Ultramafic magmas made the main contribution to PGE mineralization of ophiolite associations. An orebearing dunite-chromitite complex intruded from the mantle depth is widespread in the southern Kempirsai massif, where a large chromite deposit of Os-Ir specialization has been formed. The PGE contents (mg/t) in this type of chromitites (290 Os, 265 Ir, 200 Ru, 60 Pt, 55 Pd,18 Rh) reflect the specific character of Cr-bearing melt as an efficient carrier of PGE, while host dunite is practically free of PGE (about 20 mg/t in total). The geochemical specialization of ophiolite chromitites is displayed only for refractory PGE (Os, Ir, Ru), prevailing over fusible PGE (Rh, Pd, Pt). Therefore, the ophiolite association was classified as chromite-bearing and unpromising for PGE mineralization, as was exemplified in the Urals by Zavaritsky and Betekhtin, who opposed this rock association to PGE-bearing zonal and layered intrusions. This difference is caused by reductive conditions and high PT parameters dominating in magmatic chambers of ophiolite associations. The main conclusion that can be drawn from this study Abstract -On the basis of a representative collection of ultramafic rocks and chromite ores and a series of technological samples from the largest (Central and Western) deposits in the Rai-Iz massif of the Polar Urals and the Almaz-Zhemchuzhina and Poiskovy deposits in the Kempirsai massif of the southern Urals, the distribution and speciation of platinum-group elements (PGE) in various type sections of mafic-ultramafic massifs of the Main ophiolite belt of the Urals have been studied. Spectral-chemical and spectrophotometric analyses were carried out to estimate PGE in 700 samples of ultramafic rocks and chromite ores; 400 analyses of minerals from rocks, ores, and concentrates and 100 analyses of PGE minerals (PGM) in chromite ores and concentrates were performed using an electron microprobe. Near-chondritic and nonchondritic PGE patterns in chromitebearing sections have been identified. PGE mineralization has been established to occur in chromite ore from all parts of the mafic-ultramafic massifs in the Main ophiolite belt of the Urals. The PGE deposits and occurrences discovered therein are attributed to four types (Kraka, Kempirsai, Nurali-Upper Neiva, and Shandasha), which are different in mode of geological occurrence, geochemical specialization, and placer-forming capability. Fluid-bearing minerals of the pargasite-edenite series have been identified for the first time in the matrix of chromite ore of the Kempirsai massif (the Almaz-Zhemchuzhina deposit) and Voikar-Syn'ya massif (the Kershor deposit). The PGE grade in various types of chromite ore ranges from 0.1-0.2 to 1-2 g/t or higher. According to technological sampling, the average PGE grade in the largest deposits of the southeastern ore field of the Kempirsai massif is 0.5-0.7 g/t. Due to the occurrence of most PGE as PGM 10-100 mm in size and the proved feasibility of their recovery into nickel alloys, chromites of the Kempirsai massif can be con...
The flow of a three-dimensional sheet on a curved wall is considered . Gravity and surface tension forces act on the sheet while a droplet stream falls on its free surface. The systems of equations of viscous incompressible fluid dynamics on a curved rigid surface and the boundary conditions with allowance for the falling droplet stream are formulated . The problems of steady axisymmetric motion of the sheet on cylindrical and conical surfaces are considered . The effect of the curvature of the rigid wall on the solution is examined .Thin sheet motion on rigid surfaces in the presence of free-surface interphase exchange is of interest in connection with technical problems of heat and mass transfer . The problems of two-dimensional sheet motion on plane surfaces with allowance for various free-surface interactions with the contact medium have been considered (see detailed bibliography in [1]) . In contrast to previous investigations, below we consider the three-dimensional flow in a sheet on a curved wall with allowance for the falling droplet stream of the same fluid . The need to consider the three-dimensional sheet flow on a curved wall stems from the physical formulation of the problems, in particular, in investigating the processes taking place in open-type cooling radiators [2] . Below, omitting small terms of order higher than the first in the quantity c related with the ratio of the characteristic transverse and longitudinal dimensions, we obtain the equations and boundary conditions in the thin-sheet approximation . This system generalizes the well-known equations of thin-sheet dynamics on plane walls [1] . The solution of steady-state axisymmetric problems of sheet dynamics on cylindrical and conical surfaces is obtained. THE THIN-SHEET APPROXIMATIONAs in the case of a boundary layer near a curved surface, we introduce a special curvilinear coordinate system [3] . We denote the curvilinear coordinates of points on the rigid wall E by s t and s 2 , which have the dimension of length . As the spatial coordinate system we chooses', s 2 , and n, where n is the segment length reckoned from the wall surface along the normal to E .Then, the covariant space basis vectors E a =E a (s t ,s 2,n) are related with the basis vectors e a on E by the expressions :an Ea =ea + n , E3 =n (1 .1) as a and the components of the metric tensor g 9 can be determined from the expressions g a a =aae -2nbaa + n 2 c o >where a ag , b aa, and c ae are the coefficients of the first, second, and third quadratic forms of the surface E, respectively, n is the unit normal to E, the Greek subscripts vary from 1 to 2 and the Latin ones -from 1 to 3 .
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