Propagation Of Progressive Waves Research Articles

Acoustofluidic separation of prolate and spherical micro-objects

Most microfluidic separation techniques rely largely on object size as a separation marker. The ability to separate micro-objects based on their shape is crucial in various biomedical and chemical assays. Here, we develop an on-demand, label-free acoustofluidic method to separate prolate ellipsoids from spherical microparticles based on traveling surface acoustic wave-induced acoustic radiation force and torque. The freely rotating non-spherical micro-objects were aligned under the progressive acoustic field by the counterrotating radiation torque, and the major axis of the prolate ellipsoids was parallel to the progressive wave propagation. The specific alignment of the ellipsoidal particles resulted in a reduction in the cross-sectional area perpendicular to the wave propagation. As a consequence, the acoustic backscattering decreased, resulting in a decreased magnitude of the radiation force. Through the variation in radiation force, which depended on the micro-object morphology enabled the acoustofluidic shape-based separation. We conducted numerical simulations for the wave scattering of spherical and prolate objects to elucidate the working mechanism underlying the proposed method. A series of experiments with polystyrene microspheres, prolate ellipsoids, and peanut-shaped microparticles were performed for validation. Through quantitative analysis of the separation efficiency, we confirmed the high purity and high recovery rate of the proposed acoustofluidic shape-based separation of micro-objects. As a bioparticle, we utilize Thalassiosira eccentrica to perform shape-based separation, as the species has a variety of potential applications in drug delivery, biosensing, nanofabrication, bioencapsulation and immunoisolation.

The mechanism of fluidization in mud beds under progressive waves

ABSTRACT Wave-flume laboratory experiments were conducted to study the mechanism of fluidization of partially consolidated mud beds, under wave propagation. The mixture of commercial kaolinite and tap water was allowed to partially consolidate under its self-weight before initiating the progressive wave propagation. The vertical changes in pore water pressure in the mud bed were monitored by using sensitive pore pressure transducers, at three levels across the mud layer depth. The experiments revealed that the wave characteristics and bed properties strongly affect the complex fluidization process, in which the accumulated pore water pressure develops through four transitional stages. The accumulated pore water pressure increases sharply at the first stage, which is followed by further gradual increases in the next two stages, with different rates. The breakup of aggregated mud particles, i.e. the generation of fluid mud, is observed at the last stage, resulting in a partial dissipation of accumulated pore pressure and wave height attenuation. The measurements also revealed that the fluidization starts from the top of the mud layer, and proceeds to the underlying layers.

Analysis of energy of internal waves in a three­layer semi­infinite hydrodynamic system

Energy characteristics of waves propagation along the contact surfaces in a hydrodynamics system "liquid half-space – layer –layer with a rigid lid" are explored. Based on the solutions of first approximation to a weakly non-linear model, the integral relations for wave motion energy in each layer and for the total energy of the system were obtained. An analysis of energy of wave processes revealed that an increase in wave number causes a decrease in energy of wave motion of the upper layers, and energy of wave motion of the lower half-space at some values of wave number reaches extreme values. In this case, total energy of the system is descending in nature and rather quickly approaches its limit value.The numerical values of energy for three different cases of propagation of progressive waves were obtained: only along the upper contact surface, only along the lower contact surface, along both surfaces simultaneously. Comparison of the obtained values of energy revealed that in the case of waves propagation along both contact surfaces simultaneously, the total energy of the system is close to the sum of energies of the system at waves propagation along one of the surfaces

Improvement of moving particle semi‐implicit method for simulation of progressive water waves

SummaryPrecise simulation of the propagation of surface water waves, especially when involving breaking wave, takes a significant place in computational fluid dynamics. Because of the strong nonlinear properties, the treatment of large surface deformation of free surface flow has always been a challenging work in the development of numerical models. In this paper, the moving particle semi‐implicit (MPS) method, an entirely Lagrangian method, is modified to simulate wave motion in a 2‐D numerical wave flume preferably. In terms of consecutive pressure distribution, a new and simple free surface detection criterion is proposed to enhance the free surface recognition in the MPS method. In addition, a revised gradient model is deduced to diminish the effect of nonuniform particle distribution and then to reduce the numerical wave attenuation occurring in the original MPS model. The applicability and stability of the improved MPS method are firstly demonstrated by the calculation of hydrostatic problem. It is revealed that these modifications are effective to suppress the pressure oscillation, weaken the local particle clustering, and boost the stability of numerical algorithm. It is then applied to investigate the propagation of progressive waves on a flat bed and the wave breaking on a mild slope. Comparisons with the analytical solutions and experimental results indicate that the improved MPS model can give better results about the profiles and heights of surface waves in contrast with the previous MPS models. Copyright © 2017 John Wiley & Sons, Ltd.

