The response of liquid droplets to a vibration is typically studied with unconfined droplets on a homogenous substrate. In this configuration, researchers have provided thorough characterizations of resonance [1
], contact angle hysteresis [3
], and the movement of the contact line [6
] in response to vibrations. Similar studies have also demonstrated that droplet transport can be induced by asymmetric vibrations [8
], and sinusoidal vibrations can be converted to horizontal transport on gradient surfaces [10
], creating the basis for microfluidic systems using these principles [13
]. More recent work has leveraged this ability to rectify vertical vibrations into horizontal transport by creating patterned asymmetric surfaces that transport droplets over indefinite distances (e.g., transport does not stop at the end of a gradient) [14
]. These systems present much potential to meet a variety of applications in microfluidics, but, for some applications (particularly those that require heating or long incubation times), are limited by their high evaporation rates compared to enclosed systems [20
]. Therefore, this work demonstrates the implementation of an enclosed configuration for droplet transport based on the anisotropic ratchet conveyor system.
Anisotropic ratchet conveyors (ARCs) transport droplets through a periodic pattern of curved hydrophilic rungs, defined by a hydrophobic background. The curvature of these rungs divides the footprint of these droplets into leading and trailing edges, that experience a difference in pinning forces, as only the leading edge of the droplet conforms to the curved rungs (Figure 1
A sinusoidal vibration, applied vertically, causes the edges of the droplet to oscillate between wetting (edges of the droplet are advancing away from the centroid) and de-wetting (edges are contracting toward the centroid) phases. This combination of edge oscillation and a difference in pinning forces between leading and trailing edges results in a net force that drives droplet transport [14
]. Previous work demonstrated a first principles model that showed droplet transport was enabled by two key anisotropies on ARCs: (1) pinning forces are greater on the leading edge of the droplet, and (2) the droplet is less susceptible to the ARC pattern during wetting (i.e., the difference in contact angle between the leading and trailing edges is larger during de-wetting than wetting) [22
]. These characteristics provide for droplet transport with a ratcheting effect, wherein the droplet takes a small step backward and a larger step forward through each vibration cycle. From this foundation, additional functional capabilities of the ARC system have also been realized through the development of devices that can selectively pause, switch, and merge transported droplets [23
], demonstrating the potential of ARC systems to automate sample handling protocols and processes. However, evaporation was still a major concern for this system. Although it was known that transport of an enclosed droplet is possible [24
], the mechanics of vibrated droplets in an enclosed ARC system had yet to be investigated and it remained to be demonstrated that an enclosed ARC system could perform practical microfluidic tasks. In this work, a dual-plate ARC system was created to study how the addition of a top-plate enclosing and contacting the droplet affected the resulting transport of droplets. This system used 3D printed holders to align ARC substrates, allowing for the entire system to be vibrated. The results of this work advance the possibilities of the ARC system, providing new opportunities for innovation, and presenting new insights into droplet mechanics.