Mathematical Theory Of Liquid Interfaces Liquid Layers Capillary Interfaces Floating Drops And Particles

This book lays a unique and straightforward mathematical foundation on the aspects of liquid layers, capillary interfaces, floating drops and particles. For the first time, these topics are studied in a joint framework. Readers will acquire deeper comprehension and gain results. Practical interest are presented, making it beneficial to engineers and physicists as well as mathematicians.The text takes an insight-oriented approach that gives it immediacy and flexibility. It contains 70 problems where some are exercises, while others are open problems. It is also illustrated with 95 figures and photographs for further understanding.

In the small world of micrometer to nanometer scale many natural and industrial processes include attachment of colloid particles (solid spheres, liquid droplets, gas bubbles or protein macromolecules) to fluid interfaces and their confinement in liquid films. This may lead to the appearance of lateral interactions between particles at interfaces, or between inclusions in phospholipid membranes, followed eventually by the formation of two-dimensional ordered arrays. The book is devoted to the description of such processes, their consecutive stages, and to the investigation of the underlying physico-chemical mechanisms. The first six chapters give a concise but informative introduction to the basic knowledge in surface and colloid science, which includes both traditional concepts and some recent results. Chapters 1 and 2 are devoted to the basic theory of capillarity, kinetics of surfactant adsorption, shapes of axisymmetric fluid interfaces, contact angles and line tension. Chapters 3 and 4 present a generalization of the theory of capillarity to the case, in which the variation of the interfacial (membrane) curvature contributes to the total energy of the system. The generalized Laplace equation is applied to determine the configurations of free and adherent biological cells. Chapters 5 and 6 are focused on the role of thin liquid films and hydrodynamic factors in the attachment of solid and fluid particles to an interface. Surface forces of various physical nature are presented and their relative importance is discussed. Hydrodynamic interactions of a colloidal particle with an interface (or another particle) are also considered.Chapters 7 to 10 are devoted to the theoretical foundation of various kinds of capillary forces. When two particles are attached to the same interface (membrane), capillary interactions, mediated by the interface or membrane, appear between them. Two major kinds of capillary interactions are described: (i) capillary immersion force related to the surface wettability (Chapter 7), (ii) capillary flotation force originating from interfacial deformations due to particle weight (Chapter 8). Special attention is paid to the theory of capillary immersion forces between particles entrapped in spherical liquid films (Chapter 9). A generalization of the theory of immersion forces allows one to describe membrane-mediated interactions between protein inclusions into a lipid bilayer (Chapter 10).Chapter 11 is devoted to the theory of the capillary bridges and the capillary-bridge forces, whose importance has been recognized in phenomena like consolidation of granules and soils, wetting of powders, capillary condensation, long-range hydrophobic attraction, etc. The nucleation of capillary bridges is also examined.Chapter 12 considers solid particles, which have an irregular wetting perimeter upon attachment to a fluid interface. The undulated contact line induces interfacial deformations, which engender a special lateral capillary force between the particles. The latter contributes to the dilatational and shear elastic moduli of particulate adsorption monolayers.Chapter 13 describes how lateral capillary forces, facilitated by convective flows and some specific and non-specific interactions, can lead to the aggregation and ordering of various particles at fluid interfaces or in thin liquid films. Recent results on fabricating two-dimensional (2D) arrays from micrometer and sub-micrometer latex particles, as well as 2D crystals from proteins and protein complexes, are reviewed. Chapter 14 presents applied aspects of the particle-surface interaction in antifoaming and defoaming. The mechanisms of antifoaming action involve as a necessary step the entering of an antifoam particle at the air-water interface. The considered mechanisms indicate the factors for control of foaminess.

The book aims at describing the most important experimental methods for characterizing liquid interfaces, such as drop profile analysis, bubble pressure and drop volume tensiometry, capillary pressure technique, and oscillating drops and bubbles.

Mathematics Research Center Symposium: Waves on Fluid Interfaces covers the proceedings of a symposium conducted by the Mathematics Research Center of the University of Wisconsin-Madison on October 18-20, 1982. The book focuses on nonlinear instabilities of classical interfaces, physical structure of real interfaces, and the challenges these reactions pose to the understanding of fluids. The selection first elaborates on finite-amplitude interfacial waves, instability of finite-amplitude interfacial waves, and finite-amplitude water waves with surface tension. Discussions focus on reformulation as an integro-differential equation, perturbation solutions, results for interfacial waves with current jump, wave of zero height, weakly nonlinear waves, and numerical methods. The text then takes a look at generalized vortex methods for free-surface flows; a review of solution methods for viscous flow in the presence of deformable boundaries; and existence criteria for fluid interfaces in the absence of gravity. The book ponders on the endothelial interface between tissue and blood, moving contact line, rupture of thin liquid films, film waves, and interfacial instabilities caused by air flow over a thin liquid layer. Topics include stability analysis of liquid film, interpretation of film instabilities, simple film, linear stability theory, inadequacy of the usual hydrodynamic model, and marcomolecule transport across the artery wall. The selection is a valuable source of data for researchers interested in the reactions of waves on fluid interfaces.

