Dilute Polymer Solutions Research Articles

Keplerian turbulence in Taylor–Couette flow of dilute polymeric solutions

Turbulent flow induced by elastorotational instability in viscoelastic Taylor–Couette flow (TCF) with Keplerian rotation is analogous to a turbulent accretion disk destabilized by magnetorotational instability. We examine this novel viscoelastic Keplerian turbulence via direct numerical simulations (DNS) for the shear Reynolds number ( $Re$ ) ranging from $10^2$ to $10^4$ . The observed characteristic flow structure consists of penetrating streamwise vortices with axial length scales much smaller than the gap width, distinct from the classic centrifugally induced Taylor vortices, which have axial lengths of the gap width. These intriguing vortices persist for the wide $Re$ range considered and give rise to intriguing scaling behaviour in key flow quantities. Specifically, the characteristic axial length of the penetrating vortices is shown to scale as $Re^{-0.22}$ ; the angular momentum transport scales as $Re^{0.42}$ ; the kinetic and elastic boundary-layer thicknesses based on angular velocity and hoop stress near the inner cylinder wall scale as $Re^{-0.48}$ and $Re^{-0.49}$ , respectively. This implies that the viscoelastic Keplerian turbulence belongs to the classical turbulent regime of TCF with the Prandtl–Blasius-type boundary layer. Furthermore, we present an analytical relation between the viscous and elastic dissipation rates of kinetic energy and the angular momentum transport and in turn demonstrate its validity using our DNS data. This study has paved the way for future research to explore astrophysics-related Keplerian turbulence and angular momentum transport via the scaling relations of the analogous TCF of dilute polymeric solutions.

Lateral migration of a deformable fluid particle in a square channel flow of viscoelastic fluid

Cross-stream migration of a deformable fluid particle is investigated computationally in a pressure-driven channel flow of a viscoelastic fluid via interface-resolved simulations. Flow equations are solved fully coupled with the Giesekus model equations using an Eulerian–Lagrangian method and extensive simulations are performed for a wide range of flow parameters to reveal the effects of particle deformability, fluid elasticity, shear thinning and fluid inertia on the particle migration dynamics. Migration rate of a deformable particle is found to be much higher than that of a solid particle under similar flow conditions mainly due to the free-slip condition on its surface. It is observed that the direction of particle migration can be altered by varying shear thinning of the ambient fluid. With a strong shear thinning, the particle migrates towards the wall while it migrates towards the channel centre in a purely elastic fluid without shear thinning. An onset of elastic flow instability is observed beyond a critical Weissenberg number, which in turn causes a path instability even for a nearly spherical particle. An inertial path instability is also observed once particle deformation exceeds a critical value. Shear thinning is found to be suppressing the path instability in a viscoelastic fluid with a high polymer concentration whereas it reverses its role and promotes path instability in a dilute polymer solution. It is found that migration of a deformable particle towards the wall induces a secondary flow with a velocity that is approximately an order of magnitude higher than the one induced by a solid particle under similar flow conditions.

Dilute Polymer Droplets Show Generalized Wetting Dynamics via an Average Viscosity.

Despite the prevalence of non-Newtonian fluids in various practical applications, comprehensive dynamic wetting models are lacking. Existing models often oversimplify complex rheological behavior, limiting our ability to predict wetting dynamics. This work introduces and experimentally validates a generalized model for the dynamic wetting of non-Newtonian shear-thinning fluids (dilute polymer solutions) on solid substrates. We experimentally analyzed 12 different shear-thinning fluids using both a power-law model and Carreau-Yasuda model. The data clearly show that the dynamic contact angle can be generalized using an average viscosity to capture rheological changes during droplet spreading. The average viscosity was defined using the fluid's constitutive model over shear rates relevant to the spreading process. Using a small droplet approximation, we propose and validate a semianalytical spreading model to predict the basal radius of non-Newtonian droplets. The model agrees well with the experimental data. Additionally, the average viscosity was used to define a spreading time scale, which is capable of collapsing the spreading of different non-Newtonian fluids onto a master spreading curve. This work offers significant potential for predicting the dynamic shape and spreading of non-Newtonian fluids with complex rheologies in a range of applications and industrial processes.

