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This study reports the influence of the dead zone (DZ) formed around obstacles due to the viscoelastic fluid flow on the flow behavior and properties. It is known that when a viscoelastic fluid, which is a semi-dilute polymer solution, is infused into a channel with structures resembling a pillar, a DZ is formed around the structure owing to the shear-variation-induced viscosity changes. In this study, hydrolyzed polyacrylamide solutions were infused into a microchannel with a triangle-shaped pillar array. Furthermore, the continuous contraction and expansion flow around the pillars were investigated using a micro-particle image velocimetry. The flow measurement results showed that the shape of DZ changes depending on the Weissenberg number, and accordingly, the flow behavior around and inside the DZ changes. In particular, it was confirmed that the velocity fluctuations trend in the entire flow field increased with the growth in DZ. Moreover, it was found that the shear caused by the velocity difference between the DZ and the other region induces a non-uniform viscosity distribution in the DZ, resulting in the formation of a complex flow containing both extension and rotation behavior inside the DZ. [ABSTRACT FROM AUTHOR]

Intricate fluid displacement patterns, arising from the unstable growth of interfacial perturbations, can be driven by fluid viscoelasticity and surface tension. A soft glassy suspension ages, i.e. its mechanical moduli evolve with time, due to the spontaneous formation of suspension microstructures. The shear and time-dependent rheology of an aging suspension can be exploited to generate a wide variety of interfacial patterns during its displacement by a Newtonian fluid. Using video imaging, we report a rich array of interfacial pattern morphologies: dense viscous, dendritic, viscoelastic fracture, flower-shaped, jagged and stable, during the miscible and immiscible displacements of an aging colloidal clay suspension by Newtonian fluids injected into a radial quasi-two-dimensional geometry at different flow rates. We propose a new parameter, the areal ratio, which we define as the fully developed pattern area normalized by the area of the smallest circle enclosing it. We show that the natural logarithms of the areal ratios uniquely identify the distinct pattern morphologies, such that each pattern can be segregated in a three-dimensional phase diagram spanned by the suspension aging time, the displacing fluid flow rate, and interfacial tension. Besides being of fundamental interest, our results are useful in predicting and controlling the growth of interfaces during fluid displacements.

We study the statistical properties of the variation of the kinetic energy of a spherical Brownian particle that freely moves in an incompressible fluid at constant temperature. Based on the underdamped version of the generalized Langevin equation that includes the inertia of both the particle and the displaced fluid, we derive an analytical expression for the probability density function of such a kinetic energy variation during an arbitrary time interval, which exactly amounts to the energy exchanged with the fluid in absence of external forces. We also determine all the moments of this probability distribution, which can be fully expressed in terms of a function that is proportional to the velocity autocorrelation function of the particle. The derived expressions are verified by means of numerical simulations of the stochastic motion of a particle in a viscous liquid with hydrodynamic backflow for representative values of the time-scales of the system. Furthermore, we also investigate the effect of viscoelasticity on the statistics of the kinetic energy variation of the particle, which reveals the existence of three distinct regimes of the energy exchange process depending on the values of the viscoelastic parameters of the fluid. • Derivation of probability distribution of heat exchanged between a Brownian particle and a liquid. • Hydrodynamic backflow and viscoelasticity of the liquid give rise to non-Markovian dynamics. • The heat probability distribution is expressed in terms of the velocity autocorrelation function of the particle. • Memory effects enhance the energy transfer with respect to that taking place in a Markovian bath. [ABSTRACT FROM AUTHOR]

To investigate the Brownian motion of individual particles suspended in viscoelastic fluids, the stochastic smoothed profile method (SPm) for direct numerical simulation is developed by extending deterministic SPm for suspensions in viscoelastic media. To simulate viscoelastic flow driven by thermal fluctuations in the suspending medium, the random stress in the fluid momentum equation as well as the random driving force for the conformation tensor in the Oldroyd-B model are incorporated according to the fluctuating hydrodynamics and fluctuating viscoelasticity formalisms. The thermal equilibrium and dynamical properties calculated by using numerical simulations successfully reproduce the analytic predictions, validating the direct simulation for the coupled fluctuating Navier–Stokes and Oldroyd-B equations and for the coupling between the stochastic viscoelastic medium and individual particles. As an application of the stochastic SPm, we investigate finite system-size effects under periodic boundary conditions (PBCs) on the passive microrheological relationship between the mean-square displacement (MSD) of a Brownian particle and the medium's dynamic modulus. Comparing the modulus that was microrheologically calculated from the MSD with the input modulus reveals that the effect of periodic image cell interaction appears not only in the long-time diffusive regime but also in the short-time region. A frequency-dependent finite system-size correction is implemented by phenomenologically extending the long-time diffusive regime correction, allowing passive microrheology analysis under PBCs. This result can be directly applied to other mesoscale numerical simulations including coarse-grained molecular dynamics and dissipative particle dynamics simulations. • A direct simulation for particle dynamics in thermally driven viscoelastic flow is developed. • Fluctuating viscoelasticity is combined with Smoothed profile method. • Simulated thermally driven viscoelasitc flow and Brownian motion are validated. • Passive microrheology under periodic boundary conditions is analyzed. • Direct simulation reveals a frequency-dependent finite system-size correction. [ABSTRACT FROM AUTHOR]

