This paper is focused on the fundamental mechanism(s) of viscoelastic turbulence that lead to polymer induced turbulent drag reduction phenomenon. A great challenge in this problem is the computation of viscoelastic turbulent flows, since the understanding of polymer physics is restricted to mechanical models. An effective state-of-the-art numerical method to solve the governing equation for polymers modelled as non-linear springs, without using any artificial assumptions as usual, was implemented here for the first time on a three-dimensional channel flow geometry. The capability of this algorithm to capture the strong polymer-turbulence dynamical interactions is depicted on the results, which are much closer qualitatively to experimental observations. This allowed a more detailed study of the polymer-turbulence interactions, which yields an enhanced picture on a mechanism resulting from the polymer-turbulence energy transfers.
Lagrangian dynamics unveil polymer conformation in viscoelastic flows
Tufts University（塔夫茨大学）；Institute for Mechanobiology, Department of Bioengineering, College of Engineering, Northeastern University（东北大学生物工程学院机制生物学研究所）；Department of Mechanical Science and Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校机械科学与工程系）；Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania（宾夕法尼亚大学机械工程和应用力学系）
Viscoelastic flows are pervasive in a host of natural and industrial processes, where the emergence of nonlinear and time-dependent dynamics regulate flow resistance, energy consumption, and particulate dispersal. Polymeric stress induced by the advection and stretching of suspended polymers feeds back on the underlying fluid flow, which ultimately dictates the dynamics, instability, and transport properties of viscoelastic fluids. However, direct experimental quantification of the stress field is challenging, and a fundamental understanding of how Lagrangian flow structure regulates the distr…
We investigate previously unclarified effects of fluid elasticity on shear-thickening in dilute suspensions in an Oldroyd-B viscoelastic fluid using a novel direct numerical simulation based on the smoothed profile method. Fluid elasticity is determined by the Weissenberg number Wi and by viscosity ratio $1-β=η_p/(η_s+η_p)$ which measures the coupling between the polymer stress and flow: $η_p$ and $η_s$ are the polymer and solvent viscosity, respectively.As $1-β$ increases, while the stresslet does not change significantly compared to that in the $β\to 1$ limit, the growth rate of the normaliz…
Surface tension-driven flow techniques have recently emerged as an efficient means of shedding light into the rheology of thin polymer films. Motivated by experimental and theoretical approaches in films bearing a varying surface topography, we present results on the capillary relaxation of a square pattern at the free surface of a viscoelastic polymer film, using molecular dynamics simulations of a coarse-grained polymer model. Height profiles are monitored as a function of time after heating the system above its glass-transition temperature and their time dependence is fitted to the theory o…
The viscoelastic behavior of polymer solutions is commonly measured using oscillating shear rheometry, however, the accuracy of such methods is limited by the oscillating frequency of the equipment and since the relaxation time of the dilute polymer solutions is short, this requires measurement at very high frequencies. Microrheology has been proposed to overcome this technical challenge. Yet the equipment for resolving the statistics of particle displacements in microrheology is expensive. In this work, we measured the viscoelastic behavior of Methocel solutions at various concentrations usin…
Simulations of undulatory swimming in viscoelastic fluids with large amplitude gaits show concentration of polymer elastic stress at the tips of the swimmers.We use a series of related theoretical investigations to probe the origin of these concentrated stresses. First the polymer stress is computed analytically at a given oscillating extensional stagnation point in a viscoelastic fluid. The analysis identifies a Deborah number (De) dependent Weissenberg number (Wi) transition below which the stress is linear in Wi, and above which the stress grows exponentially in Wi. Next, stress and velocit…
We investigate the rapid spreading dynamics of a viscoelastic drop on a solid. Upon contact, surface tension drives a fast motion of the contact line along the substrate. Here, we resolve this motion for viscoelastic liquids by experiments on aqueous polymer solutions of varying concentration. It is found that while the contact line motion is only mildly affected by the polymers, the interface profile becomes much sharper owing to singular polymer stress. This behaviour is reminiscent of that observed for viscoelastic drop coalescence; in this light we revisit the analogy between spreading and…
We show that viscoelastic plane Poiseuille flow becomes linearly unstable in the absence of inertia, in the limit of high elasticities, for ultra-dilute polymer solutions. While inertialess elastic instabilities have been predicted for curvilinear shear flows, this is the first ever report of a purely elastic linear instability in a rectilinear shear flow. The novel instability continues upto a Reynolds number ($Re$) of $O(1000)$, corresponding to the recently identified elasto-inertial turbulent state believed to underlie the maximum-drag-reduced regime. Thus, for highly elastic ultra-dilute …
Interface-resolved direct numerical simulations are performed to examine the combined effects of soluble surfactant and viscoelasticity on the structure of a bubbly turbulent channel flow. The incompressible flow equations are solved fully coupled with the FENE-P viscoelastic model and the equations governing interfacial and bulk surfactant concentrations. The latter coupling is achieved through a non-linear equation of state which relates the surface tension to the surfactant concentration at the interface. The two-fluid Navier-Stokes equations are solved using a front-tracking method, augmen…
When a dilute polymer solution experiences capillary thinning, it forms an almost uniformly cylindrical thread, which we study experimentally. In the last stages of thinning, when polymers have become fully stretched, the filament becomes prone to instabilities, of which we describe two: A novel "breathing" instability, originating from the edge of the filament, and a sinusoidal instability in the interior, which ultimately gives rise to a "blistering" pattern of beads on the filament. We describe the linear instability with a spatial resolution of 80 nm in the disturbance amplitude. For suffi…
The effects of polymer additives on Rayleigh--Taylor (RT) instability of immiscible fluids is investigated using the Oldroyd-B viscoelastic model. Analytic results obtained exploiting the phase-field approach show that in polymer solution the growth rate of the instability speeds up with elasticity (but remains slower than in the pure solvent case). Numerical simulations of the viscoelastic binary fluid model confirm this picture.
