Figure 1: Experimental set-up
Investigation of the Shape and Dynamic of Fast Microparticles with a Single-Shot-Micro-CCD
Dipl.-Ing. T. Leclaire
Dr.-Ing. F. Schmidt
Prof. Dr.-Ing. K. G. Schmidt
Gerhard-Mercator-Universität Duisburg, Mechanical Engineering
Microparticles
Shape
Dynamic
Video Microscopy
Sparkflash Light
Several aspects of the formation, dynamic
and interaction of airborne microparticles can be well investigated
observing monodisperse and equidistant droplet chains of different
liquids or solutions. The variability of droplet chains is limited
by minimum initial velocity, feasible frequency ranges and restricted
coherence length. Investigations are further constricted by the
ability of the observation methods used.
The actual experimental set-up consists of a Berglund-Liu generator
fixed on a software driven scanning table, a light microscope
with a long working distance objective combined with a CCD-camera
and a short exposure sparkflash light. With the present investigations
a correlation of frequency dependent jet disintegration and the
electrical charge of the droplets could be evidenced.
Introduction
Small droplets and particles especially in the micrometer range are of great interest in many application fields in chemical engineering or other technical processes. These are e.g. spray drying, aerosol coating, ink-jet printing or medical inhalation.
Investigation methods based on light or laser scattering and reflection are very powerful tools but cannot give information about the shape of individual particles. This, however, is possible with a videomicroscopic device as long as the objects can be observed in the focus region of the microscope. With such a method shape and interaction of microdroplets or other particles can be investigated not only in a resting but also in a moving state. In particular the different modes and locations of disintegration and collision of droplets have been observed as well as special phenomena concerning these processes.
Experimental Set-up
A sketch of the experimental set-up is shown in fig. 1. The particles to be examined in the present investigations are generated by a Vibrating Orifice Aerosol Generator (VOAG) of a Berglund-Liu type [1] without dispersion cap. The liquid feed rate is determined by a defined pressure on the reservoir as described by Lin et al. [2]. The generated droplet chain is positioned by a software driven scanning table under a light microscope. The microscope is equipped with a long working distance objective and a high-speed CCD-camera.
The piezoelectric ceramic of the VOAG is positioned not at the orifice containing cap but on the top of the generator, so that the cap could be designed very small (fig. 2). This and the long working distance objective make it possible to observe the region where the jet exits the orifice. The respective distance between the orifice and the position of observation can be gathered from the control device of the scanning table.
We first used the video microscopy together with a synchronised LED lamp as a stroboscope to visualise the droplet chain. This gives good results in the case of a highly uniform droplet chain, where the many individual droplets passing the viewpoint in the period of investigation have the same size, shape and velocity. Otherwise the fixed image becomes unclear or indefinable.
To obtain analysable microphotographs even under non ideal conditions we use a triggered high-speed sparkflash light. It produces bright pulses of few nanoseconds. This allows a very short exposure time and to snapshot particles with velocities of e.g. 20 m/s. The digital photographs sampled show single objects and no superposition. Droplet diameter and interdroplet distance can be measured using an image processing and analysing program after spacial calibration.
For measuring the average electric charge of the droplets a shielded collector and a nano ampere meter were used. Other effects could be investigated with a plate capacitor placed at the position of observation.
Experimental Results
In fig. 3 the jet disintegration and droplet formation can be seen at two different locations and different times. The photographs have been taken from one droplet chain under the same operating conditions. In this case it was a jet leaving a 20 mm diameter vibrating orifice (200 kHz) with a jet velocity of about 16 m/s. The occurrence and disappearance of satellite droplets as well as the periodic deviation from the spherical shape of the droplets until stabilisation can easily be detected with this method.
The development of the droplet chain at longer distances is shown in fig. 4. The deviation from equidistance and then with occurring collisions from monodispersity can be regarded. Varying feed rate, generator frequency or voltage leads to different conditions of droplet formation, which result in respective droplet diameter, interdroplet distance and jet disintegration length.
The deflection of the droplets in a plate capacitor has been observed. At fixed operating conditions and constant voltage the droplets show uniform behaviour. This leads to the conclusion, that the droplets are uniformly charged.
