Creeping flow of a viscous fluid in a uniformly porous slit with porous medium: An application to the diseased renal tubules

In this paper, exact solutions for the creeping flow of Newtonian fluid through a porous slit with uniform reabsorption at the porous walls and a porous medium in between are presented. The momentum equation is converted into the form of stream function and is then solved exactly. The solutions for corresponding problem without porous filling in the channel are also deduced and they match exactly with those present in literature. Expressions for other useful physiological quantities like longitudinal and transverse velocities, pressure difference, mean pressure drop across the slit, volume flow rate, wall shear stress, fractional reabsorption and leakage flux are derived. The absorption velocity for renal tubule in a rat kidney is computed for the relevant fractional reabsorption of 80%. The data are then used to tabulate pressure differences corresponding to various values of medium porosity. The results are also presented graphically and it is shown that there is a possibility of reverse flow, usually farther along the length of the slit, when the values of initial flow rate are not high or when the values of absorption velocity are too high.     

Diffusion tensor imaging to study anisotropy in a particular porous system: the trabecular bone network

During the last decade, considerable effort has been invested into the development of diffusion tensor imaging (DTI) mainly used to investigate cerebral morphology. The aim of this paper is to review and to discuss our recent results about high magnetic field DTI application to study spongy bone tissue. Due to its peculiar properties, spongy bone represents a particular porous system sample. Strategies to perform DTI on porous systems and issues linked to DTI outcome interpretation are presented on the basis of our results concerning trabecular bone network characterization.     

流体-孔隙介质圆柱界面波传播特性

研究流体-孔隙介质圆柱界面波传播特性,分析孔隙介质孔隙率等参数对频散曲线的影响。理论上建立了无限大流体包裹孔隙介质圆柱界面波的模型,利用孔隙介质弹性波动理论,通过数值模拟计算得到流体-孔隙介质圆柱的频散曲线及时域波形,并分析了孔隙介质为开孔和闭孔状态下孔隙介质圆柱半径、孔隙率及渗透率对频散曲线的影响。结果表明,时域上斯通利波可以被明显区分开,孔隙介质圆柱半径的变化改变了圆柱尺度,孔隙率的变化改变了孔隙介质的纵、横波波速,因此对于斯通利波频散曲线的影响较大。而渗透率的变化既不改变圆柱的尺度也不改变孔隙层的纵、横波速度,因此对斯通利波频散曲线影响较小。     

Thermosolutal convection in a Maxwellian viscoelastic fluid in porous medium

The thermosolutal convection in a layer of Maxwellian viscoelastic fluid heated and soluted from below in porous medium is considered. The effects of uniform magnetic field and uniform rotation on the thermosolutal convection are also considered. For stationary convection, the Maxwellian viscoelastic fluid behaves like a Newtonian fluid. The sufficient conditions for the nonexistence of overstability are obtained. The critical Rayleigh number is found to increase with the increase in magnetic field, rotation and stable solute gradient.     

Scattering of gaussian beam by a ferrite cylinder

The scattering of a Gaussian beam by a ferrite cylinder is analyzed using two methods. The spatial pictures in the amplitude of the total Gaussian beam near the cylinder resulting from the two methods are both clarified and compared. The scattering by a ferrite cylinder coating a dielectric sleeve is also presented.     

Scattering of electromagnetic waves by a chiral cylinder

We consider the problem of three-dimensional diffraction of electromagnetic waves excited by an elementary source on a chiral infinite cylinder of arbitrary radius. Effective scattering cross sections of a chiral cylinder in the case of two-dimensional diffraction are numerically analyzed. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 10, pp. 872–883, October 2008.     

Scattering by a homogeneous anisotropic-coated conducting elliptic cylinder

A solution to the two-dimensional scattering properties of a conducting elliptic cylinder coated with a homogeneous anisotropic elliptical shell is obtained. The conducting elliptic cylinder and the shell have the same eccentricity. The transmitted and scattered fields of the anisotropic shell are expressed as Mathieu functions in elliptic coordinates. The unknown coefficients of the scattered and transmitted fields are solved with the aid of the boundary conditions and the Galerkin's method. Only the transverse magnetic (TM) polarization is presented and the transverse electric (TE) polarization can be obtained in the same way. Some numerical results are presented and discussed. As expected the result is in agreement with that available when the coated elliptic cylinder degenerates to a coated circular one.     

Critical fluctuations of a binary fluid mixture confined in a porous medium

We have performed small angle neutron scattering experiments on the binary fluid mixture n-C₆H₁₄+n-C₈F₁₈ imbibed inside porous Vycor glass in the thermodynamic region corresponding to the bulk critical one. The resulting structure can be represented as the sum of a temperature dependent Lorentzian term and a term describing the interference between the porous matrix, a shell part richer in one component coating the glass surface, and a core part richer in the other component. We observe critical fluctuations extending over distances markedly larger than the mean pore size. Received 20 May 1999     

Scattering of Lamb waves by a circular cylinder.

