222 Part. Part. Syst. Charact. I1 (1994) 222-226

Particle Breakup in Shock Waves Studied by Single Particle Light Scattering

Jorg J. F. Strecker, Paul Roth"

(Received: 19 November 1993)

Abstract

The breakup of suspended, agglomerated submicron particles was studied by exposing the aerosol to weak shock waves of varying strength under conditions 400 ms-' 5 v 5 880 ms-'. A newly developed laser light-scattering diagnostic employing a top hat laser profile was used to size the particles passing through a very small scattering volume. By comparing the op-

tically measured particle size in front of and behind shock waves, the breakup of agglomerated particles could be clearly identified. The experiments indicate that the aerodynamic forces behind an incident shock overcome the particle binding force resulting in disintegration of the submicron agglomerates. The results are presented in form of a modified Weber number.

1 Introduction

Breakup, coagulation and adhesion of solid particles are impor- tant physical phenomena with applications in science and technology. They affect both dust deposition and mixing pro- cesses, and provide limitations in applying various mechanical separation methods. If the primary particles are in the micron or submicron size range, the interactive adhesion forces exceed the volumetric forces by several orders of magnitude. It is therefore difficult to disintegrate agglomerates in this size range. The breakup of droplets by aerodynamic forces is usually described by the dimensionless Weber number, which is the ratio of external and internal forces:

p . v 2 We = ~

a

In this equation p . v 2 is the dynamic pressure of the surround- ing fluid with the gas density p and the relative velocity v be- tween the gas and particle phase. The quantity in the deno- minator of Eq. (1) is the internal force keeping the particle material together. In the case of droplets, o is represented by

o = T/d , (2)

where d is the droplet diameter and T the surface tension. The first breakup phenomena of droplets occur at a critical Weber number of Wecri, = 10 followed by five additional disintegra- tion modes [l]. In the case of solid agglomerates, no general breakup theory exist and only a few experimental data [2] and some considera- tions (31 are available. For dry agglomerates of two smooth, spherical, monosized particles of diameter d*, the van der Waals attraction is known to be the dominant adhesion

* Dip1.-Ing. J. J . R Strecker, Prof. Dr.-Ing. I! Roth, Institut fur Ver- brennung und Gasdynamik, Universitat Duisburg, 47048 Duisburg (Federal Republic of Germany).

mechanism. The tensile strength a can be calculated according to Rumpf [4] by

(3)

where A represents the Hamaker constant and a, is the particle adhesion distance. In the present investigation, the aerodynamic force p . v 2 was generated by exposing the aerosol consisting of agglomerated submicron particles to weak shock waves. The flow field behind the wave is characterized by a nearly instantaneous acceleration of the fluid phase, which in turn starts to accelerate the suspended agglomerates. The resulting particle drag forces, which are well characterized, can overcome the particle adhe- sion force and break the agglomerate structures. The breakup process was measured by sizing the particles in front and behind the shock wave by laser light scattering.

2 Experimental Set-up

The test facility used is illustrated in Figure 1. It consists of a 50 mm inner diameter shock tube with vacuum tank, an expan- sion wave driven aerosol generator, a single-particle laser light- scattering system and a particle filter sampling system with SEM analysis.

2.1 Shock Tube

The stainless-steel shock tube consists of a low- and high- pressure section of 5.50 and 2.5 m in length, respectively. The end of the low-pressure section is connected to a vacuum tank of 80 1 volume separated by a thin diaphragm allowing absorp- tion of the shock wave. Hydrogen, nitrogen and argon were used as high-pressure driver gases. The pressure ranged between 2 and 20 bar. The low-pressure tube could be evacuated below 0.05 mbar. For each run the low-pressure section was first filled with argon and then connected to the aerosol generator,

0 VCH Verlagsgesellschaft mbH, D-69469 Weinheim, 1994 0934-0866/94/0306-0222 $5.00 + .25/0

Part. Part. Svst. Charact. I1 (1994) 222-226 223

Fig. 1 : Schematic diagram of the shock tube apparatus.

