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A method is presented for measuring the concentrations of flow components from their static complex dielectric constants. The initial equations are derived, and also a solution to the inverse treatment by a nonconvex programming method. A description is given of the measurement system.It is difficult to overestimate the importance of determining the compositions of mixtures flowing in closed pipes. There is a wide range of physical methods (optical, acoustic, and radio-frequency ones), but only the latter are suitable because the characteristic scales of the flow inhomogeneities are much less than the corresponding wavelengths, while the metal walls give closely defined boundary conditions, in contrast to the conditions in acoustic methods.The method involves measuring the real and imaginary parts of the dielectric constant in three mutually perpendicular directions by reference to the measured resonant frequencies and quality factors of the corresponding cavities, where one utilizes the initial calibrated values.The data processing involves specifying an electrostatic model for the mixture, which incorporates the directions of the anisotropy (flow direction, gravity, and so on) and solving the inverse treatment for determining the concentrations by reference to the dielectric constants.Electrostatic Model, We use a coordinate system related to the symmetry axes of the pipeline and employ the theorem on the mean [ I ] ( 1) Here we have used the fact that although the components of the mixture are isotropic, the mixture itself is anisotropic because of deviations from symmetry due to the direction of the flow velocity and that of the field of gravity.We split up the volume into finite parts and group them by components (subscript i) and suspended-particle shapes (subscript j) on the assumption that the fields within the identical particles Ek, ij are identical:

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