Body Waves in Composite Solid Matrix Containing Two Immiscible Fluids

This paper establishes the concept of elastic wave propagation in a multi-porous medium with different permeabilities by assuming there are n distinct pore fluid phases. The dynamic equation of motion of elastic wave propagation through this multi-porous medium is derived based on Lagrangian mechanics. In this regard, the generalized form of mass coefficients and then the energy loss due to the fluid phases in terms of dissipation coefficients are presented for low-frequency limits with the help of Darcy’s Law of multi-phases system. The elastic coefficients of the constitutive equation in terms of compliance matrix are identified using a series of Gedanken experiments. Some significant results regarding the compressional and rotational waves in a multi-porosity medium are derived. The validation of the theory has been shown by comparing it with the existing theory of single and double porosity. It is observed that there are ( n + 1 ) compressional waves corresponding to solid and fluid phases, whereas only one rotational wave is associated with the solid phase. The concept of multi-porosity theory can contribute to a deeper understanding of wave behaviour in a porous medium.

Monte Carlo computer simulations have been used to study the solid and fluid phase properties as well as phase equilibrium in a flexible, united atom, hard sphere chain model of n-heptane/n-octane mixtures. We describe a methodology for calculating the chemical potentials for the components in the mixture based on a technique used previously for atomic mixtures. The mixture was found to conform accurately to ideal solution behavior in the fluid phase. However, much greater nonidealities were seen in the solid phase. Phase equilibrium calculations indicate a phase diagram with solid–fluid phase equilibrium and a eutectic point. The components are only miscible in the solid phase for dilute solutions of the shorter chains in the longer chains.

Purpose – The purpose of this paper is to analyze two different approaches (Models A and B) for an adiabatic boundary condition at the wall of a channel filled with a porous medium. The analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are derived and compared with numerical solutions. The phenomenon of heat flux bifurcation for Model A is demonstrated. The effects of pertinent parameter C on the applicability of the Models A and B are discussed. Analytical solutions for the overall Nusselt number and the heat flux distribution at the channel wall are derived and the influence of pertinent parameters Da and k on the overall Nusselt number and the heat flux distribution is discussed. Design/methodology/approach – Two approaches (Models A and B) for an adiabatic boundary condition in porous media under local thermal non-equilibrium (LTNE) conditions are analyzed in this work. The analysis is applied to a microchannel which is modeled as a porous medium. Findings – The phenomenon of heat flux bifurcation at the wall for Model A is demonstrated. The effect of pertinent parameter C on the applicability of each model is discussed. Model A is applicable when C is relatively large and Model B is applicable when C is small. The heat flux distribution is obtained and the influence of Da and k is discussed. For Model A, ϕAfin increases and ϕAsub, ϕAcover decrease as Da decreases and k is held constant, ϕAsub increases and ϕAfin, ϕAcover decrease as k increases while Da is held constant; for Model B, ϕBfin increases and ϕBsub decreases either as Da decreases or k decreases. The overall Nusselt number is also obtained and the effect of Da and k is discussed: Nu increases as either Da or k decrease for both models. The overall Nusselt number for Model A is larger than that for Model B when Da is large, the overall Nusselt numbers for Models A and B are equivalent when Da is small. Research limitations/implications – Proper representation of the energy equation and the boundary conditions for heat transfer in porous media is very important. There are two different models for representing energy transfer in porous media: local thermal equilibrium (LTE) and LTNE. Although LTE model is more convenient to use, the LTE assumption is not valid when a substantial temperature difference exists between the solid and fluid phases. Practical implications – Fluid flow and convective heat transfer in porous media have many important applications such as thermal energy storage, nuclear waste repository, electronic cooling, geothermal energy extraction, petroleum processing and heat transfer enhancement. Social implications – This work has important fundamental implications. Originality/value – In this work the microchannel is modeled as an equivalent porous medium. The analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are obtained and compared with numerical solutions. The first type of heat flux bifurcation phenomenon, which indicates that the direction of the temperature gradient for the fluid and solid phases is different at the channel wall, occurs when Model A is utilized. The effect of pertinent parameter C on the applicability of the models is also discussed. The analytical solutions for the overall Nusselt number and the heat flux distribution at the channel wall are derived, and the effects of pertinent parameters Da and k on the overall Nusselt number and the heat flux distribution are discussed.

Analytical characterization and conceptual assessment of solid and fluid temperature differentials in porous media

This paper concentrates on an investigation of the temperature difference between the fluid and solid phases during heating of a porous slab initially at a low temperature by a flow of a higher temperature incompressible fluid for the case of a random heat transfer coefficient between the fluid and solid phases. A two energy equation model is employed to simulate the temperature difference between the solid and fluid phases. It is shown that the temperature difference forms a wave localized in space. The stochastic response of the temperature difference wave is presented in terms of the mean value and the standard deviation. In numerical examples, the probability density functions of both the uniform and truncated normal distributions are considered to simulate the random behavior of the heat transfer coefficient.

The research problem aims to investigate the effect of heat and moisture on the propagation of plane waves in a micropolar hygro-thermoelastic medium. The governing equations of a hygro-thermoelastic micropolar medium are developed and solved to determine the velocity equation. The plane-wave solution reveals that the medium is propagated by two coupled transverse displacement waves, namely Coupled Transverse Micropolar wave (CTM-wave) and Coupled Transverse Displacement wave (CTD-wave). Additionally, three coupled longitudinal waves are observed: thermal diffusion TD-wave, longitudinal displacement P-wave, and moisture diffusion mD-wave. To assess the characteristics of these waves in the micropolar hygrothermal medium, the speed and distance of propagation are calculated for each wave type. This analysis provides information on how fast and how far the P-wave, TD-wave, mD-wave, CTM-wave, and CTD-wave can travel in the medium. Furthermore, the research problem determines the equations for the coefficient of reflection and energy ratio when a coupled plane wave is incident on the medium. These coefficients quantify the amount of reflected energy compared to the incident energy and provide insights into the wave behavior at the interface of the medium. Finally, the variations in energy ratio and reflection coefficient are depicted graphically, allowing for a visual representation of how these quantities change with different parameters or conditions. These graphs provide a comprehensive understanding of the wave behavior and the effects of heat and moisture on the propagation characteristics in the micropolar hygrothermal medium.