In melt-blowing processes mico- and nanofibers are produced by the extrusion of polymeric jets into a directed, turbulent high-speed airflow. Up to now the physical mechanism for the drastic jet thinning is not fully understood, since in the existing literature the numerically computed/predicted fiber thickness differs several orders of magnitude from those experimentally measured. Recent works suggest that this discrepancy might arise from the neglect of the turbulent aerodynamic fluctuations in the simulations. In this paper we confirm this suggestion numerically. Due to the complexity of th…
The linear amplification of disturbances is critical in setting up transition scenarios in viscoelastic channel and Couette flow, and may also play an important role when such flows are fully turbulent. As such, it is of interest to assess how this amplification, defined as the steady-state variance maintained under Gaussian white noise forcing, scales with the main nondimensional parameters: the Reynolds ($Re$) and Weissenberg ($Wi$) numbers. This scaling is derived analytically in the two limits of strong and weak elasticity for when the forcing is streamwise-constant. The latter is the rele…
Nontrivial steady flows have recently been found that capture the main structures of the turbulent buffer layer. We study the effects of polymer addition on these "exact coherent states" (ECS) in plane Couette flow. Despite the simplicity of the ECS flows, these effects closely mirror those observed experimentally: Structures shift to larger length scales, wall-normal fluctuations are suppressed while streamwise ones are enhanced, and drag is reduced. The mechanism underlying these effects is elucidated. These results suggest that the ECS are closely related to buffer layer turbulence.
As the first endeavour, we have analyzed the pulsatile flow of Oldroyd-B viscoelastic fluid where the combined effects of fluid elasticity and pulsation parameters on the flow characteristics are numerically studied at a low Reynolds number. Computations are performed using a finite-volume based open-source solver OpenFOAM by appending the log-conformation tensor approach to stabilize the numerical solution at high Deborah number. Significant flow velocity enhancement is achieved by increasing the viscoelastic behaviour of the fluid. High-velocity gradient zones and high polymeric stress regio…
Polymer additives are commonly utilized to manipulate bubbly flows in various applications. Here, we investigate the effects of clean and contaminated bubbles driven upwards (upflow) in Newtonian and viscoelastic turbulent channel flows. Interface-resolved direct numerical simulations are performed to examine sole and combined effects of soluble surfactant and viscoelasticity using an efficient 3D finite-difference/front-tracking method. The incompressible flow equations are solved fully coupled with the FENE-P viscoelastic model and the equations governing interfacial and bulk surfactant conc…
Particles migrate in the transverse direction of the flow due to the existence of normal stress anisotropy in weakly viscoelastic liquids. We test the ability of theoretical predictions to predict the transverse velocity migration of particles in a confined Poiseuille flow according to the viscoelastic constitutive parameters of dilute polymers solutions. Firstly, we carefully characterize the viscoelastic properties of two families of dilute polymer solutions at various concentrations using shear rheometry and capillary breakup experiments. Secondly, we develop a specific 3D particle tracking…
We briefly review the recent advances in the rheology of entangled polymers and identify emerging research trends and outstanding challenges, especially with respect to branched polymers. Emphasis is placed on the role of well-characterized model systems, as well as the synergy of synthesis-characterization, rheometry and modeling/simulations. The theoretical framework for understanding the observed linear and nonlinear rheological phenomena is the tube model which is critically assessed in view of its successes and shortcomings, whereas alternative approaches are briefly discussed. Finally, i…
This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-defini…
We propose numerical simulations of viscoelastic fluids based on a hybrid algorithm combining Lattice-Boltzmann models (LBM) and Finite Differences (FD) schemes, the former used to model the macroscopic hydrodynamic equations, and the latter used to model the polymer dynamics. The kinetics of the polymers is introduced using constitutive equations for viscoelastic fluids with finitely extensible non-linear elastic dumbbells with Peterlin's closure (FENE-P). The numerical model is first benchmarked by characterizing the rheological behaviour of dilute homogeneous solutions in various configurat…
Interior stagnation point flows of viscoelastic liquids arise in a wide variety of applications including extensional viscometry, polymer processing and microfluidics. Experimentally, these flows have long been known to exhibit instabilities, but the mechanisms underlying them have not previously been elucidated. We computationally demonstrate the existence of a supercritical oscillatory instability of low-Reynolds number viscoelastic flow in a two-dimensional cross-slot geometry. The fluctuations are closely associated with the "birefringent strand" of highly stretched polymer chains associat…
