Wetting phenomena are ubiquitous in nature and technology. A solid substrate exposed to the environment is almost invariably covered by a layer of fluid material. In this review, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid. Depending on the nature of the surface forces involved, different scenarios for wetting phase transitions are possible; recent progress allows us to relate the critical exponents directly to the nature of the surface forces which lead to the different wetting scenarios. Thermal fluctuation effects, which can be greatly enhanced for wetting of geometrically or chemically structured substrates, and are much stronger in colloidal suspensions, modify the adsorption singularities. Macroscopic descriptions and microscopic theories have been developed to understand and predict wetting behavior relevant to microfluidics and nanofluidics applications. Then the dynamics of wetting is examined. A drop, placed on a substrate which it wets, spreads out to form a film. Conversely, a nonwetted substrate previously covered by a film dewets upon an appropriate change of system parameters. The hydrodynamics of both wetting and dewetting is influenced by the presence of the three-phase contact line separating "wet" regions from those that are either dry or covered by a microscopic film only. Recent theoretical, experimental, and numerical progress in the description of moving contact line dynamics are reviewed, and its relation to the thermodynamics of wetting is explored. In addition, recent progress on rough surfaces is surveyed. The anchoring of contact lines and contact angle hysteresis are explored resulting from surface inhomogeneities. Further, new ways to mold wetting characteristics according to technological constraints are discussed, for example, the use of patterned surfaces, surfactants, or complex fluids.

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Wetting and Spreading

The review deals with drop impacts on thin liquid layers and dry surfaces. The impacts resulting in crown formation are referred to as splashing. Crowns and their propagation are discussed in detail, as well as some additional kindred, albeit nonsplashing, phenomena like drop spreading and deposition, receding (recoil), jetting, fingering, and rebound. The review begins with an explanation of various practical motivations feeding the interest in the fascinating phenomena of drop impact, and the above-mentioned topics are then considered in their experimental, theoretical, and computational aspects.

Drop Impact Dynamics: Splashing, Spreading, Receding, Bouncing ...

The numerical simulation of flows with interfaces and free-surface flows is a vast topic, with applications to domains as varied as environment, geophysics, engineering, and fundamental physics. In engineering, as well as in other disciplines, the study of liquid-gas interfaces is important in combustion problems with liquid and gas reagents. The formation of droplet clouds or sprays that subsequently burn in combustion chambers originates in interfacial instabilities, such as the Kelvin-Helmholtz instability. What can numerical simulations do to improve our understanding of these phenomena? The limitations of numerical techniques make it impossible to consider more than a few droplets or bubbles. They also force us to stay at low Reynolds or Weber numbers, which prevent us from finding a direct solution to the breakup problem. However, these methods are potentially important. First, the continuous improvement of computational power (or, what amounts to the same, the drop in megaflop price) continuously extends the range of affordable problems. Second, and more importantly, the phenomena we consider often happen on scales of space and time where experimental visualization is difficult or impossible. In such cases, numerical simulation may be a useful prod to the intuition of the physicist, the engineer, or the mathematician. A typical example of interfacial flow is the collision between two liquid droplets. Finding the flow involves the study not only of hydrodynamic fields in the air and water phases but also of the air-water interface. This latter part

Direct numerical simulation of free-surface and interfacial flow

Surface-tension-driven flows and, in particular, their tendency to decay spontaneously into drops have long fascinated naturalists, the earliest systematic experiments dating back to the beginning of the 19th century. Linear stability theory governs the onset of breakup and was developed by Rayleigh, Plateau, and Maxwell. However, only recently has attention turned to the nonlinear behavior in the vicinity of the singular point where a drop separates. The increased attention is due to a number of recent and increasingly refined experiments, as well as to a host of technological applications, ranging from printing to mixing and fiber spinning. The description of drop separation becomes possible because jet motion turns out to be effectively governed by one-dimensional equations, which still contain most of the richness of the original dynamics. In addition, an attraction for physicists lies in the fact that the separation singularity is governed by universal scaling laws, which constitute an asymptotic solution of the Navier-Stokes equation before and after breakup. The Navier-Stokes equation is thus continued uniquely through the singularity. At high viscosities, a series of noise-driven instabilities has been observed, which are a nested superposition of singularities of the same universal form. At low viscosities, there is rich scaling behavior in addition to aesthetically pleasing breakup patterns driven by capillary waves. The author reviews the theoretical development of this field alongside recent experimental work, and outlines unsolved problems.

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Nonlinear dynamics and breakup of free-surface flows

Jets, ie collimated streams of matter, occur from the microscale up to the large-scale structure of the universe Our focus will be mostly on surface tension effects, which result from the cohesive properties of liquids Paradoxically, cohesive forces promote the breakup of jets, widely encountered in nature, technology and basic science, for example in nuclear fission, DNA sampling, medical diagnostics, sprays, agricultural irrigation and jet engine technology Liquid jets thus serve as a paradigm for free-surface motion, hydrodynamic instability and singularity formation leading to drop breakup In addition to their practical usefulness, jets are an ideal probe for liquid properties, such as surface tension, viscosity or non-Newtonian rheology They also arise from the last but one topology change of liquid masses bursting into sprays Jet dynamics are sensitive to the turbulent or thermal excitation of the fluid, as well as to the surrounding gas or fluid medium The aim of this review is to provide a unified description of the fundamental and the technological aspects of these subjects

Physics of liquid jets

PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method

It is shown that the Timoshenko beam can be uniformly stabilized by means of a boundary control. A numerical study on the spectrum is also presented.

Boundary control of the Timoshenko beam

Fundamentals of two-fluid dynamics

This paper gives an overview of the issues posed by the science and technology of transporting heavy oils in a sheath of lubricating water. It touches on measures of energy efficiency, industrial experience, fouling, stability, models of levitation, and future directions.

Yuriko Renardy

Papers

PROST: a parabolic reconstruction of surface tension for the volume-of-fluid method

Boundary control of the Timoshenko beam

Fundamentals of two-fluid dynamics

Core-annular flows

Numerical simulation of moving contact line problems using a volume-of-fluid method