Bendotaxis - when droplets are self-propelled in response to bending

We’re all familiar with liquid droplets moving under gravity (especially if you live somewhere as rainy as Oxford). However, emerging applications such as lab-on-a-chip technologies require precise control of extremely small droplets; on these scales, the forces associated with surface tension become dominant over gravity, and it is therefore not practical to rely on the weight of the drops for motion. Many active processes (requiring external energy inputs), such as those involving the use of temperature gradients, electric fields, and mechanical actuation, have been used successfully to move small droplets. Recently, however, there has been increasing interest in passive processes, which do not require external driving. One example of this is durotaxis, in which droplets spontaneously move in response to rigidity gradients (similar to the active motion of biological cells, which generally move to stiffer regions of a deformable substrate). Here, the suffix ‘taxis’ refers to the self-propulsive nature of the motion. In a recent study, Oxford Mathematicians Alex Bradley, Finn Box, Ian Hewitt and Dominic Vella introduced another such mechanism; Bendotaxis is self-propelled droplet motion in response to bending. What is particularly interesting is that the motion occurs in the same direction, regardless of whether the drop has an affinity to (referred to as ‘wetting’) the channel walls or not (‘non-wetting’), which is atypical for droplet physics.

A small drop confined to a channel exerts a force on the walls, as a result of surface tension; this force pulls the walls together when the drop wets them, and pushes them apart otherwise. By manipulating the geometry of the channel (leaving one end free, and clamping the other end), the deformation that results from this surface tension force is asymmetric—it creates a tapering in the channel. The drop subsequently moves in response to this tapering, which is towards the free end in both the wetting and non-wetting cases.

Using a combination of scaling arguments and numerical solutions to a mathematical model of the problem, the team were able to verify that it is indeed the capillary induced elastic deformation of the channel that drives the experimentally observed motion. This model allowed them to understand the dynamic nature of bendotaxis, and predict the motion of drops in these deformable channels. In particular, they identified several interesting features of the motion; counter-intuitively, it is predicted (and observed) that the time taken for a drop to move along the channel decreases as it increases in length. However, relatively long channels are susceptible to ‘trapping’, whereby the force exerted by the drop is sufficient to bring the channel walls into contact. It is hoped that understanding the motion will pave the way for its application on a variety of scales - for example, drug delivery on a laboratory-scale, and self-cleaning surfaces on a micro-scale.