Nonlinear wave processes in media containing cracks partially filled with a viscous liquid

A nonlinear (in the cubic approximation) relaxation equation of state is derived for a rod containing cracks partially filled with an incompressible viscous liquid. The nonlinear effects of the self-action and interaction of low-and high-frequency longitudinal elastic waves propagating in such a rod are studied for the cases of identical and size-varied cracks. Linear and nonlinear acoustic parameters characterizing the self-action and interaction of elastic waves in a cracked rod are determined.     

Nonlinear wave interactions in porous media filled with a quantum fluid

The problem of the nonlinear interaction between the fourth sound and an acoustic wave propagating in a porous medium filled with superfluid helium is solved. Based on the Landau equations of quantum fluid dynamics and on the Biot theory of mechanical waves in a porous medium, nonlinear wave equations are derived for studying the aforementioned interaction. An expression is obtained for the vertex that determines the excitation of an acoustic wave by two waves of the fourth sound. The possibility of an experimental observation of this process is estimated.     

Acoustic wave dispersion in a cylindrical elastic tube filled with a viscous liquid

This paper deals with the study of the velocity and the attenuation of an acoustic wave propagating inside a cylindrical elastic tube filled with a viscous liquid. A theory describing the propagation of the axisymmetrical modes in such waveguides is presented, with special attention given to the absorption produced by the viscous mechanisms in the liquid. One of these mechanisms is related to the momentum transfer between the compression and rarefaction regions of a propagating wave. The other viscous mechanism is due to the momentum transport inside the viscous boundary layer, close to the tube wall. Numerical calculations were carried out to investigate the influence of different parameters (frequency, tube radii, viscosity coefficient) on the propagation of acoustic waves.     

Acoustic nonlinearity of cracks partially filled with a viscous liquid: A quadratic approximation

A mechanism that accounts for the acoustic nonlinearity of cracks partially filled with a viscous liquid is proposed. The mechanism is related to the nonlinear dependences of the capillary and viscous pressures in liquid on the distance between the crack surfaces and on the rate of change of this distance. The nonlinear equation of state is obtained for this type of cracks, and the parameters of this equation are determined. It is shown that the presence of a viscous liquid can lead to a considerable increase in the acoustic nonlinearity of such cracks, as compared to the cracks filled with an ideal liquid.     

Nonlinear waves in a waveguide partially filled with a plasma

Nonlinear waves have been studied in a circular waveguide partially filled with a cold magnetized collisionless plasma. The solution obtained is periodical with the frequency increasing as a square root of the amplitude of the solution in the first approximation.The author is indebted to K.Jungwirth, R.Klíma and J.Preinhaelter for valuable discussions.     

Analysis of coaxial waveguide partially filled with chiral media

In this paper, the canonical problem of coaxial waveguide partially filled with chiral media is analyzed by a new equivalent transmission line network method. Both radial transmission lines in the cross section and multi-mode transmission lines in the longitudinal direction are introduced. The symmetrical properties of the structure are also discussed. Therefore, this method brings a clear physical picture into the wave propagation phenomena. Based on the analysis, the notable features and the role of the chirality parameter of the medium on the reflected and transmitted guided waves are discussed.     

NMR investigations of polymer dynamics in a partially filled porous matrix

The interior surface of well-defined porous alumina membranes (Anopore) of 20 nm and 200 nm pore diameter, respectively, was coated with polymer layers generated from solution by the solvent evaporation method. Deposits of poly(dimethyl siloxane) (PDMS) with nominal thicknesses ranging from 0.15 to 4.5 nm --corresponding to submonolayer to multilayer films--were investigated, and were compared to poly(butadiene) (PB) as an example for non-wetting polymers. Molecular weights below and above the critical value were studied since the bulk dynamics of such polymers are known to be qualitatively different. First results of NMR relaxation dispersion experiments on these systems are presented, supplemented by transverse relaxation times and double-quantum measurements obtained from high-field NMR. A systematic decrease of relaxation times at low fields with decreasing polymer amount is found for PDMS, but molecules retain a high degree of mobility irrespective of molecular weight. The relaxation dispersion results are supported by T2 data and 1H residual dipolar coupling (RDC) constants, and are discussed in terms of molecular order and reorientational dynamics.     

Nonlinear wave processes in a deformable solid as a hierarchically organized system

Theoretical predictions and experiments demonstrate that solid state mechanics should consider, along with a structurally equilibrium 3D crystalline subsystem, a structurally nonequilibrium planar subsystem as a complex of all surface layers and internal interfaces with broken translation invariance. Primary plastic flow of a loaded solid develops in its structurally nonequilibrium planar subsystem as channeled nonlinear waves of local structural transformations that determine the self-organization law of multiscale plastic flow. These waves initiate mesoscale rotational deformation modes, giving rise to all types of microscale strain-induced defects in the planar subsystem. The strain-induced defects are emitted into the crystalline subsystem as an inhibitor of nonlinear waves of plastic flow in the planar subsystem. Plastic deformation of solids, whatever the loading type, evolves in the field of rotational couple forces. Loss of hierarchical self-consistency by rotational deformation modes culminates in fracture of material as an uncompensated rotational deformation mode on the macroscale.     

Stability of steady rotation of a rotor partly filled with a viscous floating liquid

The problem of low-speed stability of steady rotation of a rotor with a cylindrical cavity partly filled with a viscous incompressible floating liquid is considered. The resultant force exerted by the liquid on the rotor performing small-radius circular precession is determined. The D-partition into regions with different degrees of instability of the plane of parameters of viscoelastic fixations of the rotor axis is constructed.     

