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Experimental measurement of the normal coefficient of restitution of micro-particles impacting on plate surface in different humidity
Accepted Manuscript Experimental measurement of the normal coefficient of restitution of micro-particles impacting on plate surface in different humidity
Ming Dong, Yaokui Mei, Xue Li, Yan Shang, Sufen Li PII: DOI: Reference:
S0032-5910(18)30384-X doi:10.1016/j.powtec.2018.05.022 PTEC 13395
To appear in:
Powder Technology
Received date: Accepted date:
26 March 2018 10 May 2018
Please cite this article as: Ming Dong, Yaokui Mei, Xue Li, Yan Shang, Sufen Li , Experimental measurement of the normal coefficient of restitution of micro-particles impacting on plate surface in different humidity. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Ptec(2017), doi:10.1016/j.powtec.2018.05.022
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ACCEPTED MANUSCRIPT Experimental measurement of the normal coefficient of restitution of micro-particles impacting on plate surface in different humidity Ming Dong*, Yaokui Mei, Xue Li, Yan Shang, Sufen Li
School of Energy and Power Engineering, Key Laboratory of Ocean Energy Utilization and
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Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian 116024, China
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Corresponding author: Ming Dong, School of Energy and Power Engineering, Key Laboratory
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of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, 2 Linggong Road, Ganjingzi District, Dalian, Liaoning, 116024, People's Republic
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of China, Tel: +86-0411-84708460, Fax: +86-0411-84708460
E-mails: [email protected]; [email protected]; [email protected];
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[email protected]; [email protected].
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Abstract
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The coefficient of restitution is widely used to characterize the energy loss rate in numerical simulations of discrete element modelling. The accurate input parameters can obtain the accurate simulation results for discrete element modelling. The determination of the coefficient of
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restitution for the single component particle is the relatively simple process, however, when considering multicomponent particles like fly-ash and humidity environment, the unpredictable
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property of particle after impact makes the analysis of the coefficient of restitution more complicated. This paper presents an experimental setup to determine normal coefficient of restitution using the high-speed digital camera in different humidity condition. The normal coefficient of restitution was measured for fly-ash micro-particles with different relative velocities and humidity, with a focus on collision velocities below 7 m/s. Therefore, this work focused on the effect of humidity and incident velocity on the normal coefficient of restitution. Keywords：Normal coefficient of restitution; critical capture velocity; relative humidity; normal impaction; micro-particle.
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Nomenclature m particle mass
the normal coefficient of restitution
limiting velocity
the kinetic energy for the incoming particle
particle density
the impact energy dissipated due to
limiting kinetic energy
plastic deformation
total adhesion energy
the elastic energy stored in the area of plastic deformation
radius of plastic deformation contact circle
elastic deformation
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the surface energy developed over the interfacial contact total projected radius of contact
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the elastic energy stored in the area of
adhesion energy caused by capillary forces
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the mechanical energy due to the surface
T environmental temperature
contact
θ1 contact angle between surface and water Poisson ratio for the material of object i
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θ2 contact angle between particle and water
maximum radius of contact circle under
molar volume of water
σ surface tension of water against air
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the Young’s modulus for the material of
purely elastic compression
object i
R
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Y elastic yield limit of material
molar gas constant
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1. Introduction
Particle dynamic processes are widely used in various industries, such as electrostatic precipitators (ESPs), fluidized beds, chemical, and food. Especially agglomeration processes,
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particles interact with each other, deposition in low temperature ESPs. The discrete element modelling (DEM) is becoming a more commonly used tool for simulating dynamic processes
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involving solid particles [1]. DEM traces the movement of all particles in a system and can provide particle-level information, which is often difficult to achieve by experiments [2]. One of the required input parameters for DEM simulations is the coefficient of restitution, e, which can describe the energy losses during particle collisions and is important for proper modelling of particle dynamics [1,3]. The coefficient of restitution is defined as the ratio of the rebound velocity and incident velocity. There have been many published studies into the normal collisions for the dry condition. Dahneke researched the normal impact of polystyrene latex micro-particles with surfaces in vacuum conditions and defined the critical capture velocity, above which bouncing and below
ACCEPTED MANUSCRIPT which sticking occur [4-5]. Rogers and Reed measured the critical capture velocity for copper particles (15-40μm) by using a high-speed camera [6]. Wall et al. researched the process of particle energy change after ammonium fluorescein particles impact different material plats by using a laser Doppler velocimetry system [7]. Their study also determined the critical capture velocity under different collision conditions. Dong et al. applied a dynamic model to investigate the rebound behaviour of fly-ash particles normally impacting a planar surface, and analysed the
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effect of particle size on the critical capture velocity and of particle’s incident velocity on the
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damping coefficient, as well as the collision contact time [8]. Dong et al. researched critical capture velocity of SiO2 particles impact with the surface under different temperatures [9]. Their
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study found that the collision process was influenced by surface temperature, which leads to higher critical capture velocity. Kuuluvainen et al. researched the effect of materials on the critical
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capture velocity with variable nozzle area impactor, and provided comparisons to previous research results with silver particles obtained by the same method [10].
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Real flue gases entering an ESP have certain humidity. Thus, a thin liquid layer can be condensed on the surface of particles. The forming of liquid bridge force produced by the liquid
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layer is given in favour of particle deposition. Many researchers focus on experimental research of
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millimeter-sized particles against flat surfaces with a liquid layer. Davis et al. measured the rebound velocity of spheres dropped from different heights onto a plat quartz surface coated with a thin layer of the viscous fluid [11]. Ma et al set up an experimental collision system to demonstrate
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that rebound behaviours differ with different liquid layer thickness and viscosity [12-13]. Then, a
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modified Stokes number was proposed:
where m is the particle mass,
Stm mVi dh
(1)
is the incident velocity, μ is the dynamic viscosity of the liquid, d
is the diameter of the particle, and h is the thickness of the liquid layer. Under humid conditions, the effect of adhesion is increased by capillary force, which makes particle deposition much easier and researched on fine particles. Zarate et al. calculated the adhesion forces of hydrophilic versus hydrophobic particles in different humidity conditions [14]. Givehchi and Tan presented a new model for airborne nanoparticle filtration with considering the influences of plastic behaviour collision and capillary force [15]. They concluded that the capillary force between the filter
ACCEPTED MANUSCRIPT surface and particle increased with increasing humidity. Pakarinen et al. computed the meniscus profile using the Kelvin equation and the values for different particle shapes, separation distance, and contact angles [16]. Xu et al., Sedin et al., Xiao et al. and Zitzler et al. measured the adhesion force between a nanoparticle and flat surface with an atomic force microscope under different humidity conditions [17-20]. Dörmann and Schmid investigated the effect of particle diameter and
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relative humidity on the capillary force. They calculated the capillary force for particle-particle and particle-wall collisions [21]. Micron-sized particles compare with millimeter-sized
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particles in impact process. There is a fundamental change in the force between particles, and many phenomena can’t be explained by traditional macroscopic contact
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theory. For example, plastic deformation and jump phenomena in contact process. These phenomena can be attributed to surface deformation and contact of particle
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surface molecules and atoms. In ash deposition, filtration, and agglomerates field, it is vital to study micron-sized particle collisions.
