Registration of high-frequency waves on the surface by the interference methods

Capillary waves are frequently used to measure the surface tension of liquids. However, this approach has not found wide application in the manufacture of modern commercial tensiometers because of the limitations imposed by capillary wave excitation techniques and the labor input associated with its practical implementation. In this paper we introduce a modified version of the capillary wave method which allows one to avoid the existing limitations and disadvantages. The distinguishing features of the proposed technique are as follows: acoustic wave generation and application of an interferometry technique for 3D surface profile reconstruction. A dynamic speaker with controlled vibration frequency and amplitude is used to produce acoustic vibrations. Application of a conventional Fizeau interferometer and the spatial phase shifting method makes it possible to perform surface form measurements with a high accuracy. For calculating wavelengths and the damping co-efficient, the surface profile is fitted with a decaying cylindrical wave equation. The accuracy of surface tension measurement by the modified capillary wave technique is 0.3 %. Owing to the non-contact way of wave generation and the small amounts of the examined fluid, the proposed method can be used in different studies.

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A nonlinear Schrödinger equation for gravity–capillary water waves on arbitrary depth with constant vorticity. Part 1

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.627 ◽

2018 ◽

Vol 854 ◽

pp. 146-163 ◽

Cited By ~ 7

Author(s):

H. C. Hsu ◽

C. Kharif ◽

M. Abid ◽

Y. Y. Chen

Keyword(s):

Surface Tension ◽

Growth Rate ◽

Gravity Waves ◽

Capillary Wave ◽

Modulational Instability ◽

Capillary Waves ◽

Rate Of Growth ◽

Positive Vorticity ◽

Constant Vorticity ◽

Wave Trains

A nonlinear Schrödinger equation for the envelope of two-dimensional gravity–capillary waves propagating at the free surface of a vertically sheared current of constant vorticity is derived. In this paper we extend to gravity–capillary wave trains the results of Thomas et al. (Phys. Fluids, 2012, 127102) and complete the stability analysis and stability diagram of Djordjevic & Redekopp (J. Fluid Mech., vol. 79, 1977, pp. 703–714) in the presence of vorticity. The vorticity effect on the modulational instability of weakly nonlinear gravity–capillary wave packets is investigated. It is shown that the vorticity modifies significantly the modulational instability of gravity–capillary wave trains, namely the growth rate and instability bandwidth. It is found that the rate of growth of modulational instability of short gravity waves influenced by surface tension behaves like pure gravity waves: (i) in infinite depth, the growth rate is reduced in the presence of positive vorticity and amplified in the presence of negative vorticity; (ii) in finite depth, it is reduced when the vorticity is positive and amplified and finally reduced when the vorticity is negative. The combined effect of vorticity and surface tension is to increase the rate of growth of modulational instability of short gravity waves influenced by surface tension, namely when the vorticity is negative. The rate of growth of modulational instability of capillary waves is amplified by negative vorticity and attenuated by positive vorticity. Stability diagrams are plotted and it is shown that they are significantly modified by the introduction of the vorticity.

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Particle trajectories in linear periodic capillary and capillary–gravity water waves

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2007.2005 ◽

2007 ◽

Vol 365 (1858) ◽

pp. 2241-2251 ◽

Cited By ~ 25

Author(s):

David Henry

Keyword(s):

Surface Tension ◽

Linear Theory ◽

Significant Role ◽

Water Waves ◽

Small Amplitude ◽

Capillary Wave ◽

Capillary Waves ◽

Particle Trajectories ◽

Particle Paths

Surface tension plays a significant role as a restoration force in the setting of small-amplitude waves, leading to pure capillary and gravity-capillary waves. We show that within the framework of linear theory, the particle paths in a periodic gravity–capillary or pure capillary wave propagating at the surface of water over a flat bed are not closed.

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Measurement of high frequency capillary waves on steep gravity waves

Journal of Fluid Mechanics ◽

10.1017/s0022112078001202 ◽

1978 ◽

Vol 86 (3) ◽

pp. 401-413 ◽

Cited By ~ 29

Author(s):

John H. Chang ◽

Richard N. Wagner ◽

Henry C. Yuen

Keyword(s):

Surface Tension ◽

High Resolution ◽

Gravity Wave ◽

Gravity Waves ◽

Deep Water ◽

High Frequency ◽

Qualitative Agreement ◽

Capillary Wave ◽

Capillary Waves ◽

Good Qualitative Agreement

The properties of high frequency capillary waves generated by steep gravity waves on deep water have been measured with a high resolution laser optical slope gauge. The results have been compared with the steady theory of Longuet-Higgins (1963). Good qualitative agreement is obtained. However, the quantitative predictions of the capillary wave slopes cannot be verified by the data because the theory requires knowledge of an idealized quantity - the crest curvature of the gravity wave in the absence of surface tension - which cannot be measured experimentally.

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A study on surface morphology and tension in laser powder bed fusion of Ti-6Al-4V

The International Journal of Advanced Manufacturing Technology ◽

10.1007/s00170-020-06221-w ◽

2020 ◽

Vol 111 (9-10) ◽

pp. 2891-2909

Author(s):

Mahyar Khorasani ◽

AmirHossein Ghasemi ◽

Umar Shafique Awan ◽

Elahe Hadavi ◽

Martin Leary ◽

...

