# Difference between revisions of "Non-stick water"

Entry by Richie Tay for AP 225 Fall 2012

## General

Authors: Pascale Aussillous, David Quéré

Keywords: Wetting, Contact Angle, Surface tension

## Introduction

Transporting liquid droplets across a solid surface is a great challenge, since most solid-liquid interactions are wetting, and small surface defects lead to contact-angle hysteresis and consequent capillary forces that oppose motion. Various strategies have been attempted to reduce surface wetting, including chemically treating the surface (e.g. coating with a hydrophobic material), modifying the physical characteristics of the surface (e.g. introducing micro-roughness), and applying external fields (e.g. electrostatic, electromagnetic, acoustic) to induce levitation, but many of these methods are not robust, reproducible or easy to implement outside of a controlled setting.

The authors have chosen an inverse strategy: to engineer the liquid drop rather than the surface. They coated water droplets with a hydrophobic material to create "liquid marbles", effectively soft solids that roll across surfaces very quickly with minimal viscous dissipation.

## Results and Discussion

Figure 1. A liquid marble on a glass surface: 1 mm water droplet coated in 20 mm silane-treated Lycopodium grains. Figure from Ref. [1]
Figure 2. Drop velocity (V) normalized by the puddle velocity (Vo) plotted against the drop radius (R) normalized by the capillary length ($\kappa^{-1}$), for different liquid viscosities ($\eta$) and slopes ($\alpha$). Figure from Ref. [1]
Figure 3. Different shapes taken by a liquid marble in the inertial regime. In the upper panels both the camera and the plane are tilted. Figure from Ref. [1]

Liquid marbles were created by adding water droplets to silane-coated Lycopodium spores. The grains separated to the water-air interface and formed a monolayer, conferring superhydrophobicity to the droplet surface. These droplets formed slightly flattened spheres on glass surfaces (Fig. 1) and even floated on pools of water! This non-wetting character is influenced by the droplet size (for a range of liquid viscosities, grain material and surfaces): when the radius of the droplet, $R$, is significantly larger than its capillary length, $\kappa^{-1}=\sqrt{\gamma \over \rho g}$, the drop collapses into something more resembling a puddle under gravitational pull.

More interesting observations were made with the drops under dynamic conditions. Unlike partially-wetting droplets, which slide down inclined surfaces and usually leave a trail of liquid, these liquid marbles were capable of rolling down relatively gentle slopes (< 10°) at fairly high velocities (~ 1 cm/s) with no wetting, even with liquid viscosities as high as 103 mPa s. If these were real marbles, one would expect their rolling velocity to scale proportionally with their radius, but here, because there is viscous dissipation at the liquid-solid contact zone, and this retarding dissipative force increases with droplet size and contact area, large droplets actually roll more slowly than smaller ones (Fig. 2). The velocity $V$ scales with radius as follows: $V \approx {V_0 \kappa^{-1} \over R}$, where $V_0$ is the theoretical velocity of a puddle. This applies so long the droplet shape remains fairly constant (i.e. inertial and viscous forces do not significantly deform the spherical shape).

If the drop is made to roll faster along a steeper incline (24°), the inertial force eventually overcomes the surface tension keeping the spherical shape, and the drop transforms into toroidal and peanut shapes (Fig. 3, top panels). The peanut shape was previously observed for normal liquid drops rotating in space, but this was the first observation of a toroidal shape for a revolving drop. The torus shape is metastable (its stability here is hypothesized to be promoted by the inclined surface), as it frequently evolved into the peanut during the descent, and always transformed into the peanut shape if the inclined plane was removed (Fig. 3, bottom).

In summary, the authors have devised a novel way that allows small liquid droplets to be transported across solid substrates using only weak fields (gravity was presented in this paper, but they claimed that they have also been successful with weak electric and magnetic fields). Although there is still much to learn about the robustness and shape changes of these liquid marbles, their ease of manufacture and elastic-like behavior make them potentially useful as rapid, wear-free micromachines in electromechanical actuators and valves, or as lubricating liquid ballbearings [2].