similar to that for Newtonian fluids. [ABSTRACT FROM AUTHOR]

The combined influence of temperature dependent viscosity and internal heat source on the onset of convection in porous enclosures saturated by a viscoelastic fluid is studied using linear and weak nonlinear stability theories. The enclosures are taken to be rectangular, square, and slender. For the viscoelastic fluid, the Oldroyd‐B type model is used, whereas the Darcy's model is taken for porous medium. The linear theory based on normal mode technique is used to find the criteria for the onset of marginal and oscillatory convections, and weakly nonlinear analysis based on minimal representation of truncated Fourier series is considered to discuss the convective heat transport in the system. It is observed that the beginning of convection will be oscillatory only if the strain retardation parameter is not greater than the stress relaxation parameter. The influence of raising the viscosity variation parameter, the internal heating parameter, and the stress relaxation parameter is to fast the onset of convection and also boost the heat transmission through the porous enclosures, but an opposite tendency is identified by raising the strain retardation parameter and the heat capacity ratio. The heat transmission decreases with the aspect ratio for rectangular enclosure, whereas this outcome is revered for the slender enclosure. [ABSTRACT FROM AUTHOR]

In this work, we studied the linear stability analyses of thermal convection, in a viscoelastic fluid saturated rotating anisotropic porous layer heated from below. The influence of hydrodynamic anisotropy and of rotation on the convective phenomenon are considered and investigated by extending the modified Darcy-Maxwell-Jeffrey model to include the Coriolis force term. It is shown that the anisotropic permeability ratio K , the inclination angle of the principal axes ( φ) of the porous medium, the relaxation time ( ε), the retardation time ( ζ) and the Taylor Darcy number ( T D ) have a strong influence on the convective flow. [ABSTRACT FROM AUTHOR]

The hydrodynamics of a steady-state nonisothermal flow of a viscoelastic polymer medium in a plane channel and heat transfer in it under boundary conditions of the first kind have been investigated. Fluid flow with a low Reynolds number and a high Péclet number was investigated, which made it possible to neglect the gravity and inertial forces, as well as the longitudinal thermal conductivity of the medium. From the rheological viewpoint, the polymer melt represents a viscoelastic fluid; therefore the Phan-Thien–Tanner fluid model was used as a rheological model of the fluid, with viscosity depending on temperature and pressure. A high-viscosity medium was considered; therefore a dissipation term was included into the equation of the energy of its flow. With the use of the indicated rheological model the velocity profile of fluid flow was obtained in an explicit form from the equation of fluid motion. It has been established that the dependence of the fluid viscosity on temperature and pressure exerts a noticeable influence on the distribution of the Nusselt number and of bulk temperature of the fluid along the channel length. It is shown that account for the temperature dependence of fluid viscosity leads to a decrease in the role of energy dissipation of its flow in the process of flow heating and that, conversely, the dependence of the fluid viscosity on pressure considerably enhances the dissipation effect. The problem has been solved numerically by the method of finite differences. [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]

In this article, we explore the three-dimensional boundary-layer flow over an exponentially stretching surface in two parallel ways. Constitutive equations of a second-grade fluid are used. Instead of classical Fourier's law, Cattaneo–Christov heat flux model is employed for the formulation of the energy equation. This model can predict the effects of thermal relaxation time on the boundary layer. The resulting partial differential equations are reduced into ordinary differential equations by similarity transformations. Homotopy Analysis Method (HAM) is employed to solve the non-linear problem. Physical impact of emerging parameters on the momentum and thermal boundary-layer thickness are studied. [ABSTRACT FROM AUTHOR]

