A modified electroresistivity probe technique for steady- and unsteady-state measurements in fine dispersions—III: Theoretical basis of signal processing in unequal drop dispersions

✍ Scribed by Michael S. Hoffer; William Resnick

• Publisher: Elsevier Science
• Year: 1975
• Tongue: English
• Weight: 765 KB
• Volume: 30
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(75)80019-4

✦ Synopsis

Significant modifications of the electroresistivity probe technique of Neal and Bankoff were made so as to permit its use in liquid-liquid dispersions with drops in the range of 0.1-0.3 mm diameter. Modifications of both hardware and signal processing theory were necessary because sensor length is no longer negligible with respect to bubble or drop size and a multi-level rather than a two-level signal is produced. Part I describes the principle of operation, the hardware, the mode of operation under different conditions, instrument calibration, techniques and final expressions used for signal processing. Parts II and III treat the theory of signal processing. Part II deals with the signal obtained in a dispersion containing drops of equal diameter. Part III extends the results obtained in Part II to dispersions with a non-uniform particle-size distribution. It was proven theoretically that for sensors of non-negligible length, the statistical properties of the signal obtained depend only on local holdup, local size distribution and sensor length; a new and easier method of deriving the appropriate mathematical expressions was found, based on a conceptual model which does not affect the generality of the expressions. The point-sensor equations developed by previous investigators are particular cases of the more general equations for finite-size sensors as developed in the present work. The theoretical aspects of finding the local size-distribution from the measured steady-state signal were investigated and elucidated in the present Part (III) of the paper. A.lNTRODUCTION B.GRNRRALIZATIONOF THR'RQUAL-DROP MODEL' TO UNEQUAL DROP DISPERSIONS The analysis in Part II of this series [4] assumed that the dispersion was composed of drops of equal diameter.