Quick Liquid Propagation on a Linear Array of Micropillars

Capillary-driven horseshoe vortex forming around a micro-pillar

HYPOTHESIS

Horseshoe vortices are known to emerge around large-scale obstacles, such as bridge pillars, due to an inertia-driven adverse pressure gradient forming on the upstream-side of the obstacle. We contend that a similar flow structure can arise in thin-film Stokes flow around micro-obstacles, such as used in textured surfaces to improve wettability. This could be exploited to enhance mixing in microfluidic devices, typically limited to creeping-flow regimes.

EXPERIMENTS

Numerical simulations based on the Navier-Stokes equations are carried out to elucidate the flow structure associated with the wetting dynamics of a liquid film spreading around a 50 μm diameter micro-pillar. The employed multiphase solver, which is based on the volume of fluid method, accurately reproduces the wetting dynamics observed in current and previous (Mu et al., Langmuir, 2019) experiments.

FINDINGS

The flow structure within the liquid meniscus forming at the foot of the micro-pillar evinces a horseshoe vortex wrapping around the obstacle, notwithstanding that the Reynolds number in our system is extremely low. Here, the adverse pressure gradient driving flow reversal near the bounding wall is caused by capillarity instead of inertia. The horseshoe vortex is entangled with other vortical structures, leading to an intricate flow system with high-potential mixing capabilities.

Effect of Micropillar Array Morphology on Liquid Propagation Coefficient Enhancement

Roughness on hydrophilic surfaces allows for fast propagation of liquids. In this paper, the hypothesis is tested which theorizes that pillar array structures with nonuniform pillar height levels can enhance wicking rates. In this work, within a unit cell, nonuniform micropillars were arranged with one pillar at constant height, while other shorter pillars were varied in height to study these nonuniform effects. Subsequently, a new microfabrication technique was developed to fabricate a nonuniform pillar array surface. Capillary rising-rate experiments were conducted with water, decane, and ethylene glycol as working liquids to determine the behavior of propagation coefficients that were dependent on pillar morphology. It is found that a nonuniform pillar height structure leads to a separation of layers in the liquid spreading process and the propagation coefficient increases with declining micropillar height for all liquids tested. This indicated a significant enhancement of wicking rates compared to uniform pillar arrays. A theoretical model was subsequently developed to explain and predict the enhancement effect by considering capillary force and viscous resistance of nonuniform pillar structures. The insights and implications from this model thus advance our understanding of the physics of the wicking process and can inform the design of pillar structures with an enhanced wicking propagation coefficient.

Predicting Hemiwicking Dynamics on Textured Substrates

The ability to predict liquid transport rates on textured surfaces is key to the design and optimization of devices and processes such as oil recovery, coatings, reaction-separation, high-throughput screening, and thermal management. In this work we develop a fully analytical model to predict the propagation coefficients for liquids hemiwicking through micropillar arrays. This is carried out by balancing the capillary driving force and a viscous resistive force and solving the Navier-Stokes equation for representative channels. The model is validated against a large data set of experimental hemiwicking coefficients harvested from the literature and measured in-house using high-speed imaging. The theoretical predictions show excellent agreement with the measured values and improved accuracy compared to previously proposed models. Furthermore, using lattice Boltzmann (LB) simulations, we demonstrate that the present model is applicable over a broad range of geometries. The scaling of velocity with texture geometry, implicit in our model, is compared against experimental data, where good agreement is observed for most practical systems. The analytical expression presented here offers a tool for developing design guidelines for surface chemistry and microstructure selection for liquid propagation on textured surfaces.

Enhancement of Meniscus Pump by Multiple Particles

We numerically investigate the behavior of a droplet spreading on a smooth substrate with multiple obstacles. As experimental works have indicated, the macroscopic contact line or the three-phase boundary line of a droplet exhibits significant deformation resulting in a local acceleration by successive interactions with an array of tiny obstacles settled on the substrate (Mu et al., Langmuir 2019, 35). We focus on the menisci formation and the resultant pressure and velocity fields inside a liquid film in a two-spherical-particle system to realize an optimal design for the effective liquid-transport phenomenon. Special attention is paid to the meniscus formation around the second particle, which influences the liquid supply related to the pressure difference around the first particle as a function of the distance between the two particles. We find that the meniscus around the first particle plays an additional role as the reservoir of the liquid supplied toward the second particle, which is found to enhance the total pumping effect.