Journal of Colloid and Interface Science 323 (2008) 133–140 Contents lists available at ScienceDirect Journal of Colloid and Interface Science www.elsevier.com/locate/jcis Elasticity-driven droplet movement on a microbeam with gradient stiffness: A biomimetic self-propelling mechanism Xiu-Peng Zheng, Hong-Ping Zhao, Ling-Tian Gao, Jian-Lin Liu, Shou-Wen Yu, Xi-Qiao Feng ∗ FML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China article info abstract Article history: Received 1 February 2008 Accepted 16 April 2008 Available online 20 April 2008 Keywords: Surface tension Substrate stiffness Directional motion Elasticity Solid/liquid interface Directional movement of liquid droplets is of significance not only for certain physiological processes in nature but also for design of some microfluidic devices. In this study, we report a novel way to drive directional movement of liquid droplets on a microbeam with a varying or gradient stiffness. We use the energy method to theoretically analyze the interaction between a droplet and the elastic microbeam. The system tends to have the minimum potential energy when the droplet moves to the softer end of the beam. Therefore, a gradient change of the bending stiffness may be utilized to help the directional motion of droplets. Similarly, one can also drive droplets to move in a designed direction by varying the cross sectional geometry of the beam. Finally, some possible applications of this self-propelling mechanism are suggested.  2008 Elsevier Inc. All rights reserved. 1. Introduction Liquid directional movement at micro scale is crucial for some physiological processes in animals and plants. For examples, Texas horned lizard drinks water with its feet, by utilizing capillary ac- tion of water through thin channels that extend from the feet to mouth [1]. The microstructures of butterfly wings can easily make rain droplets roll off and avoid the entrance of droplets into its body [2]. Another example is the anisotropic microstructures of rice leaves that can guide liquid droplets to move directionally [3]. Controlling the directional motion of liquid droplets is also of significance for design and fabrication of microfluidic devices and for many other applications in, for instance, bioassays, microre- actors, and chemical or biological sensing [4,5]. The directional movement of droplets may be driven by unbalanced capillary force or surface tension on solid surfaces with spatially varying wetting properties or surface morphologies [6–10]. One can also realize the directional movement of droplets by utilizing temperature gradi- ent [6] or concentration gradient of the environmental liquid [7]. A bislug of two immiscible liquids with different surface tensions in a glass capillary tube can move spontaneously [8–10]. A drop in a capillary tube whose interior surface is partially coated to induce a discontinuous wetting condition can also move toward the more hydrophilic zone [11]. Chaudhury et al. [12,13] reported that a droplet on a substrate with a spatially varying surface ten- sion can quickly run from the hydrophobic to the hydrophilic zone, and even climb uphill on an inclined plane. Additionally, some par- * Corresponding author. Fax: +86 10 62772934. E-mail address: fengxq@tsinghua.edu.cn (X.-Q. Feng). ticularly designed geometric structures can also induce directional movement of droplets. Lorenceau and Quere [14] investigated ex- perimentally the behavior of a droplet deposited on a conical hy- drophilic fiber and found that the droplet spontaneously moves towards its thick end due to the Laplace pressure gradient along the fiber. Droplets bounded by two nonparallel hydrophilic sur- faces can move toward the converging end with an increasing speed [15]. Moreover, it has also been found that a wetting liq- uid plug placed in an open conical hydrophilic tube can migrate toward the cone tip [16–18]. Besides the gradient hydrophobicity and surface curvature, the elasticity of the substrate may also influence the motion of liquid droplets. For example, when two flexible lamellae are adhered by a liquid layer, the liquid may ascend to a certain height due to the deformation of the lamellae [19–22]. In view of the interaction between elasticity and capillarity, very recently, Py et al. [23] sup- plied a novel idea to produce three-dimensional structures through the wrapping of a liquid droplet by a flexible sheet. Additionally, the interaction of elastic deformation and capillary process is cru- cial for the vessel wall in the cardiovascular and respiratory sys- tem [24]. In this paper, we will suggest a novel self-propelling mechanism of liquid droplets deposited on a substrate by utilizing the elastic- ity of the latter. Using the energy method, we theoretically analyze a droplet on an elastic microbeam with stiffness varying along its length direction. The droplet–substrate interaction was firstly mod- eled to formulate the total potential energy of the system. It is found that the droplet tends to move along the direction with a negative stiffness gradient (i.e., from the stiffer to the softer end of the beam). Similarly, the directional movement of liquid droplets 0021-9797/$ – see front matter  2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2008.04.033