Minimum number of turbidity measurements required for the determination of particle size distributions

It has been claimed [D. H. Melik and H. S. Fogler, J. Colloid Interface Sci.92, 161 (1983)] that by combining the turbidity ratio and the wavelength exponent, a two-parameter size distribution of the particles in a suspension can be estimated from only two turbidity measurements at two widely separated wavelengths, in other words that one is able to estimate three independent parameters (number concentration of particles and the two parameters of the particle size distribution) from only two measurements. It is shown here that this claim is strictly a result of an approximation that was used, and the solution obtained depends only upon the error of this approximation and upon the measurement errors, and has no relationship to the true particle size distribution. Furthermore it is shown that the turbidity ratio and the wavelength exponent methods are essentially the same technique for particle size determination.