A note on the progressive wave solution of the perturbed Korteweg–deVries equation with variable dissipation

In this note, utilizing the method presented in Engelbrecht (1991) and Demiray (2002) we have studied the propagation of progressive waves in perturbed KdV equation with variable dissipation coefficient. The cases of constant and variable dissipation coefficient are studied separately and the results are compared with each other. It is seen that for both cases the amplitude and wave speed decrease with increasing time.

Lagrangian solution for irrotational progressive water waves propagating on a uniform current: Part 1. Fifth-order analysis

A three-dimensional (3D) Lagrangian solution up to the fifth-order is found for the Boundary Value Problem (BVP) of irrotational, progressive water waves propagating in the presence of uniform current in water of constant depth. The BVP is formulated in the Lagrangian framework which uses Lagrangian label (a,b,c) and time t as the independent variables. The (a,b,c) of a particle in wave motion are the coordinates of the particle position in the still water. In the solution, wave–current interaction is embedded in the Lagrangian velocity potential in such way that pressure is not affected by current in the wave–current field. In this study, we present motion properties of particles such as the particle motion period, drift velocity, the Lagrangian mean level, and the 3D particle trajectory and streakline, aspects that are hardly described by the Eulerian solution. It is found that the particle motion period is always larger than the progressive wave period. As the wave–current becomes steady motion, the stable wavy track of the particle motion may exist in the wave–current field. When currents vanish, the present solution deduces to the same solution of the progressive wave propagation by Chen et al. (2010).

On some properties of 2D spectral finite elements in problems of wave propagation

A computational analysis of plane progressive wave propagation in plane stress body is presented. The initial-boundary value problem of linear elastodynamics of Cauchy continuum is approximated spatially by specially designed multi-node C0 displacement-based isoparametric quadrilateral spectral finite elements. To integrate element matrices the Gauss–Lobatto–Legendre quadrature rule is used. The temporal discretization is carried out by Newmark type algorithm reformulated to accommodate the structure of local element matrices. The developed multi-node spectral elements with Gauss–Lobatto–Legendre nodes are validated by running some statics and dynamics tests to investigate the presence of locking effect and of spurious zero-energy modes. Dynamic tests, dedicated to wave propagation in L-shaped structure, are concentrated on energy propagation through right-hand angle of the construction.

Strong ellipticity and progressive waves in elastic materials with voids

In the present paper, we investigate a model for propagating progressive waves associated with the voids within the framework of a linear theory of porous media. Owing to the use of lighter materials in modern buildings and noise concerns in the environment, such models for progressive waves are of much interest to the building industry. The analysis of such waves is also of interest in acoustic microscopy where the identification of material defects is of paramount importance to the industry and medicine. Our analysis is based on the strong ellipticity of the poroelastic materials. We illustrate the model of progressive wave propagation for isotropic and transversely isotropic porous materials. We also study the propagation of harmonic plane waves in porous materials including the thermal effect.

Examples of the influence of the geometry on the propagation of progressive waves

In this paper, we give examples of the influence of the domain of propagation on progressive waves. More precisely, we numerically investigate the propagation of reaction diffusion waves in cylinders with variable radius. We show that, when the radius rapidly expands from a very small radius to a larger one, depending on the viscosity and the nonlinearity, the travelling wave may be blocked. The aim of this paper is to give numerical illustrations and quantifications of this effect, and to propose some conjectures which could be interesting subjects for further mathematical investigations. This work is linked to the study of spreading depression (SD), a propagative mechanism in brain and various tissues which has been observed in vivo and in vitro in many species since their discovery in 1944 by Leao. As a matter of fact, their direct observation in Man is still controversial. The complex structure of gray and white matter in humans may block the propagation of SD over large distances in brain and thus explain the difficulty of observing it. Medical consequences of the current numerical studies are detailed in [M.A. Dronne, et al., Influence of brain geometry on spreading depressions: A computationnal study, Progress in Biophysics and Molecular Biology 97 (1) (2008) 54–59] and a first mathematical approach given in [M.A. Dronne, E. Grenier, H. Gilquin, Modelization of spreading depressions following Nedergaard, preprint, 2003].

On the Propagation of Progressive Waves in Prestressed, Linearly Elastic, Transversely Isotropic, Kirchhoff Plate-Like Bodies

In the context of the linear elastic theory where Kirchhoff-Love’s hypotheses are treated as internal constraints, the linearized response mapping for prestressed Kirchhoff plate-like bodies is given. The case of a material having the maximum of symmetry is considered. The conditions of propagation for progressive elastic waves are discussed.

