Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA.
Langmuir. 2010 Oct 5;26(19):15070-5. doi: 10.1021/la102645u.
Prediction and optimization of liquid propagation rates in micropillar arrays are important for various lab-on-a-chip, biomedical, and thermal management applications. In this work, a semianalytical model based on the balance between capillary pressure and viscous resistance was developed to predict liquid propagation rates in micropillar arrays with height-to-period ratios greater than 1 and diameter-to-period ratios less than 0.57. These geometries represent the most useful regimes for practical applications requiring large propagation rates. The capillary pressure was obtained using an energy approach where the meniscus shape was predicted using Surface Evolver simulations and experimentally verified by interference microscopy. The combined viscous resistance of the pillars and the substrate was determined using Brinkman's equation with a numerically obtained permeability and corroborated with finite element simulations. The model shows excellent agreement with one-dimensional propagation experiments of deionized water in silicon micropillar arrays, highlighting the importance of accurately capturing the details of the meniscus shape and the viscous losses. Furthermore, an effective propagation coefficient was obtained through dimensionless analysis that is functionally dependent only on the micropillar geometry. The work offers design guidelines to obtain optimal liquid propagation rates on micropillar surfaces.
预测和优化微柱阵列中的液体传播速率对于各种微流控芯片、生物医学和热管理应用都非常重要。在这项工作中，开发了一种基于毛细压力和粘性阻力平衡的半解析模型，用于预测高度与周期比大于 1 且直径与周期比小于 0.57 的微柱阵列中的液体传播速率。这些几何形状代表了需要大传播速率的实际应用中最有用的区域。毛细压力通过能量方法获得，其中使用 Surface Evolver 模拟预测了弯月面形状，并通过干涉显微镜进行了实验验证。使用 Brinckman 方程和数值获得的渗透率确定了柱子和基底的组合粘性阻力，并与有限元模拟进行了比较。该模型与去离子水在硅微柱阵列中的一维传播实验非常吻合，突出了准确捕捉弯月面形状和粘性损失细节的重要性。此外，通过无量纲分析获得了有效传播系数，该系数仅功能上依赖于微柱几何形状。这项工作为在微柱表面获得最佳液体传播速率提供了设计指南。
