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

In developing its new engineering accreditation criteria, ABET reaffirmed a set of “hard” engineering skills while introducing a second, equally important, set of six “professional” skills. These latter skills include communication, teamwork, and understanding ethics and professionalism, which we label process skills, and engineering within a global and societal context, lifelong learning, and a knowledge of contemporary issues, which we designate as awareness skills. We review these skills with an emphasis on how they can be taught, or more correctly learned, citing a number of examples of successful and/or promising implementations. We then examine the difficult issue of assessing these skills. We are very positive about a number of creative ways that these skills are being learned, particularly at institutions that are turning to global and/or service learning in combination with engineering design projects to teach and reinforce outcome combinations. We are also encouraged by work directed at assessing these skills, but recognize that there is considerable research that remains to be done.

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The ABET “Professional Skills” — Can They Be Taught? Can They Be Assessed?

The aim of this paper is to describe the development of the method of fundamental solutions (MFS) and related methods over the last three decades. Several applications of MFS-type methods are presented. Techniques by which such methods are extended to certain classes of non-trivial problems and adapted for the solution of inhomogeneous problems are also outlined.

https://msvlab.hre.ntou.edu.tw/grades/meshless/MFS98.pdf

The method of fundamental solutions for elliptic boundary value problems

Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

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Liquid Sloshing Dynamics

A recurring question in the study of fish biomechanics and energetics is the mechanical power required for tail-swimming at the high speeds seen among aquatic vertebrates. The quest for answers has been driven by conceptual advances in fluid dynamics, starting with ideas on the boundary layer and drag initiated by Prandtl, and in measurement techniques starting with force balances focussing on drag and thrust. Drag (=thrust) from measurements on physical models, carcasses, kinematics as inputs to hydromechanical models, and physiological power sources vary from less than that expected for an equivalent rigid reference to over an order of magnitude greater. Estimates of drag and thrust using recent advances largely made possible by increased computing power have not resolved the discrepancy. Sources of drag and thrust are not separable in axial undulatory self propulsion, are open to interpretation and Froude efficiency is zero. Wakes are not easily interpreted, especially for thrust evaluation. We suggest the best measures of swimming performance are velocity and power consumption for which 2D inviscid simulations can give realistic predictions. Steady swimming power is several times that required for towing an equivalent flat plate at the same speed.

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Power Requirements of Swimming: Do New Methods Resolve Old Questions?

SUMMARY The concept of desingularization in three-dimensional boundary integral computations is re-examined. The boundary integral equation is desingularized by moving the singular points away from the boundary and outside the problem domain. We show that the desingularization gives better solutions to several problems. As a result of desingularization, the surface integrals can be evaluated by simpler techniques, speeding up the computation. The effects of the desingularization distance on the solution and the condition of the resulting system of algebraic equations are studied for both direct and indirect versions of the boundary integral method. Computations show that a broad range of desingularization distances gives accurate solutions with significant savings in the computation time. The desingularization distance must be carefully linked to the mesh size to avoid problems with uniqueness and ill-conditioning. As an example, the desingularized indirect approach is tested on unsteady non-linear three-dimensional gravity waves generated by a moving submerged disturbance; minimal computational difficulties are encountered at the truncated boundary. Boundary integral methods provide a powerful technique for the solution of linear, homogeneous boundary value problems. The method employs a fundamental solution, which satisfies the differential equation (and possibly part of the boundary conditions), to reformulate the problem as an integral equation on the boundary. In conventional boundary integral formulations, singularities of the fundamental solution are placed on the domain boundary. This requires special evaluation of singular integrands, which can result in costly numerical calculations. In time-dependent non-linear free surface problems' - a boundary integral problem is solved at each time step. Since most of the computation time is devoted to the boundary integral problem, an effective solution method is critical in the time-marching procedure. When the singularity of the fundamental solution is placed away from the boundary and outside the domain of the problem, a desingularized boundary integral equation is obtained. We will show two advantages to this desingularization: a more accurate solution can be obtained for a given truncation, and a numerical quadrature can be used to reduce the computational time to obtain the algebraic system representing the discretized boundary integral problem. There are two types of non-singular boundary integral formulations: direct and indirect. In the direct method, Green's second identity is used to derive the boundary integral equation, and the solution of the problem is obtained directly by solving the boundary integral equation. In the

/pdf/three-dimensional-desingularized-boundary-integral-methods-4pzrtgq8fg.pdf

Three-dimensional desingularized boundary integral methods for potential problems

▪ Abstract We concentrate on the rich effects that surface tension has on free and forced surface waves for linear, nonlinear, and especially strongly nonlinear waves close to or at breaking or their limiting form. These effects are discussed in the context of standing gravity and gravity-capillary waves, Faraday waves, and parasitic capillary waves. Focus is primarily on post-1989 research. Regarding standing waves, new waveforms and the large effect that small capillarity can have are considered. Faraday waves are discussed principally with regard to viscous effects, hysteresis, and limit cycles; nonlinear waveforms of low mode numbers; contact-line effects and surfactants; breaking and subharmonics; and drop ejection. Pattern formation and chaotic and nonlinear dynamics of Faraday waves are mentioned only briefly. Gravity and gravity-capillary wave generation of parasitic capillaries and dissipation are considered at length. We conclude with our view on the direction of future research in these areas.

Capillary Effects on Surface Waves

A numerical model combining the methods of enthalpy, effective-viscosity and volume-of-fluid is developed to simulate the metal transfer process in gas metal arc welding. The model describes not only the influence on droplet profile and transfer frequency of electromagnetic force, surface tension, and gravity, but it can also model the nonisothermal phenomena such as heat transfer and phase change. The model has been used to study the shape of the melting interface on the welding wire, the droplet oscillation at wire tip, the characteristics of relevant physical variables and their roles in metal transfer. We find that the taper formation in spray transfer is closely related to the heat input on the unmelted portion of the welding wire, and the taper formation affects the globular–spray transition by decelerating the transfer process. The formation of satellite drops during the metal transfer process is also considered. High-speed photography, laser-shadow imaging, and metallographic analysis validate the numerical model, and recommendations are made on the topics that require further consideration for a more accurate metal transfer model.

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Modelling and analysis of metal transfer in gas metal arc welding

Axisymmetric Newtonian viscous fibers are examined under isothermal conditions. An expansion based on lubrication scaling is used to derive systematically the one‐dimensional equations for the fiber. At lowest order these are identical with those obtained by others, e.g., Matovich and Pearson. One‐dimensional theory limitations on jet shape and inertial, gravitational, and surface tension effects are obtained from higher‐order approximations. Similar approaches can be used to analyze fibers having complex rheological behaviors.

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William W. Schultz

Papers

Power Requirements of Swimming: Do New Methods Resolve Old Questions?

Three-dimensional desingularized boundary integral methods for potential problems

Capillary Effects on Surface Waves

Modelling and analysis of metal transfer in gas metal arc welding

One-Dimensional Liquid Fibers