Development of porous media theories — A brief historical review

For a complete understanding of the complex theories in continuum mechanics, e.g., porous media theories, an extensive investigation of their historical development is helpful. Indeed, it was first with activities in this field that fundamental effects in saturated porous solids, e.g., uplift, friction, capillarity, and the effect of effective stresses, could be clarified.The theory of porous media was pioneered by Reinhard Woltman in 1794 when he introduced the concept of volume fractions. Last century, important contributions were published by Adolf Fick, Henry Darcy, and Josef Stefan.In the twentieth century, the scientific discussion on porous media theories was started by Paul Fillunger in 1913 in a paper about the uplift problem in saturated rigid porous solids. In subsequent papers, he investigated the effects of friction and capillarity and discovered the effect of effective stresses. In 1923 Karl von Terzaghi, founder of modern soil mechanics, started his investigations on saturated deformable porous solids within the framework of the calculation of the permeability coefficient of clay. For the derivation of his famous differential equation, he formulated a linear constitutive relation between the increments of the porosity and the effective stresses. In 1936, Paul Fillunger founded the concept of the modern theory of liquid-saturated porous solids. However, his findings are almost completely forgotten.Today, two important directions of the porous media theory are commonly acknowledged. The first one is based on investigations by Maurice Biot, the second one proceeds from the mixture theory, extended by the concept of volume fractions.Currently on sabbatical leave at the University of California, Los Angeles (UCLA).     

Invariant Solutions of the Thermal-Diffusion Equations for a Binary Mixture in the Case of Plane Motion

The group properties of the thermal-diffusion equations for a binary mixture in plane flow are studied. Optimal systems of first-and second-order subalgebras are constructed for the admissible Lie operator algebra, which is infinite-dimensional. Examples of the exact invariant solutions are given, which are found by solving ordinary differential equations. Exact solutions are found that describe thermal diffusion in an inclined layer with a free boundary and in a vertical layer in the presence of longitudinal temperature and concentration gradients. The effect of the thermal-diffusion parameter on the flow regime is studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 95–108, January–February, 2006.     

An elastoplasticity model in porous media theories

In this article, porous media theories are referred to as mixture theories extended by the well-known concept of volume fractions. This approach implies the diverse field functions of both the porous solid matrix and the pore fluid to be represented by average functions of the macroscale.The present investigations are based on a binary model of incompressible constituents, solid skeleton, and pore liquid, where, in the constitutive range, use is made of the second-grade character of general heterogeneous media. Within the framework of geometrically finite theories, the paper offers a set of constitutive equations for the solid matrix, the viscous pore liquid and the different interactions between the constituents. The constitutive model applies to saturated as well as to empty solid materials, taking into account the physical nonlinearities based on elasto-plastic solid deformations. In particular, the constitutive model concentrates on granular materials like soil or concrete, where the elastic deformations are usually small and the plastic range is governed by kinematically hardening properties.     

两相混合流体的非线性本构理论

本文从连续介质力学的基本原理出发,建立了微极流体与经典流体两相流动的非线性扩散理论。给出了混合流体本构方程的一般形式。对单相流体、单相微极流体及稀悬浮体三种特殊情形,得到了具体形式的二阶非线性本构方程,并同已有的理论进行了比较。     

Description of a Flow of a Gas‐Condensate Mixture in an Axisymmetric Capillary Tube by the Density‐Functional Method

An isothermal flow of a twophase multicomponent mixture through a smalldiameter capillary tube is examined by the densityfunctional method. For low ratios of the characteristic radius of the capillary to its length, a general form of the dominating term in the asymptotic solution is found. An improved version of the law of mixture transfer is obtained. The form of possible corrections to the Darcy law for the filtration rates of the phases is discussed.     