Keyword(s):

Surface Tension ◽

Process Parameters ◽

Surface Profile ◽

Test Case ◽

Powder Bed Fusion ◽

Laser Powder Bed Fusion ◽

Data Set ◽

Powder Bed ◽

Case Morphology ◽

Melting Pool

Abstract When reporting surface quality, the roughest surface is a reference for the measurements. In LPBF due to recoil pressure and scan movement, asymmetric surface is shaped, and surface roughness has different values in different measurement orientations. In this research, the influence of the laser powder bed fusion (LPBF) process parameters on surface tension and roughness of Ti-6AI-4 V parts in three orientations are investigated. To improve the mechanical properties, heat treatment was carried out and added to the designed matrix to generate a comprehensive data set. Taguchi design of experiment was employed to print 25 samples with five process parameters and post-processing. The effect and interaction of the parameters on the formation of surface profile comprising tension, morphology and roughness in various directions have been analysed. The main contribution of this paper is developing a model to approximate the melting pool temperature and surface tension based on the process parameters. Other contributions are an analysis of process parameters to determine the formation and variation of surface tension and roughness and explain the governing mechanisms through rheological phenomena. Results showed that the main driving factors in the variation of surface tension and formation of the surface profile are thermophysical properties of the feedstock, rheology and the temperature of the melting pool. Also, the results showed that while the value of surface tension is the same for each test case, morphology and the value of roughness are different when analysing the surface in perpendicular, parallel and angled directions to laser movement.

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Asymptotic Analysis of Nonlinear Resonance Interaction of Capillary Waves of Arbitrary Symmetry on Moving Charged Jet at Multimode Initial Deformation

Elektronnaya Obrabotka Materialov ◽

10.52577/eom.2021.57.3.72 ◽

2021 ◽

Vol 57 (3) ◽

pp. 72-82

Author(s):

S. Shiryaeva ◽

Keyword(s):

Surface Tension ◽

Nonlinear Resonance ◽

Radial Electric Field ◽

Resonant Interaction ◽

Capillary Waves ◽

Initial Deformation ◽

Physical Parameters ◽

Dimensionless Amplitude ◽

Material Environment ◽

The Waves

The problem of research of a nonlinear resonance between capillary waves on a surface of the charged jet at multimode initial deformation moving regarding the material environment is considered. It is shown in analytical asymptotic calculations of the second order on the dimensionless amplitude of oscillations that on a surface of a jet an internal nonlinear resonant interaction of capillary waves of any symmetry, both degenerate and secondary combinational, takes place. Positions of resonances depend on physical parameters of the system: the values of the coefficient of a surface tension and of the radial electric field at a surface of a jet, the velocity of its movement regarding the material environment, the values of the wave and azimuthal numbers of the interacting waves, a range of the waves defining initial deformation.

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Local structure at a ferrofluid surface: chain-like aggregates revealed by non-specular X-ray reflection

Journal of Applied Crystallography ◽

10.1107/s0021889802023361 ◽

2003 ◽

Vol 36 (2) ◽

pp. 244-248 ◽

Cited By ~ 4

Author(s):

I. Takahashi ◽

N. Tanaka ◽

S. Doi

Keyword(s):

Surface Tension ◽

Fractal Dimension ◽

Local Structure ◽

Fine Particles ◽

Capillary Waves ◽

Aggregation Kinetics ◽

X Ray ◽

Surface Fluctuations ◽

Irreversible Aggregation ◽

A Chain

The surface structure of a ferrofluid was investigated by means of non-specular X-ray reflection. Strong intensity that is impossible to explain by surface fluctuations due to capillary waves was observed. It can be related to lateral correlation within aggregates of super-paramagnetic fine particles in the vicinity of the specimen surface. The fractal dimension of these surface-induced aggregates and the surface-tension coefficient of the ferrofluid were simultaneously determined. The fractal dimension was found to be around 1.1, indicating a chain-like character of the aggregates that have few branches. Strong and anisotropic interaction among the particles, as well as irreversible aggregation kinetics must be the origin of such a high-density and low-fractal-dimension system of dipolar 10 nm sized particles. The temperature variation of the fractal dimension indicated that the fractal aggregates stabilize themselves by losing their branches at increasing temperatures.

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Locally Perturbed Inaccessible Rough Surface Profile Reconstruction via Phaseless Scattered Field Data

IEEE Transactions on Geoscience and Remote Sensing ◽

10.1109/tgrs.2021.3105257 ◽

2021 ◽

pp. 1-8

Author(s):

Ahmet Sefer

Keyword(s):

Rough Surface ◽

Scattered Field ◽

Field Data ◽

Surface Profile ◽

Profile Reconstruction

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Wavelet Transforms in Fractal-Based Form Tolerancing

5th International Conference on Design Theory and Methodology ◽

10.1115/detc1993-0007 ◽

1993 ◽

Author(s):

R. S. Srinivasan ◽

Kristin L. Wood

Keyword(s):

Wavelet Transforms ◽

Design Research ◽

Profile Analysis ◽

Synthesis Method ◽

Surface Profile ◽

Synthesis Methods ◽

Geometric Tolerancing ◽

Analysis And Synthesis ◽

Cost Implications ◽

Profile Reconstruction

Abstract Tolerancing is a crucial problem for mechanical designers, as it has quality and cost implications on product design. Research in tolerancing has addressed specific areas of the problem. Building upon previous research, a unified approach for geometric tolerancing with fractal-based parameters has been recently proposed. This paper explores an alternative error profile analysis and synthesis method, based on wavelets, that maintains and extends the use of fractals for surface error abstraction. An overview of the theory of wavelets is provided, and the link between fractals and wavelets is established. Experimental data are used to illustrate the application of wavelet theory to surface profile reconstruction and synthesis. The synthesis methods are then implemented in the design of ball-bearing elements, demonstrating the utility of fractal-based tolerancing. Plans for further study and implementation conclude the paper.

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