A light transmittance probe for interfacial area measurements of dispersed two phase flows with small particles

An optical probe measuring interfacial area () by light attenuation has been designed with a special emphasis on flows with sub-millimetric particles. It permits measurements in liquid-liquid or gas-liquid dispersions without need of introducing empirical correcting factors for the standard exponential decay law of light intensity while keeping an extended application range. This probe was successfully tested with an air-glass particle flow, the parameters of which were carefully determined basically by hold-up methods. The volume fraction of the dispersed phase was varied between 0.05% and 5%, and the particle size between 10 m and 300 m.List of symbols D diameter of spherical particle - D _S Sauter diameter - E ₀ irradiance on a surface perpendicular to light propagation 226E;=(1/l) averaged density function along y axis - f density function of a dispersion - f ₁, f ₂ focal length of the lenses L ₁, L ₂ - g granulometry function of a powder (probability density) - h granulometry function of a powder (unnormalized) - I ₀, I light beam intensity respectively before and after passing through the dispersion - j volumetric powder flow - K ₁, K ₂, K ₃ dimensionless constants - l optical path length of the beam in the dispersion - L experimental pipe width along x axis - m mass of a sample - n optical index of the continuous phase - p _a, p ₀ respectively slope of _a and ₀ straight line - r distance between particles - S _d scattering cross-section - V volume of dispersion - averaged particles velocity - x, y, z spatial coordinates - interfacial area - _a absolute interfacial area (by unit volume of dispersion) - ₀ interfacial area measured by light attenuation method - _d angle (around the initial direction of light propagation) within which a particle diffracts - _dr detector aperture angle - light wavelength - _d scattering cross section by unit volume of dispersion - light beam diameter - ₁, ₂ L₁, and L₂ lenses diameters - local volumetric fraction of dispersed phase - averaged fraction of dispersed phase along x axis - ₂ averaged fraction of dispersed phase along x and y axis - volumetric mass of particles