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The evolution in developed countries has taken a role in global warming and natural disasters such as flash flood, El-Nino, earthquake and groundwater contamination. The underground storage tank leakage problems and spillage of hydrocarbon liquid leading to the contamination of non-aqueous phase liquids (NAPLs) into the groundwater could reduce the quality of groundwater. This chapter is intended to investigate the behaviour and the pattern of NAPL migrations in double-porosity soil under vibration and intact conditions. The experimental model is developed by using kaolin soil type S300 and toluene as NAPLs. The kaolin soil was mixed with 25% of moisture content to produce kaolin granules in the soil column and vibrate under 0.98 Hz of frequency within 60 seconds. As a result, both specimen liquids completely migrated to the bottom of soil column: sample 1 has higher permeability compared to sample 2. This is due to the fracture in double-porosity soil under vibration effect and loosened the soil structure in sample 1 compared to good intact soil sample 2 with stronger and compact soil structure. In conclusion, this study proves that the dangerous hydrocarbon NAPL migration in fractured double-porosity soil has very harmful effect on the environment and groundwater resources.

The purpose of this paper to construct the fundamental solution of partial differential equations in the generalized theory of thermoelastic diffusion materials with double porosity.

The paper deals with the study of pseudo oscillations in the generalized theory of thermoelastic diffusion materials with double porosity.

The paper finds the fundamental solution of partial differential equations in terms of elementary functions.

Assuming the displacement vector, volume fraction fields, temperature change and chemical potential functions in terms of oscillation frequency in the governing equations, pseudo oscillations have been studied and finally the fundamental solution of partial differential equations in case of pseudo oscillations in terms of elementary functions has been constructed.

The purpose of this paper is to study the reflection of plane waves in thermoelastic medium with double porosity structure.

A two-dimensional model is considered of an isotropic thermoelastic half-space with double porosity. Thermoelasticity with one relaxation time given by Lord and Shulman (1967) has been used to study the problem. It is found that there exists four coupled longitudinal waves, namely, longitudinal wave (P), longitudinal thermal wave (T), longitudinal volume fractional wave corresponding to pores (PVI) and longitudinal volume fractional wave corresponding to fissures (PVII), in addition to an uncoupled transverse wave (SV).

The formulae for amplitude ratios of various reflected waves are obtained in closed form. It is found that these amplitude ratios are functions of angle of incidence. Effect of porosity and thermal relaxation time is shown graphically on the amplitude ratios with angle of incidence for a particular model.

Reflection of plane waves is of great practical importance. There are many organic and inorganic deposits beneath the earth surface. Wave propagation is the simplest and most economical technique to detect these. The model discussed in the present paper can provide useful information for experimental researchers working in the field of geophysics and earthquake engineering, along with seismologist working in the field of mining tremors and drilling into the crust of the earth.

The impact of climate change towards water surface resources is crucial, particularly in developing and non-developing countries. Groundwater as a main water resource is thus an essential. However, contamination due to hydrocarbon spills affects the groundwater as a water resource, especially as a main source of drinking water. This chapter investigates the light non-aqueous phase liquid (LNAPL) penetrations in double-porosity soil with different moisture contents and with or without vibration impact. It also explains the LNAPL penetration phenomena by employing image analysis. The physical laboratory experiments were implemented using an acrylic cylinder, a mirror, toluene and a Nikon D90 DSLR digital camera. Prepared soil was poured in an acrylic cylinder and compressed with compressor until it became 10 cm in height. LNAPL was then poured instantaneously onto the acrylic cylinder that was filled with soil sample. The LNAPL penetration patterns were recorded and monitored using a Nikon D90 DSLR digital camera. The processing technique was conducted at predetermined time intervals using Surfer software and Matlab routine to plot the LNAPL pattern. The results showed that a higher penetration rate of LNAPL occurred with higher moisture content and without vibration impact. The penetration time for LNAPL to reach the bottom of the soil sample was found to be longer for the soil that had low moisture content and with vibration impact.

The purpose of this study is to investigate the reflection of plane waves in a double-porosity (DP) thermoelastic medium.

To derive the theoretical formulas for elastic wave propagation velocities through the potential decomposition of wave-governing equations. The boundary conditions have been designed to incorporate the unique characteristics of the surface pores, whether they are open or sealed. This approach provides a more accurate and realistic mathematical interpretation of the situation that would be encountered in the field. The reflection coefficients are obtained through a linear system of equations, which is solved using the Gauss elimination method.

The solutions obtained from the governing equations reveal the presence of five inhomogeneous plane waves, consisting of four coupled longitudinal waves and a single transverse wave. The energy ratios of reflected waves are determined for both open and sealed pores on the stress-free, the thermally insulated surface of DP thermoelastic medium. In addition, the energy ratios are compared for the cases of a DP medium and a DP thermoelastic medium.

A numerical example is considered to investigate the effect of fluid type in inclusions, temperature and inhomogeneity on phase velocities and attenuation coefficients as a function of frequency. Finally, a sensitivity analysis is performed graphically to observe the effect of the various parameters on propagation characteristics, such as propagation/attenuation directions, phase shifts and energy ratios as a function of incident direction in double-porosity thermoelasticity medium.

