Session R17: Microfluids Mixing

Measuring Convective and Diffusive Mixing in Inertial Droplet-Pair Collisions

Complete mixing, dilution, and sample homogenization are essential processes in modern Lab on a Chip and Micro Total Analysis Systems and these seemingly simple tasks remain a major obstacle. A new mixing technique has been proposed that accelerates mixing rates in droplets through controlled, high speed droplet-pair collisions. The collisions take place inside a confined microchannel and the droplet generation and entrainment processes are provided by an inertial gaseous flow. The fast time scales, small length scales, and highly Lagrangian nature of discrete droplet collisions makes optical diagnostics the obvious choice for understanding, characterizing, and quantifying mixing processes. Presented here is a simple and robust visualization and measurement technique that captures convective and diffusive mixing inside droplets using differential fluorescence. High speed digital imagery, custom image processing, and fluorescent intensity statistical analysis are employed to examine the contribution of convective rearrangement and tracer diffusion to droplet mixing following inertial droplet-pair collisions.   

Mixing in Three Dimensional Linear Spiral Microchannels

Since its introduction a decade ago, soft lithography has drastically changed our understanding of fluid physics under confinement by enabling rapid production of microchannels and microdevices. Despite its popularity however, soft lithography has some limitations, including fabrication of thoroughly three dimensional passages without using multiple layers. In this talk, we first introduce the fabrication of a simple three dimensional linear spiral microchannel in a polydimethylsiloxane (PDMS) mold. In two dimensional planar spiral microchannels, Dean number increases or decreases with each consecutive rotation as the radius of curvature decreases or increases, respectively. In our three dimensional spiral microchannel, however, the radius of curvature is constant and as a result the Dean number assumes a constant value. The mixing performance of two miscible fluids in this microchannel is characterized using digital image processing techniques. The influence of flow rate as well as the length of the spiral pitch on the mixing performance is studied. Other possible applications are also discussed.   

Optimal Blinking-Flow Microfluidic Mixers

The performance of blinking-flow microfluidic mixers is explored in order to identify optimal mixer designs. A two-dimensional lid-driven flow model is defined that approximates the cross-channel flow in three-dimensional grooved mixers. On either side of a specified separatrix location on the channel floor, the model imposes two different transverse velocities that generate a pair of counter-rotating vorticies of differing sizes. Blinking-flow mixers are then defined by alternating two such fields with the separatrix location for each field chosen independently. An exhaustive search of this design space demonstrates that the best blinking flow mixers are not symmetric, i.e., the second velocity field is not the mirror image of the first. The best mixers combine a field with the separatrix near the channel centerline with a field with separatrix near one of the side walls. Results are compared to comparable three-dimensional grooved channel mixers, and implications of these results for optimizing general mixer designs are discussed.   

Use of Eulerian Indicators to Predict Best Mixing Configurations for a Blinking 2D Lid-Driven Flow

The 2D lid driven model with an alternating flow between two double gyres whose relative size differs is used as the basis of a study to determine the predictive capabilities of two Eulerian Indicators (EI), dubbed the ``transversality'' and ``mobility'' with respect to the degree of mixing achieved. The ``transversality'' EI measures the angular difference between the two alternating velocity vectors at a given position in the flows domain. Experiments have indicated that streamline crossing between two alternating flows is associated with regions of good mixing. The ``mobility'' EI measures the percentage of the flows domain that contributes the most to particle transport. In the parameter space under study, the product of the two EI's is shown to correlate well with the variance of concentration for the fluid, calculated as a Lagrangian metric. The computational efficiency gained by calculating Eulerian Indicators compared to Lagrangian metrics allows for a more efficient search through this systems parameter space, suggesting configurations which are better suited to mix well, effectively cutting the design time for optimizing new mixing designs.   

Fluid Mixing from Viscous Fingering

Fluid mixing is an important and complex phenomenon. It plays a fundamental role in natural processes, including groundwater flows in heterogeneous media, reactive flows, mantle convection, debris gravity currents, and bacterial locomotion. Mixing at low Reynolds numbers is a notoriously difficult problem because it cannot rely on turbulence. Mixing efficiency at low Reynolds numbers can be enhanced by exploiting hydrodynamic instabilities that induce heterogeneity and disorder in the flow. The unstable displacement of fluids with different viscosities, or viscous fingering, provides a powerful mechanism to increase fluid-fluid interfacial area and enhance mixing. Here we describe the dissipative structure of miscible viscous fingering, and propose a two-equation model for the scalar variance and its dissipation rate. Our analysis predicts the optimum range of viscosity contrasts that, for a given P\'eclet number, maximizes interfacial area and minimizes mixing time. In the spirit of turbulence modeling, the proposed two-equation model permits upscaling dissipation due to fingering at unresolved scales.   

