Bridging kinematics and concentration content in a chaotic micromixer

Linking mixing and flow topology in porous media: An experimental proof

Transport processes in porous media are controlled by the characteristics of the flow field which are determined by the porous material properties and the boundary conditions of the system. This work provides experimental evidence of the relation between mixing and flow field topology in porous media at the continuum scale. The setup consists of a homogeneously packed quasi-two-dimensional flow-through chamber in which transient flow conditions, dynamically controlled by two external reservoirs, impact the transport of a dissolved tracer. The experiments were performed at two different flow velocities, corresponding to Péclet numbers of 191 and 565, respectively. The model-based interpretation of the experimental results shows that high values of the effective Okubo-Weiss parameter, driven by the changes of the boundary conditions, lead to high rates of increase of the Shannon entropy of the tracer distribution and, thus, to enhanced mixing. The comparison between a hydrodynamic dispersion model and an equivalent pore diffusion model demonstrates that despite the spatial and temporal variability in the hydrodynamic dispersion coefficients, the Shannon entropy remains almost unchanged because it is controlled by the Okubo-Weiss parameter. Overall, our work demonstrates that under highly transient boundary conditions, mixing dynamics in homogeneous porous media can also display complex patterns and is controlled by the flow topology.

Plume deformation, mixing, and reaction kinetics: An analysis of interacting helical flows in three-dimensional porous media

Heterogeneity and macroscopic anisotropy of porous media play an important role for dilution and reaction enhancement of conservative and reactive plumes. In this study, we perform numerical simulations to investigate steady-state flow and transport in three-dimensional heterogeneous porous media. We consider two macroscopic anisotropic inclusions resulting in helical flows with twisting streamlines in a three-dimensional flow-through domain. The inclusions are obtained by alternating two layers of angled slices of coarse and fine porous media with different hydraulic conductivity. We investigate flow and transport scenarios considering different geometry and relative position of the two anisotropic inclusions yielding helical flow fields with different extent of interaction. We use metrics of stretching and folding to characterize the flow field and entropy-based metrics for the analysis of the conservative and reactive transport problems. The outcomes show that the two helices result in different patterns of twisting streamlines, which cause distinct deformation of the plumes. However, mixing and reaction enhancement could not be directly related to the extent of the flow field deformation: Configurations with strong deformation can result in only moderate mixing enhancement, whereas configurations with limited deformation of the flow field can lead to significant mixing of the solute plume. Finally, we explore the impact of different degradation rates on reactive transport and the role of reaction kinetics on the entropy balance for a reactant undergoing transport and mixing-controlled degradation in the twisting flow fields. The results show that strong mixing enhancement due to helical flow increases the importance of the reaction kinetics that becomes the rate-limiting process for solute reactive transport.

Three-Dimensional Fabrication for Microfluidics by Conventional Techniques and Equipment Used in Mass Production

This paper presents a simple three-dimensional (3D) fabrication method based on soft lithography techniques and laminated object manufacturing. The method can create 3D structures that have undercuts with general machines for mass production and laboratory scale prototyping. The minimum layer thickness of the method is at least 4 µm and bonding strength between layers is over 330 kPa. The performance reaches conventional fabrication techniques used for two-dimensionally (2D)-designed microfluidic devices. We fabricated some 3D structures, i.e., fractal structures, spiral structures, and a channel-in-channel structure, in microfluidic channels and demonstrated 3D microfluidics. The fabrication method can be achieved with a simple black light for bio-molecule detection; thus, it is useful for not only lab-scale rapid prototyping, but also for commercial manufacturing.

Experimental Evidence of Helical Flow in Porous Media

Helical flow leads to deformation of solute plumes and enhances transverse mixing in porous media. We present experiments in which macroscopic helical flow is created by arranging different materials to obtain an anisotropic macroscopic permeability tensor with spatially variable orientation. The resulting helical flow entails twisting streamlines which cause a significant increase in lateral mass exchange and thus a large enhancement of plume dilution (up to 235%) compared to transport in homogenous media. The setup may be used to effectively mix solutes in parallel streams similarly to static mixers, but in porous media.

How a "pinch of salt" can tune chaotic mixing of colloidal suspensions

Efficient mixing of colloids, particles or molecules is a central issue in many processes. It results from the complex interplay between flow deformations and molecular diffusion, which is generally assumed to control the homogenization processes. In this work we demonstrate on the contrary that despite fixed flow and self-diffusion conditions, the chaotic mixing of colloidal suspensions can be either boosted or inhibited by the sole addition of a trace amount of salt as a co-mixing species. Indeed, this shows that local saline gradients can trigger a chemically driven transport phenomenon, diffusiophoresis, which controls the rate and direction of molecular transport far more efficiently than the usual Brownian diffusion. A simple model combining the elementary ingredients of chaotic mixing with diffusiophoretic transport of the colloids allows rationalization of our observations and highlights how small-scale out-of-equilibrium transport bridges to mixing at much larger scales in a very effective way. Considering chaotic mixing as a prototypal building block for turbulent mixing suggests that these phenomena, occurring whenever the chemical environment is inhomogeneous, might bring interesting perspectives from micro-systems to large-scale situations, with examples ranging from ecosystems to industrial contexts.