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the experiments as mentioned above considered the particle size as millimeters, little attention has been paid on micrometer-scale particle collision under humid conditions. In this
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paper, we investigated the effect of humidity on particle-wall collision behaviour by experimental
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and theoretical analysis. In section 2, the experimental set-up was described to study the particle-wall collision behaviour. In section 3, theoretical analysis model for normal impaction of fly-ash particles with the surface was introduced. In section 4, firstly, we discussed the
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experimental results on the variation of the normal coefficient of restitution with the incident velocity. Secondly, the effect of humidity on rebound behaviour and critical capture velocity was
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analysed. Finally, energy loss of collision process was investigated systematically. 2. Experimental analyses 2.1 Experimental system The experimental device was developed to investigate the collision of fly-ash particles on the surface under dry and humid conditions. This system, which is illustrated in Fig. 1, is used for measuring the normal impact velocity. Take in Figure 1.
This system is composed of the fluid-flow system, impact unit, humidity control system and high-speed camera system. The fluid-flow system consists of a nitrogen supply device, two mass
ACCEPTED MANUSCRIPT flowmeters, and an atomizer. The fluid-flow was divided into two parts to provide the required humidity environment. The humidity control system consists of two mass flow meters and one BGI collision device (atomizer aerosol generator, BGI Inc., USA). The system can provide the required humidity condition, and therefore, we can change the humidity and velocity by adjusting the mass flow meters.
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The fly ash particle enters the thoroughly mixed air stream through the particle generator for vertical impacting onto the disassembling planar surface made of stainless steel (diameter of 2
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mm). The surface roughness is 0.2μm showed in Fig. 2 using FlatMaster200, so the effect of roughness could be neglect. The humidity of the outlet gases in the experiment is measured by a
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hygrometer, which offers a full range of digital output calibration for the determination of humidity value.
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Take in Figure 2.
The high-speed camera system (Phantom V12.1, Vision Research Inc., Wayne, NJ, USA)
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consists of a point source, M×10microscopic lens, and a computer. The fly-ash particle was recorded using the high-speed camera at a resolution of 256×128 at an exposure time of 6.22 μs.
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The frame rate was 120,000 frames/s. The images were showed in Fig. 3, the time interval of
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which was two frames. The diameter and impaction velocity of the particle in the picture is 6μm and 5.72m/s respectively.
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2.2 Particles
Take in Figure 3.
The experimental fly ash particles were obtained from Fushun bituminous coal in the
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Liaoning province of China. Fly ash particles are created by burning coal powder in a muffle furnace at 800 ℃. We used an X-ray fluorescence spectrometer to analyse all total element analysis of the fly ash particles, and the results are given in Table 1. A laser scattering particle analyser was used to determine the particle size distribution as shown in Fig. 4. The diameter of the particle was selected 7μm ± 2 in this study. Take in Table 1. Take in Figure 4.
X-ray diffraction (XRD) is used to analyse the content of crystallization phase and amorphous phase that were measured in Fig. 5 and the data are given in Table 2. MDI Jade
ACCEPTED MANUSCRIPT software is used to calculate the weight percentage of fly ash crystallinity. The results were illustrated in Table 3. Take in Figure 5. Take in Table 2. Take in Table 3.
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Through the data analysis, the value of density and Young's modulus were calculated as follows and the results are listed in Table 4 [22].
flyash SiO VSiO CaSO VCaSO glassVglass 2
4
4
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2
(3)
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E flyash E SiO2VSiO2 E CaSO4VCaSO4 E glassVglass
(2)
where V is the volume fraction, E is the Young’s modulus, and the subscripts fly ash, SiO2, CaSO4
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and glass denote the fly ash, SiO2, CaSO4 and glass phase, respectively. Take in Table 4.
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3. Theoretical analysis
The fly-ash particle has an elastic-plastic behaviour. The collision process between particle
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and surface is divided into two stages: approaching stage and rebounding stage. The approaching
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stage is further divided into two stages. The first stage is at the moment of initial contact of the particle and characterized by the purely elastic deformation of the particle. With the pressure of collision progresses increases until the peak pressure reached the elastic yield limit Y of the
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fly-ash particle. The second stage is characterized by the appearance of plastic deformation region of the fly-ash particle and until the collision bodies have zero relative velocity.
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A schematic diagram of the energy balance of the collision process of fly-ash particle and planar surface for humidity condition is shown in Fig. 6. The energy balance equation for the collision is:
Ki Ke K pe K p Ev where
is the incident particle kinetic energy;
deformation region;
is the energy stored in the elastic
is the energy stored in the plastic deformation region;
collision energy loss for plastic deformation;
(4)
is the
is the adhesion energy loss due to capillary forces
for humidity condition. Take in Figure 6.
ACCEPTED MANUSCRIPT The Hertz equation is applied for only elastic collision. The elastic yield limit Y can be used to determine the limiting velocity Vy, above which plastic deformation begins to occur.
as
[6,23]:
Vy 2 3K 2 5 Y 5/2 2
1/2
(5)
where ρ is the fly-ash particle density and
K 4 3 k1 k2 , where
is the Young’s modulus for the material
is determined by the bulk material properties and is independent of particle
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of object i.
is the Poisson ratio,
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with
(6)
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diameter [7].
The energy stored in elastic deformations is just the limiting kinetic energy, , can be shown as [6,23]:
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An expression of the collision energy loss for plastic deformation,
.
