Session CM: Microfluids: General II

Computational sensitivity analysis of geometric parameters in laminar superhydrophobic microchannels

This talk presents 3-D numerical simulations of laminar flow through a microchannel of height $h$ containing superhydrophobic surfaces (SHS) along the top and bottom walls. The SHS is modelled as an array of longitudinal shear-free surfaces having width $w$ and inclination angle $\alpha$. The simulations allow for a phase offset $\ell$ between the shear-free surfaces on the top and bottom walls. The sensitivity of velocity, wall shear stress, and slip-length with respect to infinitesimal changes in the geometrical design parameters ($w$, $\alpha$, $\ell$, and $h$) was examined using the Sensitivity Equation Method and Complex Step Differentiation. These techniques differ from traditional parametric studies in that sensitivities are obtained more accurately by direct numerical solution of a separate set of PDEs for the sensitivity derivatives. In this manner, the present sensitivity results can be used to reliably predict the percent drag savings achievable for a unit increase in $w$ and $h$. Sensitivity results also indicate that an increase in $\alpha$ translates into enhanced mixing, albeit with a drag penalty. Finally, the talk discusses how the present sensitivity results may be incorporated in to a gradient-based optimization algorithm toward improved microchannel design.   

Effect of wall pattern configurations on Stokes flow through a microchannel with superhydrophobic slip

The present work aims to study low-Reynolds-number flow through a microchannel with superhydrophobic surfaces, which contain a periodic array of parallel ribs on the upper and lower walls. Mimicking impregnation, the liquid is allowed to penetrate the grooves between the ribs which are filled with an inviscid gas. The array of ribs and grooves gives a heterogeneous wall boundary condition to the channel flow, with partial-slip boundary condition on the solid surface and no-shear boundary condition on the liquid-gas interface. Using the method of eigenfunction expansions and domain decomposition, semi-analytical models are developed for four configurations. Two of them are for longitudinal flow and the others are for transverse flow. For each flow orientation, in-phase and out-phase alignments of ribs between the upper and lower walls are analyzed. The effect of the phase alignments of ribs is appreciable when the channel height is sufficiently small. In-phase alignment gives rise to a larger effective slip length in longitudinal flow. On the contrary, out-phase alignment will yield a larger effective slip length in transverse flow. This work was supported by the Research Grants Council of the Hong Kong Special Administrative Region, China, through Project HKU 7156/09E.   

Surface Energy Characterization of Superhydrophobic Surfaces under Varying Ambient Temperatures

A Cassie state is a state where a liquid droplet sits on top of a rough surface while maintaining a gas layer under the liquid interface. This state decreases the solid surface energy, and the contact angle is consequently increased. The contact angle of liquid droplets formed under the Cassie state is a function of the surface roughness and surface energies, dependent primarily on temperature, involved. We studied the surface energy variation of polymeric surfaces under different ambient temperatures, including surfaces that induce Cassie state. A highly rough PDMS (poly-dimethylsiloxane) pillar arrayed surface was used as the substrate. To study these properties, we employed Zisman plots for a number of liquids at different temperatures. A Zisman plot displays variation in contact angles of droplets with different surface energies, thus allowing us to determine the surface energies involved. Such experiments required a methodology that calculated each surface property independently and the subsequent use of image decomposition analyses. We computed the contact angle using similar analyses. These two parameters allowed for the successful construction of the Zisman plot.   

Streaming potential generated by a pressure-driven flow over a super-hydrophobic surface

The streaming potential generated by a pressured-driven flow over a weakly charged striped slip-stick surface (the zeta potential of the surface is smaller than the thermal potential (25 mV) with an arbitrary double layer thickness is theoretically studied by solving the Poisson-Boltzmann equation and Stokes equation. A series solution of the streaming potential is derived. Approximate expressions for the streaming potential in the limits of thin double layers and thick double layers are also presented, in excellent agreement with the full solution. The streaming potential is compared against that over a homogenously charged smooth surface. Our results indicate that the streaming potential over a super-hydrophobic surface only can be enhanced when the liquid-gas interface is charged. In addition, as the double layer thickness increases, the advantage of the super-hydrophobic surface diminishes. The impact of a slip-stick surface on the streaming potential might provide guidance for designing novel and efficient microfludic energy conversion devices using a super-hydrophobic surface.   

