A general correlation has been proposed to estimate various flow characteristic quantities of developed gas-liquid two-phase steady flows, such as void fraction, lengths of large bubble and passing frequency of large bubble in slug flows, film thickness in annular flows, and so on. The concept used in this derivation is extended to derive correlations for volumetric fractions of each phase in developed steady solid-fluids multiphase flows. Empirical correlations are proposed for volumetric fractions of each phase in liquid-solid two-phase flows, and in gas-liquid-solid three-phase flows using experimental data obtained from various kinds of experimental conditions.

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An accurate method for evaluating surface tension force was proposed. The method utilizes a solution of the Cahn-Hilliard equation for the color function of the Continuum Surface Force model. Curvature vectors on three surfaces of revolution, i.e., sphere, distorted spheroid and spherical-cap were accurately evaluated by the method. Interface tracking simulations of a flow around a neutrally buoyant fluid sphere and of a drop rising through a stagnant liquid demonstrated that the proposed method could significantly reduce pseudo parasitic currents caused by numerical errors in surface tension force.

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