In this paper, we consider the magnetohydrodynamic (MHD) flow of an incompressible Phan-Thien–Tanner (PTT) fluid in two space dimensions. We focus upon the sharp time decay rates (upper and lower bounds) and global-in-time stability of large strong solutions for the PTT system with magnetic field. Firstly, the convergence of large solutions to the equilibrium have been investigated and these convergence rates are shown to be sharp. We then show that two large solutions converge globally in time as long as two initial data are close to each other. One of the main objectives of this paper is to develop a way to capture L 2 -convergence result via auxiliary logarithmic time decay estimates with the initial data in L p (R 2) ∩ L 2 (R 2). Improving time decay rates for the high-order derivatives of large solutions by using interpolation inequalities. In addition, time-weighted energy estimate, Fourier time-splitting method, semigroup method and iterative scheme have also been utilized. [ABSTRACT FROM AUTHOR]

We investigate the initial-boundary value problem of the three-dimensional compressible viscoelastic fluids with the electrostatic effect, in which the Dirichlet-Neumann mixed boundary condition for the electrostatic potential is imposed. We prove that there exists a unique global-in-time small strong solution in H 2 Sobolev space. Moreover, we show that such a solution converges to the constant equilibrium state with an exponential decay rate as time tends to infinity. [ABSTRACT FROM AUTHOR]

This paper is concerned with the two dimensional motion of a finite number of homogeneous rigid disks in a cavity filled with incompressible viscoelastic fluids which obey constitutive laws of differential type. We focus here on two types of differential constitutive laws which are commonly used to describe the flow of dilute solutions of polymeric liquids: the first one corresponds to the regularized Oldroyd model whereas the other one corresponds to the Oldroyd model. The movement of rigid bodies modifies the fluid domain and hence we are dealing with a free boundary problem. By using fixed point theorem, we prove the existence and uniqueness of local-in-time strong solutions of the considered moving-boundary problem for both models. [ABSTRACT FROM AUTHOR]

It is well-known that viscoelasticity is a material property that exhibits both viscous and elastic characteristics with deformation. In particular, an elastic fluid strains when it is stretched and quickly returns to its original state once the stress is removed. In this review, we first introduce some mathematical results, which exhibit the stabilizing effect of elasticity on the motion of viscoelastic fluids. Then we further briefly introduce similar stabilizing effect in the elastic fluids. [ABSTRACT FROM AUTHOR]

We study control properties of a linearized fluid–structure interaction system, where the structure is a rigid body and where the fluid is a viscoelastic material. We establish the approximate controllability and the exponential stabilizability for the velocities of the fluid and of the rigid body and for the position of the rigid body. In order to prove this, we prove a general result for this kind of systems that generalizes in particular the case without structure. The exponential stabilization of the system is obtained with a finite-dimensional feedback control acting only on the momentum equation on a subset of the fluid domain and up to some rate that depends on the coefficients of the system. We also show that as in the case without structure, the system is not exactly null-controllable in finite time. [ABSTRACT FROM AUTHOR]

This paper presents the numerical analysis of the three-field stabilized formulation based on the one-level local projection stabilization (LPS) for computations of the coupled Navier-Stokes and Oldroyd-B viscoelastic constitutive equations. Due to dominating convective terms, the velocity-pressure-stress formulation suffers from numerical instability in viscoelastic flows. The other challenges are the necessity of the inf-sup conditions for the velocity-pressure and stress-velocity couplings in equal-order interpolations. One-level local projection stabilization scheme allows us to use equal-order interpolation spaces for the velocity and the viscoelastic stress, whereas inf-sup stable finite elements are used for the velocity and the pressure approximations. The local projection method is based on a projection π h : V h → D h of finite element approximation space V h into a discontinuous space D h . In one-level LPS, the approximation and projection spaces are defined on the same mesh, with an enriched approximation space. We prove the stability and a priori error analysis, ensuring the optimal order of convergence of the proposed numerical scheme. The numerical result validates the theoretical estimates. [ABSTRACT FROM AUTHOR]

Fused deposition modelling is one of the most widely used additive manufacturing techniques and the diffusion of 3D printers has increased in popularity even further in recent times. Since high precision is required in 3D printing, a good control over the extrusion process is necessary. In this regard, a crucial phenomenon to be accounted for is the die or extrudate swell, i.e., the enlargement of the cross-section of the strand when coming out of the printer nozzle. While this phenomenon has been studied in large scale extruders, it has not yet been investigated in depth for 3D printing processes. In this work, the die swell phenomenon observed in a printed PLA filament is studied by experiments and fluid dynamic simulations. A novel, easy-to-use, accurate and fast procedure for measuring the value of the die swell ratio during the printing process is developed, accounting for typical errors related to a non-constant strand diameter and possible oscillations of the filament with respect to the extrusion direction. As the printing velocity is increased, a linearly increasing swelling ratio is observed at low printing speeds. The trend flattens at moderate speed values. A sudden increase is found at high printing velocities. The swelling ratio measured with the proposed technique is compared with the results of multi-mode viscoelastic simulations at different temperatures. A fair agreement between the experimental measurements and the numerical predictions is found for printing velocities that are typically employed in commercial 3D printers, supporting the reliability of the developed procedure.

