Session GN: Micro Fluids III

Asymptotic study of flow in reactive microchannels

The influence of thermal expansion on the dynamics of thick premixed flames (flame thickness less than the channel height) for a variable density flow in a narrow, rectangular channel or pipe is explored. Adiabatic, non-adiabatic and axial heat conducting channel walls are considered. In each case, small Peclet number asymptotic solutions are developed for steady variable density flame propagation in the narrow channel. Configurations including flame propagation from the closed to the open end of the channel, toward the closed end of the channel, and toward the channel inlet where a Poiseuille flow (flame assisting or flame opposing) is imposed are studied. Finally, comparisons of the finite Peclet number dynamics are made with the behavior of the small Peclet number solutions.   

Osmotically driven flows in microchannels separated by a semipermeable membrane

Osmotically driven flows in microchannels are studied experimentally and theoretically. The propagation of the front of sugar solutions has been measured using dye and particle tracking in $200~\mu$m wide and 50, 100, and 200~$\mu$m high polymer-based microchannels. Each of these microchannels was separated by a semipermeable membrane from a reservoir containing pure water. We have also established a theoretical model of this system. In the limit of low axial flow resistance, our model predicts the propagation speed of the sugar front as a function of sugar concentration and channel geometry. The theoretical predictions agree well with the measurements. Our motivations for studying osmotically driven flows are that they are believed to be responsible for the translocation of sugar in plants and that they can be used as the driving mechanism in micropumps with no moveable parts.\\[5mm] This work was supported by the Danish National Research Foundation, Grant No. 74.   

Electromagnetic Activation of Capillary Switches

By designing coupled droplet pairs with the appropriate length scale to promote surface tension as the dominant force, one can create bi-stable capillary switches. This bi-stability can be triggered by pressure pulses, surface chemistry, electroosmosis, or body forces. To exploit the latter, we designed a capillary switch with electromagnetic activation. The resulting setup consists of a sub-millimeter tube, overfilled with a ferrofluid, surrounded by a wire coil to generate a magnetic field. Evidence of this capillary switching will be presented along with some theoretical basis in fluid- and electro-dynamics. The approach may also be used to investigate other transport phenomena in electromagnetically-coupled microfluidic systems, including the relative effects of translational motion of the ferrofluid (both particles and solvent molecules) versus the rotational effects of the individual magnetic grains. These individually addressable capillary switches offer intriguing applications including high-speed adaptive optics, actuators at the microscale, and possible PCB integration.   

Gas motion induced by unsteady boundary heating in a small-scale gap

We study the response of a gas confined in a small-scale gap to a small, time-dependent change in the temperature of its boundaries. Using the collisionless Boltzmann equation, a general scheme for the calculation of the probability density function and the respective hydrodynamic fields in response to any heating history is developed. Asymptotic results are obtained for the cases of ``ramp'' (linearly varying with a cutoff value) and oscillatory heating. The ``ramp'' solution may be used to approximate arbitrarily slow and fast process timescales (compared to the mean free time) and thus complements and bridges previous analyses. For oscillatory heating at frequencies higher than the collision frequency it is shown that, in steady state, hydrodynamic fields decay proportionally to $\exp[-(\omega \delta_{\textrm w})^{2/3}]$, where $\omega$ is the oscillation frequency and $\delta_{\textrm w}$ is the distance from the wall. The steady state gas motion is thus confined to narrow layers in the vicinity of each wall. Our results are compared with low-variance particle simulations of the linearized Boltzmann equation using the low-variance deviational simulation Monte Carlo (LVDSMC) method. The good agreement found between the two methods of calculation suggests the former as an accurate and simple means of calculating the response of systems of arbitrary size within one mean free path from the heated boundary.   

Instability of electroosmotic channel flow with streamwise conductivity gradients

This work considers the stability of an electroosmotic microchannel flow with streamwise electrical conductivity gradients, a configuration common in microfluidic applications such as field amplified sample stacking. Previous work on such flows has focused on how streamwise conductivity gradients set a non-uniform electroosmotic velocity which results in dispersion of the conductivity field. However, it has been known for many years that electric fields can couple with conductivity gradients to generate unstable flows. This work demonstrates that at high electric fields such an electrohydrodynamic instability arises and the basic mechanisms of this instability are explored through numerical simulations. The instability in this configuration is unique in that the non-uniform electroosmotic flow sets the shape of the underlying conductivity field in a way that makes it susceptible to instability. However, the instability is the direct result of electric body forces due to slight departure from electro-neutrality in the fluid bulk. A simple stability map is created where two dimensionless numbers can predict system stability reasonably well, even though the system formally depends on six dimensionless groups.   

