Nonisothermal viscoplastic fluid flow through porous media

The Alishaev model [1] is extended to the case of nonisothermal flow. Neglecting conductive heat transfer, it is shown that for the model in question in the plane of the complex potential not only are the problems linear but the decoupling of the thermal and hydrodynamic problems is also allowed. The latter is reduced to a mixed problem for an analytic function. This makes it possible to use the wellknown methods and results of the theory of limiting equilibrium pillars for isothermal flow [2–5]. It is also established that the solutions of the unsteady problems tend asymptotically to the solutions of the corresponding steady-state problems and can be obtained from the latter by simpler conversion. The effectiveness of the approach proposed is illustrated with reference to the problem of a source-sink system [1–4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 117–122, July–August, 1990.     

Problems of nonlinear flow through porous media in regions with curved boundaries

The investigation of two-dimensional problems of nonlinear flow through porous media in regions with given curved boundaries involves considerable mathematical difficulties due to the fact that neither the hodograph transformation nor transition to the plane of the complex potential leads to a simplification of the problem. Attention is drawn to a transformation which in the case of circular boundaries maps the flow region onto a canonical domain (half-plane), while the transformed system, which remains, in general, nonlinear, has a much simpler structure than the initial system. For a previously introduced model of the resistance law it is shown that it is possible to construct exact solutions of the problem of an eccentric well within a circular supply contour and the problem of a circular group of wells in an annular (circular) reservoir. The dependence of the dimensionless flow rate on the eccentricity is found and the boundaries of the stagnant zones are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 103–108, January–February, 1989.     

The effect of temperature and pressure on the optical absorption edge in Cu6PS5X (X=Cl,Br,I) crystals

The absorption edge of monocrystalline Cu₆PS₅X (X=Cl,Br,I) superionic ferroelastics was studied in the 77–303 K temperature range and the mechanisms of exciton–phonon interactions resulting in exponential absorption edges and Urbach tails were analysed. Various types of disordering, affecting the optical absorption tails, were studied. The investigation of the influence of hydrostatic pressure (up to 400 MPa) on optical transitions of Cu₆PS₅X at 295 K revealed that the increase of pressure causes an increase of the optical pseudogap as well as the increase of the slope of the absorption edge indicating pronounced ordering in most disordered crystals. Data obtained from the pressure studies confirmed the predominant contribution of exciton–phonon interaction to the temperature shift of the Urbach absorption edge.     

Exact solutions of boundary-value problems for nonlinear flow in porous media

Exact solutions for flow problems in porous media with a limiting gradient in the case when the flow region in the hodograph plane is a half-strip with a longitudinal cut [1] are known only for two models of the resistance law [2–6]. The present study gives a one-parameter family of flow laws, and argues the possibility of effective determination of exact and approximate analytical solutions on the basis of successive reduction to boundary-value problems for the Laplace equation or for the equation studied in detail in [1]. It should be noted that the characteristics of the flow are determined without additional quadratures.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 107–112, May–June, 1985.