A new concept of semi-compressible fluids is introduced for slightly compressible visco-elastic fluids (typically rather liquids than gasses) where mass density variations are negligible in some sense, while being directly controlled by pressure which is very small in comparison with the elastic bulk modulus. The physically consistent fully Eulerian models with specific dispersion of pressure-wave speed are devised. This contrasts to the so-called quasi-incompressible fluids which are described not physically consistently and, in fact, only approximate ideally incompressible ones in the limit. After surveying and modifying models for the quasi-incompressible fluids, we eventually devise some fully convective models complying with energy conservation and capturing phenomena as pressure-wave propagation with wave-length (and possibly also pressure) dependent velocity. [ABSTRACT FROM AUTHOR]

In this work, we present a numerical study on the development length (the length from the channel inlet required for the velocity to reach 99 % of its fully-developed value) of a pressure-driven viscoelastic fluid flow (between parallel plates) modelled by the generalised Phan–Thien and Tanner (gPTT) constitutive equation. The governing equations are solved using the finite-difference method, and, a thorough analysis on the effect of the model parameters α and β is presented. The numerical results showed that in the creeping flow limit ( R e = 0 ), the development length for the velocity exhibits a non-monotonic behaviour. The development length increases with W i . For low values of W i , the highest value of the development length is obtained for α = β = 0.5 ; for high values of W i , the highest value of the development length is obtained for α = β = 1.5 . This work also considers the influence of the elasticity number. [ABSTRACT FROM AUTHOR]

Chyme is propelled through large and small intestines by peristalsis which is a wavelike propulsion of muscular contraction and relaxation. Chyme is a strongly rheological biofluid and requires non-Newtonian models for accurate simulation. Motivated by gastric transport applications, in this paper, a peristaltic transport model is developed to analyze the hydrodynamics of chyme movement through the large intestine. Chyme is modelled with the generalized (fractional) Maxwell viscoelastic model. The geometry for the large intestine is approximated as a two-dimensional curved channel. The analysis is carried out under the lubrication theory and low Reynolds number approximation. The approximate solutions of the governing equations under complex boundary conditions are obtained by deploying the Reduced Differential Transformation Method. Trapping phenomena are also analyzed graphically. The effects of fractional parameter, relaxation time, curvature and amplitude on the pressure difference and friction force are visualized graphically and interpreted in detail. The present simulations are applicable in gastric transport phenomena and the design of novel intestinal devices (colonoscopy) in biomedical engineering. [ABSTRACT FROM AUTHOR]

Elasto-inertial turbulence (EIT), a new turbulent state found in polymer solutions with viscoelastic properties, is associated with drag-reduced turbulence. However, the relationship between EIT and drag-reduced turbulence is not currently well-understood, and it is important to elucidate the mechanism of the transition to EIT. The instability of viscoelastic fluids has been studied in a canonical wall-bounded shear flow to investigate the transition process of EIT. In this study, we numerically deduced that an instability occurs in the linearly stable viscoelastic plane Couette flow for lower Reynolds numbers, at which a non-linear unstable solution exists. Under instability, the flow structure is elongated in the spanwise direction and regularly arranged in the streamwise direction, which is a characteristic structure of EIT. The regularity of the flow structure depends on the Weissenberg number, which represents the strength of elasticity; the structure becomes disordered under high Weissenberg numbers. In the energy spectrum of velocity fluctuations, a steep decay law of the structure’s scale towards a small scale is observed, and this can be recognized as a ubiquitous feature of EIT. The existence of instability in viscoelastic plane Couette flow supports the idea that the transitional path toward EIT may be mediated by subcritical instability.

Two-dimensional steady laminar natural convection of a viscoelastic fluid represented by generalized second-grade fluid model in a square enclosure is studied. The cavity is submitted at its vertical sides to a uniform density of heat flux while the horizontal walls are insulated, without slipping conditions at all the solid boundaries. The governing conservation and constitutive equations with the corresponding boundary conditions are solved by finite volume method in a collocated grid system. The contributions of shear rate dependent and elastic characteristics of the viscoelastic fluid are investigated on momentum and heat transport. The effects of elastic number (E) in the range 0 - 1 on heat transfer and fluid motion are interpreted for a power-law index (n) in the range 1.4 - 0.6 and nominal values of Rayleigh number (Ra) range of 10³ to 105. [ABSTRACT FROM AUTHOR]

Polymer solutions are often described as viscoelastic fluids, whose rheological behavior dynamically evolves according to the flow shear rate due to successive contractions and relaxations of inner deformable components. Contrary to shear-thickening and shear-thinning fluids, viscoelastic fluids can undergo an increase in the normal stress-differences even in simple geometries, leading to counterintuitive flow patterns. In this paper, we investigate numerically the monophasic flow of viscoelastic fluids through microfluidic devices. The objective is to qualitatively assess how modification of the rheological properties and the geometry of porous media representative element affect the flow regime at microscale. Deviations from equivalent Newtonian model are analyzed to quantify the contribution of elasticity in the flow. It is demonstrated that depending on the geometry, flow of polymer solution can display anisotropic features and flow resistance at relatively low viscoelastic numbers, which is coherent with previous microscopic experimental and numerical studies. Ensued applications of the formulated microscale model are discussed. [ABSTRACT FROM AUTHOR]

The main aim of this research work is to establish, under fully developed conditions, an analytical solution for viscoelastic fluids flow obeying the constitutive Phan–Thien–Tanner (PTT) and Finely Extensible Nonlinear Elastic-Peterlin (FENE-P) models. In fact, a unified formulation for laminar, stationary and fully developed flow in the cases of circular and flat ducts geometries is obtained for velocity profile involving PTT and FENE-P models. In this investigation, the effect of pressure gradient on velocity profile, shear stress, shear rate and shear viscosity is explored. Effects of pressure gradient and Weissenberg number on normal stress are also studied and discussed. [ABSTRACT FROM AUTHOR]