The absolute electrostatic charge of the droplets, that results from the disintegration process, has been measured as follows. The droplets have been sampled in a shielded Faraday cup, while their charges lead to a small electric current that has been measured with a nano ampere meter connected with the cup. Such measurements have been performed first with distilled water. Varying the operation frequency of the droplet generator the detected current shows some local minima (fig. 5). For higher frequencies the current does not change. The detected minimum at about 150 kHz belongs to the optimal frequency range for the used orifice diameter and feed rate. Therefore a correlation between the jet disintegration process and the measured current was supposed. At each frequency marked in fig. 5 photos of the developing droplets have been taken at 5 mm distance from the orifice, because at that place the differences could be seen at best. The scaled down pictures are put into the diagram to emphasise the correlation that could be found. The better the drops have already been formed the lower the current and vice versa. The longer the filament bridge between the tearing off droplets (compare with the right side of fig. 3) the higher the current. This can be explained with the disruption of the electric double layer at the water air interface.
Drop formation optima and current minima occur at different frequencies. The lowest current can be found at the optimum frequency following the relation of Rayleigh [1]. The other three minima belong to integer divisors of this frequency. The appearance of those additional frequency ranges as feasible for jet disintegration has already been mentioned by Brenn and Lackermeier [6].
Calculations
In addition to the above mentioned experiments a model was developed to describe the dynamic of the droplets theoretically. This includes the numerical integration of the trajectory of evaporating and therefore shrinking droplets as a transient and non isothermal process.
Because of the relatively high initial velocities (10 to 20 m/s) the drag force cannot be determined with the Stokes law but with empirical Re-dependent formulas for the transition regime (e.g. Abraham [3] or Clift [4]). These equations have been developed for single spheres. In the case of droplet chains, however, the drag force acting on individual droplets is reduced by their neighbour droplets. The ratio of the interaction drag force to that of the single droplet case can be determined e.g. with a correlation of Kleinstreuer and Wang [5].
As the final velocity of the particles is much lower than the initial velocity, the interdroplet distance becomes smaller with flying time and distance (while the interdroplet distance remains constant for fixed locations). Collision occurs, when the interdroplet distance becomes zero or the distance of neighbouring droplet centres reaches the droplet diameter. For ideal conditions (equidistant behaviour) the collision point can be determined. It depends on the droplet diameter, the initial velocity and the initial interdroplet distance. The latter results from the initial velocity and the generator frequency, while the initial velocity results from the feed rate and the orifice diameter.
In the experiments irregular collision always occurs earlier than predicted with the above mentioned calculations. In the photographs taken from the droplet chain (fig. 4) it can be seen, that deviations from the equidistant behaviour takes place, which obviously results from small external influences and irregularities. These deviations are responsible for the catch-ups that appear at lower distances than predicted.
Figure 2: Vibrating Orifice Generator used with piezoelectric
ceramic on top
Figure 3: Example for the observation of jet disintegration
and droplet formation (left: at orifice, right: at 0.4 mm distance)
Figure 4: Example for droplet chains of different
quality concerning monodispersity and equidistance depending on
the distance from the orifice
Figure 5: Measured current of the charged droplets
versus generator frequency correlated with the disintegration
of the liquid jet at 5 mm distance from the orifice
Literature
[1] Berglund, Richard N.; Liu, Benjamin Y. H.: Generation of Monodisperse Aerosol Standards, Environmental Science and Technology, Vol. 7, No. 2, Feb. 1973, pp. 147-153
[2] Lin, H.-B.; Eversole, J. D.; Campillo, A. J.: Vibrating orifice droplet generator for precision optical studies, Rev. Sci. Instrum. 61 (3), March 1990
[3] Schade, H.; Kunz, E.: Strömungslehre, Verlag de Gruyter, Berlin, New York, 1989
[4] Hinds, William C.: Aerosol Technology, John Wiley and Sons, New York, 1999
[5] Kleinstreuer, C; Wang, T.-Y.: Approximate Analysis of Interacting Vaporizing Fuel Droplets, Int. J. Multiphase Flow, Vol. 16, No. 2, 295-304, 1990
[6] Brenn, G.; Lackermeier, U.: Drop formation from a vibrating orifice generator driven by modulated electrical signals, Phys. Fluids 9 (12), Dec. 1997