Modeling thermocapillary flow on superhydrophobic surfaces

A liquid in Cassie-Baxter state confined between two microstructured superhydrophobic surfaces has a large free surface fraction while at the same time being in close contact to a solid. As such this configuration is predestined for thermocapillary transport when applying a temperature gradient along the structured substrate. We analytically and numerically investigate the thermocapillary flow over superhydrophobic arrays of fins, with the temperature gradient applied in parallel and transverse directions. At the gas-liquid interface Marangoni stresses exert a force on the liquid driving it towards the regions of higher surface tension. This leads to a spatially varying near-wall flow profile extending a distance of the order of the fin spacing into the liquid, while a plug flow prevails in the bulk of the liquid. In the Stokes limit we are able to relate the bulk flow velocity to the hydrodynamic slip length for pressure-driven flow over such surfaces. The numerical results indicate that this relation serves as an upper bound for the achievable flow velocities at large temperature gradients. Since even moderate temperature gradients of the order of a few K/cm can induce flow velocities of several mm/s for water-based systems, this setup lends itself for microfluidic pumping.   

3-D CFD Simulations of Liquid Laminar Flow over Superhydrophobic Surfaces for two scenarios: (1) Shear-driven Flow with Square Post Geometries, (2) Pressure-driven Flow with Rectangular Post Geometries

We numerically investigate the influence of post patterned superhydrophobic surfaces on the drag reduction for liquid flow through microchannels. Hydrophobically coated surfaces exhibiting microscale structures such as ribs/cavities and posts/cavities can significantly reduce the liquid-solid contact. Preventing liquid from entering the cavities increases the fraction of liquid-gas interface, which results in reduced surface friction. Fully developed steady state laminar flow for two scenarios is considered here. The effects of aspect ratio, cavity fraction, and relative module width on the slip length and on the Darcy friction factor-Reynolds number product, \textit{fRe}, were explored numerically. Various aspect ratios, cavity fractions, and relative module widths were explored. The present results are compared with those for surfaces exhibiting square posts in pressure-driven liquid laminar flow. As the aspect ratio of the posts increased or decreased, the \textit{fRe} values asymptotically approached those of surfaces exhibiting longitudinal and transverse ribs, respectively.   

Amplification of the electroosmotic velocity by induced charges at fluidic interfaces

The performance of microfluidic devices like electroosmotic pumps is strongly limited by drag forces at the channel walls. In order to replace the standard no-slip condition at the wall with a more favorable slip condition, superhydrophobic surfaces are employed. In the Cassie-Baxter state, air is entrapped in the surface cavities, so that a significant fraction of water-air interfaces at which slip does occur is provided. However, such surfaces do not enhance electroosmotic flow. Since no net charge accumulates at the water-air interfaces, the driving force is reduced, and no flow enhancement is obtained. We consider electrodes incorporated in the superhydrophobic structure to induce charges at these interfaces, thereby increasing the driving force. A theoretical model is set up, yielding an understanding of the influence of the surface morphology on the flow, which serves as a basis for ongoing experimental work. While a considerable enhancement of the electroosmotic velocity is already expected for standard superhydrophobic surfaces, greater amplifications of one order of magnitude may be achieved by substituting the air in the surface cavities by oil, reducing the risk for electric breakdown or transition to the unfavorable Wenzel state.   

Dynamics of the Liquid Meniscus in Micropillar Arrays

Liquid dynamics in superhydrophilic micropillar arrays is of broad interest in microfluidics for lab-on-a-chip, biomedical, and thermal management applications. Accurate prediction and optimization of propagation rates in such microstructures require detailed understanding of the evolution of the liquid meniscus. In this work, we experimentally investigated microfabricated circular pillar arrays with diameters of 2.5 $\mu $m and 5 $\mu $m, periods ranging from 5 $\mu $m to 30 $\mu $m, and heights ranging from 10 $\mu $m to 30 $\mu $m. By coupling interference microscopy and high-speed imaging, the dynamics of the advancing liquid front were precisely captured. Two distinct time scales in the wetting process were observed associated with the liquid sweeping across the bottom surface and rising along the sides of the pillars, which is dependent on the height-to-period ratio of the pillar array,. This behavior was modeled by using an energy-based approach. This work provides important insights towards accurately predicting propagation rates for a range of micropillar arrays and can be extended to other microstructure geometries.   

Disjoining pressure in thin liquid films on charged structured surfaces

We consider thin liquid films on various structured surfaces and compute the electrostatic component of disjoining pressure in the film. The regions of solid phase in contact with the liquid are assumed to be at a constant electrical potential. Presence of ions in the liquid implies that the electrical field there is described by the Poisson-Boltzmann equation. Situations are considered when liquid fills the spaces between the elements of the structure (e.g. grooves) and when pockets of air remain trapped there. The formulas for disjoining pressure are incorporated into a numerical method for calculation of deformations of air-liquid interfaces. Applications of our mathematical model to recent experiments on evaporation of thin liquid droplets on structured surfaces are discussed.