Millions of years of evolution have led to a wealth of highly adapted functional surfaces in nature. Among the most fascinating are superhydrophobic surfaces which are highly water-repellent and shed drops very easily owing to their chemical hydrophobicity combined with micropatterning. Superhydrophobic materials have attracted a lot of attention due to their practical applications as ultra-low friction surfaces for ships and pipes, water harvesters, de-humidifiers and cooling systems. At small length scales, where surface tension dominates over gravity, these surfaces show a wealth of phenomena interesting to physicists, such as directional flow, rolling, and drop bouncing. This thesis focuses on two examples of dynamic drop interactions with micropatterned surfaces and studies them by means of a lattice Boltzmann simulation approach. Inspired by recent experiments, we investigate the phenomenon of the self-propelled bouncing of coalescing droplets. On highly hydrophobic patterned surfaces drop coalescence can lead to an out-of-plane jump of the composite drop. We discuss the importance of energy dissipation to the jumping process and identify an anisotropy of the jumping ability with respect to surface features. We show that Gibbs' pinning is the source of this anisotropy and explain how it leads to the inhibition of coalescence-induced jumping. The second example we study is the novel phenomenon of pancake bouncing. Conventionally, a drop falling onto a superhydrophobic surface spreads due to its inertia, retracts due to its surface tension, and bounces off the surface. Here we explain a different pathway to bouncing that has been observed in recent experiments: A drop may spread upon impact, but leave the surface whilst still in an elongated shape. This new behaviour, which occurs transiently for certain impact and surface parameters, is due to reversible liquid imbibition into the superhydrophobic substrate. We develop a theoretical model and test it on data from experiments and simulations. The theoretical model is used to explain pancake bouncing in detail.

Surfactants are amphiphilic molecules which self-assemble at the interface in oil-water-surfactant mixtures such that the hydrophobic part, called tail, stays in oil and the remaining part, called head, resides in hydrophilic en-vironment. Depending upon concentration of individual components, these mixtures form several microphases, such as bilayers, micelles, columnar and lamellar phases. A lamellar phase, at equilibrium, is made up of alternat-ing layers of water and oil separated by surfactants, or of alternate layers of water and surfactant bilayers such that the hydrophilic heads are in contact with water. This equilibrium state is rarely achieved in macroscopic samples due to thermodynamic and kinetic constraints; instead, a lamellar fluid is usually disordered with a large number of defects. These defects have significant effect on the flow behaviour of the lamellar mesophase systems. They are known to alter the flow field, resulting stresses and in turn could get distorted or annihilated by the flow. In present work, we analyse this two way coupling between lamellar structure and flow field. The structural and rheological evolution of an initially disordered lamellar phase system under a shear flow is examined using a mesoscale model based on a free energy functional for the concentration field, which is the scaled difference in the concentration between the hydrophilic and hydrophobic components. Two distinct modes of structural evolution are observed depending only on Peclet number, which ratio of inertial forces to mass diffusivity, in-dependent of system size. At low Peclet number, local domains are formed which are then rotated and stretched by shear. A balance between defect creation and annihilation is reached due to which the system never reaches the equilibrium layer configuration. In the opposite limit, partially formed layers break and reform so as to form a nearly aligned lamellar phase con-figuration with residual defects. Viscosity of lamellar phase system increases with layer moduli, differences in viscosity of individual components, fluidity of the lamellae due to shear banding and defect pinning. These factors however, do not have any effect on alignment mechanism.