Band Dispersion During Isoelectric Focusing in a Microchip

Ampholyte based isoelectric focusing (IEF) is simulated for a two-dimensional horse shoe microchannel. Mobility correction for proteins and ampholytes are considered in the model because the mobility of both large molecules (proteins) and small molecules (ampholytes) varies with ionic strength in the IEF process. Four model proteins are allowed to focus in the presence of 25 biprotic carrier ampholytes in a horse shoe microchannel. Normalized variances of protein bands are calculated from numerical results using moment method. We particularly show dispersion behavior of proteins in IEF and discuss the differences between linear electrophoretic transports and nonlinear IEF in a horse shoe microchannel. Our numerical results show that protein spreading is induced by a turn during gradient formation stage, but the dispersed bands are rearranged and straighten as double peaks of a protein start to focus at the focal point. The rearrangement of spreading band is very unique compared to other linear electrokinetic phenomena (electroosmotic flow and capillary zone electrophoresis) and is independent of channel position and channel shape. Hence, one can perform the IEF to separate proteins in complex geometry without incorporating hyperturns.   

Dynamic assembly with enhanced ac polarization induced by a conducting microwire

In this work, we design a new microfluidic platform for active manipulation of colloidal suspensions with high-frequency ac electric fields. The strategy invokes a micron-sized metal wire placed under a large conducting plane, acting like a line electrode with an intensified electric field capable of producing strong polarization effects on fluids and suspended colloids. A diversity of polarization phenomena are observed, including rapid dieletrophoretic assembly/segregation of polarized colloids, chaining and clustering due to interactions between these colloids, and dense columning of pearl chains along the wire due to their fluidization by ac electro-osmotic vortices. The underlying physics are also discussed in line with simple scalings that elicit how the phenomena depend on the particle concentration, applied field conditions, and relevant length scales.   

Particle electrokinetic focusing in curved microchannels

Particle focusing is usually a necessary step in continuous flow particle separation. It may be achieved using sheath flows to pinch the particle stream or external forces to manipulate particles directly. We present in this talk a novel electrokinetic technique for particle focusing in curved microchannels. Such focusing is attributed to the dielectrophoretic forces induced around the turns when a DC electric field is applied to drive the particle stream through a curved microchannel by electrokinetic flow. Particle focusing is demonstrated using 5 $\mu $m and 10 $\mu $m polystyrene beads in a 50 $\mu $m wide channel at low electric fields. A numerical model is also developed to simulate the particle focusing process.   

Interface dynamics during the formation of bubbles and droplets at microfluidic junctions

We describe how the size of bubbles and droplets -- created at microfluidic T-junctions -- scales with the shape of the junction. The shape of the junction plays a crucial role as it sets the shape of the bubble. Due to interfacial tensions, the bubble cannot conform to the channel walls. Hence, fluid upstream and downstream of the bubble communicates via so-called gutters between the wall and the bubble. In this work, we show that -- depending on the Capillary number and the ratio between the height and width of the main channel -- significant flows of carrier liquid by-pass the bubble during its growth. We compared our experiments, in which we measured the interface evolution from high-speed micrographs for junctions with different shapes operated at Capillary numbers below 0.01, with a simple model. In this model, a geometrical description of the interface was coupled to a continuity and momentum balance. We balanced the pressure drop over the emerging bubble due to the difference in radii of curvature at the front and rear with the pressure drop due to the flow through the gutters. This model shows good agreement with the experiments, explains the rapid 3-D pinch-off, and shows how the size of bubbles and droplets scales with the T-junction geometry.   

Micro Jet Generation with Annular Plasma Actuators

The effectiveness of dielectric barrier discharge plasma actuators for use in micro thrusters and internal duct aerodynamics are investigated. The primary flow is driven by tha zero-net mass flux jet at the wall in a closed circumferential arrangemen that then entrains fluid in the core of the duct. This results in a unique configuration for studying impulsively started jet phenomena. Laser flow visualization is utilized to observe detailed flow structure wherein multiple vortex rings are formed immediately after pulsed actuation and evolve into a turbulent jet downstream. Measurements are made using PIV and the effects of modulation frequency and the duty cycle on the induced velocity and resulting thrust are observed. The values of the induced velocities increase with the forcing frequency and duty cycle although there is a peak value for the forcing frequency after which the velocity and thrust decrease. The influence of the length-to-diameter ($l/d_i$) ratio is also significant; the velocities and thrust increase as the inner diameter of the tubes are increased. Velocity profiles show a great difference with this ratio. As the inner diameter is increased, a recirculation region at the center of the tube with negative velocities can be observed. The effect of freestream on the induced veloicty profiles is also studied wherein the duct is placed inside a wind tunnel and tests are conducted at different $Re$.