The importance of initial extension rate on elasto-capillary thinning of dilute polymer solutions

This work focuses on inferring the molecular state of the polymer chain required to induce stress relaxation and the accurate measure of the polymer’s longest relaxation time in uniaxial stretching of dilute polymer solutions. This work is facilitated by the discovery that constant velocity applied at early times leads to initial constant extension rate before reaching the Rayleigh–Plateau instability. Such constant rate experiments are used to correlate initial stretching kinematics with the thinning dynamics in the final thinning regime. We show that there is a minimum initial strain-rate required to induce rate independent elastic effects, and measure the longest relaxation time of the material. Below the minimum extension rate, insufficient stretching of the chain is observed before capillary instability, such that the polymer stress is comparable to the capillary stress at long times and stress relaxation is not achieved. Above the minimum strain-rate, the chain reaches a critical stretch before instability, such that during the unstable filament thinning the polymer stress is significantly larger than the capillary stress and rate-independent stress relaxation is observed. Using a single relaxation mode FENE model, we show that the minimum strain rate leads to a required initial stretch of the chain before reaching the Rayleigh–Plateau limit. These results indicate that the chain conformation before entering the Rayleigh Instability Regime, and the stretching induced during the instability, determines the elastic behavior of the filament. Lastly, this work introduces a characteristic dimensionless group, called the stretchability factor, that can be used to quantitatively compare different materials based on the overall material deformation/kinematic behavior, not just the relaxation time. Overall, these results demonstrate a useful methodology to study the stretching of dilute solutions using a constant velocity stretching scheme.

Analytical and Numerical Investigation of Star Polymers in Confined Geometries.

The analysis of the impact of the star polymer topology on depletion interaction potentials, depletion forces, and monomer density profiles is carried out analytically using field theory methods and techniques as well as molecular dynamic simulations. The dimensionless depletion interaction potentials and the dimensionless depletion forces for a dilute solution of ideal star polymers with three and five legs (arms) in a Θ-solvent confined in a slit between two parallel walls with repulsive surfaces and for the case where one of the surfaces is repulsive and the other inert are obtained. Furthermore, the dimensionless layer monomer density profiles for ideal star polymers with an odd number (f˜ = 3, 5) of arms immersed in a dilute solution of big colloidal particles with different adsorbing or repelling properties in respect of polymers are calculated, bearing in mind the Derjaguin approximation. Molecular dynamic simulations of a dilute solution of star-shaped polymers in a good solvent with N = 901 (3 × 300 + 1 -star polymer with three arms) and 1501 (5 × 300 + 1 -star polymer with five arms) beads accordingly confined in a slit with different boundary conditions are performed, and the results of the monomer density profiles for the above-mentioned cases are obtained. The numerical calculation of the radius of gyration for star polymers with f˜ = 3, 5 arms and the ratio of the perpendicular to parallel components of the radius of gyration with respect to the wall orientation for the above-mentioned cases is performed. The obtained analytical and numerical results for star polymers with an odd number (f˜ = 3, 5) of arms are compared with our previous results for linear polymers in confined geometries. The acquired results show that a dilute solution of star polymer chains can be applied in the production of new functional materials, because the behavior of these solutions is strictly correlated with the topology of polymers and also with the nature and geometry of confined surfaces. The above-mentioned properties can find extensive practical application in materials engineering, as well as in biotechnology and medicine for drug and gene transmission.