Cuttings transport from wellbore annulus to the surface via drilling fluids is one of the most important problems in gas and oil industries. In the present paper, the effects of viscoelastic property of drilling fluids on flow through wellbore annulus are studied numerically by use of computational fluid dynamics simulation in OpenFOAM software. This problem is simulated as the flow between two coaxial annulus cylinders and the inner cylinder is rotating through its axes. Here, the Giesekus model is used as the nonlinear constitutive equation. This model brings the nonlinear viscosity, normal stress differences, extensional viscosity and elastic property. The numerical solution is obtained using the second order finite volume method by considering PISO algorithm for pressure correction. The effect of elasticity, Reynolds number, Taylor number and mobility factor on the velocity and stress fields, pressure drop, and important coefficient of drilling mud flow is studied in detail. The results predicted that increasing elastic property of drilling mud lead to an initial sharp drop in the axial pressure gradient as well as Darcy-Weisbach friction coefficient. Increasing the Reynolds number at constant Taylor number, resulted an enhancing in the axial pressure drop of the fluid but Darcy-Weisbach (f) friction coefficient mainly reduced. [ABSTRACT FROM AUTHOR]

In this paper we present the numerical analysis of a finite element method for a linearized viscoelastic flow problem. In particular, we analyze a linearization of the logarithmic reformulation of the problem, which in particular should be able to produce results for Weissenberg numbers higher than the standard one. In order to be able to use the same interpolation for all the unknowns (velocity, pressure and logarithm of the conformation tensor), we employ a stabilized finite element formulation based on the Variational Multi-Scale concept. The study of the linearized problem already serves to show why the logarithmic reformulation performs better than the standard one for high Weissenberg numbers; this is reflected in the stability and error estimates that we provide in this paper. [ABSTRACT FROM AUTHOR]

Cell‐derived microvesicles (MVs, also known as microparticles, MPs) are known as important biomarkers of various diseases including cardiovascular diseases, infectious diseases, and cancer. Development of techniques for blood cell removal and MV isolation is required for downstream analyses in biological and clinical applications. A sheathless, label‐free, viscoelastic microfluidic device is proposed for the separation of submicrometer platelet‐derived MPs (PDMPs) from whole blood. Flow rate and channel length dependent performance of the device is evaluated using 2‐µm particles as analogs to platelets and hematocrit (Hct) dependent flow characteristics of red blood cells (RBCs) are observed. In addition, the removal rate of nanoparticles of sizes 300, 500, 700, and 1000 nm is evaluated, and finally, the device is applied to examine the recovery of PDMPs from diluted whole blood sample. At Q = 200 µL min−1 in a 15‐mm long microchannel, RBCs at 5% Hct and platelets are removed to the central outlet without platelet activation, while PDMPs are successfully isolated to the side outlets within ≈2 min. The PDMPs collected from the device are analyzed by flow cytometry. The device exhibits ≈4.8‐fold enhanced isolation performance compared to the centrifugation method. [ABSTRACT FROM AUTHOR]

This paper presents a numerical evaluation of two different artificial stress diffusion techniques for the stabilization of viscoelastic Oldroyd-B fluid flows at high Weissenberg numbers. The standard artificial diffusion in the form of a Laplacian of the extra stress tensor is compared with a newly proposed approach using a discrete time derivative of the Laplacian of the extra stress tensor. Both methods are implemented in a finite element code and demonstrated in the solution of a viscoelastic fluid flow in a two-dimensional corrugated channel for a range of Weissenberg numbers. The numerical simulations have shown that this new temporal stress diffusion not only efficiently stabilizes numerical simulations, but also vanishes when the solution reaches a steady state. It is demonstrated that in contrast to the standard tensorial diffusion, the temporal artificial stress diffusion does not affect the final solution.

A mathematical investigation on the combined effect of oscillation and conjugation on the enhancement of heat transfer in a heat pipe called Dream Pipe is carried out, when viscoelastic fluids (CPyCl/NaSal) are employed as the heat carriers. Closed-form solutions for the momentum and heat equations are presented. The physical and thermal properties of the polymer solution used are obtained by experiments. The effects of thermal conductivity and thickness of the wall, fluid thickness, Womersley number (α), Deborah number and Prandtl number on the enhancement of heat transfer are examined. Results obtained in the present analysis are in excellent agreement with those of the existing literature. The effective thermal diffusivity (κe) is maximized at optimum α where the fluid flow exhibits a resonant behavior. Several maxima occur in κe for several resonant frequencies and the dramatic increase in κe due to oscillation for the viscoelastic fluid is 5.63 x 109 times higher than that obtained by the molecular motion. This increase is much higher than that (1.84 x 104 times) obtained for the Newtonian fluid. κe is increased with increasing wall thermal conductivity and thickness in the viscous regime whereas in the elastic regime the effect of conjugation is saturated. In the viscous regime, a maximum increase of 50.63% in κe is obtained by optimizing the wall thickness. Also κe increases with increasing molar ratio of concentrations of counterion to surfactant. A maximum heat flux of 4.54 x 1010 W/m2 is achieved using a viscoelastic fluid with thermally conducting wall and this highest heat flux is 207 times higher than that (2.19 x 108 W/m2) obtained with the Newtonian fluid (liquid metal). Hence, viscoelastic fluids are preferable to liquid metals as working fluids in the Dream Pipe. The new insights gained by the present investigation are useful while designing viscoelastic Dream Pipes and micro channel heat exchangers.

