Evaluation of drop size distribution from chord length measurements

The relationship between the chord length distribution (CLD) obtained by a point sensor and the drop size distribution (DSD) in a liquid‐liquid dispersion is investigated. Based on analysis of the frequency of drop‐cuttings by the sensor, a physical model is built to derive the probability density function of chord lengths for a given DSD, and vice versa. The effect of biased sampling towards larger drops relevant to point sensors, which is often ignored by investigators, is included in this relationship. A new algorithm is introduced to solve the problem of noisy or even negative DSD values by adding smoothing equations while performing the backward conversion. The effects of parameters, such as the number of drop size groups used, the noise level, and the smoothing factor value, on the backward transform are further studied. Both forward and backward transforms are shown to be in good agreement with ideal data when using continuous (e.g., log‐normal, uniform) distributions and with data obtained from Monte‐Carlo simulations. Good agreement is also found between the DSD obtained from chord length measurements and drop size data determined by direct observation. © 2005 American Institute of Chemical Engineers AIChE J, 2006