Newtonian pipe flow is known to be linearly stable at all Reynolds numbers. We report, for the first time, a linear instability of pressure driven pipe flow of a viscoelastic fluid, obeying the Oldroyd-B constitutive equation commonly used to model dilute polymer solutions. The instability is shown to exist at Reynolds numbers significantly lower than those at which transition to turbulence is typically observed for Newtonian pipe flow. Our results qualitatively explain experimental observations of transition to turbulence in pipe flow of dilute polymer solutions at flow rates where Newtonian …
Viscoelastic properties of polymer melts are particularly challenging to compute due to the intrinsic stress fluctuations in molecular dynamics (MD). We compared equilibrium and non-equilibrium MD approaches for extracting the storage (G') and loss moduli (G") over a wide frequency range from a bead-spring chain model, in both unentangled and entangled regimes. We found that, with properly chosen data processing and noise reduction procedures, different methods render quantitatively equivalent results. In equilibrium MD (EMD), applying the Green-Kubo relation with a multi-tau correlator method…
Long-chained, viscoelastic surfactant solutions (VES) have been widely employed in the oil and gas industry, particularly in hydraulic fracturing and gravel-packing operations, where turbulence is commonly reached due to high pumping rates. With this motivation, we experimentally investigate the turbulent duct flow of an under-studied class of wormlike micellar solutions that forms a gel at room temperature. The fluid is characterized via rotational rheometry, and the turbulent velocity and Reynolds stress profiles are measured via Laser Doppler Anemometry (LDA). Three surfactant concentration…
We study the physics of turbulent/non-turbulent interface of an isolated turbulent region in dilute polymer solutions and Newtonian fluid. The performance of a FENE-P model with a localized homogeneous forcing is verified using the specially designed experimental setup of a turbulent patch growing in water/dilute polymer solution, without mean shear and far from the walls. The results of the small scale dynamics of vorticity and strain help to reveal the key mechanism of polymer action in turbulent flows without mean shear. Modified degrees of alignment between vorticity, the polymer conformat…
An analytic, asymptotic approximation of the nonlinear steady-state equations for viscoelastic creeping flow, modeled by the Oldroyd-B equations with polymer stress diffusion, is derived. Near the extensional stagnation point the flow stretches and aligns polymers along the outgoing streamlines of the stagnation point resulting in a stress-island, or birefringent strand. The polymer stress diffusion coefficient is used, both, as an asymptotic parameter and a regularization parameter. The structure of the singular part of polymer stress tensor is a Gaussian aligned with the incoming streamline …
In this study, the OpenFOAM platform, based on the finite volume method, is applied to investigate the two-dimensional viscoelastic flow past a circular cylinder. The FENE-P model, which considers the bounded elongation of polymer molecules, is chosen to describe the elastic constitutive relationship of the polymer solution. The maximum molecular chain lengths of L = 10, 50, 100, and 200 are considered, which describe the molecular conformation characteristics of the polymer solution. To improve the numerical instability of the viscoelastic flow simulation, three different methods, i.e., the t…
Amplification of deterministic disturbances in inertialess shear-driven channel flows of viscoelastic fluids is examined by analyzing the frequency responses from spatio-temporal body forces to the velocity and polymer stress fluctuations. In strongly elastic flows, we show that disturbances with large streamwise length scales may be significantly amplified even in the absence of inertia. For fluctuations without streamwise variations, we derive explicit analytical expressions for the dependence of the worst-case amplification (from different forcing to different velocity and polymer stress co…
By tracking small particles in the bulk of an intensely turbulent flow, we show that even a very small concentration of long-chain polymers disrupts the usual turbulent energy cascade. The polymers affect scales much larger than their physical size, from the dissipation range to the inertial range. The effect depends strongly on the polymer concentration. While the dissipative-scale statistics change continuously as the polymer concentration is increased, the inertial-range energy transfer rate is only altered by the polymer additives when the concentration is above a threshold (approximately …