Based on a bootstrap instability method, we prove the existence of unstable strong solutions in the sense of L 1 -norm to an abstract Rayleigh–Taylor (RT) problem arising from stratified viscous fluids in Lagrangian coordinates. In the proof we develop a method to modify the initial data of the linearized abstract RT problem by exploiting the existence theory of a unique solution to the stratified (steady) Stokes problem and an iterative technique, such that the obtained modified initial data satisfy the necessary compatibility conditions on boundary of the original (nonlinear) abstract RT problem. Applying an inverse transform of Lagrangian coordinates to the obtained unstable solutions and taking then proper values of the parameters, we can further obtain unstable solutions of the RT problem in viscoelastic, magnetohydrodynamics (MHD) flows with zero resistivity and pure viscous flows (with/without interface intension) in Eulerian coordinates. [ABSTRACT FROM AUTHOR]

In this work, we establish the unique global solvability of the stochastic two dimensional viscoelastic fluid flow equations, arising from the Oldroyd model for the non-Newtonian fluid flows perturbed by multiplicative Gaussian noise. A local monotonicity property of the linear and nonlinear operators and a stochastic generalization of the Minty–Browder technique are exploited in the proofs. The Laplace principle for the strong solution of the stochastic system is established in a suitable Polish space using a weak convergence approach. The Wentzell–Freidlin large deviation principle is proved using the well known results of Varadhan and Bryc. The large deviations for shot time are also considered. We also establish the existence of a unique ergodic and strongly mixing invariant measure for the stochastic system with additive Gaussian noise, using the exponential stability of strong solutions. [ABSTRACT FROM AUTHOR]

Summary: A three‐field local projection stabilized (LPS) finite element method is developed for computations of a three‐dimensional axisymmetric buoyancy driven liquid drop rising in a liquid column where one of the liquid is viscoelastic. The two‐phase flow is described by the time‐dependent incompressible Navier‐Stokes equations, whereas the viscoelasticity is modeled by the Giesekus constitutive equation in a time‐dependent domain. The arbitrary Lagrangian‐Eulerian (ALE) formulation with finite elements is used to solve the governing equations in the time‐dependent domain. Interface‐resolved moving meshes in ALE allows to incorporate the interfacial tension force and jumps in the material parameters accurately. A one‐level LPS based on an enriched approximation space and a discontinuous projection space is used to stabilize the numerical scheme. A comprehensive numerical investigation is performed for a Newtonian drop rising in a viscoelastic fluid column and a viscoelastic drop rising in a Newtonian fluid column. The influence of the viscosity ratio, Newtonian solvent ratio, Giesekus mobility factor, and the Eötvös number on the drop dynamics are analyzed. The numerical study shows that beyond a critical Capillary number, a Newtonian drop rising in a viscoelastic fluid column experiences an extended trailing edge with a cusp‐like shape and also exhibits a negative wake phenomena. However, a viscoelastic drop rising in a Newtonian fluid column develops an indentation around the rear stagnation point with a dimpled shape. [ABSTRACT FROM AUTHOR]

In this work, we consider the two-dimensional viscoelastic fluid flow equations, arising from the Oldroyd model for the non-Newtonian fluid flows. We investigate the well-posedness of such models in two-dimensional bounded and unbounded (Poincaré domains) domains, both in deterministic and stochastic settings. The existence and uniqueness of weak solution in the deterministic case is proved via a local monotonicity property of the linear and nonlinear operators and a localized version of the Minty-Browder technique. Some results on the exponential stability of stationary solutions are also established. The global solvability results for the stochastic counterpart are obtained by a stochastic generalization of the Minty-Browder technique. The exponential stability results in the mean square as well as in the pathwise (almost sure) sense are also discussed. Using the exponential stability results, we finally prove the existence of a unique invariant measure, which is ergodic and strongly mixing. [ABSTRACT FROM AUTHOR]

This theoretic study focuses on investigating the Jeans instability excitation dynamics in strongly correlated astrofluid media confined in a vast spherically symmetric volume. A spherically symmetric normal mode analysis over the perturbed spherical medium leads to a quadratic dispersion relation of atypical analytic construct. It is specifically shown that the effect of geometrical curvature introduces a compound viscous influence onto the dispersion relation against the earlier reports analytically based on a planar parallel geometry instead. A numerical illustrative platform based on judicious multiparametric values is provided to see the various fluid stabilizing and destabilizing factors against the nonlocal gravity. An interesting non-trivial outcome found herein is that larger clouds with fixed mass and density are gravitationally more stabilized, and vice-versa. Astronomical implications and applications of our findings are summarily actualized. [ABSTRACT FROM AUTHOR]

In this study, we optimise two types of multi-stream configurations (a T-junction and a flow-focusing design) to generate a homogeneous extensional flow within a well-defined region. The former is used to generate a stagnation point flow allowing molecules to accumulate significant strain, which has been found very useful for performing elongational studies. The latter relies on the presence of opposing lateral streams to shape a main stream and generate a strong region of extension in which the shearing effects of fluid–wall interactions are reduced near the region of interest. The optimisations are performed in two (2D) and three dimensions (3D) under creeping flow conditions for Newtonian fluid flow. It is demonstrated that in contrast with the classical-shaped geometries, the optimised designs are able to generate a well-defined region of homogeneous extension. The operational limits of the obtained 3D optimised configurations are investigated in terms of Weissenberg number for both constant viscosity and shear-thinning viscoelastic fluids. Additionally, for the 3D optimised flow-focusing device, the operational limits are investigated in terms of increasing Reynolds number and for a range of velocity ratios between the opposing lateral streams and the main stream. For all obtained 3D optimised multi-stream configurations, we perform the experimental validation considering a Newtonian fluid flow. Our results show good agreement with the numerical study, reproducing the desired kinematics for which the designs are optimised. [ABSTRACT FROM AUTHOR]