Multi‐Scenario Applications of Fluoro‐Free Super Liquid‐Repellent Particles Prepared Through Excluded Volume Effect

AbstractSuperhydrophobic surfaces garner tremendous research attention due to their potential applications in the fields of oil–water separation membrane, self‐cleaning, and anti‐icing systems. However, the reported superhydrophobic materials that achieve low‐surface‐tension (<60 mN m−1) liquid repellency are typically prepared using perfluorinated compounds (PFCs), which pose significant risks to the natural environment and human health. Here a concept based on the excluded volume effect in polymer dilute solutions is explored to achieve a hydrophobic flexible polymer‐chain wrapping of multidimensional particles, which forms a nonadherent soft‐shell‐hard‐core structure and maintains the original structural integrity of particles. The prepared fluoro‐free super‐repellent multidimensional particles can be spray‐coated and dip‐coated on different substrates to prepare large‐scale superhydrophobic coatings, which exhibit excellent low‐surface‐tension (42.6−50 mN m−1) liquid repellency superior to the reported fluoro‐free superhydrophobic materials. Benefiting from the strong interaction of super‐repellent particles with flexible polymer chains, the superhydrophobic coatings show unexpected wear resistance and durability. This first demonstration of hydrophobic polymer‐wrapped particles for repelling low‐surface‐tension liquids provides insights into next‐generation fluoro‐free superhydrophobic materials.

Anti-turbulent efficiency of oil-soluble polymer solutions and colloid systems flowing through cylindrical channel

Relevance. The use of anti-turbulent additives for transporting hydrocarbon liquids through main pipelines allows reducing significantly the energy consumption of pumping power stations. Aim. Comparative analysis of the anti-turbulent efficiency of high-molecular polymers and compositions of surfactants. Methods. Laboratory-scale experimentation aimed to study the flow of dilute polymer solutions and dispersed surfactant systems through a cylindrical channel of a turbulent rheometer. Results. The author has carried out the comparative experimental studies of the anti-turbulent efficiency of extremely dilute solutions of polymers and colloidal systems. The results were obtained that suggest a higher anti-turbulent efficiency of high-molecular-weight polymers compared to micellar surfactant systems. Solutions of high molecular weight polybutadiene and aluminum polyhydroxydicarboxylates in gasoline were used as samples for the experimental comparison of hydrodynamic efficiency. The paper describes the laboratory setup, on which the studies were carried out, and introduces the formulas used for quantitative calculations. The structure of polymer solutions and colloidal systems is considered and a theoretical explanation is given for the preferential use in industrial practice of high-molecular polymers in extremely low concentrations in real pipelines. It was found out that the mechanisms of degradation of antiturbulent properties of polymer solutions and dispersed surfactant systems are different. This is due to the difference in the structure of macromolar coils of polymer with an immobilized solvent and that of micelles from low molecular amphiphilic compounds. The paper introduces the arguments that explain the degradation of the antiturbulent properties of polymers not by the destruction of carbon-chain macromolecules, but by decomposition in a turbulent flow of the original large associates, consisting of a large number of chains, into individual and smaller macromolecular coils with an immobilized solvent.

Orientational order and topological defects in a dilute solutions of rodlike polymers at low Reynolds number.

The relationship between the polymer orientation and the chaotic flow, in a dilute solution of rigid rodlike polymers at low Reynolds number, is investigated by means of direct numerical simulations. It is found that the rods tend to align with the velocity field in order to minimize the friction with the solvent fluid, while regions of rotational disorder are related to strong vorticity gradients, and therefore to the chaotic flow. The "turbulent-like" behavior of the system is therefore associated with the emergence and interaction of topological defects of the mean director field, similarly to active nematic turbulence. The analysis has been carried out in both two and three spatial dimensions.

Enhanced heat transfer in a two-dimensional serpentine micro-channel using elastic polymers