1/2 1/2 K p Ki K y 16 15K y 16
2
(7)
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From energy balance of dry condition, Rogers and Reed determined the necessary condition for particle rebound after the collision to be [6]:
Ki K p Ea
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is the total adhesion energy from the equilibrium circle of contact, Ki K p is the
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where
available elastic energy for rebound. If Ki K p is less than
, the particle will be adhere. If
, the particle will be rebound. Johnson et, al. presented that the total
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Ki K p is greater than
adhesive energy is the sum of a mechanical energy
and a surface energy
Ea Em Es
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where
(8)
is the mechanical energy due to the surface contact,
[24], such as (9)
is the surface energy
developed over the interfacial contact. The calculation method was discussed in the literature [6] in detail, thus this paper will not describe it. Humidity has a significant influence on particle rebound, which can be explained by the adhesion energy contributed by capillary forces [25]. The adhesion energy as a result of capillary forces is represented as:
Ev 8 2Vm RT c 2 2R ln RH 100
(10)
ACCEPTED MANUSCRIPT c cos 1 cos 2 2 where
(11)
is the molar volume of water, σ is the surface tension of water against air, T is the
environmental temperature, R is the molar gas constant, θ1 is the contact angle between the surface and liquid, and θ2 is the contact angle between the particle and liquid. Under the humidity condition, the particle rebound condition after the collision is:
Ki K p Ea Ev
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(12)
4. Results and discussion
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4.1 Normal coefficient of restitution
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In the present experiments, the incident and rebound velocities of fly-ash particles of different humidity were measured. The diameter range of the particle in the error curve is 7 μm±2
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by screening; therefore, the influence of particle diameter could be ignored. The particle collision process was plotted under four different humidity, which was shown as follows: Case (Ⅰ) the
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environmental was dry; Case ( Ⅱ ) the environmental humidity was 35%; Case ( Ⅲ ) the environmental humidity was 50%; Case (Ⅳ) the environmental humidity was 65%, respectively.
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The definition of humidity in this paper is relative humidity. The drag force calculation was
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discussed in the literature [26] in detail, the flow influence could be neglected, thus this paper will not describe it.
The normal coefficient of restitution (en) is defined as the ratio of normal rebound-to-incident
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velocity. Fig. 7 shows en versus the normal incident velocity (Vin) under four cases. The experiment was performed five times for each group, for each group could obtain several
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experiment dates, and then the error curve is obtained. For all cases, Vin is less than the critical capture velocity leads to particle stick to the surface, Vin is larger than but close to the critical capture velocity, the steep tendencies of normal coefficient of restitution with increasing Vin are most apparent. And then en has a smooth transition. However, with increasing Vin further, the en will obviously decrease. Also, owing to the additional capillary force, the energy loss increased with increasing humidity. The particles for Case (Ⅳ) are easily captured than other cases. The results show that the stick process of ash-particle easily occurs for higher humidity. Take in Figure 7.
In terms of energy loss analysis, there are several reasons for energy loss, the main ones
ACCEPTED MANUSCRIPT being viscoelasticity of material and plastic deformation energy loss with low-velocity collision and high-velocity collision, respectively [27]. When the collision strength is lower, the elastic deformation occurs in the contact area. When the impact strength is higher, plastic and elastic deformation occur in the centre of contact area, and elastic deformation occurs at the edge contact area. Elastic deformation can be restored, while plastic deformation is permanent. Actual particles
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are not fully ideal elastic material and exhibit viscoelasticity, and viscoelastic energy loss increases with increasing contact time. During low-velocity collision, viscoelastic energy loss plays a
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dominant role in energy loss. When the elastic deformation occurs in the contact area, the contact time decreases with increasing Vin. The proportion of viscoelastic energy loss of kinetic energy
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decreases with increasing Vin. Therefore, en curve shows an increasing tendency. As increasing Vin, the plastic deformation occurs in the contact area and plays a dominant role in energy loss. The
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proportion of plastic deformation energy loss of kinetic energy increases with increasing Vin. Therefore, en curve shows a decreasing tendency.
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4.2 Effect of humidity on impact process
The above experimental results indicate that the normal coefficient of restitution depends
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strongly on the incident velocity and humidity. In order to explore the relation between the normal
Stokes number
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coefficient of restitution and these parameters. We analysed that en versus the Stokes number. The is defined as the ratio between the inertia of the particle and the
viscosity of fluid, where
is the diameter of the particle,
is
is the viscosity of the fluid. A critical Stokes number Stc is used as
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the incident velocity,
is the density of the particle,
parameters within this paper. Stc is the smallest Stokes number if the particle rebound. The
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particle will stick to the surface for StStc. Stc can be determined experimentally by critical capture velocity. Fig. 8 is en versus the Stokes number. The en is zero for StStc. Then en has a smooth transition. But with the St further increases, the en will slightly decrease. In addition, for a constant St, en decreases with humidity increases. Further, the interaction contact forces between particles and plate surface most likely to be relevant to this study are van der Waals and capillary force. Contact forces may be shielded by capillary forces, except for under dry conditions, van der Waals forces may be small compared to other forces, and capillary forces usually dominate other surface forces for particles impacting the plate [28]. An
ACCEPTED MANUSCRIPT attractive force is caused by a liquid meniscus between the lyophilic particle and the plate surface. The attractive force is known as capillary force and is dependent on humidity. The meniscus may be formed by capillary condensation or an accumulation of adsorbed liquid. The meniscus generates an attractive force for two reasons [29-31]: one is the direct effect of the liquid surface tension around the periphery of the meniscus draws the particles and the plate surface together;
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another is the internal stress of the meniscus declines compared to the external pressure by the capillary pressure developed by the Laplace equation, due to the meniscus curvature. This pressure
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difference affects the intersecting surface of the meniscus and attracts the particles towards the plate surface. The capillary pressure contribution (acting over the intersecting surface of the
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meniscus) is predicted to drop steeply with increasing humidity. However, the surface tension contribution (acting around the circumference of the meniscus) increases drastically with humidity.
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According to the cone-on-flat model developed by Coughlin et al. [31], a significant increase in capillary forces was predicted with increased humidity, due to the dominant effect of the surface
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tension term, and this was validated by experimental data [32]. The capillary forces between the particle and plate surface are strengthened as the humidity increases; therefore, the normal
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coefficient of restitution decreases.
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Take in Figure 8.
