Elastic turbulence in a curvilinear channel flow

Electro-Elastic Instability and Turbulence in Electro-osmotic Flows of Viscoelastic Fluids: Current Status and Future Directions

The addition of even minute amounts of solid polymers, measured in parts per million (ppm), into a simple Newtonian fluid like water significantly alters the flow behavior of the resulting polymer solutions due to the introduction of fluid viscoelasticity. This viscoelastic behavior, which arises due to the stretching and relaxation phenomena of polymer molecules, leads to complex flow dynamics that are starkly different from those seen in simple Newtonian fluids under the same conditions. In addition to polymer solutions, many other fluids, routinely used in various industries and our daily lives, exhibit viscoelastic properties, including emulsions; foams; suspensions; biological fluids such as blood, saliva, and cerebrospinal fluid; and suspensions of biomolecules like DNA and proteins. In various microfluidic platforms, these viscoelastic fluids are often transported using electro-osmotic flows (EOFs), where an electric field is applied to control fluid movement. This method provides more precise and accurate flow control compared to pressure-driven techniques. However, several experimental and numerical studies have shown that when either the applied electric field strength or the fluid elasticity exceeds a critical threshold, the flow in these viscoelastic fluids becomes unstable and asymmetric due to the development of electro-elastic instability (EEI). These instabilities are driven by the normal elastic stresses in viscoelastic fluids and are not observed in Newtonian fluids under the same conditions, where the flow remains steady and symmetric. As the electric field strength or fluid elasticity is further increased, these instabilities can transition into a more chaotic and turbulent-like flow state, referred to as electro-elastic turbulence (EET). This article comprehensively reviews the existing literature on these EEI and EET phenomena, summarizing key findings from both experimental and numerical studies. Additionally, this article presents a detailed discussion of future research directions, emphasizing the need for further investigations to fully understand and harness the potential of EEI and EET in various practical applications, particularly in microscale flow systems where better flow control and increased transport rates are essential.

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.

Towards Predicting the Onset of Elastic Turbulence in Complex Geometries

Abstract

Flow of complex fluids in porous structures is pertinent in many biological and industrial processes. For these applications, elastic turbulence, a viscoelastic instability occurring at low Re—arising from a non-trivial coupling of fluid rheology and flow geometry—is a common and relevant effect because of significant over-proportional increase in pressure drop and spatio-temporal distortion of the flow field. Therefore, significant efforts have been made to predict the onset of elastic turbulence in flow geometries with constrictions. The onset of flow perturbations to fluid streamlines is not adequately captured by Deborah and Weissenberg numbers. The introduction of more complex dimensionless numbers such as the M-criterion, which was meant as a simple and pragmatic method to predict the onset of elastic instabilities as an order-of-magnitude estimate, has been successful for simpler geometries. However, for more complex geometries which are encountered in many relevant applications, sometimes discrepancies between experimental observation and M-criteria prediction have been encountered. So far these discrepancies have been mainly attributed to the emergence from disorder. In this experimental study, we employ a single channel with multiple constrictions at varying distance and aspect ratios. We show that adjacent constrictions can interact via non-laminar flow field instabilities caused by a combination of individual geometry and viscoelastic rheology depending (besides other factors) explicitly on the distance between adjacent constrictions. This provides intuitive insight on a more conceptual level why the M-criteria predictions are not more precise. Our findings suggest that coupling of rheological effects and fluid geometry is more complex and implicit and controlled by more length scales than are currently employed. For translating bulk fluid, rheology determined by classical rheometry into the effective behaviour in complex porous geometries requires consideration of more than only one repeat element. Our findings open the path towards more accurate prediction of the onset of elastic turbulence, which many applications will benefit.

Article Highlights

Continuous Pathway between the Elasto-Inertial and Elastic Turbulent States in Viscoelastic Channel Flow

Viscoelastic plane Poiseuille flow is shown to become linearly unstable in the absence of inertia, in the limit of high elasticities, for ultradilute 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 up to 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 ultradilute polymer solutions, a single linearly unstable modal branch may underlie transition to elastic turbulence at zero Re and to elasto-inertial turbulence at moderate Re, implying the existence of continuous pathways connecting the turbulent states to each other and to the laminar base state.

Elastic Turbulence of Aqueous Polymer Solution in Multi-Stream Micro-Channel Flow

Viscous liquid flow in micro-channels is typically laminar because of the low Reynolds number constraint. However, by introducing elasticity into the fluids, the flow behavior could change drastically to become turbulent; this elasticity can be realized by dissolving small quantities of polymer molecules into an aqueous solvent. Our recent investigation has directly visualized the extension and relaxation of these polymer molecules in an aqueous solution. This elastic-driven phenomenon is known as 'elastic turbulence'. Hitherto, existing studies on elastic flow instability are mostly limited to single-stream flows, and a comprehensive statistical analysis of a multi-stream elastic turbulent micro-channel flow is needed to provide additional physical understanding. Here, we investigate the flow field characteristics of elastic turbulence in a 3-stream contraction-expansion micro-channel flow. By applying statistical analyses and flow visualization tools, we show that the flow field bares many similarities to that of inertia-driven turbulence. More interestingly, we observed regions with two different types of power-law dependence in the velocity power spectra at high frequencies. This is a typical characteristic of two-dimensional turbulence and has hitherto not been reported for elastic turbulent micro-channel flows.

