Composing chaos: An experimental and numerical study of an open duct mixing flow

Development of Test Procedures Based on Chaotic Advection for Assessing Polymer Performance in High-Solids Tailings Applications

Post-thickener polymer addition to initiate rapid tailings dewatering has gained considerable interest for tailings storage facility (TSF) management. However, the highly viscous and non-Newtonian rheology of dense suspensions presents unique challenges for mixing with polymer solutions. Such mixing is highly inefficient, often resulting in polymer overdosing and wide variations in deposited tailings characteristics, with the potential to significantly compromise TSF performance. In this study, a new type of mixer based on the principles of chaotic advection was used for treating kaolin suspensions with high molecular weight (MW) anionic copolymer solutions. Chaotic advection imparts efficient mixing by gently stretching and folding flows in a controlled manner, as opposed to random, high-shear flows associated with turbulent mixing, and this lower shear stress allows for the controlled formation of larger aggregate structures with vastly improved dewatering characteristics. A pre-conditioning pipe reactor prior to this mixer can also be advantageous in terms of providing a short burst of high shear for initial polymer distribution. Seven acrylamide/acrylate copolymers of a fixed anionic charge density (30%) spanning a distinct MW range, as characterized by intrinsic viscosity, were applied at elevated dosages to high-solids (20–30 wt %) kaolin suspensions in continuous flow through the chaotic mixer described above. Medium-to-high MW polymers were generally preferred, with further increases in MW resulting in significantly diminished dewatering outcomes. Direct analysis of polymer solution properties through oscillatory rheology gave a better indication of a polymer’s potential performance compared with intrinsic viscosity, offering a more robust basis for polymer selection. This represented the first systematic study into the effects of polymer properties on deposition behavior after dosing at high solids, which was only possible through the ability to apply controlled shear across the entire suspension during sample preparation.

Rapid detection of Hendra virus antibodies: an integrated device with nanoparticle assay and chaotic micromixing

Current diagnosis of infectious diseases such as Hendra virus (HeV) relies mostly on laboratory-based tests. There is an urgent demand for rapid diagnosis technology to detect and identify these diseases in humans and animals so that disease spread can be controlled. In this study, an integrated lab-on-a-chip device using a magnetic nanoparticle immunoassay is developed. The key features of the device are the chaotic fluid mixing, achieved by magnetically driven motion of nanoparticles with the optimal mixing protocol developed using chaotic transport theory, and the automatic liquid handling system for loading reagents and samples. The device has been demonstrated to detect Hendra virus antibodies in dilute horse serum samples within a short time of 15 minutes and the limit of detection is about 0.48 ng ml^-1. The device platform can potentially be used for field detection of viruses and other biological and chemical substances.

Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state

Countless theoretical/numerical studies on transport and mixing in two-dimensional (2D) unsteady flows lean on the assumption that Hamiltonian mechanisms govern the Lagrangian dynamics of passive tracers. However, experimental studies specifically investigating said mechanisms are rare. Moreover, they typically concern local behavior in specific states (usually far away from the integrable state) and generally expose this indirectly by dye visualization. Laboratory experiments explicitly addressing the global Hamiltonian progression of the Lagrangian flow topology entirely from integrable to chaotic state, i.e., the fundamental route to efficient transport by chaotic advection, appear non-existent. This motivates our study on experimental visualization of this progression by direct measurement of Poincaré sections of passive tracer particles in a representative 2D time-periodic flow. This admits (i) accurate replication of the experimental initial conditions, facilitating true one-to-one comparison of simulated and measured behavior, and (ii) direct experimental investigation of the ensuing Lagrangian dynamics. The analysis reveals a close agreement between computations and observations and thus experimentally validates the full global Hamiltonian progression at a great level of detail.

Viscous pumping inspired by flexible propulsion

Fluid-suspended microorganisms have evolved different swimming and feeding strategies in order to cope with an environment dominated by viscous effects. For instance, ciliated organisms rely on the collective motion of flexible appendages to move and feed. By performing a non-reciprocal motion, flexible filaments can produce a net propulsive force, or pump fluid, in the absence of inertia. Inspired by such a fundamental concept, we propose a strategy to produce macroscopic pumping and mixing in creeping flow. We measured experimentally the net motion of a Newtonian viscous fluid induced by the reciprocal motion of a flapper. When the flapper is rigid no net motion is induced. In contrast, when the flapper is made of a flexible material, a net fluid pumping is measured. We quantify the effectiveness of this pumping strategy and show that optimal pumping is achieved when the length of the flapper is on the same order as the elasto-hydrodynamic penetration length. We finally discuss the possible applications of flexible impellers in mixing operations at low Reynolds numbers.

Control mechanisms for the global structure of scalar dispersion in chaotic flows

Scalar dispersion has complex interactions between advection and diffusion that depend on the values of the scalar diffusivity and of the (possibly large) set of parameters controlling the flow. Using a spectral method which is three to four orders of magnitude faster than traditional methods, we calculate the fine-scale structure of the global solution space of the advection-diffusion equation for a physically realizable chaotic flow. The solution space is rich: spatial pattern locking, an order-disorder transition, and optima in dispersion rates that move discontinuously with Peclét number and boundary condition type are some of the discoveries. We uncover the mechanisms which control pattern locking and govern the global structure of dispersion across the parameter space and Peclét number spectrum.

