Session EC: Microfluidics IV: Mixing-1

Micromixers for studies of protein folding kinetics

We are developing microfluidic mixers with mixing dead time of microseconds and sample consumption of femtomoles for use in studies of protein folding kinetics. Our mixer uses hydrodynamic focusing of pressure-driven flow to form a sub-micron wide stream, which reduces diffusion length and results in fast mixing. We discuss the design, optimization, and characterization of these mixers. In the original mixer (Hertzog et al., Anal. Chem. 2004) with cross-shaped microchannels, the mixing time and the mixing uniformity are limited. The limitation to the mixing time arises due to formation of Dean vortices at high flow rates, while the photolithographically defined nozzles limit mixing uniformity. We addressed these two problems in two individual designs with reduced side channel curvatures and shape-optimized nozzles, respectively. The final design that we will present combines both of these features and achieves optimized performance. We quantified the mixing performance of these four designs by numerical simulation of coupled Navier-Stokes and convection-diffusion equations, and experiments using both dye quenching and FRET-labeled DNA.   

Microfluidic mixing through electrowetting-driven droplet oscillations

We used electrowetting to trigger periodic oscillations of millimeter-sized sessile droplets of water-glycerol mixtures in a viscosity range from 1 to 65 mPa s. We stained the drops partially with fluorescent dyes of variable mass to study the mixing within the droplets and we inserted tracer particles to characterize the flow patterns using particle image velocimetry (PIV). We found that mixing is completed within 100--2000 oscillation cycles for low and high viscosities, respectively. The absolute time for mixing is reduced by two orders of magnitude compared to pure diffusion. For dye molecules of variable mass, we find that the number of cycles required for mixing, scales with the logarithm of the P\'{e}clet number, in agreement with models based on chaotic advection. PIV data suggest that the origin of the irreversibility in the time-periodic flow fields inside the drop is related to the difference in contact angle between the spreading and the receding phase of the oscillatory drop motion. Part of the results was published in F. Mugele, J.-C. Baret, and D. Steinhauser. Appl. Phys. Lett. 88, 204106 (2006).   

Mixing by steady flows in thermocapillary driven droplets

We consider mixing via chaotic advection in microdroplets suspended at the free surface of a liquid substrate and driven using the thermocapillary effect. We illustrate that the mixing properties of the flow inside the droplet can vary dramatically as a function of the physical properties of the fluids and the imposed temperature profile. We show that proper characterization of the mixing quality requires introduction of two different metrics. The first metric determines the relative volumes of the domains of chaotic and regular streamlines. The second metric describes the time for homogenization inside the chaotic domain. We compute both metrics using perturbation theory in the limit of weak temperature dependence of the surface tension coefficient at the free surface of the substrate.   

Nature-Inspired Active Mixing in a Microchannel

Many applications of microfluidics require efficient mixing of two or more liquid streams. Mixing at the microscale mostly occurs through a rather slow diffusion process given the inherent laminar flow conditions. To speedup mixing, we propose an active mixer configuration, inspired by the motion of ciliated micro-organisms, that consists of an array of individually addressable micro-flaps covering microchannel walls, that can be actuated by an external stimulus. We developed a computational fluid-structure interaction model based on a fictitious domain method that simulates both the micro-flap motion as well as the concomitant fluid flow. We will first demonstrate the feasibility of our concept through a simple two micro-flap design in a cavity. We found that when a proper actuation scheme is used, two micro-flaps can indeed induce effective mixing by chaotic advection in a microchannel. For optimal mixing, it seems that the two micro-flaps should be placed as close to each other as possible, obviously taking care to avoid collision, and they should preferably be actuated 90$^{\circ}$ out of phase. Next, the simulated 2D flow field from multiple elements is translated to a 3D scenario to assess the design as a continuous micromixer.   

Chaotic advection using passive and active rigid particles in a two-dimensional serpentine channel flow

We studied flow and mixing due to the presence and active manipulation of rigid particles in a two-dimensional serpentine channel. The motion of a freely suspended particle in this flow is time periodic and the streamlines from the perturbed velocity are hyperbolic in nature. From Poincar\'e~ sections we observe two chaotic mixing zones separated by Kolmogorov-Arnold-Moser (KAM) boundaries along the path of the particle. In the case of the time-periodic flow of two-particles, two interacting hyperbolic points are present which give rise to three chaotic mixing zones. The efficiency of the mixing process can be greatly enhanced by adding a time-periodic external force working on the particle(s). The larger the force, the larger the strength of the perturbation of the flow. The size and presence of global chaotic mixing zones is positively influenced, as demonstrated by Poincar\'e~ sections, while the enhanced rate of mixing is computed via the deformation of a material strip undergoing stretching and folding around the particle. Actuation indeed makes the separating KAM boundaries disappear leading to almost global chaotic advection.   

Swirling of viscous threads in microchannels

We experimentally investigate the stability of viscous threads that are swept along in the flow of a less viscous miscible liquid in a square microchannel. Thin threads near the walls become unstable to shear-induced disturbances, which ultimately cause the threads to break-up and form arrays of viscous swirls, the miscible counterparts of droplets. We investigate the deformation morphologies of the threads during the swirling instability as well as the hydrodynamic coupling between the threads, which can produce intermingling phase-locked multiple folding. Our study highlights the possibility of forming and controlling the size and the shape of discrete and well-defined viscous elements without surface tension at the microscale.   

On the roughness-hydrophobicity coupling in nano and micro-channel flows

An approach based on a lattice version of the Boltzmann kinetic equation for describing multi-phase flows in nano- and micro-corrugated devices is proposed. We specialize it to describe the wetting/dewetting transition of fluids in presence of nanoscopic grooves etched on the boundaries. This approach permits to retain the essential {\it supra-molecular} details of fluid-solid interactions without surrendering -actually boosting- the computational efficiency of continuum methods. The method is used to analyze the importance of conspiring effects between hydrophobicity and roughness on the global mass flow rate of the microchannel. In particular we show that ``smart surfaces'' can be tailored to have strongly different mass throughput by changing the bulk pressure. The mesoscopic method is also validated quantitatively against Molecular Dynamics (MD) results of {\it Cottin-Bizonne et al.} [Nature Mater. {\bf 2} 237-240 (2003)].   

Size-controllable flow passage in a microchannel

Particle handling method in microchannels is an important process in the bioanalysis and biochemical array analysis. Existing methods utilize converging and diverging channel to accelerate and separate particles. This study adopts a straight channel and judiciously combines pressure-driven and elctrokinetically-driven flow to form a size-controllable flow passage. The combined flow results in the generation of recirculation flow, which changes the effective flow passage. Particles can be accelerated when passing through the passage along the straight microchannel. Analytical and experimental methods are used to investigate the flow. Particles passing through the recirculation flow region are detected and visualized. The effect of electrical field, particle trajectory, particle motions and particle separation distance in microchannel are examined.