From the point of view of energy analysis, the energy loss of particle collision can be divided into three sections: the first represents the adhesion energy associated with the viscoelasticity of
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the particle itself, the second is the energy loss caused by the particle’s plastic deformation of particle, and the third is the adhesion energy relative to the meniscus, which plays dominant role
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in the three types of energy loss. Fig. 9 shows the relationship between the adhesion energy caused by the meniscus. The adhesion energy caused by the meniscus rises steeply at high humidity. Nevertheless, in this study, the particle size is 7μm ± 2, resulting in the low kinetic energy of particles. The ratio of adhesion energy caused by the meniscus to the kinetic energy of the particles is large. Therefore, the humidity significantly affects particle rebound at higher humidity. The adhesion energy as a result of capillary forces obtained from Eq. (10) as developed by Bateman [25], the adhesion energy associated with the meniscus increases with increasing humidity. However, other forms of energy loss are independent of the humidity. The normal coefficient of restitution decreases and particle rebound weakens with increasing humidity.
ACCEPTED MANUSCRIPT Take in Figure 9.
4.3 Critical capture velocity of particle The critical capture velocity is a crucial parameter for the dynamic collision. The particle will be captured by the surface or agglomerate when the incident velocity is below critical capture velocity. Furthermore, the critical capture velocity reflects the relative strength of adhesion. It is
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known that the viscoelastic effect and the plastic deformation play import roles in energy loss during low-velocity and high-velocity collision, respectively [27]. The plastic deformation effect
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is considered to be negligible when the incident velocity close to the critical capture velocity. Table 5 shows the experimental critical capture velocity under four cases. The critical capture
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velocity approximately is 0.85, 1.5, 1.82, and 2.1 m/s under case (Ⅰ), Case (Ⅱ), Case (Ⅲ) and Case (Ⅳ), respectively. The maximum critical capture velocity is about 2.1 m/s under four
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working conditions. Obviously, there is humidity has the significant influence on the critical capture velocity and impact behaviour. The critical capture velocity increases with increasing
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humidity because of viscous damping by humidity increases. Therefore, as in this work, the critical capture velocity with case (Ⅰ) is 0.85 m/s, which increases to 2.1 m/s for the case (Ⅳ).
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Take in Table 5.
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4.4 Analysis of energy loss
To understand the dependence of the normal coefficient of restitution on humidity, it is helpful to analyse the associated energy loss. The dissipated energy can be treated as the sum of two parts:
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the part transferred into the solid body
, and the other part was taken by the humidity
, that
is shown in Eq. (9) and (10), respectively. Fig. 10 shows the plots of adhesion energy versus
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normal incident velocity. From Fig. 10, the surface energy developed over the interfacial contact remains unchanged when
is lower than the
. Rogers and Reed considered that the surface
energy developed over the interfacial contact can be determined by the total projected radius of contact
(
purely elastic compression, and
), where
is the maximum radius of the contact circle under
is the plastic deformation contact circle radius, which forms
at the centre of contact upon further compression once the yield limit is reached. When elastic deformation occurs, Rogers and Reed considered that Rt is the maximum radius of the contact circle under purely elastic compression and has a constant value[6]. Therefore, the surface energy
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is lower than the
However, the surface energy increases with increasing normal incident velocity when higher than the
. The reason for this is that the total projected radius of contact
. is
increases
when the normal incident velocity is higher than the yield velocity. The changing trends of the mechanical energy associated with the surface contact and adhesion energy due to the contact
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radius are identical. The mechanical energy is several orders of magnitude smaller than the adhesion energy, due to the equilibrium circle of contact and the surface energy developed over
surface energy developed over interfacial contact.
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Take in Figure 10
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interfacial contact. Therefore, the total adhesion energy size is generally the same as that of the
Fig. 11 shows that the energy loss associated with plastic deformation increases rapidly with . The plastic deformation energy loss is several orders of magnitude larger than the
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increasing
adhesion energy, which derived from the equilibrium circle of contact. The plastic deformation
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energy loss plays a dominant role in the high-velocity collision [27]. Take in Figure 11.
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Fig. 12 shows the relative percentages of three different energy loss under humidity 50%.
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The adhesion energy percentage associated with the meniscus relative to the total energy loss basically remains unchanged with the normal incident velocity increase and is close to 1 before plastic deformation occurs. The reason is that other energy loss is small and no plastic deformation
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energy loss occurs before plastic deformation. The percentage of adhesion energy due to the equilibrium circle of contact relative to the total energy loss is less than 0.01 and remains
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unchanged with normal incident velocity. This indicates that adhesion energy due to the meniscus plays the dominant role in energy loss before plastic deformation occurs. As plastic deformation occurs, the percentage of adhesion energy due to the equilibrium circle of contact relative to the total energy loss decreases rapidly with increasing normal incident velocity. The percentage of adhesion energy associated with the meniscus relative to the total energy loss also begins to decrease with incident velocity. However, plastic deformation energy loss relative to the total energy loss increases with normal incident velocity. The plastic deformation energy loss surpasses the adhesion energy due to the meniscus when the normal incident velocity is more than 6.8 m/s. This indicates that the plastic deformation energy loss gradually becomes more dominant in
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5. Conclusion In this study, we presented an experimental setup to determine the normal coefficient of restitution using the high-speed digital camera in different humidity condition. The normal
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coefficient of restitution was measured for fly-ash micro-particles with different velocities and humidity, with a focus on small collision velocities. The primary results can be summarized as
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follows.
Firstly, for Vin is larger than the critical capture velocity but close to the critical capture
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velocity, the steep tendencies of normal coefficient of restitution with increasing Vin are most obvious. And then en has a smooth transition. However, with increasing Vin further, the en will
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obviously decrease. The particles with humidity 65% are easily captured than other cases. The results show that the stick process of ash-particle has easily occurred for higher humidity.
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Secondly, the capillary forces between the particle and plate surface are strengthened as the humidity increases. The adhesion energy caused by the meniscus rises steeply at high humidity.
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Therefore, the normal coefficient of restitution decreases and particle rebound weakens with
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increasing humidity.
Thirdly, there is humidity has the significant influence on the critical capture velocity and impact behaviour. The critical capture velocity increases with increasing humidity because of
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viscous damping by humidity increases. Therefore, as in this work, the critical capture velocity with case (Ⅰ) is 0.85 m/s, which increases to 2.1 m/s for the case (Ⅳ).