Flow fluctuations in wormlike micelle fluids

We investigate the unstable flow of wormlike micelle solutions in pressure driven capillary flow, with a focus on the effect of entrance geometry on the fluid fluctuations. The flow is measured at different points in the capillary using particle image velocimetry while simultaneously measuring the pressure drop across the entire capillary. The fluctuations are characterized by rapid flow rate jumps that correspond with a decrease in the pressure drop followed by a longer recovery period. Velocimetry measurements in the entrance region show a transition to unstable flow above a critical flow rate, where large flow circulations are observed in the tapered geometry and localized jets are observed in an abrupt contraction. The transition to this unstable flow is shown to occur at a similar dimensionless extension rate normalized by the micelle relaxation time. A rapid breakdown in micelle alignment is observed in polarized light microscopy at the onset of the flow rate jump, indicating the importance of rapid micelle structural changes on the fluctuations. We characterize the system by analyzing the power spectral densities and develop a dynamical systems model to describe the relationship between pressure and flow rate. These developments provide understanding to control flow fluctuations and motivation for more detailed study of the coupling of fluid microstructure transitions and flow fluctuations.

Emergence of chaos in a viscous solution of rods

It is shown that the addition of small amounts of microscopic rods in a viscous fluid at low Reynolds number causes a significant increase of the flow resistance. Numerical simulations of the dynamics of the solution reveal that this phenomenon is associated to a transition from laminar to chaotic flow. Polymer stresses give rise to flow instabilities which, in turn, perturb the alignment of the rods. This coupled dynamics results in the activation of a wide range of scales, which enhances the mixing efficiency of viscous flows.

On the role of initial velocities in pair dispersion in a microfluidic chaotic flow

Chaotic flows drive mixing and efficient transport in fluids, as well as the associated beautiful complex patterns familiar to us from our every day life experience. Generating such flows at small scales where viscosity takes over is highly challenging from both the theoretical and engineering perspectives. This can be overcome by introducing a minuscule amount of long flexible polymers, resulting in a chaotic flow dubbed 'elastic turbulence'. At the basis of the theoretical frameworks for its study lie the assumptions of a spatially smooth and random-in-time velocity field. Previous measurements of elastic turbulence have been limited to two-dimensions. Using a novel three-dimensional particle tracking method, we conduct a microfluidic experiment, allowing us to explore elastic turbulence from the perspective of particles moving with the flow. Our findings show that the smoothness assumption breaks already at scales smaller than a tenth of the system size. Moreover, we provide conclusive experimental evidence that 'ballistic' separation prevails in the dynamics of pairs of tracers over long times and distances, exhibiting a memory of the initial separation velocities. The ballistic dispersion is universal, yet it has been overlooked so far in the context of small scales chaotic flows.Elastic turbulence, a random-in-time flow, can drive efficient mixing in microfluidics. Using a 3D particle tracking method, the authors show that the smoothness assumption breaks at scales far smaller than believed and the ballistic pair dispersion holds over much longer distances than expected.

Elastic turbulence in entangled semi-dilute DNA solutions measured with optical coherence tomography velocimetry

The flow instabilities of solutions of high molecular weight DNA in the entangled semi-dilute concentration regime were investigated using optical coherence tomography velocimetry, a technique that provides high spatial (probe volumes of 3.4 pL) and temporal resolution (sub μs) information on the flow behaviour of complex fluids in a rheometer. The velocity profiles of the opaque DNA solutions (high and low salt) were measured as a function of the distance across the gap of a parallel plate rheometer, and their evolution over time was measured. At lower DNA concentrations and low shear rates, the velocity fluctuations were well described by Gaussian functions and the velocity gradient was uniform across the rheometer gap, which is expected for Newtonian flows. As the DNA concentration and shear rate were increased there was a stable wall slip regime followed by an evolving wall slip regime, which is finally followed by the onset of elastic turbulence. Strain localization (shear banding) is observed on the boundaries of the flows at intermediate shear rates, but decreases in the high shear elastic turbulence regime, where bulk strain localization occurs. A dynamic phase diagram for non-linear flow was created to describe the different behaviours.

Oscillatory elastic instabilities in an extensional viscoelastic flow

Dilute polymer solutions are known to exhibit purely elastic instabilities even when the fluid inertia is negligible. Here we report the quantitative evidence of two consecutive oscillatory elastic instabilities in an elongation flow of a dilute polymer solution as realized in a T-junction geometry with a long recirculating cavity. The main result reported here is the observation and characterization of the first transition as a forward Hopf bifurcation resulted in a uniformly oscillating state due to breaking of time translational invariance. This unexpected finding is in contrast with previous experiments and numerical simulations performed in similar ranges of the Wi and Re numbers, where the forward fork-bifurcation into a steady asymmetric flow due to the broken spatial inversion symmetry was reported. We discuss the plausible discrepancy between our findings and previous studies that could be attributed to the long recirculating cavity, where the length of the recirculating cavity plays a crucial role in the breaking of time translational invariance instead of the spatial inversion. The second transition is manifested via time aperiodic transverse fluctuations of the interface between the dyed and undyed fluid streams at the channel junction and advected downstream by the mean flow. Both instabilities are characterized by fluid discharge-rate and simultaneous imaging of the interface between the dyed and undyed fluid streams in the outflow channel.