ABSTRACT
The motion of droplets on solid surfaces in response to an external gradient is a fundamental problem with a broad range of applications, including water harvesting, heat exchange, mixing and printing. Here we study the motion of droplets driven by a humidity gradient, i.e. a variation in concentration of their own vapour in the surrounding gas phase. Using lattice-Boltzmann simulations of a diffuse-interface hydrodynamic model to account for the liquid and gas phases, we demonstrate that the droplet migrates towards the region of higher vapour concentration. This effect holds in situations where the ambient gradient drives either the evaporation or the condensation of the droplet, or both simultaneously. We identify two main mechanisms responsible for the observed motion: a difference in surface wettability, which we measure in terms of the Young stress, and a variation in surface tension, which drives a Marangoni flow. Our results are relevant in advancing our knowledge of the interplay between gas and liquid phases out of thermodynamic equilibrium, as well as for applications involving the control of droplet motion.
ABSTRACT
The empirical laws of dry friction between two solid bodies date back to the work of Amontons in 1699 and are pre-dated by the work of Leonardo da Vinci. Fundamental to those laws are the concepts of static and kinetic coefficients of friction relating the pinning and sliding friction forces along a surface to the normal load force. For liquids on solid surfaces, contact lines also experience pinning and the language of friction is used when droplets are in motion. However, it is only recently that the concept of coefficients of friction has been defined in this context and that droplet friction has been discussed as having a static and a kinetic regime. Here, we use surface free energy considerations to show that the frictional force per unit length of a contact line is directly proportional to the normal component of the surface tension force. We define coefficients of friction for both contact lines and droplets and provide a droplet analogy of Amontons' first and second laws but with the normal load force of a solid replaced by the normal surface tension force of a liquid. In the static regime, the coefficient of static friction, defined by the maximum pinning force of a droplet, is proportional to the contact angle hysteresis, whereas in the kinetic regime, the coefficient of kinetic friction is proportional to the difference in dynamic advancing and receding contact angles. We show the consistency between the droplet form of Amontons' first and second laws and an equation derived by Furmidge. We use these liquid-solid Amontons' laws to describe literature data and report friction coefficients for various liquid-solid systems. The conceptual framework reported here should provide insight into the design of superhydrophobic, slippery liquid-infused porous surfaces (SLIPS) and other surfaces designed to control droplet motion.
ABSTRACT
Contact-line pinning and dynamic friction are fundamental forces that oppose the motion of droplets on solid surfaces. Everyday experience suggests that if a solid surface offers low contact-line pinning, it will also impart a relatively low dynamic friction to a moving droplet. Examples of such surfaces are superhydrophobic, slippery porous liquid-infused, and lubricant-impregnated surfaces. Here, however, we show that slippery omniphobic covalently attached liquid-like (SOCAL) surfaces have a remarkable combination of contact-angle hysteresis and contact-line friction properties, which lead to very low droplet pinning but high dynamic friction against the motion of droplets. We present experiments of the response of water droplets to changes in volume at controlled temperature and humidity conditions, which we separately compare to the predictions of a hydrodynamic model and a contact-line model based on molecular kinetic theory. Our results show that SOCAL surfaces offer very low contact-angle hysteresis, between 1 and 3°, but an unexpectedly high dynamic friction controlled by the contact line, where the typical relaxation time scale is on the order of seconds, 4 orders of magnitude larger than the prediction of the classical hydrodynamic model. Our results highlight the remarkable wettability of SOCAL surfaces and their potential application as low-pinning, slow droplet shedding surfaces.