This paper investigates interaction between two particles in acoustic field. It is shown that additional oscillating movements of particles occur as a result of plain acoustic wave action. This sufficiently increases the probability of collisions between particles. Micro-displacements in the collision zone help to remove various pollutants, oxidation products and adsorbed gas molecules from surfaces of particles. Strong adhesive bonds are formed in the contact area between the particles

Darius Ozarovskis

Rolandas Zaremba

Vadim Mokšin

Vladas Vekteris

Vytautas Striška

Journal of Vibroengineering

English

Vekteris, Vladas

Striška, Vytautas

Mokšin, Vadim

Ozarovskis, Darius

Zaremba, Rolandas

Vilniaus Gedimino Technikos Universitetas: VGTU Talpykla / Vilnius Gediminas Technical University: VGTU Repository

Tribological adhesion of particles in acoustic field

  VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 2012. VOLUME 14, ISSUE 2. ISSN 1392-8716 
509 
774. Tribological adhesion of particles in acoustic field 
 
Vladas Vekteris1, Vytautas Striška2, Vadim Mokšin3, 
Darius Ozarovskis4, Rolandas Zaremba5 
Vilnius Gediminas Technical University, Department of Machine Engineering, Lithuania 
E-mail: 1vekteris@vgtu.lt, 2vytautas.striska@vgtu.lt, 3vadim@vgtu.lt, 
4darius.o@vilpra.lt, 5roliuxas@gmail.com 
  
(Received 12 September 2011; accepted 14 May 2012) 
 
Abstract. This paper investigates interaction between two particles in acoustic field. It is shown 
that additional oscillating movements of particles occur as a result of plain acoustic wave action. 
This sufficiently increases the probability of collisions between particles. Micro-displacements 
in the collision zone help to remove various pollutants, oxidation products and adsorbed gas 
molecules from surfaces of particles. Strong adhesive bonds are formed in the contact area 
between the particles. 
 
Keywords: acoustic field, particles, adhesion, aggregation.  
 
Introduction  
 
Surfaces of solid particles dispersed in the atmosphere are fouled by oxidation products and 
have high moisture content [1]. Chemical bonds (short-range forces) between surfaces of 
particles reach their peak value under the action of these pollutants [2]. If two particles come 
into contact with each other only Van Der Waals interaction become sufficient for adhesion, 
because chemical bonds reach peak value and total thickness of fouling layer is bigger than 
action interval of mentioned surface forces. However, if the interaction of particles takes place in 
the presence of acoustic field, additional tangential force occurs. This force can break the fouling 
layer thereby removing pollutants and increasing the contact area between the particles. It is 
considered that small displacements occur on the separation surfaces of particles under the 
action of tangential forces. This results in several-fold increase in adhesion and higher degree of 
aggregation of particles.  
When two particles approach one another, Van Der Waals attraction forces start to act 
between them. These forces occur due to fluctuations in the charge distribution of atoms and 
molecules of particles. These charges form continuously moving dipoles. As a first solid body 
approximation, it can be considered that Van Der Waals force acting between atoms or 
molecules has additive character. Therefore total force can be calculated by summing pairs of 
atoms of the both surfaces. With this assumption, Casimir [3] first derived the formula for 
adhesion force acting on interface of two mirror polished surfaces: ,240 40
2 zAcFA piℏ=  
where: pi2/h=ℏ , h is the Planck’s constant, c is the speed of light, z0 is the separation between 
surfaces, 20zA >>  is the area. 
It is established [4] that Van Der Waals adhesion force acts between all the materials which 
are brought together at the nanometric distance. If the separation between surfaces is less than 1 
nm, various chemical bonds are formed between surfaces depending on chemical composition of 
surfaces.   
Fuller and Tabor [5] proposed the “adhesive parameter”: ,2/12/3 γ∆ββθ Ez=  where E is 
the effective Young modulus, z is the separation of average lines of two bodies, β is the 
curvature radius of asperities, ∆γ is the variation of surface energy. Quantity β∆γ is related to the 
adhesion force and quantity 2/12/3 βEz  – to the surface force between asperities which appears 
when surfaces are torn apart.  
If Fuller-Tabor parameter is small the adhesion plays a central role, if large – asperities 
dominate, adhesion becomes weak. 
 774. TRIBOLOGICAL ADHESION OF PARTICLES IN ACOUSTIC FIELD. 
VLADAS VEKTERIS, VYTAUTAS STRIŠKA, VADIM MOKŠIN, DARIUS OZAROVSKIS, ROLANDAS ZAREMBA 
 
 
 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 2012. VOLUME 14, ISSUE 2. ISSN 1392-8716 
510 
This work investigates the impact of acoustic field on particle adhesion for large values of θ.  
 
Object of investigation    
 
The interaction between two general shape SiO2 particles 1 and 2 (Fig. 1) in the acoustic 
field was chosen as object of investigation. Let the radii of the particles be r1 and r2 respectively, 
separation between them is denoted by l. Value of interaction angle φ may vary and can be 
stochastic. 
 
 
 
Fig. 1. Scheme of particle motion in the acoustic 
field: 1, 2 – particles, l – separation between 
particles, φ – interaction angle, x – coordinate 
Fig. 2. Approximate composition of surface layer 
of the particle: 1 – fouling layer, 2 – adsorbed gas 
layer, 3 – oxidation products, 4 – particle material 
 
The scheme of the surface layer of particles before collision can be presented as shown in 
Fig. 2. 
 