Nonlinear development of capillary waves in a viscous liquid jet

The one-dimensional approximate equations describing the dynamics of a Newtonian viscous fluid are used to analyze the nonlinear development of capillary waves in a jet. It is shown that the size of satellite droplets resulting from a nonuniform jet breakup decreases with the Reynolds number at a constant wavenumber. The satellite-droplet formation ceases at a certain value of the Reynolds number, which depends on the wavenumber and initial perturbation amplitude.     

The heterogeneous distribution of the liquid phase in partially filled porous glasses and its effect on self-diffusion

The spatial distribution of the liquid phase in a typical, partially filled, porous glass (VitraPor #5) has been examined with the aid of magnetic resonance microscopy and field gradient nuclear magnetic resonance diffusometry techniques. The correlation length of the material turned out to be long enough to permit the visualization of the microscopic heterogeneity of the material by magnetic resonance imaging. Contrasts are dominated by transverse relaxation depending on local filling degree, which in turn depends on local microstructure. The bimodal heterogeneity of the latter was also visualized by scanning electron microscopy. The effect of heterogeneity on an effective diffusion coefficient has been examined for polar (water) and nonpolar (cyclohexane) molecules.     

Nonlinear waves in porous media saturated with live oil

A nonlinear equation is obtained for waves propagating in porous media of arbitrary consolidation (relative rigidity) saturated with live (i.e., air-bearing) oil. The equation describes the evolution of fast and slow Biot-Frenkel longitudinal acoustic waves propagating in both directions and allows one to analyze the reflected waves and their interaction. For a wave of the second kind, the diffusion coefficient is determined. The dependences of the dispersion and dissipation parameters on the rigidity of the oil pool structure and on the depth of the oil pool occurrence are analyzed.     

Methane hydrate crystal growth in a porous medium filled with methane-saturated liquid water

The nucleation, growth and ageing of methane hydrate crystals were observed visually in a porous medium filled with liquid water presaturated with methane. The pore space dimensions of the porous medium were 1.0?×?10²?µm. The pressure?temperature conditions at which hydrate formation was initiated corresponded to system subcoolings of 3.4?K, 6.7?K, 12.3?K and 14.1?K, respectively, where the system subcooling denotes the difference of the system temperature from the triple methane?hydrate?water equilibrium temperature under a given pressure. Faceted (skeletal) hydrate crystals grew and bridged the pore spaces without intervention of a liquid water layer when the subcoolings were equal or smaller than 6.7?K. The faceted crystals may form a physical bonding with the walls of the porous medium. At the higher subcoolings, the dispersive formation of dendritic crystals and subsequent morphological change into particulate crystals were observed. The bridging of the dendritic crystals is unlikely in the absence of a large amount of additional methane supply due to the dispersive spatial distribution of the dendritic crystals that have dimensions smaller than those of the pore spaces. As a result of the interpretation of the observed variation in the crystal morphology of the methane hydrate formed in liquid water, the dependence of the crystal morphology on the magnitude of the mass transfer of methane molecules in liquid water observed in the porous medium was consistent with that previously observed in a bulk methane–water system.     

Three-dimensional non-stationary processes in a vertically falling film of a viscous liquid

Three-dimensional wave processes in vertically falling films of viscous liquid are considered. The 3D localized perturbations, which are studied insufficiently, are of a particular interest. The numerical method for watching evolution of initial perturbations was developed. The final stage of this evolution is formation of the 3D localized structures: solitons. The boundaries of 3D soliton stability were determined.     

Acoustic nonlinearity of cracks partially filled with liquid: cubic approximation.

The theoretical investigation of mechanisms of the acoustic nonlinearity (elastic and inelastic) of cracks partially filled with an ideal and viscous liquid and associated with the nonlinear dependence of the capillary and viscous pressure in the liquid on the distance between the crack surfaces and the velocity of the change of this distance is proposed. The nonlinear (in cubic approximation) equations of the state of these cracks is obtained, and its parameters are defined. It is shown that the presence of the viscous liquid may lead to the considerable increase of the acoustic nonlinearity of such cracks in comparison with cracks filled with the ideal liquid.     

Nonlinear effects in photonic crystal fibers filled with nematic liquid crystals

We have investigated the nonlinear propagation of light in photonic crystal fibers filled with nematic liquid crystals. We analyzed a configuration with a periodic modulation of the refractive index corresponding to a matrix of waveguides. Matrices of coupled waveguides allow observing a variety of new phenomena both for low power light beam propagation and with an existence of nonlinear effects. The opportunity for the creation of solitary waves caused by the interplay between diffraction and nonlinear effects in these kinds of fibers is investigated. At low power the propagating light beam spreads as it couples to more and more waveguides. When the intensity is increased the light modifies the refractive index distribution, inducing a defect in the periodic structure. The creation of such a defect can lead to a situation in which the light becomes self-localized and its diffractive broadening is eliminated. Eventually, in the case of positive Kerr-type nonlinearity, a discrete soliton can be created. In the case of negative nonlinearity the refractive index decreases with the optical power and can lead to bandgap shifting. The incident beam, with a frequency initially within the bandgap, is then turned outside the bandgap resulting in the changing of the propagation effect for the discrete diffraction effect. As a consequence the delocalization of the light can be observed. Presented at 9-th International Workshop on Nonlinear Optics Application, NOA 2007, May 17–20, 2007, Świnoujscie, Poland