Following our previous attempt at the scattering from a cylinder in a slab to the incidence of a guided shear wave, we hereby discuss the scattering by an elastic cylinder embedded in an isotropic plate for a variety of bonding states to incidence of the fundamental Lamb wave modes S0 and A0 at the low-frequency regime. The plate is divided up into three regions by introducing two imaginary planes located symmetrically some distance from the cylinder and perpendicular to surfaces of the plate. The wave fields in various regions are expanded either into cylinder wave modes or into Lamb wave modes. A system of equations determining the coefficients of expansion is obtained according to the traction-free boundary conditions on the plate walls and the displacement and stress continuity conditions across the virtual planes. By taking an appropriate finite number of terms of the infinite expansion series and some selected points on the two properly chosen imaginary planes and the surfaces of the plate through convergence and precision tests, a matrix equation to numerically evaluate the expansion coefficients is found. Coefficients of the reflection and transmission versus the normalized radius of the cylinder in welded, slip, and cracked interfacial conditions are numerically computed. In the low-frequency range, the relative errors are found to be less than 1%. Contrast curves of the reflection coefficient for the cylinder of nearly all permissible size in perfect and imperfect interfacial bonding are shown and prominent differences are noted.     

Stability analysis of a Maxwell fluid in a porous medium heated from below

Based on a modified-Darcy–Brinkman–Maxwell model, stability analysis of a horizontal layer of Maxwell fluid in a porous medium heated from below is performed. By solving the eigenvalue problems, the critical Rayleigh number, wave number and frequency for overstability are determined. It is found that the critical Rayleigh number for overstability decreases as the relaxation time increases and the elasticity of a Maxwell fluid has a destabilizing effect on the fluid layer in porous media. On the other hand, the critical Rayleigh number for overstability increases by increasing the porous parameter which acts to stabilize the system. In limiting cases, some previous results for viscoelastic fluids in nonporous media are recovered from our results.     

R'2 measured in trabecular bone in vitro: relationship to trabecular separation.

Measurement of key parameters of the microstructure of trabecular bone is critical to the study of osteoporosis and bone strength. Density based methods cannot provide this information, and give only the total amount of bone present, and not its arrangement. Magnetic resonance imaging has shown the potential to provide information related to the microarchitecture of the trabecular bone matrix. Twelve samples (8 x 8 x 8 mm3 bone cubes) were cut from sheep vertebrae such that the trabeculae ran either parallel or perpendicular to each face. Detailed measurements of the structure of these bone cubes were made by histomorphometry, and compared to R'2 and R*2 measured with a spin and gradient-echo sequence, Partially Refocused Interleaved Multiple Echo, at 1.5 Tesla. The precision of the R'2 measurement (% coefficient of variation) was 8.7+/-5.1, and 7.7+/-4.3 for R*2. Uncorrected values of R'2 and R*2 were significantly correlated to density measured by quantitative computed tomography (r = 0.87, p = 0.0005, and r = 0.90, p = 0.0002, respectively), and trabecular bone area measured by histomorphometry (r = 0.80, p = 0.002, and r = 0.83, p = 0.0008, respectively). Density correction was effected by imaging the same slice of bone in two orientations (90 degrees and 0 degrees ) to the main magnetic field. For both R'2 and R*2 there was a significant difference between measurements in the 90 degrees and 0 degrees orientations (p < 0.01). The difference between the two values was used, and termed R'2net or R*2net. The net parameters were independent of bone mass. R'2net and R*2net were significantly correlated to trabecular separation (p < 0.05) with r = -0.58 and r = -0.62, respectively. These results demonstrate the ability of magnetic resonance imaging to characterize a key measure of the trabecular microstucture. An increase in trabecular separation has important biomechanical consequences in osteoporosis. This result also strengthens the hypothesis that the sensitivity of R'2 to osteoporosis-related bone changes is due to magnetic susceptibility effects in which rapid transitions between bone and marrow create local magnetic field inhomogeneities that result in an increase in R'2 values.     

Reflexion of a spherical wave by the plane interface between a perfect fluid and a porous medium

By using the Fourier transform of the system of equations and continuity conditions, it is easy to obtain the Fourier transform of the solution. This last function is decomposed into several terms which are identified as Fourier images of known functions. An exact representation of the scattered sound pressure field is obtained as a combination of the radiation of the image source and layer potentials. Approximations are given when the point spherical source is located on the interface.