Wave–structure interaction using coupled structured–unstructured finite element meshes

The interaction of inviscid gravity waves with submerged fixed horizontal structures is modelled in two-dimensions using a finite element numerical wave tank. An adaptive hybrid coupled mesh is utilised that tracks the free surface through vertical movement of the free surface nodes in a Lagrange–Eulerian scheme. The hybrid mesh consists of a combination of structured and Voronoi unstructured meshes, with the submerged structure located in the Voronoi mesh region. Validation tests include free and forced sloshing in a rectangular tank, regular progressive wave propagation in a flume, and regular wave loading on a horizontal cylinder. The results are found to be in close agreement with analytical potential theory solutions for waves of small amplitude. Non-linear effects are noted for steeper waves. The wave-induced force components on the horizontal cylinder match the expected results from Ogilvie's [J Fluid Mech 16 (1963) 451] linear theory and Vada's [J Fluid Mech 174 (1987) 23] second order model. Wave interactions with a pair of submerged horizontal cylinders spaced at half the wavelength of undisturbed regular waves are examined.

Progressive Wave Propagation in the Meridian Plane of a 6 mm-Type Piezoelectric Crystal Subject to Initial Fields

The purpose of this paper is to derive the conditions of the propagation of progressive waves in the meridian plane of 6 mm-type piezoelectric crystal subject to mechanical and electrical initial fields. The author obtains the velocities of propagation as closed-form solutions and analyzes the polarization of the respective waves. The influence of the initial fields on the shape of slowness surfaces is shown.

The electrostrictive effect on wave propagation in isotropic solids subjected to initial fields

THE ELECTROSTRICTIVE EFFECT ON WAVE PROPAGATION IN ISOTROPIC SOLIDSSUBJECTED TO INITIAL FIELDSO. Simionescu-PanaitDepartment of Mechanics, Bucharest University, Str. Academiei 14, 70109 Bucharest 1, Romania.IntroductionIn the last years many authors have paid attention to the dynamics of electroelastic materials,which are subjected to initial mechanical and electric flelds (see [1-4], [7-10]). The basic equationsof piezoelectric bodies for inflnitesimal deformations and flelds superposed on the initial deforma-tions and electric flelds, were given by Eringen and Maugin in their monograph [4]. An alternatederivation of the equations of this type was obtained by Baesu et al. [1]. Using the equationsderived by Baesu et al. [1], we assume that the elastic dielectric is linear and homogeneous, theinitial homogeneous deformations are inflnitesimal, and that the initial applied electric fleld is ofsmall intensity. In this case the constitutive equations, describing the incremental behaviour ofthe material, are expressed by linear relations containing coe–cients which depend on the materialconstants and on the initial applied flelds.In the papers [7-9] we have obtained the conditions when the progressive waves can propagate inpiezoelectric crystals of 6-mm type. There, we derived the wave velocities and the polarizationdirections, as closed form solutions. Also, we deflned new coupling coe–cients, and we showedwhat in°uence have the initial flelds on the shape of slowness surfaces. We analyzed there, thecharacteristics of the obtained waves, and the physical limits of the approximations made.In this paper we study the electrostrictive efiect on the progressive wave propagation in an isotropicsolid subjected to initial mechanical and electric flelds. In this case, even the piezoelectric efiect is,obviously, absent, we flnd that the initial flelds in°uence signiflcantly the

Wave Propagation in Piezoelectric Crystals Subjected to Initial Deformations and Electric Fields

In the present paper, we study interactions between initial elastic deformations and electric fields in a piezoelectric crystal with respect to the propagation of progressive waves in such crystals. We assume the elastic dielectric to be linear and homogeneous, the initial homogeneous deformations are infinitesimal, and the initial applied electric field has small intensity. For a 6-mm-type crystal, we show that progressive waves can propagate along the symmetry axis, respectively in the plane normal to the symmetry axis.

The influence of initial fields on wave propagation in piezoelectric crystals

In the present paper we study the effects of initial deformations and electric fields on the behaviour of the electromechanical coupling coefficients and on the shape of the slowness curves, in the case of progressive wave propagation in 6mm-type piezoelectric crystals along the symmetry axis, resp. in the plane normal to the previous axis.

Axisymmetric propagation modes in a liquid-filled elastic waveguide

Using Del Grosso’s theoretical treatment [V. A. Del Grosso, ‘‘Errors in Ultrasonic Propagation Parameter Measurements. Part 4—Effect of Finite Thickness Solid Tubes Enclosing the Liquid Cylinder of Interest,’’ NRL Report 6852, Naval Research Laboratory, Washington, DC (1968)] as a foundation, axisymmetric modes of progressive wave propagation in a liquid-filled elastic waveguide are studied. The waveguide system consists of a liquid cylinder surrounded by a hollow cylinder of elastic solid of arbitrary thickness. Dispersion curves and particle displacement profiles for propagating modes are calculated for several liquid/solid combinations. Modal characteristics are compared to those in the extreme cases of the rigidly bound cylinder and the empty hollow elastic cylinder. It is also shown that certain liquid/solid combinations can produce a near-plane-wave mode propagating at the intrinsic sound speed of the liquid over a range of frequencies. Experimental measurements demonstrating modal properties are presented. [Work supported by ONR.]