Temperature-composition phase diagrams of binary lipid mixtures under conditions of constant pressure and excess water show that component immiscibility is the rule rather than the exception in these systems. Phase immiscibility is particularly noted in the solid phase but several cases are known where immiscibility is apparent even in the fluid phase. Using the fluorescence recovery are photobleaching (FRAP) technique, we have examined the long-range translational diffusion (over several micrometers) of fluorescent lipid derivatives, soluble only in the fluid phase, in bilayers under conditions of temperature and composition where solid and fluid phases are co-existent. These experiments provide information regarding barriers to free diffusion of the reporter molecules in these systems. The barriers are solid phase domains that are impenetrable to the reporter molecules, and may either exist as a discontinuous (non-percolating) archipelago of solid phase 'islands' in as continuous (percolating) fluid phase 'sea', or as continuous (percolating) solid phase domain cluster with non-connected (non-percolating) 'lakes' of the fluid phase domains. The transition from one state to the other is the so-called 'percolation threshold'. In FRAP experiments the former case is manifested as a reduction of the measured long-range diffusion coefficient (increased recovery time) with complete fluorescence recovery, whereas in the latter case both the apparent recovery times and the percent recoveries are altered. The position of the percolation threshold as a function of temperature and composition within the phase diagram permits a reasonably exact estimation of the mass fractions of the two phases in the system at this threshold and, with certain assumptions, an estimation of solid phase domain symmetry.(ABSTRACT TRUNCATED AT 250 WORDS)

The propagation of acceleration waves in a fluid-saturated porous medium is considered. The two-phase medium is the system consisting of a porous elastic solid skeleton, filled with a viscous compressible fluid. Two types of the media are taken into account: the medium composed of definite conductors and the medium composed of non-conductors. The method of singular surfaces has been used in these considerations. The acceleration waves in the medium consisting of non-conductors are not homentropic, in general. In this paper the conditions are determined which must be fulfilled to satisfy the acceleration waves to be homentropic. The propagation conditions of the waves are formulated and analysed. As usual in such a two-phase medium two longitudinal waves and one transverse wave are propagated. The growth equations of homothermal and homentropic waves are derived, and their solutions are analysed.

Purpose. Propagation of a shear wave in sandy marine sediments is considered. The acoustic properties of a shear wave are the phase velocity and the attenuation coefficient. It is known that in dry sandy sediments, the attenuation coefficient is directly proportional to frequency. In the saturated mediums, there are the deviations from this law that implies existence of two physical mechanisms of losses – the intergranular friction and viscous loss. The study is aimed at developing a two-phase theoretical model of the shear wave propagation in the unconsolidated marine sediments, and at identifying the dissipative effects caused by the fluid relative movement in the pore space. Methods and Results. The intergranular friction is modeled using a springpot, which represents an element combing conservative properties of a spring and dissipative ones of a dashpot. The equation of motion is applied, where a part of fluid is assumed to be associated with the media solid phase and another part is considered to be mobile. For a harmonic displacement, the equations of state and the equation of motion yield a new two-phase dispersion relation (the theory of Grain Shearing + Effective Density, or GS + EDs, for short). The results of the GS + EDs theory are compared with the data of the velocity and attenuation measurements taken from the open sources. It is shown that during propagation of the compressional and shear waves, the mechanisms of interaction between the granules, and between the granules and fluid are not similar. Character of the changes in the grain-to-grain friction parameters when the pore space is saturated with fluid, is analyzed. Conclusions. Manifestation of the dissipative effects resulting from the pore saturation with fluid depends on the density of the granules packing. In case of a dense packing, there are no conditions for the fluid relative movement, and the sandy sediments exhibit the property of constant Q-factor. If the packing is loose, the viscous losses make a significant contribution, and the attenuation frequency dependence is nonlinear. The effective pore sizes for the compression and shear waves do not coincide.

The numerical assessment of volume averaging method in heat transfer modeling of tissue-like porous media

In the frame of the spinor formalism of the electromagnetic field, the propagation of a plane wave in a random medium with a view to obtaining the moments of the energy density is considered. Using two different approximations to the solution of the spinor wave equation, it is shown that the energy conservation requires, on the statistics of the refractive index, some extra conditions difficult (eventually impossible) to satisfy. For the variance of the light intensity, a result valid for weakly scattering media is given. It is concluded that ‘‘dishonest’’ methods (in Keller’s terminology) have to be used.

Influence of fluid flow and heat transfer on crack propagation in SOFC multi-layered like material with anisotropic porous layers

Bio-heat diffusion under local thermal non-equilibrium conditions using dual-phase lag-based Green’s functions

A thermal non-equilibrium model with Cattaneo effect for convection in a Brinkman porous layer

A systematic perturbation approach to elastic-wave processes in a weakly anisotropic medium is discussed. As a simple practical example, the propagation of plane waves in a homogeneous medium is considered in detail. The limitations of perturbation theory are described. The second-order corrections for velocity and polarization are found in the case of general weak anisotropy. The particular case of transverse isotropy is considered.