The formation of drops of a complex fluid, for instance including dissolved polymers and/or solid particles, has practical implications in several industrial and biophysical processes. In this Letter, we experimentally investigate the generation of drops of a viscoelastic suspension, made of non-Brownian spherical particles dispersed in a dilute polymer solution. Using high-speed imaging, we characterize the different stages of the detachment. Our experiments show that the particles primarily affect the initial Newtonian necking by increasing the fluid viscosity. In the viscoelastic regime, pa…
Minute amount of long chain flexible polymer dissolved in a turbulent flow can drastically change flow properties, such as reducing the drag and enhancing mixing. One fundamental riddle is how these polymer additives interact with the eddies of different spatial scales existing in the turbulent flow and in turn alter the turbulence energy transfer. Here we show how turbulent kinetic energy is transferred through deferent scales in the presence of the polymer additives. In particular, we observed experimentally the emerging of a new scaling range, referred to as the elastic range, where increas…
We use numerical simulations to address locomotion at zero Reynolds number in viscoelastic (Giesekus) fluids. The swimmers are assumed to be spherical, to self-propel using tangential surface deformation, and the computations are implemented using a finite element method. The emphasis of the study is on the change of the swimming kinematics, energetics, and flow disturbance from Newtonian to viscoelastic, and on the distinction between pusher and puller swimmers. In all cases, the viscoelastic swimming speed is below the Newtonian one, with a minimum obtained for intermediate values of the Wei…
Bubbles rising in viscoelastic liquids may exhibit a jump discontinuity of the rise velocity as a critical bubble volume is exceeded. The phenomenon has been extensively investigated in the literature, both by means of experiments as well as via numerical simulations. The occurrence of the velocity jump has been associated with a change of the bubble shape under the formation of a pointed tip at the rear end and to the appearance of a so-called negative wake with the liquid velocity behind the bubble, pointing in the opposite direction to that in viscous Newtonian fluids. We revisit this topic…
This paper describes the isothermal die swell using our recent quasi-1D model for fast (high Deborah number) contraction flows of polymers melts. Because the model analyzes the flow in several flow regions as one continuous process, it makes possible to evaluate the die swell as a qusi-1D extrudate flow in dies of various lengths. Using the asymptotic matching condition for the change in flow type at the die exit allowed us to find the swelling profile for extrudate along the flow direction. The calculations in paper performed using a multi-mode viscoelastic constitutive equation of differenti…
Axisymmetric viscoelastic pipe flow of Oldroyd-B fluids has been recently found to be linearly unstable by Garg et al. Phys. Rev. Lett., 121.024502 (2018). From a nonlinear point of view, this means that the flow can transition to turbulence supercritically, in contrast to the subcritical Newtonian pipe flows. Experimental evidences of subcritical and supercritical bifurcations of viscoelastic pipe flows have been reported, but these nonlinear phenomena have not been examined theoretically. In this work, we study the weakly nonlinear stability of this flow by performing a multiple-scale expans…
We extend the analysis of the friction factor for turbulent pipe flow reported by G. Gioia, P. Chakraborty and N. Goldenfeld (GCG) (G. Gioia and P. Chakraborty, Phys. Rev. Lett. 96, 044502 (2006), N. Goldenfeld, Phys. Rev. Lett. 96, 044503 (2006)) to the case where drag is reduced by polymer additives.
Measurements of heat transport, as expressed by the Nusselt number $Nu$, are reported for turbulent Rayleigh-Bénard convection of water containing up to 120 ppm by weight of poly-[ethylene oxide] with a molecular weight of $4\times10^6$ g/mole. Over the Rayleigh number range $ 5\times 10^9 \alt Ra \alt 7 \times 10^{10}$ $Nu$ is smaller than it is for pure water by up to 10%.
Creeping flow of polymeric fluid without inertia exhibits elastic instabilities and elastic turbulence accompanied by drag enhancement due to elastic stress produced by flow-stretched polymers. However, in inertia-dominated flow at high $\mbox{Re}$ and low fluid elasticity $El$, a reduction in turbulent frictional drag is caused by an intricate competition between inertial and elastic stresses. Here, we explore the effect of inertia on the stability of viscoelastic flow in a broad range of control parameters $El$ and $(\mbox{Re}, \mbox{Wi})$. We present the stability diagram of observed flow r…
The perturbations of the laminar shear-thinning viscoelastic pipe flow under Finitely Extensible Nonlinear Elastic model with Peterlin approximation (FENE-P) are shown to exhibit leading-order power-law behaviours, and the expected odd-even parities with respect to the radial coordinate that depend on the azimuthal wave\-number, $n$. The analysis helps regularizing the governing system of equations at the centreline, and allows for a complete stability analysis of three-dimensional perturbations for a general integer value of $n$, which has hitherto remained a challenge for FENE-P models. It i…
