Study of Steady State Mean Drop Size and Drop Size Distribution Produced in Turbulent Liquid-Liquid Dispersions at High Hold up Ratios

In this investigation, the mean drop size and the drop size distribution which are the most important factors in the liquid-liquid dispersions were studied over a wide range of phase ratio for four different non viscous dispersed phases (namely ethyl hexanoate, toluene, kerosene and phenetole) in water. The dispersed phases have been used at concentrations of 5 to 50 (% v/v) that were agitated by Rushton turbine impeller with the revolution speed varied from 300 to 700 rpm. Drop size distributions were measured by an endoscope technique. The drop size distributions in the agitated dispersions resulted from the dynamic equilibrium existing between the breaking and coalescing drops. Since the common modulated correlation, d32(1+const)We-0.6 estimate fairy inaccurate the Sauter mean diameter especially at high hold up ratios and the linearity dependence on hold up ratio is doubtful, in frame of the classical Hinze-Kolmogorov theory, a new two-parametric relation was established which correlated the Sauter mean drop diameter to the Weber number and to the volume phase fraction much more reliably. Also, in this work the linear normal distribution function in cumulative form was used to fit the experimental data with appropriate agreement. The variations of the related standard deviation were correlated to the Sauter drop diameter and to the phase ratios. For modeling drop size distribution, the population balance equation was solved by discrete formulation methods. Drop breakage and coalescence frequency were described by famous Coulaloglou and Tavlarides model and the parameters of the model were obtained by least squares error method. The results showed that if the parameters obtained for a specified revolution speed was used the experimental and simulated data agreed well, but since the parameter depended on the power input to the system, this model should be improved.