Fluid interfaces are promising candidates for confining different types of materials, e.g., polymers, surfactants, colloids, and even small molecules, to be used in designing new functional materials with reduced dimensionality. The development of such materials requires a deepening of the physicochemical bases underlying the formation of layers at fluid interfaces as well as on the characterization of their structures and properties. This is of particular importance because the constraints associated with the assembly of materials at the interface lead to the emergence of equilibrium and features of dynamics in the interfacial systems, which are far removed from those conventionally found in traditional materials. This Special Issue is devoted to studies on the fundamental and applied aspects of fluid interfaces, and attempts to provide a comprehensive perspective on the current status of the research field.

Physically correct boundary conditions on vapor-liquid interfaces are essential in order to make an analysis of flows of a liquid including bubbles or of a gas including droplets. Suitable boundary conditions do not exist at the present time. This book is concerned with the kinetic boundary condition for both the plane and curved vapor-liquid interfaces, and the fluid dynamics boundary condition for Navier-Stokes(fluid dynamics) equations. The kinetic boundary condition is formulated on the basis of molecular dynamics simulations and the fluid dynamics boundary condition is derived by a perturbation analysis of Gaussian-BGK Boltzmann equation applicable to polyatomic gases. The fluid dynamics boundary condition is applied to actual flow problems of bubbles in a liquid and droplets in a gas.

In this book experts discuss research and applications in interfacial fluid dynamics.

Update your knowledge of the chemical, biological, and physical properties of liquid-liquid interfaces with Liquid-Liquid Interfaces: Theory and Methods. This valuable reference presents a broadly based account of current research in liquid-liquid interfaces and is ideal for researchers, teachers, and students. Internationally recognized investigators of electrochemical, biological, and photochemical effects in interfacial phenomena share their own research results and extensively review the results of others working in their area. Because of its unusually wide breadth, this book has something for everyone interested in liquid-liquid interfaces. Topics include interfacial and phase transfer catalysis, electrochemistry and colloidal chemistry, ion and electron transport processes, molecular dynamics, electroanalysis, liquid membranes, emulsions, pharmacology, and artificial photosynthesis. Enlightening discussions explore biotechnological applications, such as drug delivery, separation and purification of nuclear waste, catalysis, mineral extraction processes, and the manufacturing of biosensors and ion-selective electrodes. Liquid-Liquid Interfaces: Theory and Methods is a well-written, informative, one-stop resource that will save you time and energy in your search for the latest information on liquid-liquid interfaces.

Despite factoring in countless natural, biological, and industrial processes, fixed attention on the singular attributes and behavior of fluids near or at interfaces has not received enough attention in the surface science literature. Liquid Interfacial Systems assembles and analyzes concepts and findings as an inclusive summation of fluid-fluid interfacial phenomena. This book covers excitation, stabilization, and suppression of instability at liquid interfaces. From the influential original research and scholarship of leaders in the discipline comes a volume to impart and explain definitions, scales, governing equations, and boundary conditions used in liquid interfacial system research.

Particle-laden interfaces have promising potentials in many fields because the particulate nature can endow the surface with physical properties that are not readily obtained from molecular-scale surfactants. In this dissertation, we first focus on measuring capillary forces on particles at fluid interfaces in order to assess the key parameters that yield effective stabilizing particles. In experiment, the force and the displacement of a millimeter-scale particle passing through a liquid interface were recorded. We find that the peak force needed to detach a particle from an interface crowded with other particles is consistently smaller than the force at a clean interface. By ruling out other possibilities, we attribute the force reduction to the perturbation of interface shape due to the constraints imposed by free particles. Then we study the mechanics of particulate assemblies by measuring the force response under a normal indentation. We find that there exist two linear regions with different slopes. The small-slope regime starts at the beginning and persists over a range of indentations much less than capillary length. Once the system entered the higher plateau region, it has the same stiffness as a pure liquid interface. Further, from top-view images, we showed that, as long as the indenter was larger than the size of a single particle, the azimuthal compression can be relaxed through the in-plane rearrangement of particles. These features are independent of the difference in fluid mass densities, the radius of the indenter and the species of particles. Although the presence of floating particles at an interface does not change its capillary nature under a wide range of poking depth, we show that the existence of the particle raft makes the original interface tougher in terms of both the maximum force it can sustain and the largest indentation an indenter can reach. These results provide an important step toward understanding the mechanics of particulate assemblies at interfaces. Finally, we study the formation of organic 2D material in aqueous media for the purpose of potential applications in passivating objects in suspension. We optimized the conditions for the self-assembly of bola-amphiphilic molecules, and directly observed 2D sheets in optical microscope under dark-field illumination. We find that stacking is not preferred by sheets because of the likely electrostatic repulsion. Our method provides an effective way to better understand the properties of those sheets.