described below. The gas-particle mixture flowed slowly from the aerosol generator through the low-pressure section of the shock tube initiated by a vacuum pump located near the high- pressure diaphragm. During the flow the pressure is reduced from 800 mbar to its final value of 400 mbar. By this procedure a very homogeneous particle concentration distribution along the full length of the low-pressure tube was realized. The test section located at the end of the low-pressure tube was equipped with cylindrical BK7 glass windows placed at fixed angles of O", 90", 180" and 270" in one cross-section plane of the tube 0.70 m apart from the vessel diaphragm. This device allows scattered light flux measurements perpendicular to the tube axis. The windows are mounted flush with the inside wall of the test section to minimize distortion of the shock wave. Two flush-mounted Kistler pressure transducers are located 5 mm before and behind the test section to monitor the shock-induced pressure rise. The output signals from the pressure transducers were fed to fast electronic counters to measure the shock velocity and to trigger the particle detection system. For more details, see References [5-81.

2.2 Aerosol Generation

A small conventional shock tube of 50 mm inner diameter also shown in Figure 1 was employed to generate the test aerosol. The high-pressure part is 500 mm and the low-pressure part 1000 mm in length. A glass vessel of 20 1 volume used as an aerosol chamber is located at the end of the shock tube. The powder to be dispersed was deposited on a flat plate inserted near the high-pressure diaphragm. For each run the low- pressure tube and the glas vessel were evacuated and the high- pressure tube was filled with the dispersion.fluid. After bursting of the diaphragm, the generated shock and expansion waves dispersed the powder. It is a basic advantage of this type of aerosol generator that any material that is available in finely divided form can be dispersed. A few micrograms of powdered material, especially very expensive and valuable solids or highly toxic powders, can be transferred into aerosol form. Another advantage of this type of particle redispersion is the possibility of the controlled formation of particle agglomerates. More details and results of this shock and expansion wave-driven powder disperser have been published earlier [9- 111.

2.3 Laser Light Scattering System and Calibration

The breakup process was monitored by in situ laser light scatter- ing of individual particles. Every particle passing a very small optically defined scattering volume generates a scattered light flash, the height of which is proportional to the particle size. This well known measurement principle suffers from two prac- tical difficulties: the Gaussian intensity profile of the illumi- nating laser beam and the border zone problem of the scattering volume. The Gaussian intensity profile has the effect that large particles passing the boundary zone of the beam can produce a signal of the same amplitude as small particles crossing the axis of the beam. To overcome this difficulty, the intensity distribution of the laser beam must be transformed into a top hat distribution, which can be achieved by different approaches. Characteristics of the absorption method and the beam stop method are high energy losses of about 90% [12]. The beam segmentation approach is accompanied by high diffraction losses and destructive interference phenomena, and requires considerable beam dimensions [13]. Other available techniques with high efficiency, for example beam refraction, diffraction or reflection, imply high expenditure, in particular when hologram images are used [14, 151. This paper gives an application of laser beam shaping by means of a multimode fibre with an overall optical efficiency of 60-70%. The border zone problem of the scattering volume can lead to a systematic error due to in- complete collection of the scattered light by the detectors and incomplete illumination of particles passing the border zone of the scattering volume, both resulting in an underestimation of the particle size. In the present case, a measurement system reported by Umhauer [16] was used in a version modified for fast flow conditions. The light-scattering system is shown in more detail in Figure 2. An argon ion laser beam operating at a wavelength of 1 = 488 nm was coupled into a multimode fibre with an aperture of 600 pm. The intensity distribution of the unpolarized outcom- ing beam has a top hat profile with a residual ripple of less than 10% and an edge steepness of 4460 m-'. The beam was focused into the low-pressure section of the shock tube. Two scattered light detection systems arranged perpendicular to the incoming beam were used. The light fluxes of the two optical test volumes entered the photomultipliers and the resulting electrical signals were recorded and stored in a

224 Part. Part. Syst. Charact. I I (1994) 222-226

particle f l ow direction

volume1 volume 2 imoging lens

Fig. 2: sizing.

Shock tube cross-section with optical diagnostic for particle

transient recorder connected to a PC. The scattering volumes of the two detection systems, which have different sizes, were defined by the images of two slits. The larger measuring volume contains the smaller one. A particle passing through both scat- tering volumes produces a scattered light flash recorded by both optical detection systems. If the heights are of comparable size the signals are further processed. For more details, see Reference [16]. The height of the measured scattered light flash signals is propor- tional to the particle size. For absolute particle sizing, the propor- tionality factors between the measured signals and the respective Mie intensity functions [17, 181 must be determined. This was done by calibration experiments with monodisperse latex par- ticles of known size. The generated aerosol was filled into the low- pressure section and passed through the test volume. The resul- ting scattered light signals obtained were compared with SEM analysis of sampled particles. The optical arrangement was fur- ther tested by flowing aerosols with agglomerated particles through the measurement section of the shock tube.

