Fracture of a viscous liquid.
TL;DR: The critical velocity of entrainment of this phase is characterized and compared with recent predictions by Eggers, and a law is defined for the collapse of the tip that explains both the cusplike shape of this region, and the instability of the cusp if increasing the impact velocity.
Abstract: When a viscous liquid hits a pool of liquid of the same nature, the impact region is hollowed by the shock. Its bottom becomes extremely sharp if increasing the impact velocity, and we report that the curvature at that place increases exponentially with the flow velocity, in agreement with a theory by Jeong and Moffatt. Such a law defines a characteristic velocity for the collapse of the tip, which explains both the cusplike shape of this region, and the instability of the cusp if increasing (slightly) the impact velocity. Then, a film of the upper phase is entrained inside the pool. We characterize the critical velocity of entrainment of this phase and compare our results with recent predictions by Eggers.
Citations
More filters
TL;DR: In this article, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid is examined, while 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.
Abstract: 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.
2,501 citations
14 Sep 2007
TL;DR: In this article, the key to the moving contact line problem is discussed and a discussion of the missing physics and the paradoxes of modeling it is presented. But the authors focus mainly on the dynamics of free-surface flows in nature and industry.
Abstract: PREFACE INTRODUCTION Free-surface flows in nature and industry Scope of the book FUNDAMENTALS OF FLUID MECHANICS Main concepts Governing equations Elements of thermodynamics Classical boundary conditions Physically meaningful solutions and paradoxes of modeling MOVING CONTACT LINES: AN OVERVIEW Essence of the problem Experimental observations Molecular dynamics simulations Review of theories The key to the moving contact-line problem BOUNDARY CONDITIONS ON FORMING INTERFACES Modeling of interfaces Conservation laws Liquid-gas and liquid-solid interfaces Liquid-liquid interfaces Summary Open questions and possible generalizations MOVING CONTACT LINES: MATHEMATICAL DESCRIPTION Flow in the immediate vicinity of a moving contact line Dynamic wetting at small capillary numbers De-wetting and re-wetting Comparison with experiments and some estimates Examples: flows in a quasi-static regime Dynamic wetting at finite capillary numbers Liquid-liquid displacement Summary and outstanding modeling issues CUSPS, CORNERS AND COALESCENCE OF DROPS Singularities of free-surface curvature in experiments Conventional modeling "Missing" physics Singularity-free solution: cusp or corner? Coalescence of drops BREAKUP OF JETS AND RUPTURE OF FILMS Background Drop formation: emerging singularity Experiments on capillary pinch-off "Missing" physics and its qualitative verification Axisymmetric capillary pinch-off: singularity-free solution Pinch-off from a molecular viewpoint Rupture of films Summary APPENDIX A: Elements of vector and tensor calculus APPENDIX B: Equations of fluid mechanics in curvilinear coordinates APPENDIX C: Complex representation of biharmonic functions APPENDIX D: Physical properties of some fluids REFERENCES INDICES
228 citations
TL;DR: The subject is reviewed by providing an overview of the relevant key mechanisms of bubble generation within a coherent hydrodynamic context; and different foaming techniques which exploit these mechanisms are discussed.
186 citations
Cites background from "Fracture of a viscous liquid."
...It creates a thin threadwhich starts at the tip of an elongated bubble/drop, where it has a non-trivial shape [74]....
[...]
TL;DR: In this article, the authors address recent research on how air is entrained during the impact of a liquid stream on a pool of the same material in a variety of scenarios, including the prototype flows of impacting stationary laminar and turbulent steady jets, the transient impact of isolated masses of liquid, and jets with organized disturbances, and translating steady and transient jets.
Abstract: Air entrainment in liquids is a complex phenomenon that has important applications in industry and the environment. This article addresses recent research on how air is entrained during the impact of a liquid stream on a pool of the same material in a variety of scenarios. At the fundamental level, these scenarios include the prototype flows of impacting stationary laminar and turbulent steady jets, the transient impact of isolated masses of liquid, the impact of jets with organized disturbances, and translating steady and transient jets. Although significant advances have been made recently, the complexity of this multiphase, three-dimensional, and frequently turbulent flow phenomenon leaves many unanswered questions. To help elucidate the problems still to be addressed in future research, the final section of the article examines air entrainment in the more complex application of plunging breaking waves and points out the many parts of this process that are poorly understood.
181 citations
TL;DR: In this article, a water drop that is gently deposited on a very cold surface freezes into a pointy ice-drop with a very sharp tip, and the formation of this singular shape originates from the reduction of mass density during the freezing process and can be explained using a simplified model for which the universal structure of the singularity is revealed in full detail.
Abstract: A water drop that is gently deposited on a very cold surface freezes into a pointy ice-drop with a very sharp tip. The formation of this singular shape originates from the reduction of mass density during the freezing process and can be explained using a simplified model for which the universal structure of the singularity is revealed in full detail. The combination of a relatively simple, static experiment, and the accessible asymptotic analysis makes this system an ideal introduction to the topic of singularities
103 citations