When a polymer is extruded freely from a rectangular die of large cross‐sectional aspect ratio, wrinkles are observed. While not present in extruded Newtonian materials, such wrinkles develop in extruded viscoelastic sheets and are understood as an elastic stress‐driven instability. The present study is devoted in developing a transient finite element method, which combines the matrix‐logarithm‐based formulation of the conformation tensor and the single‐phase level set method, for simulating wrinkles that form during sheet extrusion of viscoelastic fluids. Numerical analyses of sheet extrusion were conducted over a wide range of flow rate and width‐to‐thickness ratio of the die exit cross section, χ, to determine critical conditions for the onset of wrinkling of extruded sheets. For large aspect ratios, that is, χ >> 1, wrinkles develop at moderate extrusion flow rate, corresponding to a Weissenberg number of about 29. Calculations based on Rayleigh's energy method show that the critical compressive stress, σc, for the onset of wrinkling of an elastic sheet scales like σc~1/χ2, with a significant drop for χ >> 1. As next to the die exit lip, compressive normal stresses are induced in the extruded sheet, wrinkling will take place for large χ (σc being small), in accordance with numerical predictions. [ABSTRACT FROM AUTHOR]

Vibration characteristics of elastic nanostructures embedded in fluid medium have been used for biological and mechanical sensing and also to investigate the materials mechanical properties. The fluid medium surrounding the nanostructure is typically modeled as a Newtonian fluid. A novel approach based on the exact theory has been developed in this paper, to accurately predict the various vibration scenarios of an elastic sphere, in a compressible viscous fluid. Then, the analysis is extended to a viscoelastic medium using the Maxwell fluid model. To demonstrate the accuracy of the present approach, a comparison is made with the published theoretical results in the literature in some particular cases, which shows a very good agreement. The effects of fluid compressibility and viscoelasticity are discussed in details, and we demonstrate that the fluid compressibility plays a significant role in the vibration modes of an elastic sphere. Results also show that the different vibration modes of a sphere trigger a viscoelastic response in water–glycerol mixtures similar to that of literature. In addition, the obtained results can serve as benchmark solution in design of liquid sensors. [ABSTRACT FROM AUTHOR]

Heat and mass transmission taking place in a magnetohydrodynamics fluid of substantial viscosity via a permeable object has been currently a subject of study inviting research. This transmission takes place along an infinite expanding vertical surface showing Soret and Dufour effects. Differential forms of nonlinear nature such as energy, momentum, and equations defining concentration are ascertained by means of similarity transformation with the existing buoyancy force, and by making use of the homotopy analysis method, the equations have been analytically resolved. The impacts arising out of applied factors on temperature, velocity, and concentration forms have been appropriately designed and established. [ABSTRACT FROM AUTHOR]

We report a 6D nonlinear dynamical system for thermo-viscoelastic fluid by selecting higher modes of infinite Fourier series of flow quantities. This nonlinear system demonstrates overstable convective motion and some organized structures such as period-bubbling and Arnold tongue-like structures. Studies reveal that the stability of the conduction state does not alter for the new 6D system in comparison with the lowest order 4D system of Khayat [1995]. However, the stabilities of the convective state have some differences. The onset of unsteady convection in the 6D system is delayed for weak elasticity of the fluid. There exists a critical range of fluid elasticity where the 4D system exhibits subcritical Hopf bifurcation while the 6D system shows supercritical Hopf bifurcation, which ensures the increase of the domain of stability. In this range, catastrophic route to chaos occurs in the 4D system, whereas the 6D system exhibits intermittent onset of chaos. Comparing the two-parameter dependent dynamics for the two systems, the chaotic zones enclosed by periodic regions are suppressed in the 6D system, so the flow behaviors become more predictable. Owing to interacting thermal buoyancy and fluid elasticity, both the models exhibit period-bubbling transition to chaos, but the period-bubbling cascade in the 6D model occurs at lower Rayleigh number than the 4D model. The convergence rate of the period-bubbling process slows down compared to usual period-doubling and approaches the square root of the Feigenbaum constant asymptotically. [ABSTRACT FROM AUTHOR]

