Ultrasonic attenuation spectroscopy is a well suitable method to measure the PSD of colloids, dispersions, slurries and emulsions. The basic concept is to measure the frequency-dependent attenuation or velocity of the ultrasound as it passes through the sample. The attenuation includes contributions from the scattering or absorption of the particles in the measuring zone, and is depending on the size distribution and the concentration of the dispersed material. [ISO 20998:2006 Particle Characterization by Acoustic Methods Part 1: Ultrasonic attenuation spectroscopy].
In a typical set-up (see FIG. 1) an electrical high frequency generator is connected to a piezoelectric ultrasonic transducer. The generated ultrasonic waves are coupled into the suspension and interact with the suspended particles. After passing the measuring zone the ultrasonic plane waves are received by an ultrasonic detector and converted into an electrical signal, which is amplified and measured. The attenuation of the ultrasonic waves is calculated from the ratio of the signal amplitudes on the generator and detector side.
FIG. 1 Set-up of an ultrasonic attenuation system for particle size analysis.
PSD and concentration can be calculated from the attenuation spectrum by either using complicated theoretical calculations requiring a large number of parameters or an empirical approach using a reference method for calibration. Following [U. Riebel, Die Grundlagen der Partikelgrößenanalyse mittels Ultraschallspektrometrie, PhD-Thesis, University of Karlsruhe], the ultrasonic extinction of a suspension of monodisperse particles with the diameter x can be described by Lambert-Beer’s law. The extinction ln(I/I0)> at a given frequency f is linear dependent on the thickness of the suspension layer Dl, the projection area-concentration CPF and the related extinction cross section K. In a polydisperse system the extinctions of single particles overlay:
When the extinction is measured at different frequencies fi this equation becomes a linear equation system, which can be solved for CPF and q2(x). The key for the calculation of the particle size distribution is the knowledge of the related extinction cross section K as a function of the dimensionless wave number s = 2px/l.
This disadvantage is compensated by a wide size range covered from below 10µm to above 3mm and the fact, that PSDs can be measured at very high concentrations (0.5% to >50% of volume) without dilution. This eliminates the risk of affecting the dispersion state and makes this method ideal for in-line monitoring of e.g. crystallizers, etc. [A. Pankewitz, H. Geers, LABO, 5'2000, In-line Crystal Size Distribution Analysis in industrial Crystallisation Processes by Ultrasonic Extinction].
Current instruments use different techniques for the attenuation measurement: with static or variable width of the measuring zone, measurement in transmission or reflection, with continuous or sweeped frequency generation, with frequency burst or single pulse excitation.
For process environment, probes are commercially available with a frequency range of 100kHz to 200MHz and a dynamic range of >150dB, covering 1 to 70% of volume concentration, 0 to 120°C, 0 to 40bar, pH 1 to 14 and hazardous areas as an option.
|Dynamic Light Scattering|
|Singe Particle Light Scattering|
|Small Angle X-ray Scattering|
|Electrical Sensing Zone|
Sympatec's publications about ultrasonic extionction.