The purpose of this study is to analyze the thermo-diffusion process in a semi-infinite nonlocal fiber-reinforced double porous thermoelastic diffusive material with voids (FRDPTDMWV) in light of the fractional-order Lord–Shulman thermo-elasto-diffusion (LSTED) model. By virtue of Eringen’s nonlocal elasticity theory, the governing equations for the considered material are developed. The free surface of the substrate is governed by the inclined mechanical load and thermal and chemical shocks.

With the aid of the normal mode technique, the solutions of the nondimensional coupled governing equations have been obtained.

The expressions of field variables are obtained analytically. By using MATHEMATICA software, various graphical implementations are presented to describe the impacts of angle of inclination, fractional-order and nonlocality parameters. The present model is also validated on the basis of some comparative studies with some preestablished cases.

As observed from the literature survey, many different studies have been carried out by taking into account the deformation analysis in nonlocal double porous thermoelastic material structures and thermo-mechanical interaction in fiber-reinforced medium under fractional-order thermoelasticity theories. However, to the best of the authors’ knowledge, no research emphasizing the thermo-elasto-diffusive interactions in a nonlocal FRDPTDMWV has been carried out. Moreover, the effect of fractional-order LSTED theory on fiber-reinforced thermoelastic diffusive half-space with double porosity has not been illuminated till now, which significantly defines the novelty of the conducted research.

This paper aims to study photothermal excitation process in an initially stressed semi-infinite double porous thermoelastic semiconductor with voids subjected to Eringen’s nonlocal elasticity theory under the fractional order triple-phase-lag thermoelasticity theory. The considered substrate is governed by the mechanical and thermal loads at the free surface.

The normal mode technique is used to carry out the investigation of photothermal transportation. By virtue of the MATHEMATICA software, each distribution is exhibited graphically.

The expressions of the displacements, temperature, volume fractions of both kinds of voids, carrier density and stresses are determined analytically. With the help of the numerical data for silicon (Si) material, graphical implementations are presented on the basis of initial stress, fractional order, nonlocality and thermoelectric coupling parameters.

The present study fabricates the association of Eringen’s nonlocal theory and the stress analysis in a semiconducting double porous thermoelastic material with voids, which significantly implies the originality of the conducted work.

For this purpose, a linear stability analysis based on the Navier–Stokes and Maxwell equations is made leading to an eigenvalue differential equation of the modified Orr–Sommerfeld type which is solved numerically by the spectral collocation method based on Chebyshev polynomials. Unlike previous studies, blood is considered as a non-Newtonian fluid. The effects of various parameters such as volume fraction of nanoparticles, Casson parameter, Darcy number, Hartmann number on flow stability were examined and presented. This paper aims to investigate a linear stability analysis of non-Newtonian blood flow with magnetic nanoparticles with an application to controlled drug delivery.

Targeted delivery of therapeutic agents such as stem cells and drugs using magnetic nanoparticles with the help of external magnetic fields is an emerging treatment modality for many diseases. To this end, controlling the movement of nanoparticles in the human body is of great importance. This study investigates controlled drug delivery by using magnetic nanoparticles in a porous artery under the influence of a magnetic field.

It was found the following: the Casson parameter affects the stability of the flow by amplifying the amplitude of the disturbance which reflects its destabilizing effect. It emerges from this study that the taking into account of the non-Newtonian character is essential in the modeling of such a system, and that the results can be very different from those obtained by supposing that the blood is a Newtonian fluid. The presence of iron oxide nanoparticles in the blood increases the inertia of the fluid, which dampens the disturbances. The Strouhal number has a stabilizing effect on the flow which makes it possible to say that the oscillating circulation mechanisms dampen the disturbances. The Darcy number affects the stability of the flow and has a stabilizing effect, which makes it possible to increase the contact surface between the nanoparticles and the fluid allowing very high heat transfer rates to be obtained. It also emerges from this study that the presence of the porosity prevents the sedimentation of the nanoparticles. By studying the effect of the magnetic field on the stability of the flow, it is observed that the Hartmann number keeps the flow completely stable. This allows saying that the magnetic field makes the dissipations very important because the kinetic energy of the electrically conductive ferrofluid is absorbed by the Lorentz force.

The originality of this paper resides on the application of the linear stability analysis for controlled drug delivery.

The mechanical response of the skeleton of a porous medium is highly dependent on its seepage behaviour as pore pressure modifications affect the in situ stress field. The purpose of this paper is to describe how u‐p formulation is employed using an explicit time integration scheme where fully saturated and single‐phase partially saturated analyse are incorporated for 2D and 3D cases.

Owing to their inherent simplicity, low‐order elements provide an excellent framework in which contact conditions coupled with crack propagation can be dealt with in an effective manner. For linear elements this implies single point integration which, however, can result in spurious zero‐energy modes which necessitates introduction of a stabilization technique to provide reliable results.

The success of the modelling strategy ultimately depends on the inter‐dependence of different phenomena. The linking between the displacements components, network and pore pressures represents an important role in the efficiency of the overall coupling procedure. Therefore, a master‐slave technique is proposed to link seepage and network fields, proving to be particularly attractive from a computational cost point of view. Another development that has provided substantial savings in CPU times is the use of an explicit‐explicit subcycling scheme.

Significant reduction in computational cost is achievable using a master‐slave procedure to link seepage and fracture network‐flows and an explicit‐explicit subcycling scheme. Special attention is focused on the investigation of the influence of plastic zones in oil production problems.