Lamination and mixing in three fundamental flow sequences driven by electromagnetic body forces

This article pursues the idea that the degree of striations, called lamination, could be engineered to complement stretching and to design new sequential mixers. It explores lamination and mixing in three new mixing sequences experimentally driven by electromagnetic body forces. To generate these three mixing sequences, Lorentz body forces are dynamically controlled to vary the flow geometry produced by a pair of local jets. The first two sequences are inspired from the "tendril and whorl" and "blinking vortex" flows. The third novel sequence is called the "cat's eyes flip." These three mixing sequences exponentially stretch and laminate material lines representing the interface between two domains to be mixed. Moreover, the mixing coefficient (defined as 1-σ(2)/σ(0)(2) where σ(2)/σ(0)(2) is the rescaled variance) and its rate grow exponentially before saturation. This saturation of the mixing process is related to the departure of the mixing rate from an exponential growth when the striations' thicknesses reach the diffusive length scale of the measurements or species and dyes. Incidentally, in our experiments, for the same energy or forcing input, the cat's eyes flip sequence has higher lamination, stretching, and mixing rates than the tendril and whorl and the blinking vortex sequences. These features show that bakerlike in situ mixers can be conceived by dynamically controlling a pair of local jets and by integrating lamination during stirring stages with persistent geometries. Combined with novel insights provided by the quantification of the lamination, this paper should offer perspectives for the development of new sequential mixers, possibly on all scales.

Transport phenomena in chaotic laminar flows

In many important chemical processes, the laminar flow regime is inescapable and defines the performance of reactors, separators, and analytical instruments. In the emerging field of microchemical process or lab-on-a-chip, this constraint is particularly rigid. Here, we review developments in the use of chaotic laminar flows to improve common transport processes in this regime. We focus on four: mixing, interfacial transfer, axial dispersion, and spatial sampling. Our coverage demonstrates the potential for chaos to improve these processes if implemented appropriately. Throughout, we emphasize the usefulness of familiar theoretical models of transport for processes occurring in chaotic flows. Finally, we point out open challenges and opportunities in the field.

Moving walls accelerate mixing

Mixing in viscous fluids is challenging, but chaotic advection in principle allows efficient mixing. In the best possible scenario, the decay rate of the concentration profile of a passive scalar should be exponential in time. In practice, several authors have found that the no-slip boundary condition at the walls of a vessel can slow down mixing considerably, turning an exponential decay into a power law. This slowdown affects the whole mixing region, and not just the vicinity of the wall. The reason is that when the chaotic mixing region extends to the wall, a separatrix connects to it. The approach to the wall along that separatrix is polynomial in time and dominates the long-time decay. However, if the walls are moved or rotated, closed orbits appear, separated from the central mixing region by a hyperbolic fixed point with a homoclinic orbit. The long-time approach to the fixed point is exponential, so an overall exponential decay is recovered, albeit with a thin unmixed region near the wall.

Transverse flow in thin superhydrophobic channels

We provide some general theoretical results to guide the optimization of transverse hydrodynamic phenomena in superhydrophobic channels. Our focus is on the canonical micro- and nanofluidic geometry of a parallel-plate channel with an arbitrary two-component (low-slip and high-slip) coarse texture, varying on scales larger than the channel thickness. By analyzing rigorous bounds on the permeability, over all possible patterns, we optimize the area fractions, slip lengths, geometry, and orientation of the surface texture to maximize transverse flow. In the case of two aligned striped surfaces, very strong transverse flows are possible. Optimized superhydrophobic surfaces may find applications in passive microfluidic mixing and amplification of transverse electrokinetic phenomena.

Print-and-peel fabricated passive micromixers

Advection driven mixing is essential for microfluidics and poses challenges to the design of microdevices. Force transducers or complex channel configurations provide means for, respectively, active or passive disrupting of laminar flows and for homogenizing the composing fluids. Print-and-peel (PAP) is a nonlithographic fabrication technique that involves direct printing of masters for molding polymer components of microdevices. PAP, hence, allows for facile and expedient preparation of microfluidic devices, without requiring access to specialized microfabrication facilities. We utilized PAP for fabrication of microfluidic devices capable of turning, expanding, and contracting microflows. We examined the mixing capabilities of these devices under flow conditions of small Reynolds numbers (0.2-20) and large Peclet numbers (260-26 000), under which advection is the dominant mode of mass transfer. We focused on mixing channels with arched shapes and examined the dependence of the mixing performance on the turns and the expansions along the direction of the microflows. Three-dimensional expansion and contraction, along with an increase in the modes of twisting of the laminar currents, improved the quality of mixing. The simplicity in the described fabrication of the investigated passive micromixers makes PAP an attractive alternative for expedient device prototyping.

Quantitative characterization of micromixing simulation

Micromixers with floor-grooved microfluidic channels have been successfully demonstrated in experiment. In this work, we numerically simulated the mixing within the devices and used the obtained concentration versus channel length profiles to quantitatively characterize the process. It was found that the concentration at any given cross-section location of the microfluidic channel periodically oscillates along the channel length, in coordination with the groove-caused helical flow during the mixing, and eventually converges to the neutral concentration value of two the mixing fluids. With these data, the specific channel length required for each helical flow to complete, the mixing efficiency of the devices, and the total channel length required to complete a mixing were easily defined and quantified, and were used to directly and comprehensively characterize the micromixing. This concentration versus channel length profile-based characterization method was also demonstrated in quantitatively analyzing the micromixing within a classic T mixer. It has clear advantages over the traditional concentration image-based characterization method that is only able to provide qualitative or semiquantitative information about a micromixing, and is expected to find an increasing use in studying mixing and optimizing device structure through numerical simulations.