The working temperature of a bituminous pavement can typically range from 75 ∘ C to − 20 ∘ C. Bitumen shows a wide spectrum of mechanical behaviour in this temperature range and these include those of a viscoelastic fluid, a viscoelastic solid and an elastic solid. Due to the amorphous nature of the material, the transitions between such mechanical responses are gradual. This investigation focuses on the transition between the viscoelastic solid and the viscoelastic fluid state of a wide class of bitumens with regard to unaged and short-term aged conditions. An unmodified binder and three modified binders were subjected to temperature sweep and frequency sweep in the viscoelastic regime across a wide range of temperatures. Depending on the material and the post-processing method followed, one could discern a viscoelastic fluid and a viscoelastic solid regime and a frequency-dependent mixture regime consisting of a viscoelastic solid and a viscoelastic fluid, across the tested temperatures and frequencies. It is shown in this investigation that parameters such as G ′ –G ′′ crossover and frequency independence of tan δ cannot be used to estimate the temperatures corresponding to the onset of either fluid-like or solid-like behaviour of the body as the temperature varies. It is also shown that the time–temperature superposition principle does not hold good in the temperature regime tested (75–25 ∘ C) due to the viscoelastic transitions exhibited by bitumen and modified bitumen. [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 investigate the combined effects of homogeneous and heterogeneous reactions in the boundary layer flow of a viscoelastic nanofluid over a stretching sheet with nonlinear thermal radiation. The incompressible fluid is electrically conducting with an applied a transverse magnetic field. The conservation equations are solved using the spectral quasi-linearization method. This analysis is carried out in order to enhance the system performance, with the source of entropy generation and the impact of Bejan number on viscoelastic nanofluid due to a partial slip in homogeneous and heterogeneous reactions flow using the spectral quasi-linearization method. Various fluid parameters of interest such as entropy generation, Bejan number, fluid velocity, shear stress heat and mass transfer rates are studied quantitatively, and their behaviors are depicted graphically. A comparison of the entropy generation due to the heat transfer and the fluid friction is made with the help of the Bejan number. Among the findings reported in this study is that the entropy generation has a significant impact in controlling the rate of heat transfer in the boundary layer region. [ABSTRACT FROM AUTHOR]

The processes of heat exchange and of nonisothermal crystallization in the formation of a plane viscoelastic polymer film are investigated. The polymer melt is forced through a plane-slitted extrusion head, subjected to uniaxial stretching and simultaneously to cooling in air, and subsequently gaining access onto a batch-off cooling roll. It is assumed that the film is wide enough, and the distance between the extruder head and the batch-off roll is minimum to such a degree that it is possible to neglect the change in the sheet width in the process of longitudinal stretching. A steady nonisothermal process is considered. It is also considered that the gravity and inertial forces and surface stretching can be neglected. From the rheological point of view, the polymer melt represents a viscoelastic fluid. The upper-convected Maxwell model is used with viscosity depending on temperature and crystallinity degree. The mathematical model is complemented by the equation of kinetics of nonisothermal crystallization. The problem has been solved numerically by the method of finite differences. [ABSTRACT FROM AUTHOR]

The model developed in this study presents a mathematical approach to the physiological transport of seminal liquid due to ciliary movements, which are attached with the lumen of the ductile efferent in the male reproductive system. The rheological properties of the seminal liquids were described using the Jeffrey liquid model. The problem described an electromagnetic mixed convective flow of a Jeffrey liquid through a vertical channel with heat and mass transfers. The effects of chemical reactions and the external heat generation were included in the formulation. The flow took place through an active porous medium (due to thick cilia mat and other deposits) and was influenced by the Lorentz magnetic force. Four basic conservation laws of mass, momentum, energy, and concentration were utilized in the mathematical modeling. These are highly nonlinear equations, which were simplified due to a physiologically valid approach known as LAT (lubrication approximation theory). Analytical solutions for temperature, concentration, and velocity profiles were evaluated. The expressions describing the pressure–volume flow rate relationships were also obtained. Analysis of various physical and geometrical factors affecting the pressure–volume (pumping) characteristics was also presented. One of the main findings of our study is that the difference between our calculated values of the flow rate and the estimated values of the flow rate in the ductile efferent was negligibly small. Moreover, our results can be implemented in the artificial cilia pumping systems in microchannels. [ABSTRACT FROM AUTHOR]