Experimental investigation of periodic lines in 3D lid-driven cylindrical cavity flows

Mixing of mass and heat by laminar flows occurs in many natural systems and industrial processes. Understanding of the basic mechanisms to enhance mixing efficiency is mostly based on mathematical analysis and numerical studies of prototype cases. Three-dimensional (3D) experiments, however, remain largely unexplored. The present investigation employs 3D Particle Tracking Velocimetry (3D-PTV) to investigate a few of these concepts in realistic experimental configurations. We focus on the observability of periodic lines in periodically lid-driven cylindrical cavity flows. Periodic lines play a central role in the transport properties. The fluid is set in motion via a time-periodic forcing protocol (piece-wise steady translations of one of the endwalls of the cylinder), 3D-PTV measurements have been performed to obtain the web of tracer paths. Experimental results confirm key features from theoretical analysis and numerical studies on the location and shape of the periodic lines. A hybrid method (numerical tracking of particles in an Eulerian flow field determined by experimental measurements) is used to extend the forcing to situations inaccessible by direct particle tracking via 3D-PTV.   

Reaction-diffusion in microdroplets: Theory \& Experiments

We study the dynamics of the reaction front that forms as two initially separated reactants meet. The reactants are initially contained in two different nanoliter droplets confined in a microfluidic device. Guiding and trapping the drops is performed using the \textit{rails} and \textit{anchors} technique. A laser pulse then triggers the chemical reaction by coalescing the drops and we monitor the integral of the reaction product. An asymptotic analysis (Trevelyan, Phys. Rev. E, 80, 2009) identifies two phases for this process. The production rate of the reaction is determined by diffusion in both. Initially the two reactants occupy different regions and have to diffuse to react. The product concentration integral then varies as $t^{3/2}$ with a prefactor that depends on the reaction kinetics. At large times, the reaction rate becomes limited by the diffusive supply of reactants which must travel over longer distances. The product concentration integral then increases as $t^{1/2}$ with a different prefactor containing the same physical ingredients. Confronting theory and experiment allows the measurement of physical and chemical constants.   

Exploiting numerical diffusion to study transport and chaotic mixing for extremely large P\'eclet values

We show that the purely convective mapping matrix approach provides an extremely versatile tool to study advection-diffusion processes for extremely large P\'eclet values ($\sim$108 and higher). This is made possible due to the coarse-grained approximation that introduces numerical diffusion, the intensity of which depends in a simple way on grid resolution. This observation permits to address fundamental physical issues associated with chaotic mixing in the presence of diffusion. Specifically, we show that in partially chaotic flows, the dominant decay exponent of the advection diffusion propagator will eventually decay as Pe-1 in the presence of quasiperiodic regions of finite measure, no matter how small they are. Examples of 2d and 3d partially chaotic flows are discussed.   

Visualizing millisecond chaotic mixing in droplets moving through a serpentine microchannel

We have developed a two-photon excitation fluorescence lifetime imaging technique to accurately and quantitatively measure mixing of two fluorescence dyes inside microdroplets. The line scanning along the microfluidic channel is passively achieved via the droplets flowing through the excitation focal point. Because the periodically generated droplets are identical, we scan multiple droplets and sum up the line signals of each droplet by cross/autocorrelation to obtain the line signal with a high signal-to-noise ratio. The droplets are scanned line by line by moving the focal point across the channel using a translation stage. The cross-sectional image of the droplet is then formed by aligning the scanning lines across the channel. A non-fitting method based on the ratio of fluorescence signals in lifetime decay is used for mixing ratio calibration. With this new imaging technique, we visualize millisecond chaotic mixing dynamics in microdroplets with 5 microsecond time resolution. The mapped chaotic mixing patterns match well with the 2D numerical simulation, performed based on the coupled Laminar two-phase flow level set model and transport of diluted species model, and also validate the characteristics of the alternative asymmetric vortex flow in droplets moving through a serpentine channel.