An experimental investigation of active noise control in ducts

This study was directed to gaining an understanding of the physical mechanism of active noise suppression in ducts for both plane waves and higher order modes. Previous work has indicated large suppressions are attainable using active control concepts for plane progressive wave propagation. However, there is little evidence suggesting the mechanism of suppression. Furthermore, it was of interest to determine whether this concept could be applied to sound carried by higher order modes in ducts. This work utilized NASA Langley's Spinning Mode Synthesizer duct facility to provide the number of control points necessary for higher order mode propagation. Pressure measurement probes were installed between the noise source and control point to provide data to define the suppression mechanism. Results indicated that for all modes suppressions of 25 dB or greater were attainable over a broad frequency range. The mechanism of suppression appeared to be a pressure minimum being forced at the control plane which caused a near perfect reflection to occur, This was true for both primary and control sources, as little net acoustic energy was actually developed.

Axially symmetric wave motion of a viscous liquid in a linearly viscoelastic tube

The problem of the propagation of progressive waves in a tube made of a linearly viscoelastic material which encloses a viscous Newtonian liquid is examined. For numerical calculations, it is proposed that the behavior of the tube wall material be described by the Voigt model. Dispersion curves are constructed for this case.

Tide and surge propagation off-shore in the Dowsing region of the North Sea

A year of simultaneous current and water level measurements at the Inner Dowsing light tower, 16 km off the Lincolnshire coast, has been analysed to investigate the tidal and shallow-water tidal components and the non-tidal water movements. These data are used in conjunction with coastal and other off-shore observations to give a detailed description of the actual off-shore tide and surge propagation in this complex region. The results are compared with analyses of elevation data elsewhere along the British coast of the North Sea. The principal tidal constituents are obtained from analysis of the year of data and from separate monthly analyses: the variability of these monthly analyses gives estimates of the errors involved when analysing data where only a single month is available. The year of current meter observations is used to determine the amplitude and phase relationship between neighbouring tidal constituents which are not separable from shorter periods of data. These relationships are close to those in the elevations. For the M2 constituent there is an annual modulation which is coherent along the length of the British coast of the North Sea, and which is substantially larger than the modulation in the astronomical forces. Some insight into the behaviour of tides in the vicinity of the Wash is obtained by representing each constituent as the sum of a progressive and a standing wave. At the Inner Dowsing the influence of the Wash is apparent. Cotidal and coamplitude charts are plotted for the constituents O1, K1, N2, M2 and S2. Similar charts are plotted for the shallow-water tidal constituents M4, MS4 and M6. At the Inner Dowsing the sense of rotation of all the shallow-water current ellipses is clockwise and this is in the opposite sense to the ellipses for the astronomical tides which rotate anticlockwise. This is shown to be due to the non-rectilinear direction of the flood and ebb currents, a phenomenon which also explains the relatively greater importance of shallow-water tides in the currents than in the elevation. Non-tidal residuals at the Inner Dowsing are not markedly smaller than at coastal stations within the Wash. For low-frequency residuals the coherence between coastal and off-shore measurements is very high, but his coherence is reduced at higher frequencies. Long-period oscillations of water level are spread across the low frequency spectrum with peaks at periods of 40 and 70 hours. Wave propagation at non-tidal frequencies is from north to south, as for the tidal waves. At the tower there is a small but significant interaction between tides and surges. The statistical distribution of residual amplitudes is closely normal for the north-south component of current, but less so for the elevations and for the weaker east-west current component. Energy fluxes are in the direction of the progressive wave propagation from north to south. Of the total energy flux 87.5% is accounted for by the M2 constituent, and only 0.35% is due to long-period surges. There is no evidence of a phase adjustment between elevations and currents to accommodate the enhanced energy dissipation at Spring tides.

Space-harmonic analysis of periodically supported beams: response to convected random loading

The solution for the response of stiffened beams due to a spatial and temporal harmonic pressure has been obtained in the form of a particular series of space harmonics, evolved from considerations of progressive wave propagation. The superiority of this method over the classical normal mode approach is indicated. It is applied to obtain the r.m.s. curvature at a point on a periodically supported beam excited by a random acoustic plane wave or boundary layer pressure fluctuation. The results obtained with different numbers of terms in the series are compared with known closed-form solutions. When seven terms are included, results bear good agreement with the exact solution and as few as three terms yield a solution of acceptable accuracy.The method of space harmonics can be adapted to the case of orthogonally stiffened plates which are excited by pressure fields convected across the plates at oblique angles to the direction of stiffeners. The general method should be applicable to the estimation of response of orthogonally stiffened cylindrical structures.