The zonal linearization method for multidimensional mass transfer problems in porous media

A number of methods have been proposed in recent years for calculating the combined flows of immiscible and miscible liquids in strata to systems of boreholes. We propose a method which can naturally be called the zonal linearization method [1]. It is more compact than the usual finite-difference method and has high accuracy, in particular, in the neighborhood of a borehole, since it is closely similar to the method of characteristics. The method can be applied to both continuous and discontinuous flows and in principle makes it possible to investigate the formation and breakdown of discontinuities. As distinct from the method of characteristics, it is well suited to programming and implementation on a computer, and it also makes it possible to obtain an approximate analytic solution of the problem in many cases and to estimate the accuracy of the solution. The method is based on the zonal linearization of the equation for mass conservation in the total flow between chosen surfaces or contour lines (lines of equal saturation or concentration). Determination of the dynamics of the contour surfaces leads to a Cauchy problem for a system of integrodifferential equations involving partial derivatives. The zonal linearization method is a development of the scheme described in [2–4], and the method of solving the Cauchy problem is a generalization of the methods described in [4–13]. The essence of the method and its convergence are illustrated by means of two-dimensional problems in two-phase filtration.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 66–80, July–August, 1973.     

A method for calculating the two-dimensional temperature field of a reservoir with thermal injection

In [1–3] and other studies devoted to the determination of the temperature field of an oil reservoir when injecting into it a fluid with a temperature different from that of the initial reservoir temperature, the one-dimensional fluid flow (linear or radial) was considered in the case of an injection gallery or a single injection well in the reservoir. The problem was formulated in [4] with an arbitrary distribution of wells, but the solution was obtained only for the integral thermal-loss characteristic. To evaluate the coverage of the reservoir by the thermal effect, we must know the temperature distribution in the multi-well reservoir system at any instant of time. In this paper we propose a method for calculating the reservoir temperature field in the case of two-dimensional fluid flow using the simplifying assumptions which were used earlier by Lauwerier [1] and other authors to describe the thermal phenomena in a reservoir.     

Terahertz split-ring metamaterials as transducers for chemical sensors based on conducting polymers: a feasibility study with sensing of acidic and basic gases using polyaniline chemosensitive layer

We report on the first application of terahertz metamaterials acting as transducers for chemical sensors based on conducting polymers. In our feasibility study aimed at sensing of gaseous hydrochloric and ammonia, a two-dimensional sensor metamaterial consisting of an array of split-ring resonators on the surface of undoped silicon wafer was prepared. The surface of the resonator was coated with a 150-μm layer of polyaniline. Binding of hydrogen chloride to polyaniline leads to distinct changes in the resonance frequency of the metamaterial. Measurements can be performed both in the reflection and transmission mode. A numerical simulation of the response revealed an increase of both the real and the imaginary components of the dielectric function of the polyaniline film. These changes are attributed to the transition from emaraldine base to emeraldine salt. The results demonstrate a new approach for formation of highly sensitive transducers for chemical sensors.

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Kinetics of nickel electroplating from methanesulfonate electrolyte

The overpotential of nickel ion electroreduction on the nickel and mercury electrodes is shown to increase in the following sequence of anions: ClO₄⁻,CH₃SO₃⁻, SO₄²⁻. On the nickel electrode, the overpotential of nickel evolution decreases as the pH^v increases from 1.5 to 4. This is associated with the increase in pH^s as the result of a parallel reaction of hydrogen evolution. It is shown that in contrast to mercury, the Tafel plots of the nickel electrode demonstrate a bend corresponding to the change in their slope from −0.044 to −0.132 V. This is accompanied by the lowering down of the reaction order in nickel ions from 2 to 1. A mechanism of nickel ion electroreduction that includes two parallel routes is proposed and substantiated by a model. In the low overpotential range, the predominant process is the electroreduction of nickel hydroxocomplexes, which is characterized by the strong dependence of the reaction rate on the potential and the concentration of electroactive species. For high overpotentials, the predominant process is the direct discharge of nickel aquacomplexes the rate of which depends weaker on the potential and the concentration of electroactive species.     

Absolute Continuity of the Spectrum of a Periodic 3D Magnetic Schrödinger Operator with Singular Electric Potential

Mathematical Notes - We prove that the spectrum of a periodic 3D magnetic Schrödinger operator whose electric potential $$V=d\mu/dx$$ is the derivative of a measure is absolutely continuous...     

On Weyl almost periodic selections of multivalued maps

We prove that Weyl almost periodic multivalued maps R∋t→F(t)∈clU have Weyl almost periodic selections, where clU is the collection of non-empty closed sets of a complete metric space U.     

Fluorescence of semiconductor nanorods in liquid-crystal composites

The fluorescence of CdSe/ZnS nanorods in liquid-crystal and anisotropic polymer composites is studied. A high degree of the fluorescence anisotropy is shown. It is found that a solubilizer strongly affects the CdSe/ZnS orientation, which opens new possibilities for creating electrically controlled liquid-crystal composites.