Regular Article
Porous micropillar structures for retaining low surface tension liquids

https://doi.org/10.1016/j.jcis.2017.12.011Get rights and content

Abstract

The ability to manipulate fluid interfaces, e.g., to retain liquid behind or within porous structures, can be beneficial in multiple applications, including microfluidics, biochemical analysis, and the thermal management of electronic systems. While there are a variety of strategies for controlling the disposition of liquid water via capillarity, such as the use of chemically modified porous adhesive structures and capillary stop valves or surface geometric features, methods that work well for low surface tension liquids are far more difficult to implement. This study demonstrates the microfabrication of a silicon membrane that can retain exceptionally low surface tension fluorinated liquids against a significant pressure difference across the membrane via an array of porous micropillar structures. The membrane uses capillary forces along the triple phase contact line to maintain stable liquid menisci that yield positive working Laplace pressures. The micropillars have inner diameters and thicknesses of 1.5–3 μm and ∼1 μm, respectively, sustaining Laplace pressures up to 39 kPa for water and 9 kPa for Fluorinert™ (FC-40). A theoretical model for predicting the change in pressure as the liquid advances along the porous micropillar structure is derived based on a free energy analysis of the liquid meniscus with capped spherical geometry. The theoretical prediction was found to overestimate the burst pressure compared with the experimental measurements. To elucidate this deviation, transient numerical simulations based on the Volume of Fluid (VOF) were performed to explore the liquid pressure and evolution of meniscus shape under different flow rates (i.e., Capillary numbers). The results from VOF simulations reveal strong dynamic effects where the anisotropic expansion of liquid along the outer micropillar edge leads to an irregular meniscus shape before the liquid spills along the micropillar edge. These findings suggest that the analytical prediction of burst Laplace pressure obtained under quasi-static condition (i.e., equilibrium thermodynamic analysis under low capillary number) is not applicable to highly dynamic flow conditions, where the liquid meniscus shape deformation by flow perturbation cannot be restored by surface tension force instantaneously. Therefore, the critical burst pressure is dependent on the liquid velocity and viscosity under dynamic flow conditions. A numerical simulation using Surface Evolver also predicts that surface defects along the outer micropillar edge can yield up to 50% lower Laplace pressures than those predicted with ideal feature geometries. The liquid retention strategy developed here can facilitate the routing and phase management of dielectric working fluids for application in heat exchangers. Further improvements in the retention performance can be realized by optimizing the fabrication process to reduce surface defects.

Introduction

Porous structures with the capacity to retain low surface tension liquids (e.g. dielectric refrigerants, oils) against an imposed pressure difference are increasingly needed in many applications, including oil transportation [1], water/oil separation [2], [3], microfluidics [4], and thermal management of micro/power electronic systems [5]. In the microelectronics industry, increasing performance demands necessitate both more memory and more central and graphics processing unit (CPU and GPU) cores, resulting in increased device density and consequent thermal management challenges. Likewise, for power electronic systems, gallium nitride (GaN) high-electron-mobility transistors (HEMT) can improve the performance of radar amplifiers, hybrid/electric vehicles, and LED arrays; however, thermal limitations prevent full exploitation of this technology, where transistor-level power densities can exceed 10 kW cm−2 [6]. For these applications, thin-film evaporative cooling in porous media (<40 μm) with a small pore size (<5 μm) can enable high heat transfer coefficients, exceeding 106 W m−2 K−1 at operating temperatures <100 °C [7], [8], [9]. However, this performance requires stable liquid-vapor interfaces in porous structures. A stable liquid-vapor interface can greatly benefit from low surface tension liquid retention in these structures under pressure, which is currently a challenge.

This problem is especially important for data centers, which represent about 2% of U.S. electricity consumption and are responsible for 2% of global CO2 emissions (similar to the aviation carbon footprint), [10], [11]. In particular, the miniaturization of computing systems and electronic circuits has culminated in three-dimensional (3D) stacked chips for high-end servers. Though offering dramatic manufacturing and electrical design advantages, this approach poses significant thermal problems in the implementation of high-performance 3D integrated circuits (3D ICs) with power densities that will soon exceed 5 kW cm–2 [12]. As a potential solution, interlayer two-phase evaporative cooling is considered a promising approach for heat removal, but it requires dielectric working fluids to avoid the difficulties associated with water in direct contact with microelectronic devices [13].

Despite the potential of dielectric liquids, most previous studies have been limited to microheat exchangers that use water as a working fluid. Previous studies have reported that venting vapor bubbles from water in microchannels through hydrophobic membranes can improve flow stability and facilitate heat transfer at the solid-liquid interface [14], [15], [16]. While thin-film evaporative microheat exchangers integrated with nanoporous alumina membranes have demonstrated heat flux removal up to 0.6 kW cm−2 [14], more recent studies have shown thin-film porous copper structures with heat flux removal exceeding 1 kW cm−2 with superheat <10 K using water, as well as the potential to implement phase separation using liquid retention membranes [9], [17]. Despite the recent advances in phase routing microheat exchangers using water as the working fluid, mechanisms for maintaining stable liquid-vapor interfaces for low surface tension liquids (i.e., γ < 0.015 N/m) are lacking.