Elastic turbulence has emerged as a promising method to enhance heat transfer performance at the microscale. However, previous studies have mainly focused on the overall convective heat transfer performance in curved channels, overlooking the fact that the chaotic flow intensity varies along the streamline, leading to diverse local heat transfer characteristics. In this study, we systematically investigate the hydraulic and thermal properties of a dilute polymer solution under elastic turbulence conditions, where the inflow conditions exhibit a vanishing Reynolds number (Re) and high Weissenberg number (Wi), enabling a comprehensive understanding of the influence of polymers on the system. Through extensive direct numerical simulations using Rheotool, a two-dimensional curvilinear channel flow of an Oldroyd-B viscoelastic fluid is analyzed. By examining the variations of the friction factor and Nusselt number along the serpentine channel, we unveil both global and local characteristics of elastic turbulence. Based on the Wi value, we identify three distinct regimes. In the first regime (0<Wi≤3), we observe approximately 10% heat transfer enhancement accompanied by a roughly 5% reduction in the friction factor compared to laminar flow, known as polymer-induced thermal conductivity enhancement. In the second regime (3<Wi≤5), we observe a steep linear increase in heat transfer (around 30%) at the expense of up to 15% enhanced friction factor. Finally, in the fully developed elastic turbulence regime (Wi>5), we observe a remarkable heat transfer enhancement of up to 60% along with a reduced friction factor. The significant enhancement of heat transfer with increasing Wi can be attributed to the intensifying elastic instability resulting from the balance between normal stresses and streamlined curvatures.

Effect of solvent depletion on electrokinetic energy conversion in viscoelastic fluids

We analyze the electrokinetic energy conversion from the pressure-driven flow of viscoelastic fluids akin to dilute polymer solutions. In contrast to the previously reported results, we account for the reduced differential capacitance over the interfacial layer and the solvent-mediated non-electrostatic interactions, cumulatively represented in an extended continuum framework. We attribute a physical basis of our consideration from the perspective of the formation of a polymer-depleted layer at the channel interface, where the explicit role of the solvent appears to dictate the electromechanics–hydrodynamics coupling over the interfacial scales. By adapting a “box-model” depicting the alterations in the solvent permittivity across the interfacial layer and accommodating a non-electrostatic interaction coefficient concomitantly, the interfacial electrokinetics are coupled with the bulk flow of the polymer-rich medium using the simplified Phan-Thien–Tanner (sPTT) constitutive model. A closed-form theory is obtained that includes only two fitting parameters, namely, the span of the interfacial layer and the strength of the non-electrostatic interactions. These parameters are estimated from comprehensive molecular simulation data. The results of the investigation are analytically tractable and enable rationalizing the “electrokinetic” implications of the polymer-depleted interfacial layer and the possibility that the electrokinetic parameters can be extracted from measurements obtained from experiments. This paves the way toward optimizing the induced streaming potential for the conversion of hydraulic energy to electrical power in polymeric solutions.

Comparison of viscoelastic flows in two- and three-dimensional serpentine channels.

Polymer solutions in the dilute regime play a significant role in industrial applications. Due to the intricate rheological properties of these highly viscoelastic fluids, especially in complex flow geometries, a thorough numerical analysis of their flow dynamics is imperative. In this research, we present a numerical investigation of purely elastic instability occurring in two- and three-dimensional serpentine channels under conditions where fluid inertia is negligible and across a broad spectrum of polymer relaxation times. Our findings reveal a strong qualitative agreement between the existing experimental results obtained from dilute solutions of flexible polymers in microfluidic devices and the numerical simulations conducted in two and three dimensions using the Oldroyd-B model. Spatial flow observations and statistical analysis of temporal flow features indicate that this purely elastic turbulent flow exhibits nonhomogeneous, non-Gaussian, and anisotropic characteristics across all scales. Additionally, our comparison of two- and three-dimensional simulations demonstrates that the elastic instability is primarily driven by the curvature of the streamlines induced by the flow geometry, rather than the weak secondary flow in the azimuthal direction. Therefore, our two-dimensional numerical simulations successfully replicate, at least qualitatively, the features observed in three-dimensional experiments. Furthermore, spectral analysis suggests that, in comparison to elastic turbulence in the dilute regime, the range of scales for the excited fluctuations is narrower.

