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Tactic behaviour is understood as the ability of a system to sense and respond to external stimuli. This tactic behaviour is present in many complex systems, many of which can be found in nature. Tactic systems are able to sense external stimuli (for example, chemical or temperature gradients) and convert this sensory information into large-scale self-propulsion. This PhD thesis aims to explore a transformative concept for tactic behaviour in soft-matter physics and smart-materials engineering called hygrotaxis, defined as the motion of a droplet on a solid surface caused by the presence of a humidity gradient. The interactions present in this effect give rise to very small forces. Hence, experiments are carried out on Slippery Omniphobic Covalently Attached Liquid-like (SOCAL) surfaces, a type of ultra-smooth surface which exhibits remarkably low contact angle hysteresis (< 3◦). Base studies on the evaporation dynamics of water droplets on ultra-smooth surfaces show that SOCAL was successfully grafted into glass substrates. Studies of the contact angle hysteresis on these surfaces shows there are different friction regimes that make measurement of contact angle hysteresis challenging. Hence, a novel method of characterisation of ultra-smooth surfaces is developed to use the relaxation of interfaces to measure contact angle hysteresis on SOCAL surfaces. The relaxation times obtained in these studies allow for the analysis of the physical mechanisms guiding the motion of the droplet, which depends on the kinematics of the contact line rather than the hydrodynamics. Lattice Boltzmann simulations are implemented to study the effect of humidity gradients on liquid droplets inside a square channel. Base simulations show that the Lattice Boltzmann algorithm is accurate in modelling the dynamics as predicted by the Cahn-Hilliard equation. Gradients inside the channel are generated by introducing a chemical potential difference in the ambient phase. These simulations show that chemical potential gradients are able to affect the liquid-gas interface, generating surface flows that guide the droplet towards more humid environments. Based on the findings in this thesis, two experimental approaches are developed to study hygrotaxis. The first approach aims to generate a gradient in relative humidity by placing two droplets of significantly different sizes in close proximity (∼ 0.1 mm) in an ambient relative humidity of 10%. The effect observed is a consistent displacement of the centre of mass of the small droplet towards the larger one. Comparisons between experiments and simulation show an overall agreement in the behaviour of the droplet in such configuration. The second approach consists of separating the exposed surface of a small amount water into two different interfaces. This is done by developing a method to coat and characterise the inside of glass capillary tubes with the SOCAL coating. Comparisons between coated and uncoated samples show that SOCAL has been successfully applied, exhibiting contact angle hysteresis measurements of 2.9◦ ±1.9◦. Although pinning events are prevalent in SOCAL coated samples, evaporation of 2μL liquid slugs indicate the possible existence of a pressure driven effect which drives the contact line to recede from the humid side rather than the dry one. Even though improvements in the experiments still have to be implemented, these results are motivating and serve a proof of concept for future studies. The methods and the results presented in this work improve our understanding of the interaction of water droplets, ultra-smooth surfaces and relative humidity gradients.

Contact-line pinning is a fundamental limitation of diffusion-limited evaporation of sessile droplets. Sessile droplet evaporation is pervasive in a wide range of situations from ink-jet printing, to pesticide sprays and spotted microarrays. Contact-line pinning drives, for example, stick-slip motion and non-uniform deposition of solute within the droplet. Moreover, contact-line pinning is problematic in a wide range of situations, such as droplet microfluidics where capillary forces dominate the motion of liquid fronts. Recently, Slippery Liquid-Infused Porous Surfaces (SLIPS) have shown excellent droplet shedding abilities by use of a lubricating liquid, imbibed into a porous structure, immiscible to droplets on the surface. However, the lubricating liquid removes the droplet-solid-interaction, can cloak the droplet, can be several microns in thickness and the porous structure can be fragile to external mechanical forces. Slippery Omniphobic Covalently Attached Liquid-Like (SOCAL) is a new type of liquid-like surface, which is an attached coating rather than a retained liquid. SOCAL promises pinning-free properties while being nanometres thick and demonstrating mechanical robustness. Few research groups have reported successful creation of SOCAL surfaces. This thesis shows an optimised methodology to make reliably, pinning-free low-hysteresis SOCAL surfaces. This is done by modifying the parameters to create SOCAL and measuring the contact-angle hysteresis. A low contact-angle hysteresis of < 1° is achieved. These surfaces then show, for the first time, constant contact angle mode evaporation of sessile water droplets from a solid surface. This allows for the accurate measurement of the diffusion coefficient of water. An unexpected feature of the evaporation sequences is a step change increase in contact angle reminiscent of a type V adsorption isotherm. Attempts are made to characterise this using Dynamic Vapour Sorption (DVS) and Quartz Crystal Microbalance (QCM) techniques. This thesis also shows voltage-programmable control of water droplets on SOCAL using electrowetting. The unexpected behaviour of droplets on SOCAL is investigated and the electrowetting device is optimised. This allows control of the constant contact angle evaporation on both SLIPS and SOCAL. This is used to study the effect on the contact angle during the evaporation of sessile water droplets. The results of this thesis will benefit the aforementioned applications overcoming contact-line pinning and introducing new methods of controlling sessile droplet evaporation.