However, there have been many recent efforts to design non-wetting surfaces for non-polar hydrocarbon-based liquids [18], [19], [20], [21] (i.e., superoleophobic or superomniphobic). Naturally occurring superoleophobic surfaces in air have been observed on Springtails (Collembola Entognatha), a wingless arthropod which lives in soil, decaying material, and on plants [22]. Their surface is composed of hierarchical structures of nanoscopic interconnected granules with re-entrant curvature, which prevents them from suffocation while immersed in polar and non-polar liquids. Thus, recent bio-inspired surfaces show that with a combination of proper surface texturing and sustaining a low solid fraction [1], [23], [24], it is possible to tune substrate wettability, even for low surface tension liquids [18], [20], [25]. Superoleophobic surfaces have been designed to yield both high and low contact angle hysteresis, (CAH) [26], [27], and recent studies have shown non-wetting surfaces for fluorinated-carbon based liquids, which have some of the lowest measured surface tensions [20], [28]. Despite the progress in development of non-wetting surfaces for non-polar liquids, there has been no demonstration of low surface tension liquid retention behind porous membrane structures against a pressure difference across the membrane.

Capillary stop valves have been used in biochemical systems for retaining wetting liquids against a driving pressure [29], [30], [31], [32]. In these structures, a sudden expansion of the capillary cross-section stops the liquid from further advancing along the channel. While capillary stop valves have been shown to restrict the advance of aqueous liquids containing surfactants [29], [33], [34], [35], [36], they have not been demonstrated to pin non-polar liquids. However, the meniscus pinning approach applied in these systems holds promise for low surface tension liquids. Most recently, we have shown contact line pinning of non-polar liquids using glass capillary structures, which allow for liquid menisci to transition from concave to convex and do not permit flow, despite pressurization of the liquid [28].

In this work, we develop a novel approach for retaining low surface tension liquids behind a porous membrane by means of the design of silicon micropillar structures on its surface. The liquid retention and bursting behavior is identified by experimental visualization as well as pressure tracing. An analytical model is developed to predict the pressure of the liquid meniscus with a 3D capped spherical shape before and after bursting, based on calculating the total free energy change during the process. The analysis provides an in-depth understanding of the physics as liquid advances along the porous micropillar, which comprises five flow regimes: (1) wicking through the inner channel of the micropillar structure, (2) pivoting from a concave to convex shape along the inner micropillar edge (only for high surface tension liquids), (3) expansion to a hemispherical cap along the outer micropillar edge, (4) expansion of the meniscus beyond a hemisphere along the outer micropillar edge, and (5) bursting of the meniscus, where the contact line advances along the outer surface of the micropillar. Because the analytical model considers only structures with perfectly sharp edges and quasi-static conditions, a transient computational model using ANSYS-Fluent is performed to predict the dynamic behavior of the meniscus and explore the associated dynamic effect on liquid pinning pressure under different flow rates [37]. Surface defects along the outer micropillar edge are considered separately by using a computation model employing Surface Evolver and Comsol Multiphysics, which predicts the static meniscus shape by computing the minimum surface energy, using a gradient-descent method [38]. To our knowledge, this paper presents the first approach to retaining liquids with small equilibrium contact angles, such as dielectric liquids (i.e. fluorinated compounds), using microfabricated micropillar structures. This approach can aid in phase management related applications that require stable liquid-vapor interfaces [39].

Section snippets

Theoretical analysis

Fig. 1 illustrates the action of the porous micropillar structure in retaining liquid and shows the contact line dynamics for a wetting liquid as it advances toward the external orifice. For very low surface tension (e.g., non-polar) liquids, the meniscus initially wicks through the inner channel of the micropillar and immediately spreads along the top surface, as shown in Fig. 1(k)–(n). After advancing to the outer micropillar edge, the meniscus is pinned and forms a hemispherical shape

Computational simulation

The pinning and bursting behaviors of two different working fluids (water and FC-40) are studied using both a quasi-static and a dynamic simulation method. Comparing the results from the different computational tools allows for determination of the flow regions under which the dynamic effect would impact the liquid retention performance of the porous micropillar structure.

Design and microfabrication of porous silicon micropillar structures

To retain both polar and non-polar liquids, we applied microfabrication techniques to create a membrane containing an array of porous silicon micropillar structures with re-entrant surface features. The design and key parameters of the porous micropillar structures are shown in Fig. 3: D is the outer micropillar diameter, d is the inner micropillar diameter, Dt is the trench diameter, t1 is the trench height, t2 is the channel height, and P is the pitch, defined as the center-to-center distance

Theoretical analysis under quasi-static condition

Fig. 4 shows the analytically predicted liquid free energy and pressure variation as liquid flows through a single porous micropillar. The meniscus initially wicks through the micropillar structure, which leads to a constant increase in the solid-liquid interfacial area and a decrease in the liquid-air interfacial area. Since the interfacial energy between the solid and liquid is far smaller than that between the liquid and air, there is a constant decrease in total free energy, which

Summary and concluding remarks

In this study, we demonstrate liquid retention using an array of identical micropillar structures with re-entrant surface geometry. While such a geometry has been used for creating superoleophobic surfaces with strong liquid repelling characteristics in extensive studies [18], [19], [20], [21], [23], [24], [25], [48], [49], [50], retention of low surface tension liquids behind porous membrane structures remains an unexplored area. Experimental visualization of the liquid advance along the

Acknowledgments

The authors gratefully acknowledge financial support from DARPA (agreement # HR0011-13-2-0011, titled: Phase Separation Diamond Microfluidics for HEMT Cooling) monitored by Dr. Avi Bar Cohen, Dr. Joe Maurer, and Dr. Kaiser Matin, and from the NSF Funded Center for Power Optimization of Electro-Thermal Systems. The authors would also like to acknowledge the support from the Institute of Materials Science and Engineering at Washington University in St. Louis. We would also like to thank James

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