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Finally, the percentage of adhesion energy associated with the meniscus relative to the total energy loss is close to 1 and basically remains unchanged before plastic deformation occurs. The percentage of adhesion energy due to the equilibrium circle of contact relative to the total energy loss remains unchanged with Vin. The percentage of plastic deformation energy loss relative to total energy loss increases with increasing Vin. However, the percentage of adhesion energy due to the meniscus relative to the total energy loss reduced with increasing Vin. Acknowledgements The authors acknowledge the National Natural Science Foundation of China (No. 51576030), the National Key Research and Development Program of China (No. 2016YFB0600602),
ACCEPTED MANUSCRIPT and Fundamental Research Funds for the Central Universities (No. DUT16ZD202). References
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microscopy, Phys. Rev. B. 66(2002)155436. [21] M. Dörmann and H.J. Schmid, Simulation of capillary bridges between nanoscale particles. Langmuir. 30 (2014)1055-1062. [22] T. Matsunaga, J. Kim, S. Hardcastle and P. Rohatgi, Crystallinity and selected properties of fly ash particles, Mat. Sci. Eng. A-Struct. 325(2002)333-343. [23] J.G.A. Bitter, A study of erosion phenomena: Part II, Wear. 6 (1963)169-190. [24] K. Johnson, K. Kendall, A. Roberts, Surface energy and the contact of elastic solids, in Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, The Royal Society, (1971)301-313. [25] A.P. Bateman, H. Belassein and S.T. Martin, Impactor apparatus for the study of particle rebound: Relative humidity and capillary forces, Aerosol Sci. Tech. 48(2014)42-52. [26] M. Dong, X. Li, Y.K. Mei, S.F. Li, Experimental and theoretical analyses on the effect of physical properties and humidity of fly ash impacting on a flat surface, J. Aerosol Sci. 117 (2018), 85-99. [27] L. Kogut and I. Etsion, Adhesion in elastic–plastic spherical microcontact, J. Colloid Interf. Sci. 261(2003)372-378. [28] H.J. Butt and M. Kappl, Normal capillary forces, Advances in colloid and interface science, 146(2009)48-60. [29] H. Princen, I. Zia, S. Mason, Measurement of interfacial tension from the shape of a rotating drop, J. Colloid Interf. Sci. 23(1967)99-107. [30] N. Cross and R. Picknett, The liquid layer between a sphere and a plane surface, Transactions of the Faraday Society, 59(1963)846-855. [31] R. Coughlin, B. Elbirli, L.V. Edwards, Interparticle force conferred by capillary-condensed liquid at contact points: I. Theoretical considerations, J. Colloid Interf. Sci. 87(1982)18-30. [32] R. Jones, H.M. Pollock, J.A. Cleaver, C.S. Hodges, Adhesion forces between glass and silicon surfaces in air studied by AFM: Effects of relative humidity, particle size, roughness, and surface treatment, Langmuir : the ACS journal of surfaces and colloids, 18(2002)8045-8055.
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FIGURE CAPTIONS Figure 1. Schematic of the experimental system
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Figure 2. Surface roughness using FlatMaster200
Figure 3. Typical recorded image for the impact of a fly ash on a flat surface.
Figure 5. Fly ash X-ray diffraction patterns
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Figure 4. Particle size distribution of fly ash
Figure 6. Diagram of particle bounce process as energy balance for normal collision, showing (a)
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process of particle impacting surface, (b) particle at full compression before rebound, and (c) rebound process
Figure 7. The normal coefficient of restitution versus normal incident velocity Figure 8. The normal coefficient of restitution versus the Stokes number
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Figure 9. Adhesion energy caused by meniscus versus humidity
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Figure 10. Energy loss versus normal incident velocity: (a) mechanical energy due to surface contact and surface energy developed over interfacial contact versus the normal incident velocity; and (b) adhesion energy loss derived from the equilibrium circle of contact versus normal incident
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velocity
Figure11. Plastic deformation energy loss versus normal incident velocity
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Figure12. Percentage of total energy loss associated with different mechanisms
TABLE CAPTIONS Table 1. The total elemental analysis of fly ash particles Table 2. Crystalline volume fractions Table 3. Experimental data for XRD experiment of fly ash particles.
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Table 5. Critical impact velocity at different conditions by experiment
ACCEPTED MANUSCRIPT Tables Table 1. The total elemental analysis of fly ash particles. SiO2 Al2O3 CaO MgO TiO2 SO3 P2O5 36.4
2.39
0.629
2.84
2.08
1.42
Na2O
SrO
NiO
0.921
0.564
0.137
0.113
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52.3
K2O
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Table 2. Crystalline volume fractions. Crystalline phase (vol%) Fly ash CaSO4
Al2O3
18.43
-
12.57
69
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SiO2
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LN
Amorphous phase (vol%)
ACCEPTED MANUSCRIPT Table 3. Experimental data for XRD experiment of fly ash particles. Integral intensities of the strongest peak of SiO2
Integral intensities of the strongest peak of CaSO4
Integral intensities of the strongest peak of Al2O3
68.77
2654
-
572
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Mass fraction of crystallization Phase
ACCEPTED MANUSCRIPT Table 4. Physical parameters of fly ash particles. Volume fraction SiO2（%） CaSO4（%） Fly ash
Density
（%）
（kg/m3）
69
2680
12.57
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18.43
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Glass phase
Young's modulus （GPa） 116.72
ACCEPTED MANUSCRIPT Table 5. Critical capture velocity at different conditions by experiment. 35% humidity (Yes/
(Yes/ vi,n
rebound)
No
vi,n
rebound)
0.71 2
1.48
1.80
1.49
0.84
1.49
7
No 8
0.85
1.50 5
0.86
1.52
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Yes
3
2.13 Yes
5
Yes 1
Yes 6
1.83
Yes
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3
2.10
Yes
4
Yes
1
Yes
6
1.82
Yes
2.09
No
9
No
7
1.81 No
2
1.93
No 8
No 6
No
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0.80
1.86 3
No 6
No rebound)
No 6
No 8
vi,n
1.79 No
0.76
No rebound)
1.48 No
4
(Yes/
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No
65% humidity
(Yes/
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vi,n
50% humidity
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Dry
Yes 8
1.90
2.20 Yes
Yes 7
ACCEPTED MANUSCRIPT Highlights
(i) The normal coefficient of restitution decreases with increasing humidity. (ii) The critical capture velocity increases with increasing humidity.