Finite-time transport in volume-preserving flows

Finite-time transport between distinct flow regions is of great relevance to many scientific applications, yet quantitative studies remain scarce to date. The primary obstacle is computing the evolution of material volumes, which is often infeasible due to extreme interfacial stretching. We present a framework for describing and computing finite-time transport in n-dimensional (chaotic) volume-preserving flows that relies on the reduced dynamics of an (n-2)-dimensional "minimal set" of fundamental trajectories. This approach has essential advantages over existing methods: the regions between which transport is investigated can be arbitrarily specified; no knowledge of the flow outside the finite transport interval is needed; and computational effort is substantially reduced. We demonstrate our framework in 2D for an industrial mixing device.

Observability of periodic lines in three-dimensional lid-driven cylindrical cavity flows

This study employs three-dimensional particle-tracking velocimetry (3D-PTV) for experimental investigation of the existence and properties of periodic lines in 3D lid-driven time-periodic flows inside a cylindrical cavity. These periodic lines, consisting of material points that periodically return to their initial position, play a central role in the transport properties of laminar flows, yet their existence has so far been demonstrated only in numerical simulations. The formation and characteristics of periodic lines are inextricably linked with spatiotemporal symmetries of the flow. 3D-PTV measurements determined that relevant symmetries, identified with previous symmetry analyses, are satisfied within experimental error bounds. These measurements subsequently isolated periodic lines in the designated symmetry planes, thus offering first experimental evidence of their physical existence and their fundamental reliance on symmetries. Experimental periodic lines are topologically equivalent to those in simulated flows with identical symmetries and exhibit the same response to changes in forcing conditions. The laboratory experiments by these observations bridge the gap from theoretical and numerical predictions on periodic lines to real 3D flows.

Toward enhanced subsurface intervention methods using chaotic advection

Many intervention activities in the terrestrial subsurface involve the need to recover/emplace distributions of scalar quantities (e.g. dissolved phase concentrations or heat) from/in volumes of saturated porous media. These scalars can be targeted by pump-and-treat methods or by amendment technologies. Application examples include in-situ leaching for metals, recovery of dissolved contaminant plumes, or utilizing heat energy in geothermal reservoirs. While conventional pumping methods work reasonably well, costs associated with maintaining pumping schedules are high and improvements in efficiency would be welcome. In this paper we discuss how transient switching of the pressure at different wells can intimately control subsurface flow, generating a range of "programmed" flows with various beneficial characteristics. Some programs produce chaotic flows which accelerate mixing, while others create encapsulating flows which can isolate fluid zones for lengthy periods. In a simplified model of an aquifer subject to balanced pumping, chaotic flow topologies have been predicted theoretically and verified experimentally using Hele-Shaw cells. Here, a survey of the key characteristics of chaotic advection is presented. Mathematical methods are used to show how these characteristics may translate into practical situations involving regional flows and heterogeneity. The results are robust to perturbations, and withstand significant aquifer heterogeneity. It is proposed that chaotic advection may form the basis of new efficient technologies for groundwater interventions.

An experimental and theoretical study of the mixing characteristics of a periodically reoriented irrotational flow

The minimum-energy method to generate chaotic advection should be to use an irrotational flow. However, irrotational flows have no saddle connections to perturb in order to generate chaotic orbits. To the early work of Jones & Aref (Jones & Aref 1988 Phys. Fluids 31, 469-485 (doi:10.1063/1.866828)) on potential flow chaos, we add periodic reorientation to generate chaotic advection with irrotational experimental flows. Our experimental irrotational flow is a dipole potential flow in a disc-shaped Hele-Shaw cell called the rotated potential mixing flow; it leads to chaotic advection and transport in the disc. We derive an analytical map for the flow. This is a partially open flow, in which parts of the flow remain in the cell forever, and parts of it pass through with residence-time and exit-time distributions that have self-similar features in the control parameter space of the stirring. The theory compares well with the experiment.

A partially open porous media flow with chaotic advection: towards a model of coupled fields

In nature, dissipative fluxes of fluid, heat and/or reacting species couple to each other and may also couple to deformation of a surrounding porous matrix. We use the well-known analogy of Hele-Shaw flow to Darcy flow to make a model porous medium with porosity proportional to local cell height. Time- and space-varying fluid injection from multiple source/sink wells lets us create many different kinds of chaotic flows and chemical concentration patterns. Results of an initial time-dependent potential flow model illustrate that this is a partially open flow, in which parts of the material transported by the flow remain in the cell forever and parts pass through with residence time and exit time distributions that have self-similar features in the control parameter space of the stirring. We derive analytically the existence boundary in stirring control parameter space between where isolated fluid regions can and cannot remain forever in the open flow. Experiments confirm the predictions.