A finite difference scheme is used to develop a numerical method to solve the flow of an unbounded viscoelastic fluid with zero to moderate inertia around a prolate spheroidal particle. The equations are written in prolate spheroidal coordinates, and the shape of the particle is exactly resolved as one of the coordinate surfaces representing the inner boundary of the computational domain. As the prolate spheroidal grid is naturally clustered near the particle surface, good resolution is obtained in the regions where the gradients of relevant flow variables are most significant. This coordinate system also allows large domain sizes with a reasonable number of mesh points to simulate unbounded fluid around a particle. Changing the aspect ratio of the inner computational boundary enables simulations of different particle shapes ranging from a sphere to a slender fiber. Numerical studies of the latter particle shape allow testing of slender body theories. The mass and momentum equations are solved with a Schur complement approach allowing us to solve the zero inertia case necessary to isolate the viscoelastic effects. The singularities associated with the coordinate system are overcome using L'Hopital's rule. A straightforward imposition of conditions representing a time-varying combination of linear flows on the outer boundary allows us to study various flows with the same computational domain geometry. For the special but important case of zero fluid and particle inertia we obtain a novel formulation that satisfies the force- and torque-free constraint in an iteration-free manner. The numerical method is demonstrated for various flows of Newtonian and viscoelastic fluids around spheres and spheroids (including those with large aspect ratio). Good agreement is demonstrated with existing theoretical and numerical results. • A finite difference method for viscoelasticity and moderate inertia around spheroids. • Prolate spheroidal coordinates efficiently resolve particle surface and large gradients. • L'Hopital rule eliminates coordinate system generated singularity. • Novel decomposition of equations allows satisfying exact integral constraints directly. • Using Schur complement reduction momentum equation is solved without time marching. [ABSTRACT FROM AUTHOR]

In this work, we present a numerical study on the development length (the length from the channel inlet required for the velocity to reach 99% of its fully-developed value) of a pressure-driven viscoelastic fluid flow (between parallel plates) modelled by the generalised Phan–Thien and Tanner (gPTT) constitutive equation. The governing equations are solved using the finite-difference method, and, a thorough analysis on the effect of the model parameters α and β is presented. The numerical results showed that in the creeping flow limit (Re=0), the development length for the velocity exhibits a non-monotonic behaviour. The development length increases with Wi. For low values of Wi, the highest value of the development length is obtained for α=β=0.5; for high values of Wi, the highest value of the development length is obtained for α=β=1.5. This work also considers the influence of the elasticity number.

The main purpose of this review is to summarize the recent advances of the Conservation–Dissipation Formalism (CDF), a new way for constructing both thermodynamically compatible and mathematically stable and well-posed models for irreversible processes. The contents include but are not restricted to the CDF’s physical motivations, mathematical foundations, formulations of several classical models in mathematical physics from master equations and Fokker–Planck equations to Boltzmann equations and quasi-linear Maxwell equations, as well as novel applications in the fields of non-Fourier heat conduction, non-Newtonian viscoelastic fluids, wave propagation/transportation in geophysics and neural science, soft matter physics, etc. Connections with other popular theories in the field of non-equilibrium thermodynamics are examined too.

This paper describes a technique for animating the behavior of viscoelastic fluids, such as mucus, liquid soap, pudding, toothpaste, or clay, that exhibit a combination of both fluid and solid characteristics. The technique builds upon prior Eulerian methods for animating incompressible fluids with free surfaces by including additional elastic terms in the basic Navier-Stokes equations. The elastic terms are computed by integrating and advecting strain-rate throughout the fluid. Transition from elastic resistance to viscous flow is controlled by von Mises's yield condition, and subsequent behavior is then governed by a quasi-linear plasticity model.

Upon stimulus by CO2, CO2-switchable viscoelastic fluids experience a deliberate transition between non-viscous and highly viscous solution states. Despite attracting considerable recent attention, most such fluids have not been applied at a large- scale due to their high costs and/or complex synthesis processes. Here, we report the development of CO2-switchable viscoelastic fluids using commercially available sodium polyacrylate (NaPAA) and N,N-dimethyl ethanol amine (DMEA)-based switchable water. Upon bubbling CO2, into the solutions under study, DMEA molecules are protonated to generate quaternary ammonium salts, resulting in pronounced decreases in solutions viscosity and elasticity due to the influence of increased ionic strength on NaPAA molecular conformations. Upon removal of CO2 via introduction of N2, quaternary salts are deprotonated to tertiary amines, allowing recovery of fluid viscosity and elasticity to near the initial state. This work provides a simple approach to fabricating CO2-switchable viscoelastic fluids, widening the potential use of CO2 in stimuli-responsive applications.