3 Results and Discussion

The aerosols used in the present shock tube experiments con- sisted of argon containing primary latex particles and ag- glomerates. Two different sorts of dry latex primaries (Fastek, Liverpool, NI: USA) were used having size parameters (mean diameter, geometric standard deviation) of (d: = 235 nm, at = 1.06) and (d; = 325 nm, a; = 1.04). The material density (polystyrene) was p: = 1.05 g cm-3 and the refractive index at A = 633 nm was m = 1.601. The optical equivalent size of the agglomerates ranged from 0.3 to 0.5 pm or from 0.4 to 0.6 pm, respectively. The breakup process of agglomerated particles was studied by varying the shock wave velocity from 400 to 880 m s-l, resulting in Mach numbers between 1.2 and 2.8. An individual shock tube experiment showing the optically measured particle size distribution both in front of and behind the shock wave is shown in Figure 3. The pre-shock aerosol (upper part of Figure 3) contains primary particles of mean diameter d;= 325 nm, and also dimers with an optical equi-

5 W

\

E

P R E - SHOCK STATE OF THE AEROSOL 0 1 2 . I I I I I I ( . , I I I I . , 1 1 .

0 10- d: = 0.325 p m :

o.o* j

optical particle diameter / pm

POST - SHOCK STATE OF THE AEROSOL 0 . 1 2 , " . ~ " " ' " 1 ~ " " , ' ,

0.04

0.02

0.00 010 0:1 0:2 0:3 014 015 0:8 0:7 018 0:9 1:O

optical particle diameter / p m

Fig. 3: vpical individual example of an optically measured particle size distributions in front (upper part) and behind (lower part) a shock wave.

valent diameter of about 0.4 pm and further agglomerates. The aerosol behind the shock wave (lower part of Figure 3) shows a very different size distribution behaviour. The number of primary particles is significantly increased and the agglomerates are reduced, indicating a breakup process. Similar results were obtained from other shock wave experiments. In order to describe the disintegration behaviour of the stressed particles, it is most convenient to employ the third moment of the count diameter [19] of a discrete size distribution, which is given by

i =d;) , . C ni M3,0 =

i

(4)

where ni and dpi are the particle number concentration and diameter of size class i, respectively. M3,o is equal to the cube of the mass average diameter d,. This moment can be related to the corresponding value Mt,o of the primary particles and leads to the definition of a dimensionless degree of agglomera- tion a3,0:

Part. Part. Syst. Charact. I1 (1994) 222-226 225

For aerosols containing only primary particles M3,o is equal to @,, resulting in a3,o = 1. If agglomerates are present in the aerosol, q 0 is always greater than 1. For every shock tube ex- periment the degree of agglomeration defined by Eq. (5) can be calculated from the optical size measurements both in front of (a3,o)I and behind (a3,o)Z the shock wave. From both these values, the efficiency q of the disintegration :

can be calculated. If the initial aerosol remains uneffected by the shock wave, q is equal to 0. On the other hand, complete disintegration of the pre-shock aerosol results in (a3,O)z = 1 or q = 100%. All shock tube experiments on agglomerate breakup performed in the present study are summarized in Figure 4. The efficiency of shock-induced disintegration q is shown as a function of the

0 0 1.0 2.0 3.0 4 0 5.0 6.0 7.0 8.0 9.0

Weber - number

Results of shock tube experiments on particle breakup: Weber number calculated with A = 3.17 * lo-’* erg [20] and uo = 0.4 nm [21].