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(iii) Systematically analysis of energy dissipation is conducted.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Ming Dong, Yaokui Mei, Xue Li, Yan Shang, Sufen Li PII: DOI: Reference:
S0032-5910(18)30384-X doi:10.1016/j.powtec.2018.05.022 PTEC 13395
To appear in:
Powder Technology
Received date: Accepted date:
26 March 2018 10 May 2018
Please cite this article as: Ming Dong, Yaokui Mei, Xue Li, Yan Shang, Sufen Li , Experimental measurement of the normal coefficient of restitution of micro-particles impacting on plate surface in different humidity. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Ptec(2017), doi:10.1016/j.powtec.2018.05.022
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ACCEPTED MANUSCRIPT Experimental measurement of the normal coefficient of restitution of micro-particles impacting on plate surface in different humidity Ming Dong*, Yaokui Mei, Xue Li, Yan Shang, Sufen Li
School of Energy and Power Engineering, Key Laboratory of Ocean Energy Utilization and
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Energy Conservation of Ministry of Education, Dalian University of Technology, Dalian 116024, China
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Corresponding author: Ming Dong, School of Energy and Power Engineering, Key Laboratory
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of Ocean Energy Utilization and Energy Conservation of Ministry of Education, Dalian University of Technology, 2 Linggong Road, Ganjingzi District, Dalian, Liaoning, 116024, People's Republic
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of China, Tel: +86-0411-84708460, Fax: +86-0411-84708460
E-mails: [email protected]; [email protected]; [email protected];
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[email protected]; [email protected].
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Abstract
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The coefficient of restitution is widely used to characterize the energy loss rate in numerical simulations of discrete element modelling. The accurate input parameters can obtain the accurate simulation results for discrete element modelling. The determination of the coefficient of
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restitution for the single component particle is the relatively simple process, however, when considering multicomponent particles like fly-ash and humidity environment, the unpredictable
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property of particle after impact makes the analysis of the coefficient of restitution more complicated. This paper presents an experimental setup to determine normal coefficient of restitution using the high-speed digital camera in different humidity condition. The normal coefficient of restitution was measured for fly-ash micro-particles with different relative velocities and humidity, with a focus on collision velocities below 7 m/s. Therefore, this work focused on the effect of humidity and incident velocity on the normal coefficient of restitution. Keywords：Normal coefficient of restitution; critical capture velocity; relative humidity; normal impaction; micro-particle.
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Nomenclature m particle mass
the normal coefficient of restitution
limiting velocity
the kinetic energy for the incoming particle
particle density
the impact energy dissipated due to
limiting kinetic energy
plastic deformation
total adhesion energy
the elastic energy stored in the area of plastic deformation
radius of plastic deformation contact circle
elastic deformation
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the surface energy developed over the interfacial contact total projected radius of contact
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the elastic energy stored in the area of
adhesion energy caused by capillary forces
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the mechanical energy due to the surface
T environmental temperature
contact
θ1 contact angle between surface and water Poisson ratio for the material of object i
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θ2 contact angle between particle and water
maximum radius of contact circle under
molar volume of water
σ surface tension of water against air
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the Young’s modulus for the material of
purely elastic compression
object i
R
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Y elastic yield limit of material
molar gas constant
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1. Introduction
Particle dynamic processes are widely used in various industries, such as electrostatic precipitators (ESPs), fluidized beds, chemical, and food. Especially agglomeration processes,
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particles interact with each other, deposition in low temperature ESPs. The discrete element modelling (DEM) is becoming a more commonly used tool for simulating dynamic processes
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involving solid particles [1]. DEM traces the movement of all particles in a system and can provide particle-level information, which is often difficult to achieve by experiments [2]. One of the required input parameters for DEM simulations is the coefficient of restitution, e, which can describe the energy losses during particle collisions and is important for proper modelling of particle dynamics [1,3]. The coefficient of restitution is defined as the ratio of the rebound velocity and incident velocity. There have been many published studies into the normal collisions for the dry condition. Dahneke researched the normal impact of polystyrene latex micro-particles with surfaces in vacuum conditions and defined the critical capture velocity, above which bouncing and below
ACCEPTED MANUSCRIPT which sticking occur [4-5]. Rogers and Reed measured the critical capture velocity for copper particles (15-40μm) by using a high-speed camera [6]. Wall et al. researched the process of particle energy change after ammonium fluorescein particles impact different material plats by using a laser Doppler velocimetry system [7]. Their study also determined the critical capture velocity under different collision conditions. Dong et al. applied a dynamic model to investigate the rebound behaviour of fly-ash particles normally impacting a planar surface, and analysed the
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effect of particle size on the critical capture velocity and of particle’s incident velocity on the
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damping coefficient, as well as the collision contact time [8]. Dong et al. researched critical capture velocity of SiO2 particles impact with the surface under different temperatures [9]. Their
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study found that the collision process was influenced by surface temperature, which leads to higher critical capture velocity. Kuuluvainen et al. researched the effect of materials on the critical
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capture velocity with variable nozzle area impactor, and provided comparisons to previous research results with silver particles obtained by the same method [10].
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Real flue gases entering an ESP have certain humidity. Thus, a thin liquid layer can be condensed on the surface of particles. The forming of liquid bridge force produced by the liquid
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layer is given in favour of particle deposition. Many researchers focus on experimental research of
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millimeter-sized particles against flat surfaces with a liquid layer. Davis et al. measured the rebound velocity of spheres dropped from different heights onto a plat quartz surface coated with a thin layer of the viscous fluid [11]. Ma et al set up an experimental collision system to demonstrate
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that rebound behaviours differ with different liquid layer thickness and viscosity [12-13]. Then, a
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modified Stokes number was proposed:
where m is the particle mass,
Stm mVi dh
(1)
is the incident velocity, μ is the dynamic viscosity of the liquid, d
is the diameter of the particle, and h is the thickness of the liquid layer. Under humid conditions, the effect of adhesion is increased by capillary force, which makes particle deposition much easier and researched on fine particles. Zarate et al. calculated the adhesion forces of hydrophilic versus hydrophobic particles in different humidity conditions [14]. Givehchi and Tan presented a new model for airborne nanoparticle filtration with considering the influences of plastic behaviour collision and capillary force [15]. They concluded that the capillary force between the filter
ACCEPTED MANUSCRIPT surface and particle increased with increasing humidity. Pakarinen et al. computed the meniscus profile using the Kelvin equation and the values for different particle shapes, separation distance, and contact angles [16]. Xu et al., Sedin et al., Xiao et al. and Zitzler et al. measured the adhesion force between a nanoparticle and flat surface with an atomic force microscope under different humidity conditions [17-20]. Dörmann and Schmid investigated the effect of particle diameter and
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relative humidity on the capillary force. They calculated the capillary force for particle-particle and particle-wall collisions [21]. Micron-sized particles compare with millimeter-sized
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particles in impact process. There is a fundamental change in the force between particles, and many phenomena can’t be explained by traditional macroscopic contact
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theory. For example, plastic deformation and jump phenomena in contact process. These phenomena can be attributed to surface deformation and contact of particle
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surface molecules and atoms. In ash deposition, filtration, and agglomerates field, it is vital to study micron-sized particle collisions.