Double diffusive convection in a binary viscoelastic fluid saturated porous layer in the presence of a cross diffusion effect and an internal heat source is studied analytically using linear and nonlinear stability analysis. The linear stability theory is based on the normal mode technique, while the nonlinear theory is based on a minimal representation of truncated double Fourier series. The modified Darcy law for the viscoelastic fluid of the Oldroyd type is considered to model the momentum equation. The onset criterion for stationary and oscillatory convection and steady heat and mass transfer have been obtained analytically using linear and nonlinear theory, respectively. The combined effect of an internal heat source and cross diffusion is investigated. The effects of Dufour, Soret, internal heat, relaxation and retardation time, Lewis number and concentration Rayleigh number on stationary, oscillatory, and heat and mass transport are depicted graphically. Heat and mass transfer are presented graphically in terms of Nusselt and Sherwood numbers, respectively. It is reported that the stationary and oscillatory convection are significantly influenced with variation of Soret and Defour parameters. An increment of the internal heat parameter has a destabilizing effect as well as enhancing the heat transfer process. On the other hand, an increment of internal heat parameter has a variable effect on mass transfer. It is found that there is a critical value for the thermal Rayleigh number, below which increasing internal heat decreases the Sherwood number, while above it increasing the internal heat increases the Sherwood number.

Viscoelastic fluids are non-Newtonian fluids that exhibit both “viscous” and “elastic” characteristics in virtue of the mechanisms used to store energy and produce entropy. Usually, the energy storage properties of such fluids are modeled using the same concepts as in the classical theory of nonlinear solids. Recently, new models for elastic solids have been successfully developed by appealing to implicit constitutive relations, and these new models offer a different perspective to the old topic of the elastic response of materials. In particular, a sub-class of implicit constitutive relations, namely relations wherein the left Cauchy–Green tensor is expressed as a function of stress, is of interest. We show how to use this new perspective in the development of mathematical models for viscoelastic fluids, and we provide a discussion of the thermodynamic underpinnings of such models. We focus on the use of Gibbs free energy instead of Helmholtz free energy, and using the standard Giesekus/Oldroyd-B models, we show how the alternative approach works in the case of well-known models. The proposed approach is straightforward to generalize to more complex settings wherein the classical approach might be impractical or even inapplicable.

The log-conformation reformulation, originally proposed by Fattal and Kupferman (2004), allows computing incompressible viscoelastic problems with high Weissenberg numbers which are impossible to solve with the typical three-field formulation. By following this approach, in this work we develop a new stabilized finite element formulation based on the logarithmic reformulation using the Variational Multiscale (VMS) method as stabilization technique, together with a modified log-conformation formulation. Our approach follows the term-by-term stabilization proposed by Castillo and Codina (2014) for the standard formulation, which is more effective when there are stress singularities. The formulation can be used when the relaxation parameter is set to zero, and permits a direct steady numerical resolution. The formulation is validated in the classical benchmark flow past a cylinder and in the well-known planar contraction 4:1, achieving very accurate, stable and mesh independent results for highly elastic fluids. [ABSTRACT FROM AUTHOR]

The influence of viscoelastic flow properties on fluid dynamics using radial impellers is investigated. The use of transparent model fluids allows for the optical measurement of general flow behavior with a fluorescence dying technique. By varying viscoelastic flow properties, size of agitators and rotational frequency, the impact of these parameters on fluid dynamics is analyzed. Toroidally shaped, cavern‐like flow compartments form around the agitators in all fluids in specific rotational frequency ranges, preventing an efficient mixing. By balancing elastic with centrifugal forces, a simple model is developed with which compartment sizes can be predicted with good accuracy. The results indicate a good suitability of the elasticity number as a scale‐up criterion. [ABSTRACT FROM AUTHOR]

• A new viscoelastic constitutive equation. • Generalisation of the PTT model using the Mittag–Leffler function. • Improving fits to experimental rheological data. In this work we propose a novel generalised form of the Phan–Thien and Tanner (PTT) model by considering a new functional form of the nonlinear expression characterizing the destruction of physical network junctions and entanglements. This new function of the trace of the stress tensor is given by the generalized Mittag–Leffler function, and contains the familiar exponential form of the original Phan–Thien and Tanner model as a limiting case, but affords additional fitting flexibility through the inclusion of one or two additional fitting constants. We perform fits to experimental data in shear and extension and show that this generalized expression allows a better description of the rheological responses for a range of complex materials such as polymer melts and semidilute polymer solutions. By using an appropriate information criterion, we also demonstrate that the resulting generelized model remains parsimonious but provides improved fits of real world data. [ABSTRACT FROM AUTHOR]

Chitosan-poly(vinyl alcohol)/clay membranes were prepared by physical blending. These hybrid systems were characterized through infrared spectroscopy, microscopy, swelling, and oscillatory rheology. Adsorption of a commercial reactive dye by these membranes was further studied. Results showed that more stable blend membranes were formed due to the strong interaction in the polymers. These membranes showed substantial percent swelling in water and shrinking in saline solution. Adsorption analysis showed the ability of the blends to fix organic dyes, and to be used in liquid waste processing. In dynamic rheology, it was observed that all measured viscoelastic properties were influenced by polymer composition and clay content. For all samples, results show a typical behavior of an entangled system in the case of low concentrated macromolecular viscoelastic fluids. The dynamic moduli exhibited higher values for blends, compared with values of the pure polymers, which is an indication of good stability and tendency of gel formation. [ABSTRACT FROM AUTHOR]

