A Study of the Bivariate Analysis of Dispersed Phase Mixing

[摘要] A method for the measurement of the bivariate drop volume-dye concentration distribution in a dispersed phase mixing vessel has been developed. The method involves extracting a sample of dispersed phase from the vessel and immediately coating it with an anticoalescence agent. The drops are then forced at a constant flow rate through a small capillary. A logarithmic photometer focused on the capillary through microscope produces an output of rectangular pulses. The length of each pulse is a measure of the volume of the drop and the height of each pulse is a measure of dye concentration in the drop. The analysis of the photometer output is performed easily and quickly on the computer. A volume balance containing a single mixing kernel to quantitatively describe the breakage and coalescence processes in a steady state mixing vessel is derived. Various space balances for the two dimensional experiment are investigated in the attempt to find a balance which would allow calculation of the mixing kernel from the experimental data. Three techniques to study the approximate calculation of the mixing kernel are developed and applied to several experiments. The uniqueness question for the mixing kernel in the two dimensional integral balance equation is investigated but not solved. The mixing kernels obtained by using the balance equation are still in question because this uniqueness question is unresolved and because the resulting kernel values seem unreasonable physically. Methods for the approximate interpretation of the data from the steady state dye mixing experiment are suggested and a particular example of some of the possible interpretations is demonstrated. In this example four experiments are run with different residence times in the vessel. The drop size distributions in the vessel for the experiments are compared with each other and with the log normal distribution. The development of the dye concentration marginal distribution with residence time is indicated. The homogenous equal drop size model is applied to the ratio of input to output concentration variance for the four experiments. For the different residence times the model fits well and indicates a mixing rate of the same order of magnitude as has been found by other investigators.

[发布机构] University of Michigan

[效力级别] dispersed

[关键词] applied sciences;dispersed;phase mixing;population;balance;Chemical Engineering