Manipulation of micro‐ and nanoparticles in complex biofluids is highly demanded in most biological and biomedical applications. A significant number of microfluidic platforms have been developed for inexpensive, rapid, accurate, and efficient particle manipulation. Due to the enormous potential of viscoelastic fluids (VEFs) for particle manipulation, various emerging microfluidic‐based VEFs techniques have been presented over the last decade. This review provides an intuitive understanding of VEF physics for particle separation in different microchannel geometries. Besides, active and passive VEF methods are critically reviewed, highlighting the potential and practical challenges of each technique for particle/cell focusing, sorting, and separation. The outcome of this study could enable recognizing deliverable VEF technology with the promising prospect in the manipulation of submicron biological samples (e.g., exosomes, DNA, and proteins). Highlights: 1.The state of the art of viscoelastic fluid (VEF) flow in microfluidics for micro‐ and nano‐(bio)particle manipulation is discussed.2.A comprehensive critical review of active and passive methods for particle manipulation in viscoelastic flows within microfluidic is provided, and the pros and cons of each method are explained.3.The promising viscoelastic microfluidic methods for particle sorting and separation are highlighted and potential future applications are presented.4.This review is intended to facilitate recognizing deliverable VEF technology with unprecedented functionality for next generation of VEF microfluidics with the application in biological sample processing and particle manipulation. [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]

This paper consists of a mathematical analysis of MHD free convective flow of viscoelastic fluid through a porous regime in an inclined channel. The flow system is permeated by a uniform moving magnetic field with strong magnetic intensity to produce Hall and ion-slip effects. The flow governing equations are obtained from the suitable field and constitutive equations and solved analytically. To accentuate the consequences of various flow controlling parameters to the nature of the flow, numerical results are discussed in assistance with graphs and tables. An important fact noted from the study that Hall current generates the flow in the direction perpendicular to the main flow while ion-slip current reduces the flow in the direction perpendicular to the main flow. It is also seen that the moving magnetic field produces less rigidity in the flow in comparison to the stationary magnetic field. [ABSTRACT FROM AUTHOR]

Viscoelastic fluids represent a major challenge both from an engineering and from a mathematical point of view. Recently, we have shown that viscoelasticity induces chaos in closed‐loop thermosyphons even when we consider binary fluids, this is, when we consider a solute in the fluid, as water and antifreezes, for example. In this work, we consider a linear friction law, and we show that in this case with the addition of a solute to the fluid we can prove, under some conditions, chaotic asymptotic behavior for suitable geometry of the circuit and heat flux or ambient temperature functions. [ABSTRACT FROM AUTHOR]

The miscible displacement of a Newtonian fluid pushed by a nonlinear viscoelastic fluid (viscous fingering instability) has been investigated via a pseudospectral method and Hartley transform. The results of the present study could be useful for enhanced oil recovery (EOR) using chemical flooding technique. Here, the Giesekus model is applied as the constitutive equation of viscoelastic fluid. In addition to the homogeneous media, the simulations are performed for a horizontal layered heterogeneous medium and the results are presented as concentration contours, transversely averaged concentration profiles, mixing length, and sweep efficiency. It is concluded that the heterogeneity of the medium has a great effect on the flow structure. The channeling regime is observed in these media. Higher layers in the heterogeneous medium reduces the intensity of instability while permeability variance acts on the contrary. This is the first attempt in simulation of the viscoelastic-Newtonian displacement (polymer flooding) in heterogeneous media. [ABSTRACT FROM AUTHOR]