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the experiments as mentioned above considered the particle size as millimeters, little attention has been paid on micrometer-scale particle collision under humid conditions. In this
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paper, we investigated the effect of humidity on particle-wall collision behaviour by experimental
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and theoretical analysis. In section 2, the experimental set-up was described to study the particle-wall collision behaviour. In section 3, theoretical analysis model for normal impaction of fly-ash particles with the surface was introduced. In section 4, firstly, we discussed the
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experimental results on the variation of the normal coefficient of restitution with the incident velocity. Secondly, the effect of humidity on rebound behaviour and critical capture velocity was
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analysed. Finally, energy loss of collision process was investigated systematically. 2. Experimental analyses 2.1 Experimental system The experimental device was developed to investigate the collision of fly-ash particles on the surface under dry and humid conditions. This system, which is illustrated in Fig. 1, is used for measuring the normal impact velocity. Take in Figure 1.
This system is composed of the fluid-flow system, impact unit, humidity control system and high-speed camera system. The fluid-flow system consists of a nitrogen supply device, two mass
ACCEPTED MANUSCRIPT flowmeters, and an atomizer. The fluid-flow was divided into two parts to provide the required humidity environment. The humidity control system consists of two mass flow meters and one BGI collision device (atomizer aerosol generator, BGI Inc., USA). The system can provide the required humidity condition, and therefore, we can change the humidity and velocity by adjusting the mass flow meters.
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The fly ash particle enters the thoroughly mixed air stream through the particle generator for vertical impacting onto the disassembling planar surface made of stainless steel (diameter of 2
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mm). The surface roughness is 0.2μm showed in Fig. 2 using FlatMaster200, so the effect of roughness could be neglect. The humidity of the outlet gases in the experiment is measured by a
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hygrometer, which offers a full range of digital output calibration for the determination of humidity value.
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Take in Figure 2.
The high-speed camera system (Phantom V12.1, Vision Research Inc., Wayne, NJ, USA)
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consists of a point source, M×10microscopic lens, and a computer. The fly-ash particle was recorded using the high-speed camera at a resolution of 256×128 at an exposure time of 6.22 μs.
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The frame rate was 120,000 frames/s. The images were showed in Fig. 3, the time interval of
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which was two frames. The diameter and impaction velocity of the particle in the picture is 6μm and 5.72m/s respectively.
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2.2 Particles
Take in Figure 3.
The experimental fly ash particles were obtained from Fushun bituminous coal in the
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Liaoning province of China. Fly ash particles are created by burning coal powder in a muffle furnace at 800 ℃. We used an X-ray fluorescence spectrometer to analyse all total element analysis of the fly ash particles, and the results are given in Table 1. A laser scattering particle analyser was used to determine the particle size distribution as shown in Fig. 4. The diameter of the particle was selected 7μm ± 2 in this study. Take in Table 1. Take in Figure 4.
X-ray diffraction (XRD) is used to analyse the content of crystallization phase and amorphous phase that were measured in Fig. 5 and the data are given in Table 2. MDI Jade
ACCEPTED MANUSCRIPT software is used to calculate the weight percentage of fly ash crystallinity. The results were illustrated in Table 3. Take in Figure 5. Take in Table 2. Take in Table 3.
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Through the data analysis, the value of density and Young's modulus were calculated as follows and the results are listed in Table 4 [22].
flyash SiO VSiO CaSO VCaSO glassVglass 2
4
4
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2
(3)
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E flyash E SiO2VSiO2 E CaSO4VCaSO4 E glassVglass
(2)
where V is the volume fraction, E is the Young’s modulus, and the subscripts fly ash, SiO2, CaSO4
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and glass denote the fly ash, SiO2, CaSO4 and glass phase, respectively. Take in Table 4.
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3. Theoretical analysis
The fly-ash particle has an elastic-plastic behaviour. The collision process between particle
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and surface is divided into two stages: approaching stage and rebounding stage. The approaching
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stage is further divided into two stages. The first stage is at the moment of initial contact of the particle and characterized by the purely elastic deformation of the particle. With the pressure of collision progresses increases until the peak pressure reached the elastic yield limit Y of the
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fly-ash particle. The second stage is characterized by the appearance of plastic deformation region of the fly-ash particle and until the collision bodies have zero relative velocity.
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A schematic diagram of the energy balance of the collision process of fly-ash particle and planar surface for humidity condition is shown in Fig. 6. The energy balance equation for the collision is:
Ki Ke K pe K p Ev where
is the incident particle kinetic energy;
deformation region;
is the energy stored in the elastic
is the energy stored in the plastic deformation region;
collision energy loss for plastic deformation;
(4)
is the
is the adhesion energy loss due to capillary forces
for humidity condition. Take in Figure 6.
ACCEPTED MANUSCRIPT The Hertz equation is applied for only elastic collision. The elastic yield limit Y can be used to determine the limiting velocity Vy, above which plastic deformation begins to occur.
as
[6,23]:
Vy 2 3K 2 5 Y 5/2 2
1/2
(5)
where ρ is the fly-ash particle density and
K 4 3 k1 k2 , where
is the Young’s modulus for the material
is determined by the bulk material properties and is independent of particle
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of object i.
is the Poisson ratio,
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with
(6)
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diameter [7].
The energy stored in elastic deformations is just the limiting kinetic energy, , can be shown as [6,23]:
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An expression of the collision energy loss for plastic deformation,
.