Delineation of the effective viscosity controls of diluted polymer solutions at various flow regimes

Carreau's model is a well-established standard in the scientific community for estimating the viscosity of polymer solutions as a function of shear rate. It accurately predicts effective viscosity in power-law and Newtonian flow regimes, distinguished by distinct asymptotic values at extremely low and high shear rates. However, existing analytical models for determining Carreau's parameters (zero-shear-viscosity, μp∘, power-law index, n, and relaxation-time constant, λ) have limitations. Typically expressed in terms of polymer solution concentration (Cp), these models often overlook critical variables such as solvent salinity (CNaCl), hardness (Cca++), solution density (ρs), and polymer molecular weight (M). Additionally, many of these models lack dimensional consistency.This study introduces a robust scientific method for modeling Carreau's parameters, integrating dimensional analysis with non-linear regression to delineate the factors influencing these parameters. The analysis indicates that the power-law index is primarily influenced by Cp, CNaCl, and Cca++. The zero-shear-viscosity (μp∘) is governed by Cp, CNaCl, Cca++, M, ρs, pressure (P), and n, while the time constant (λ) is mainly determined by Cp, CNaCl, Cca++, n, and μp∘. The derived empirical models demonstrate a direct dependence of zero-shear viscosity on P, M3,ρs6, and an exponential dependence on Cp, aligning with experimental observations. Incorporating variables like solution density, molecular weight, and pressure was crucial for enhancing the precision of μp∘ and λ predictions. These models, validated against rheological measurements of three dilute EOR polymer solutions (HPAM and AMPS-based) in various conditions, have shown superior precision and impartiality compared to prominent existing models, representing a significant advancement in the field.

Field-driven polyelectrolyte-polymer collisions in nanochannels.

Even though dilute (unentangled) polymer solutions cannot act as gel-like sieving media, it has been shown that they can be used to separate DNA molecules in capillary electrophoresis. The separation then comes from sporadic, independent DNA-polymer collisions. We study polymer-polymer collisions in nanochannels (i.e., channels that are smaller than the normal size of the polymers), a situation where a polyelectrolyte is forced to migrate "through" isolated uncharged molecules during electrophoresis. We use Langevin dynamics simulations to explore the nature of these collisions and their effect on the net motion of the two polymer chains. We identify several types of collisions, including some that are unique to nanochannels. When the uncharged polymer is much larger than the polyelectrolyte, the system is reminiscent of gel electrophoresis, and we propose a modified empirical reptation model to explain the data, with an orientation factor that depends on the tube diameter. We also observe that the duration of a collision is a non-monotonic function of the polymer size ratio when the two chains are of comparable size, a surprising resonance-like phenomenon, which, combined with the asymmetric nature of molecular conformations during collision, suggests possible ratchet-like mechanisms that could be used to sort polyelectrolytes in nanodevices.

Elastic particle model for coil-stretch transition of dilute polymers in an elongational flow

The phenomenon of the ‘coil-stretch’ (C-S) transition, wherein a long-chain polymer initially in a coiled state undergoes a sudden configuration change to become fully stretched under steady elongational flows, has been widely recognized. This transition can display intricate hysteresis behaviours under specific critical conditions, giving rise to unique rheological characteristics in dilute polymer solutions. Historically, microscopic stochastic models and Brownian dynamics simulations have shed light on the underlying mechanisms of the transition by uncovering bistable configurations of polymer chains. Following the initial work by Cerf (J. Chem. Phys., vol. 20, 1952, pp. 395–402), we introduce a continuum model in this study to investigate the C-S transition in a constant uniaxial elongational flow. Our approach involves approximating the unfolding process of the polymer chain as an axisymmetric deformation of an elastic particle. We make the assumption that the particle possesses uniform material properties, which can be represented by a nonlinear, strain-hardening constitutive equation to replicate the finite extensibility of the polymer chain. Subsequently, we analytically solve for the steady-state deformation using a polarization method. By employing this reduced model, we effectively capture the C-S transition and establish its specific correlations with material and geometric properties. The hysteresis phenomena can be comprehended through a force-balance analysis, which involves comparing the externally applied viscous forces with the intrinsic elastic responsive forces. We demonstrate that our model, while simple, unveils rich elastohydrodynamics of the C-S transition.

Electrospun Fenoprofen/Polycaprolactone @ Tranexamic Acid/Hydroxyapatite Nanofibers as Orthopedic Hemostasis Dressings.