Droplets on slippery surfaces such as Slippery Liquid Infused Porous Surfaces or Liquid - Impregnated Surfaces (SLIPS/LIS) are inherently highly mobile and therefore can be difficult to control in terms of position and motion. This thesis has explored how to return droplet control back to very slippery surfaces via four interconnected studies. The first study investigated how to return droplet control back to these slippery surfaces by adding a simple step structure to the surface. The adhesive force created by this structure has been quantified by measuring the droplet sliding angle as a function of step height and oil thickness. As the step height was increased so did the adhesive force, as the oil thickness was increased the adhesive force decreased. Given the correct conditions the adhesive force can be great enough to hold a droplet upside down. The ability of the structure to produce motion via a repulsive or attractive force has been investigated in the second study by changing where the droplet was placed onto the substrate. The type of force produced was found to not only vary with position but with oil thickness and time. The third study involved a more complex topography onto which the SLIPS coating was applied, creating a mobile surface which also shaped the droplet. As a droplet placed on to this surface evaporated it was shown that the shape of the droplet could be accurately predicted for a given droplet volume. The final study developed a SLIPS coating that could be applied to any structure, even a closed geometry, in one single step, producing sliding angles equivalent to those seen on a standard SLIPS coating. This coating has also been shown to be long lasting with the SLIPS properties remaining more than two years after it was first produced and tested.

Capillarity and wetting are the study of the interfaces that separate immiscible fluids and their interaction with solid surfaces. The interest in understanding capillary and wetting phenomena in complex geometries has grown in recent years. This is partly motivated by applications, such as the micro-fabrication of surfaces that achieve a controlled wettability, but also because of the fundamental role that the geometry of a solid surface can play in the statics and dynamics of liquids that come into contact with it. In this work, the statics and dynamics of liquids in contact with smooth, but non-planar geometries are studied. The approach is theoretical, and include mathematical modelling and numerical simulations using a new lattice-Boltzmann simulation method. The latter can account for solid boundaries of arbitrary geometry and a variety of boundary conditions relevant to experimental situations. The focus is directed to two model systems. First, an analysis on the statics and dynamics of a droplet inside wedge is performed, this is accomplished by proposing the shape of the droplet, a new shape that will be referred in this document as a “liquid barrel”. Using this assumption, the static position and shape of the droplet in response to an external body force is predicted. Then, the analysis is extended to include to dynamical situations in the absence of external forces, in which the translational motion of the liquid barrel towards equilibrium it is described. The proposed analytical model was validated by comparison with full 3D lattice-Boltzmann simulations and with recent experimental results. The applicability of these ideas is materialised with the purpose of achieving energy-invariant manipulation of a liquid barrel in a reconfigurable wedge. As a second model system, the evaporation of a sessile droplet in contact with a wavy solid surface was studied. Due to the non-planar solid topography, the droplet position in equilibrium is restricted to a discrete set of positions. It is shown that when the amplitude of the surface is sufficiently high, the droplet can suddenly readjust its shape and location to a new equilibrium configuration. These events occur in a time-scale much shorter than the evaporation time-scale, a “snap”. With numerical simulations and theoretical analysis, the study reveals the causes for the snap transitions, which lie in shape bifurcations of the droplet shapes, The analysis and results are compared against recent experiments of droplets evaporating on smooth sinusoidal surfaces. With the advent of low-friction surfaces, in which static friction is practically absent, the mobility of droplets is close to ideal, and with this, predicting and controlling them in static cases becomes a challenge. The analysis and results presented in this work can be used for manipulating the position and defining the shape of droplets via the geometry of their confinements.