Weber number, which was calculated according to Eqs. (1) and (3) based on the velocity difference between the particles and the gas flow immediately behind the shock wave and by assum- ing the Hamaker constant to be A = 3.17 e erg I201 and the adhesion distance to be a. = 0.4 nm [21]. The results clearly indicate that the agglomerated particles were disintegrated in the shock wave. The effect is dependent on the intensity of the shock characterized by the Weber number. The disintegration of agglomerates with primaries of d: = 235 and 325 nm showed a similar behaviour with a maximum at We = 0.9-1.0 followed by an abrupt decrease with a minimum at We = 3.0. The minimum value of the disintegration efficiency is q = 30% and the max- imum value is q = 90%. The breakup efficiencies of agglo- merates composed of larger primary particles is more effective than those of the smaller particles. For a more detailed understanding of the observed disintegration behaviour, two interfering processes must be considered : a) the breakup of agglomerates in the post-shock fluid flow and b) the shock-induced coagulation of particles. The first process is caused by the velocity difference between the gas flow and the particles resulting in strong drag forces, which break the agglo- merate structure. The origin of the second process is the velocity difference between two particles moving through the post-shock relaxation zone. Agglomerates having a higher velocity than primary particles can hit them and stick together and vice versa

according to a stationary or non-stationary point of view. Also, primary particles resulting from breakup of a dimer have a velocity profile which is different from that of the other primary particles in the relaxation zone. This velocity difference causes flow-induced coagulation of particles having the same size. The above concise description indicates that breakup of ag- glomerates behind shock waves can partly be compensated for by flow-induced particle coagulation. This factual sitation is further illustrated in Figure 5, which shows two sets of calculat- ed curves : i) exponentially decreasing curves representing the velocity difference between primary particles (dp* = 325 nm) or dimers (d,,, = 450 nm) and the gas velocity in the post-shock relaxation zone and ii) a curve with a maximum at x = 0.12 mm, which illustrates the velocity difference between dimers and primary particles.

0 2 0 3 0 4 0 5 06 00 01

relaxation length / mm Fig. 5 : Calculated profiles of velocity differences between particles and gas and between particles in the relaxation zone behind a shock wave.

The driving property for particle disintegration is the velocity dif- ference according to i), whereas the driving property for the parti- cle coagulation is the velocity difference according to ii). One can imagine that depending on the flow conditions and the particle properties the global disintegration process can be dominated either by i) or by ii). A further detail is also given in Figure 5. If a dimer breaks, e.g. at x = 0.1 mm behind the shock front, the two remaining primary particles have a different velocity dif- ference profile to the gas flow than the original primaries (see the dot-dashed curve). The resulting velocity difference between these primaries of different origins, which is also shown in Figure 5 as dot-dashed line with opened diamonds, can conse- quently result in flow-induced coagulation of primary particles of the same size, thus correcting again the original breakup pro- cess. The dot-dashed curve with crossed diamonds represents the velocity difference profile between the new primaries and ag- glomerates resulting in particle coagulation according again to ii). The combination and interference of all these processes described above can result in the observed particle disintegration behaviour shown in Figure 4. At Weber numbers We < 0.9 the breakup of agglomerates behind shock waves seems to be domi- nant, case a). Under conditions 0.9 5 We 4 3.0 an additional strong influence of particle coagulation (case b)) seems to become significant, leading to a decrease in the overall disintegra- tion efficiency q. The further observed increase of q at We 2 3.0 must be a result of the increasing importance of particle breakup compared with particle coagulation.

226 Part. Part. Syst. Charact. I1 (1994) 222-226

Although the present experiments clearly indicate that breakup of agglomerates was observed behind shock waves, an inter- pretation in terms of a critical Weber number well known for liquid particles is obviously not possible. The reason seems to be that the breakup of agglomerates and its interaction with shock wave-induced coagulation is more complicated than the flow-induced disintegration of liquid particles.

4 Acknowledgement

This work originated in the special research section (Sonder- forschungsbereich) 209 of the University of Duisburg. The financial support of the Deutsche Forschungsgemeinschaft is gratefully acknowledged.

5 Symbols and Abbreviations

A Hamaker constant a. adhesion distance d diameter F force n particle number concentration M moment SEM scanning electron microscope T surface tension v velocity We Weber number x relaxation length

Greek symbols a degree of agglomeration q efficiency 1 wavelength n constant p density a tensile strength B standard deviation

Subscripts aggl agglomerate crit critical g geometric rn average mass p particle v d W van der Waals

Additional definitions for any symbol or function i size class 1, 2 3 , O

* primary particle

conditions in front of and behind the shock wave e.g. M3,0: third moment (3) of the number (0) concen- tration

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