Dressings with multiple functional performances (such as hemostasis, promoting regeneration, analgesia, and anti-inflammatory effects) are highly desired in orthopedic surgery. Herein, several new kinds of medicated nanofibers loaded with several active ingredients for providing multiple functions were prepared using the modified coaxial electrospinning processes. With an electrospinnable solution composed of polycaprolactone and fenoprofen as the core working fluid, several different types of unspinnable fluids (including pure solvent, nanosuspension containing tranexamic acid and hydroxyapatite, and dilute polymeric solution comprising tranexamic acid, hydroxyapatite, and polyvinylpyrrolidone) were explored to implement the modified coaxial processes for creating the multifunctional nanofibers. Their morphologies and inner structures were assessed through scanning and transmission electron microscopes, which all showed a linear format without the discerned beads or spindles and a diameter smaller than 1.0 μm, and some of them had incomplete core-shell nanostructures, represented by the symbol @. Additionally, strange details about the sheaths' topographies were observed, which included cracks, adhesions, and embedded nanoparticles. XRD and FTIR verified that the drugs tranexamic acid and fenoprofen presented in the nanofibers in an amorphous state, which resulted from the fine compatibility among the involved components. All the prepared samples were demonstrated to have a fine hydrophilic property and exhibited a lower water contact angle smaller than 40° in 300 ms. In vitro dissolution tests indicated that fenoprofen was released in a sustained manner over 6 h through a typical Fickian diffusion mechanism. Hemostatic tests verified that the intentional distribution of tranexamic acid on the shell sections was able to endow a rapid hemostatic effect within 60 s.

Effects of chain resolution on the configurational and rheological predictions of dilute polymer solutions in flow fields with hydrodynamic interactions

In a recent study, the resolution of a polymer chain model was shown to significantly affect rheological predictions from Brownian dynamics (BD) simulations [Kumar and Dalal, “Effects of chain resolution on the configurational and rheological predictions from Brownian dynamics simulations of an isolated polymer chain in flow,” J. Non-Newtonian Fluid Mech. 315, 105017 (2023)], even in the absence of hydrodynamic interactions (HI) and excluded volume. In this study, we investigate the effects of chain resolution in the presence of HI. Toward this, we perform BD simulations of a long polymer chain, with the discretization level varying from a single Kuhn step (bead–rod model) to several tens of Kuhn-steps (bead–spring model). The chain models were subjected to flow fields of uniaxial extension (purely stretching) and steady shear (equal rates of stretching and rotation). Broadly, our results indicate an amplification of the differences observed between the differently resolved bead–rod and bead–spring models, in the presence of HI. Interestingly, all rheological predictions qualitatively fall in two groups for extensional flow, with the predictions from the bead–spring model with HI being close to those of the bead–rod model without HI. This indicates significantly reduced sensitivity of coarser bead–spring models to HI, relative to the one resolved to a single Kuhn step. However, in shear flow, the bead–spring rheological predictions fall between those of the bead–rod model with and without HI, forming a third group. This is linked to the presence of stretched and coiled states in the ensemble for shear flow. HI effects are large for the coiled states and weak for the stretched states, thereby yielding predictions that are intermediate between those for no HI and dominant HI. Thus, quite surprisingly, the quality of predictions of the bead–spring models is strongly affected by the physics of the flow field, irrespective of the parameterization.