Interaction between particles 
 
Interaction force acting between two oscillating particles can be expressed as follows [6]: 
 
( )
3 3 2
1 2 2
4
3 1 3cos ,
2
f
p f
r r u
F
l
ρ pi φ= −  (1) 
 
where ρf is the density of the flow, r1 and r2 are the radii of particles, uf is the velocity of the 
flow, l is the separation between particles (Fig. 1), φ is the interaction angle (Fig. 1). 
Velocity of the flow can be obtained from plain acoustic wave equation [7]: 
 
,2cos2 ftfxu ff pipi=  (2) 
 
where f is the frequency of the acoustic field, xf is the amplitude of the flow, t is the time. 
The force that makes the particles and flow oscillate can be expressed as follows [8]: 
 
,
4
sin
3
10
2
32








=
ss
s
c
fx
c
fJrF pipi  
 (3) 
where J is the sound intensity, x is the coordinate, cs is the speed of sound. 
Graphical representation of Eq. (1) is presented in Fig. 3.  
 
 774. TRIBOLOGICAL ADHESION OF PARTICLES IN ACOUSTIC FIELD. 
VLADAS VEKTERIS, VYTAUTAS STRIŠKA, VADIM MOKŠIN, DARIUS OZAROVSKIS, ROLANDAS ZAREMBA 
 
 
 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 2012. VOLUME 14, ISSUE 2. ISSN 1392-8716 
511 
 
a) 
 
 
b) 
 
Fig. 3. Interaction force Fp as function of size of particles and interaction angle φ: 
a) f = 10 kHz, xf = 0.5 mm, t = 2 s, l = r1 + r2; b) f = 20 kHz, xf = 0.5 mm, t = 2 s, l = r1 + r2 
 
Experimental investigations 
 
Special setup (Fig. 4) was designed and manufactured for experimental investigations. The 
scheme of the setup is presented in Fig. 4a. It consists of pipes 1 with integrated analyzers, 
acoustic chamber 2 with tone generator, throttle 3, dispenser 5, fan 4 and HEPA filter 6. “Lasair 
II” particle detecting and counting system was used. Particle shape and size analysis was 
performed using optical microscopy. 
Microscope images of particles are shown in Figs. 5 and 6. Particles have irregular shapes as 
is evident from the figures. Aggregates of particles can be clearly observed in Fig. 6. 
 774. TRIBOLOGICAL ADHESION OF PARTICLES IN ACOUSTIC FIELD. 
VLADAS VEKTERIS, VYTAUTAS STRIŠKA, VADIM MOKŠIN, DARIUS OZAROVSKIS, ROLANDAS ZAREMBA 
 
 
 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 2012. VOLUME 14, ISSUE 2. ISSN 1392-8716 
512 
 
a)  
 
 
b) 
 
Fig. 4. Experimental setup: a) – scheme; b) – photography; 1 – pipe with analyzer, 2 – acoustic chamber,                
3 – throttle, 4 – fan, 5 – dispenser, 6 – HEPA filter, 7 – aerosol diluter “Ati TDA-D100”, 8 – particle 
detecting and counting system “Lasair II”, 9 – sound level in acoustic chamber 
 
 
 
Fig. 5. Quartz sand particles after the action of acoustic field (photo from the optical microscope, 
magnification ×20) 
 774. TRIBOLOGICAL ADHESION OF PARTICLES IN ACOUSTIC FIELD. 
VLADAS VEKTERIS, VYTAUTAS STRIŠKA, VADIM MOKŠIN, DARIUS OZAROVSKIS, ROLANDAS ZAREMBA 
 
 
 VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. JUNE 2012. VOLUME 14, ISSUE 2. ISSN 1392-8716 
513 
 
 
Fig. 6. Quartz sand particles aggregation caused by the action of acoustic field (photo from the optical 
microscope, magnification ×200): 1 – two-particle aggregate, 2 – three-particle aggregate 
 
Conclusions 
 
1. Theoretical investigations show that interaction between particles occurs only if the value of 
interaction angle φ exceeds 50º. Interaction force increases as frequency of acoustic field 
decreases. 
2. Theoretical and experimental investigations demonstrate that the rate of particle aggregation 
depends on frequency of acoustic field and value of interaction angle. When interaction angle 
increases the force created by surface roughness occurs, i.e. the friction factor increases. 
3. Microscopic analysis of aggregated particles reveals that their surfaces have an irregular 
shape and approximately coincide with the surfaces shown in Fig. 6.   
 
References 
 
[1] Schmaltz G. Technische Oberflächenkunde. Berlin: Springer-Verlag, 1936. 
[2] Czichos H. A Systems Approach to the Tribology. Moscow: Mir, 1982. 
[3] Casimir H. B. G. On the attraction between two perfectly conducting plates. Proceedings of the 
Royal Netherlands Academy of Arts and Sciences, Vol. 51, 1948, p. 793 – 795. 
[4] Briscoe B. J., Tabor D. Surface forces in friction and adhesion. Faraday Special Discussions of the 
Chemical Society, Issue 2, 1972, p. 1 – 6. 
[5] Fuller K. N. G., Tabor D. The effect of surface roughness on the adhesion of elastic solids. 
Proceedings of the Royal Society A, Vol. 345, No. 1642, 1975, p. 327 – 342. 
[6] Bergman L. Ultrasound and its Application in Science and Technique. Moscow: Publishing House 
of Foreign Literature, 1957. 
[7] Vekteris V., Zaremba R., Striška V. Tribology and adhesion of particles in acoustic field. 
Proceedings of 13th International Research/Expert Conference “Trends in the Development of 
Machinery and Associated Technology”, TMT2009, Hammamet, Tunisia, 16 – 21 October, 2009,        
p. 645 – 648. 
[8] King L. V. On the acoustic radiation pressure on circular discs: Inertia and diffraction corrections. 
Proceedings of the Royal Society A, Vol. 153, No. 878, 1935, p. 1 – 16. 
 


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Tribological adhesion of particles in acoustic field

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