Connection between electrical conductivity and diffusion coefficient of a conductive porous material filled with electrolyte

The paper focuses on the cross-property connection between the effective electrical conductivity and the overall mass transfer coefficient of a two phase material. The two properties are expressed in terms of the tortuosity parameter which generalized to the case of a material with two conductive phases. Elimination of this parameter yields the cross-property connection. The theoretical derivation is verified by comparison with computer simulation

Normal and tangential compliances of interface of rough surfaces with contacts of elliptic shape

AbstractThe incremental compliances, normal and tangential, of an interface between rough surfaces are considered. Contacts are assumed to be elliptic – the shape of Hertzian contacts between any two locally smooth asperities. The ellipses may have diverse eccentricities and random or non-random orientation distribution; in the latter case, the tangential compliance is anisotropic. It is found that the Hertzian contacts and “welded” zones of the same geometry produce the same incremental compliances. Microstructural characteristics ξ of the interface that controls its incremental compliances is identified. For the circular contacts, ξ is the sum ∑Ak where Ak is kth contact area; in the more general case of elliptic contacts, each Ak enters in product with its shape factor dependent on the ellipse aspect ratio. The mentioned in-plane tangential anisotropy is relatively mild, even for parallel strongly elongated elliptic contacts. This is due to weakness of the anisotropy for a single elliptic contact (or external elliptic crack). Comparison of the latter to the internal crack of the same elliptic geometry shows that whereas the anisotropy is mild for both crack types, it is weaker for the external crack, in which case it is also less sensitive to Poisson’s ratio

Effect of spherical pores coalescence on the overall conductivity of a material

The problem about steady-state temperature distribution in a homogeneous isotropic medium containing a pore or an insulating inhomogeneity formed by two coalesced spheres of the same radius, under arbitrarily oriented uniform heat flux, is solved analytically. The limiting case of two touching spheres is analyzed separately. The solution is obtained in the form of converged integrals that can be calculated using Gauss-Laguerre quadrature rule. The temperature on the inhomogeneity’s surface is used to determine components of the resistivity contribution tensor for the insulating inhomogeneity of the mentioned shape. An interesting observation is that the extreme values of these components are achieved when the spheres are already slightly coalesce

Effective elastic properties of media containing coalescing holes

A recent study about the temperature and heat flux distributions around two nonconductive (separate or intersecting) circular holes in a plane system recently appeared in Literature [1]. These results have been used to construct the second-rank resistivity contribution tensor which allows assessing the effective thermal properties of a composite including circular inhomogeneities. Here, that study is extended to assess the overall elastic properties of an isotropic elastic matrix with two separate circular cavities or a cavity obtained by the union of two circles of generally different diameters (Figure 1). The problem is formulated in terms of stress functions expressed in Fourier series or Fourier transforms. Reference is made to bipolar cylindrical coordinates [2]. Once the displacement field u has been calculated, the extra strain due to the inhomogeneity is assessed according to (1), being n the normal vector and V the volume reference. Finally, the extra strain is used to assess the fourth-rank compliance contribution tensor varying the size of the circular arcs

Overall thermal conductivity of fibre reinforced materials

The overall thermal conductivity of composites involving cylindrical fibres of irregular shape is investigated in the present work. Isotropic and homogeneous thermal conductivity is assumed for both the matrix and fibre. The system consists of an infinite plate with an embedded fibre subjected to a remotely applied steady state heat flux q acting along a given direction. Once the alteration of the heat flux and temperature field T due to the presence of the inclusion is assessed, the homogeneized thermal properties of the composite material can be computed following the procedure reported in [1]. As an example, the dimensionless temperature distribution Tk/Rq and heat flow q/q in an infinite with a non-conductive circula fiber is sketched in Figure 1, being k the thermal conductivity of the matrix and R denotes the radius of the fiber. The study extends the results reported in [2] performed for non-conductive inclusions accounting for the real thermal conductivity of the fibres. The analysis allows assessing the effective thermal properties of a fibre reinforced material based on fibres with cross section formed by circular arcs, as polystyrene, polyacrylonitrile and sisal fibres

Thermal conductivity of solids with coalescing spherical pores

The overall thermal properties of media containing insulating cylindrical inhomogeneities has been addressed recently in [1] making reference to a 2D layout. There, the cross section of the fibers is formed by two intersecting circles to simulate a variety of nonconductive fibers (e.g. electrospinned polystyrene fibers). On the other hand, intersecting circles is a relevant layout to assess the physical properties of a variety of porous materials (e.g. Gasar metals) during the processes of pore coalescence and growth. In this work we extend the analysis addressed in [1] to a 3D framework by considering the effect of insulating inhomogeneities having the shape of intersecting spheres. The analysis aims at assessing the second-order resistivity contribution tensor, which provides the corrective temperature gradient induced by the volume V * of the inhomogeneity over the reference volume V of the background material subjected the a remotely applied heat flux q. Owing to the geometric setting, reference is made to toroidal coordinates and Mehler–Fock transforms are used to represents the perturbation temperature field due to the inhomogeneity [2]. As remarked in [3] for coalescing spheres having the same diameter, the components of tensor R display a non-monotonic trend varying the distance between their centers. In particular, unlike what is observed for spheroids, the stationary values of the components of tensor R occur when spherical pores are slightly intersecting

Effective thermal conductivity of oolitic rocks using the Maxwell homogenization method

International audienceThe present work focuses on effective thermal conductivity of oolitic lime-stones, characterized by an assemblage of porous grains (oolites), mesopores and solid grains. Two distinct scales of pores, micropores or intra oolitic pores and mesopores or inter oolitic pores are taken into account. At the first step, micropores are homogenized inside the oolites by using self consistent homogenization scheme. The second homogenization step describing transition from the mesoscale to the macroscale, is performed by using a recent reformulation of the Maxwell homogenization scheme (see [1]). At the mesoscale, porous oolitic inclusions are quasi spherical whereas two families of mesopores are considered according to analysis of photomicrographs: (1) randomly oriented oblate spheroidal pores and (2) concave pores. The proposed model is compared to a simplified one when all the pores are of ellipsoidal shape. The relevancy of the ellipsoidal approximation is then evaluated. In particular, the influence of the shape of the mesopores on the overall thermal conductivity is discussed. Comparisons between multi-scale model based on Maxwell homogenization method and experimental data show that effects of porosity and saturating fluids on overall conductivity are correctly predicted when concave pores are taken into account

Production of Miniature Glass Cells with Rubidium for Chip Scale Atomic Clock

AbstractThe main advantage of chip scale atomic clock (e.g., Knappe (2008)) (CSAC) over quartz-oscillators is the higher long-term stability. It is provided by non-aging resonance of unperturbed atoms. However it is not a simple task to suppress all possible perturbations. Hence, metrological properties of resonance depend on the way in which ensemble of atoms is localized in space and protected. The paper describes a technology of small all-glass Rb cells production. The sealing of cells is made with radiation of a СО2 lasers. The cells will be utilized in Rb CSAC based on the phenomenon of coherent population trapping (CPT). (Pat. No RU 2014101361