Cavitation in viscoelastic dilute polymer solutions through a Venturi nozzle

This research experimentally examines the influence of viscoelastic dilute water solutions of polyethylene oxide on Venturi cavitation. Variations in solutions are engineered to manipulate the viscoelastic properties that in turn affect cavitation patterns and attributes. The consequences of viscoelasticity and flow conditions on cavitation are quantified using dimensionless numbers, including the elasticity number (El), the Reynolds number (Re), and the pressure ratio (κ). The experiment identifies three distinct cavitation patterns in the solutions, with their transitions being impacted by alterations in El and κ. As El amplifies, the cavitation bubbles expand and get smoother, and the reentrant jet thickens and amplifies. The behavior of cavitation aligns with the model proposed by Zhang et al. [Phys. Fluids 31, 097107 (2019)], suggesting the critical role of the reentrant jet in the shedding of the cavity cluster. The study also substantiates that the reentrant jet intensifies with ascending El or Re. The collective influence of El, Re, and κ is discovered to shape the cavitation length and shedding frequency of cavity clusters. An increased El or a decreased Re reinforces the vorticity and the reentrant jet, which inevitably leads to a reduction in cavitation lengths and an uptick in the shedding frequency. Conversely, a larger El results in a more gradual response of the bubble to pressure alterations and pronounced rebounds, extending the cavitation length.

Some experimental results for converging flow of dilute polymer solution

This paper presents the results of experimental studies of the flow of a dilute polymer solution in a converging pipe. Three geometries with restriction rates are considered: 2.41, 3.92, and 5.65. A water–glycerin solution of 0.1% polyacrylamide was used as a working fluid. Point velocity measurements are made by using the smoke image velocimetry technique, which previously was proved by the construction of velocity profiles corresponding to the laminar viscoelastic flow in a straight pipe. The influence of the Weissenberg number and the restriction rate of the channel on the velocity profiles are established for both transverse and longitudinal directions. For small Weissenberg numbers, the experimental results are compared with the numerical results obtained using the Giesekus and exponential form of Phan-Thien–Tanner rheological models. Three flow regimes are identified: flow without vortex, vortex enhancement, and divergent flow, which is consistent with published results on the abrupt contraction and converging flows. Vortex length for a wide range of Weissenberg numbers is well predicted by a logarithm function. Modified expression of stretch rate with location of detachment plane can predict the flow regimes and the onset of unsteady flow in converging channels.

Multistability of elasto-inertial two-dimensional channel flow

Elasto-inertial turbulence (EIT) is a recently discovered two-dimensional chaotic flow state observed in dilute polymer solutions. Two possibilities are currently hypothesized to be linked to the dynamical origins of EIT: (i) viscoelastic Tollmien–Schlichting waves and (ii) a centre-mode instability. The nonlinear evolution of the centre mode leads to a travelling wave with an ‘arrowhead’ structure in the polymer conformation, a structure also observed instantaneously in simulations of EIT. In this work we conduct a suite of two-dimensional direct numerical simulations spanning a wide range of polymeric flow parameters to examine the possible dynamical connection between the arrowhead and EIT. Our calculations reveal (up to) four coexistent attractors: the laminar state and a steady arrowhead regime (SAR), along with EIT and a ‘chaotic arrowhead regime’ (CAR). The SAR is stable for all parameters considered here, while the final pair of (chaotic) flow states are visually very similar and can be distinguished only by the presence of a weak polymer arrowhead structure in the CAR regime. Analysis of energy transfers between the flow and the polymer indicates that both chaotic regimes are maintained by an identical near-wall mechanism and that the weak arrowhead does not play a role. Our results suggest that the arrowhead is a benign flow structure that is disconnected from the self-sustaining mechanics of EIT.

Purely elastic turbulence in pressure-driven channel flows

Solutions of long, flexible polymer molecules are complex fluids that simultaneously exhibit fluid-like and solid-like behavior. When subjected to an external flow, dilute polymer solutions exhibit elastic turbulence-a unique, chaotic flow state absent in Newtonian fluids, like water. Unlike its Newtonian counterpart, elastic turbulence is caused by polymer molecules stretching and aligning in the flow, and can occur at vanishing inertia. While experimental realizations of elastic turbulence are well-documented, there is currently no understanding of its mechanism. Here, we present large-scale direct numerical simulations of elastic turbulence in pressure-driven flows through straight channels. We demonstrate that the transition to elastic turbulence is sub-critical, giving rise to spot-like flow structures that, further away from the transition, eventually spread throughout the domain. We provide evidence that elastic turbulence is organized around unstable coherent states that are localized close to the channel midplane.