• Modeling interfacial rheology of buoyancy driven 3D-axisymmetric two-phase flows. • Local projection stabilized scheme for viscoelastic two-phase flows with surfactants. • Coupled arbitrary Lagrangian-Eulerian and Lagrangian approach for interface tracking. • Parametric study to analyze simultaneous effects of viscoelasticity and surfactants. • Observed features like cusp shape, dimpled shape and negative wake phenomenon. A stabilized finite element scheme is developed for computations of buoyancy driven 3D-axisymmetric viscoelastic two-phase flows with insoluble surfactants. The numerical scheme solves the Navier–Stokes equations for the fluid flow, Giesekus constitutive equation for the effects of viscoelasticity and simultaneously an evolution equation for the surfactant concentration on the interface. The interface is tracked by the coupled arbitrary Lagrangian–Eulerian (ALE) and Lagrangian approach. The interface-resolved moving meshes allow accurate incorporation of the interfacial tension force, Marangoni forces and the jumps in the material properties. Further, the tangential gradient operator technique is used to handle the curvature approximation in a semi-implicit manner. An one-level Local Projection Stabilization (LPS), which is based on an enriched approximation space and a discontinuous projection space, where both spaces are defined on a same mesh is used to stabilize the model equations. The stabilized numerical scheme allows us to use isoparametric second order conforming finite elements enriched with cubic bubble functions for velocity and viscoelastic stress, second order finite elements for surfactant concentration and discontinuous first order finite element for pressure. A number of computations are performed for a Newtonian drop rising in a viscoelastic fluid column and a viscoelastic drop rising in a Newtonian fluid column with insoluble surfactants on the interface. The influence of the Marangoni number, initial surfactant concentration and Peclet number on the dynamics of the rising drop are analyzed. The numerical study shows that a viscoelastic drop rising in a Newtonian fluid column develops an indentation around the rear stagnation point with a dimpled shape without insoluble surfactants. The presence of insoluble surfactants forces the drop to rise slowly but the drop at the tail end is pulled up more. However, a Newtonian drop rising in a viscoelastic fluid column experiences an extended trailing edge with a cusp-like shape without insoluble surfactants. The presence of surfactants pulls the tail end of the drop up slightly and makes the tail flatter with/without small undulations depending on the magnitude of the surfactant concentrations. [ABSTRACT FROM AUTHOR]

Highlights • Analytical solution of electro-osmotic oscillatory flow of multi-mode upper convective Maxwell (UCM) fluids. • Equal wall zeta potentials and case with zero potential at one wall. • Linear versus nonlinear fluid response. • Use of micro-channel electro-osmosis flow for small amplitude oscillatory shear (SAOS) rheology. Abstract This work presents an analytical solution for electro-osmotic flow (EOF) in small amplitude oscillatory shear (SAOS) as a measuring tool suitable to characterize the linear viscoelastic properties of non-Newtonian fluids in microchannel flow. The flow in the straight microchannel is driven by applying oscillating sinusoidal electric potentials. Fourier series are used to derive an expression for the velocity field, under an externally imposed generic potential field aimed at the practical application of SAOS in characterizing the rheological properties of viscoelastic fluids. This extensive investigation covers a wide range of parameters and considers the multi-mode upper-convected Maxwell (UCM) model, which represents the rheology of viscoelastic fluids in the limit of small and slow deformations. Particular focus is given to two cases of practical interest: equal wall zeta potentials at both channel walls and negligible zeta potential at one of the walls. The results show that in flows with thin electric double layers (EDL), Reynolds numbers below 0.001, and Deborah numbers below 100, corresponding to a viscoelastic Mach number of 0.32, the velocity field outside the EDLs is linear and has a large enough amplitude of oscillation, which may allow the quantification of the storage and loss moduli in the linear regime. This technique requires the use of significantly smaller sample sizes than the traditional SAOS in a rotational rheometer. [ABSTRACT FROM AUTHOR]

Highlights • Transient trajectories exploring the turbulent growth pathway are studied. • Transition in Newtonian flow involves a strong breakdown of intense turbulence. • Drag-reducing polymers stabilize primary vortices from breaking down. • Intermittent bursting events are likely governed by this transitional dynamics. • A turbulent cycle contains active turbulence, hibernation, and bursting phases. Abstract The transient process of turbulence development and vortex breakdown from a marginal flow state dominated by streaky velocity patterns is not only essential for understanding the bypass transition into turbulence, but – in the context of viscoelastic fluids – also offers unique insight into the dynamics at high-extent and maximum drag reduction (HDR and MDR). Shooting trajectories connecting the edge state and following its unstable manifold to the turbulent basin are generated. In Newtonian flow, the growth of turbulence starts with the intensification of velocity streaks and a sharp rise in the Reynolds shear stress. It is followed by a quick breakdown into high-intensity small-scale fluctuations before entering the basin of statistical turbulence. Adding drag-reducing polymers does not affect the initial growth of turbulence but stabilizes the primary streak-vortex structure. As a result, the vortex breakdown stage is circumvented. Polymer deformation is insignificant until the vortex breakdown, after which polymer stress rapidly shoots up. At high Weissenberg number Wi, loss of turbulent kinetic energy through polymer elastic conversion is comparable to viscous dissipation. Beyond bypass transition, the transient process studied here closely resembles the bursting phase of the self-sustaining cycle of turbulence. Our results indicate that at high Wi (i.e., HDR) polymer effects can significantly reduce bursting by rerouting the trajectory of turbulent dynamics. [ABSTRACT FROM AUTHOR]