Converting Vertical Vibration of Anisotropic Ratchet Conveyors into Horizontal Droplet Motion

An anisotropic ratchet conveyor is an asymmetric, periodic, micropatterned surface that propels droplets when vibrated with a sinusoidal signal at certain frequencies and amplitudes. For each input frequency, there is a threshold amplitude beyond which the droplet starts to move. In this paper, we study the parameters that initiate droplet motion and the relationship between the input frequency and threshold amplitude among droplets with different volume, density, viscosity, and surface tension. Through this investigation we demonstrate how nondimensionalization reveals consistent behavior for droplets of different volumes. Finally, we propose a compact model that captures the essential features of the system to describe how a pure vertical vibration results in horizontal droplet motion. This model provides an intuitive understanding of the underlying physics and explains how the surface asymmetry is the key for lateral droplet motion.