Differential schemes for the elastic characterisation of dispersions of randomly oriented ellipsoids

The paper deals with the elastic characterisation of dispersions of randomly oriented ellipsoids: we start from the theory of strongly diluted mixtures and successively we generalise it with a differential scheme. The micro-mechanical averaging inside the composite material is carried out by means of explicit results which allows us to obtain closed-form expressions for the macroscopic or equivalent elastic moduli of the overall composite materials. This micromechanical technique has been explicitely developed for describing embeddings of randomly oriented not spherical objects. In particular, this study has been applied to characterise media with different shapes of the inclusions (spheres, cylinders and planar inhomogeneities) and for special media involved in the mixture definition (voids or rigid particles): an accurate analysis of all these cases has been studied yielding a set of relations describing several composite materials of great technological interest. The differential effective medium scheme (developed for generally shaped ellipsoids) extends such results to higher values of the volume fraction of the inhomogeneities embedded in the mixture. For instance, the analytical study of the differential scheme for porous materials (with ellipsoidal zero stiffness voids) reveals a universal behaviour of the effective Poisson ratio for high values of the porosity. This means that Poisson ratio at high porosity assumes characteristic values depending only on the shape of the inclusions and not on the elastic response of the matrix.     

Interaction of a shock wave with a two-phase interface

The acceleration by an incident shock of a planar interface between a gas and a particle-gas mixture has been investigated experimentally and numerically. The experiments were conducted in a newly developed vertical shock tube in which the planar interface of the particle-gas mixture was generated and its particle concentration history was measured. Polydisperse corn starch particles with a mean diameter of 10m were used. We recorded the motion of the interface, as well as of the incident and reflected shock by using a 4 channel spark shadowgraph. The experimental conditions were Mach numberM _s=5.15 and initial pressurep ₁=50kPa for various particle concentrations in nitrogen. The reflected shock appears with a delay after the incident shock enters the particle-gas mixture. Numerical methods were employed to solve the two-phase governing equations. Experiments and numerical solutions are in good agreement.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Liquid viscosity of low-GWP refrigerant mixtures (R32 + R1234yf) and (R125 + R1234yf)

In this work, the viscosity of R1234yf, (R32 + R1234yf), and (R125 + R1234yf) in one-phase liquid was measured. The combined expanded uncertainty of viscosity measurement apparatus of confidence of 0.95 (k = 2) is about 2.0%. The measurements of mixtures containing (30.0, 50.0, and 70.0) wt% R32 or R125 were carried out between T = (283.0 and 323.0) K (at intervals of T = 5 K) and P = (1.58 and 2.74) MPa, with a moving piston viscometer (VISCOpro 1600, accuracy ±1.0%) and a Coriolis flowmeter (Ultramass MKII, accuracy ±0.001 g/ml). The measured data were correlated with a hard-sphere (RSH) method and the Grunberg and Nissan method. The average absolute deviations are (2.2 and 3.3)% for the (R32 + R1234yf) and (R125 + R1234yf) mixtures by RSH method, (2.8 and 1.3)% for the (R32 + R1234yf) and (R125 + R1234yf) mixtures by Grunberg and Nissan method, while (3.5 and 2.4)% for the (R32 + R1234yf) and (R125 + R1234yf) mixtures by RefProp V9.1, respectively.     

Design of advanced multicomponent ferroelectric liquid crystalline mixtures with submicrometre helical pitch

New functional multicomponent ferroelectric liquid crystalline mixtures have been designed while searching smart self-assembling materials with submicrometre periodicity of the helical structure responding definite demands for application in electro-optic devices and photonics that exploit the deformed helix ferroelectric effect. The resulting designed mixtures possess the paraelectric smectic A* and the tilted ferroelectric smectic C* phases over a very broad temperature range down below the room temperature. The mesomorphic, electro-optic and dielectric properties have been studied and discussed. The presence of a very stable enantiotropic ferroelectric smectic phase exhibiting almost temperature independent helical pitch within 150–250 nm range and reasonably high values of the tilt angle might allow these mixtures to be applicable for practical purposes.     

Low-birefringence liquid crystal mixtures for photonic liquid crystal fibres application

ABSTRACT

Series of low-birefringence liquid crystal mixtures composed of alkyl alkylbicyclohexyl carbonates and modified mixtures with other compounds have been formulated, their refractive indices and electric permittivity measured upon temperature. They exhibit the ordinary refraction index n_o lower than the refractive index of silica glass in a different range of temperature. This enables to observe in photonic liquid crystal fibres (PLCFs) a change in the light propagation mechanism from photonic band gap guiding to modified total internal reflection at different temperatures. Selected applications of PLCFs are also discussed.