Principle of the ultrasonic dispersion equipment. 

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Context 1

... ultrasonic dispersion equipment used in the present study is an adapted ultrasonic fatigue testing equipment (Mayer 2006). The probe is inserted into a soil water suspension and performs resonance vibrations at 19.1 kHz. This led to emission of pressure waves into the soil water suspension. The vibration amplitude was measured with an induction coil. Under well- defined geometrical conditions, the vibration organic matter (ISO11277 2009). Carbon and nitrogen were measured using dry combustion with a Carlo Erba NA 1500 (ISO10694 2009; ISO13878 1998) determined with flash combustion and chromatographic analysis of carbon dioxide. The difference between total carbon and inorganic carbon is expressed as organic carbon. Determination of calcium carbonate was in accordance with the Scheibler volumetric method (ISO10693 1995). SOM was calculated with C x 1.724 assuming average C-concentration of org organic matter of 58% (Blume et al. 2010). Each sample was air-dried, homogenously mixed and sieved to gain the aggregate fraction with size between 2000 μ m and 1000 μ m. This fraction is used to determine soil aggregate stability (SAS) according to OENorm L 1072 (2003). amplitude strongly correlates with the magnitude of the acoustic pressure waves emitted into the suspension that cause dispersion of soil particles (Kuttruff 1988; Millner 1987). The amplitude and resonance frequency was controlled and kept constant with very high accuracy in a closed- loop electronic circuit. Deviation of pre-selected and actual vibration amplitude was maximum ± 1%. The equipment can be run in pulsed mode to limit the temperature increase of the soil- water suspension. Commercially available equipment use ultrasonic power as a control parameter where the power setting is rather high and accuracy is low. Since ultrasonic power is derived from voltage and current signals, the efficiency of the ultrasonic transducer and other electrical and mechanical parameters of the system it is prone to errors. Subsequently, the power of these systems can be quantified with 10-20% accuracy only (Zhu et al. 2009; Schmidt et al. 1999). 2.4. Calibration procedure to determine power of the ultrasonic equipment The system operated close to the cavitation threshold of gas saturated de-ionized water, which is 0.5-0.6 μ m at 19.1 kHz frequency (Schomakers et al. 2011b). The following procedure was developed and applied to determine ultrasonic power at low vibration amplitudes. The probe was inserted in water (mass of water is m and specific heat capacity w is c ) and vibrates at constant amplitude. The The cylindrical probe used in this study had a diameter of 30 mm. The rather large diameter of the probe improves the homogeneity of the pressure field. During the experiments, the probe was dipped into de-ionized water. The insertion depth was four millimetres, which set the distance between probe and beaker bottom at about 50 mm ( Figure 1 ). This distance to the beaker bottom was chosen to avoid resonance of the acoustic waves in water (half wavelength of sound waves of 20 kHz frequency in water is 37 mm). increase of water temperature, Δ T during the time period Δ t was measured. Changes of thermal energy of water are caused by ultrasonic vibrations and by heat exchange with probe, beaker and ambient air. With the ultrasonic power, P and the heat exchange per second, us Δ Q Exchange / Δ t, change of thermal energy of water per second, m w c w Δ T/ Δ t is given by Eq. 1 in Schomakers et al. 2011b: A temperature gradient drives heat flow between water and environment due to convection or thermal conduction. Heat flow from thermic conduction (ultrasonic probe, beaker) and convection (ambient air) is proportional to the respective temperature difference. At the start of the power measurements, all mechanical components of the system are at room temperature. Only water measures a few degrees less: Δ Q Exchange / Δ t > 0 and the increase of thermal energy of water per unit time is the sum of ultrasonic power and heat flow into the water. During sonication, the water temperature increases until it is greater than the ambient temperature and Δ Q Exchange / Δ t < 0. When temperature of water and ambiance coincide Δ Q Exchange / Δ t = 0 and the ultrasonic power is directly correlated to the increase of water temperature. Ultrasonic power was determined at different vibration amplitudes for the used setup, i.e. an ultrasonic probe with diameter ø 30 mm, insertion depth 4 mm and vibration frequency 19.1 kHz. At vibration amplitude 1 μ m mean ultrasonic power was 2.9 W. At vibration amplitude 2 μ m it was 8.9 W, at 3 μ m the mean power was 14.9 W, at 4 μ m it was 20.8 W and at 5 μ m it was 26.8 W. Standard deviation was mean 0.9 ...

Context 2

... grams of air-dried soil (2 000-1 000 μ m) were placed in a plexiglass beaker (Ø 44 mm), 80 cm 3 of de-ionised water was added and the suspension was subsequently sonicated. To obtain a homogeneous distribution, the soil water suspension was stirred with a magnetic device (2 Hz, cylindrical shape with length 25 mm and thickness 8 mm), immediately prior and during the experiment ( Figure 1 ). The soil samples were subjected to a combination of ultrasonic dispersion, in accordance with OENorm L 1092 (2005). One treatment included a sonication time of 60 s at 2 μ m, the other treatment included a sonication time of 480 s at 5 μ m. With the ultrasonic power of 8.9 W and 26.8 W, respectively, the ultrasonic energies absorbed in 80 cm 3 were 0.53 kJ (i.e. 6.7 J cm -3 ) in the experiments at vibration amplitude 2 μ m, and 12.9 kJ (i.e. 161 J cm -3 ) in the experiments at vibration amplitude 5 μ m. Pulsed loading was applied to limit maximum temperature of the soil-water suspension to maximum 30 ...