1/2 1/2 K p Ki K y 16 15K y 16
2
(7)
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From energy balance of dry condition, Rogers and Reed determined the necessary condition for particle rebound after the collision to be [6]:
Ki K p Ea
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is the total adhesion energy from the equilibrium circle of contact, Ki K p is the
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where
available elastic energy for rebound. If Ki K p is less than
, the particle will be adhere. If
, the particle will be rebound. Johnson et, al. presented that the total
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Ki K p is greater than
adhesive energy is the sum of a mechanical energy
and a surface energy
Ea Em Es
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where
(8)
is the mechanical energy due to the surface contact,
[24], such as (9)
is the surface energy
developed over the interfacial contact. The calculation method was discussed in the literature [6] in detail, thus this paper will not describe it. Humidity has a significant influence on particle rebound, which can be explained by the adhesion energy contributed by capillary forces [25]. The adhesion energy as a result of capillary forces is represented as:
Ev 8 2Vm RT c 2 2R ln RH 100
(10)
ACCEPTED MANUSCRIPT c cos 1 cos 2 2 where
(11)
is the molar volume of water, σ is the surface tension of water against air, T is the
environmental temperature, R is the molar gas constant, θ1 is the contact angle between the surface and liquid, and θ2 is the contact angle between the particle and liquid. Under the humidity condition, the particle rebound condition after the collision is:
Ki K p Ea Ev
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(12)
4. Results and discussion
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4.1 Normal coefficient of restitution
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In the present experiments, the incident and rebound velocities of fly-ash particles of different humidity were measured. The diameter range of the particle in the error curve is 7 μm±2
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by screening; therefore, the influence of particle diameter could be ignored. The particle collision process was plotted under four different humidity, which was shown as follows: Case (Ⅰ) the
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environmental was dry; Case ( Ⅱ ) the environmental humidity was 35%; Case ( Ⅲ ) the environmental humidity was 50%; Case (Ⅳ) the environmental humidity was 65%, respectively.
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The definition of humidity in this paper is relative humidity. The drag force calculation was
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discussed in the literature [26] in detail, the flow influence could be neglected, thus this paper will not describe it.
The normal coefficient of restitution (en) is defined as the ratio of normal rebound-to-incident
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velocity. Fig. 7 shows en versus the normal incident velocity (Vin) under four cases. The experiment was performed five times for each group, for each group could obtain several
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experiment dates, and then the error curve is obtained. For all cases, Vin is less than the critical capture velocity leads to particle stick to the surface, Vin is larger than but close to the critical capture velocity, the steep tendencies of normal coefficient of restitution with increasing Vin are most apparent. And then en has a smooth transition. However, with increasing Vin further, the en will obviously decrease. Also, owing to the additional capillary force, the energy loss increased with increasing humidity. The particles for Case (Ⅳ) are easily captured than other cases. The results show that the stick process of ash-particle easily occurs for higher humidity. Take in Figure 7.
In terms of energy loss analysis, there are several reasons for energy loss, the main ones
ACCEPTED MANUSCRIPT being viscoelasticity of material and plastic deformation energy loss with low-velocity collision and high-velocity collision, respectively [27]. When the collision strength is lower, the elastic deformation occurs in the contact area. When the impact strength is higher, plastic and elastic deformation occur in the centre of contact area, and elastic deformation occurs at the edge contact area. Elastic deformation can be restored, while plastic deformation is permanent. Actual particles
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are not fully ideal elastic material and exhibit viscoelasticity, and viscoelastic energy loss increases with increasing contact time. During low-velocity collision, viscoelastic energy loss plays a
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dominant role in energy loss. When the elastic deformation occurs in the contact area, the contact time decreases with increasing Vin. The proportion of viscoelastic energy loss of kinetic energy
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decreases with increasing Vin. Therefore, en curve shows an increasing tendency. As increasing Vin, the plastic deformation occurs in the contact area and plays a dominant role in energy loss. The
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proportion of plastic deformation energy loss of kinetic energy increases with increasing Vin. Therefore, en curve shows a decreasing tendency.
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4.2 Effect of humidity on impact process
The above experimental results indicate that the normal coefficient of restitution depends
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strongly on the incident velocity and humidity. In order to explore the relation between the normal
Stokes number
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coefficient of restitution and these parameters. We analysed that en versus the Stokes number. The is defined as the ratio between the inertia of the particle and the
viscosity of fluid, where
is the diameter of the particle,
is
is the viscosity of the fluid. A critical Stokes number Stc is used as
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the incident velocity,
is the density of the particle,
parameters within this paper. Stc is the smallest Stokes number if the particle rebound. The
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particle will stick to the surface for St
ACCEPTED MANUSCRIPT attractive force is caused by a liquid meniscus between the lyophilic particle and the plate surface. The attractive force is known as capillary force and is dependent on humidity. The meniscus may be formed by capillary condensation or an accumulation of adsorbed liquid. The meniscus generates an attractive force for two reasons [29-31]: one is the direct effect of the liquid surface tension around the periphery of the meniscus draws the particles and the plate surface together;
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another is the internal stress of the meniscus declines compared to the external pressure by the capillary pressure developed by the Laplace equation, due to the meniscus curvature. This pressure
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difference affects the intersecting surface of the meniscus and attracts the particles towards the plate surface. The capillary pressure contribution (acting over the intersecting surface of the
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meniscus) is predicted to drop steeply with increasing humidity. However, the surface tension contribution (acting around the circumference of the meniscus) increases drastically with humidity.
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According to the cone-on-flat model developed by Coughlin et al. [31], a significant increase in capillary forces was predicted with increased humidity, due to the dominant effect of the surface
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tension term, and this was validated by experimental data [32]. The capillary forces between the particle and plate surface are strengthened as the humidity increases; therefore, the normal
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coefficient of restitution decreases.
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Take in Figure 8.
From the point of view of energy analysis, the energy loss of particle collision can be divided into three sections: the first represents the adhesion energy associated with the viscoelasticity of
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the particle itself, the second is the energy loss caused by the particle’s plastic deformation of particle, and the third is the adhesion energy relative to the meniscus, which plays dominant role
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in the three types of energy loss. Fig. 9 shows the relationship between the adhesion energy caused by the meniscus. The adhesion energy caused by the meniscus rises steeply at high humidity. Nevertheless, in this study, the particle size is 7μm ± 2, resulting in the low kinetic energy of particles. The ratio of adhesion energy caused by the meniscus to the kinetic energy of the particles is large. Therefore, the humidity significantly affects particle rebound at higher humidity. The adhesion energy as a result of capillary forces obtained from Eq. (10) as developed by Bateman [25], the adhesion energy associated with the meniscus increases with increasing humidity. However, other forms of energy loss are independent of the humidity. The normal coefficient of restitution decreases and particle rebound weakens with increasing humidity.
ACCEPTED MANUSCRIPT Take in Figure 9.
4.3 Critical capture velocity of particle The critical capture velocity is a crucial parameter for the dynamic collision. The particle will be captured by the surface or agglomerate when the incident velocity is below critical capture velocity. Furthermore, the critical capture velocity reflects the relative strength of adhesion. It is
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known that the viscoelastic effect and the plastic deformation play import roles in energy loss during low-velocity and high-velocity collision, respectively [27]. The plastic deformation effect
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is considered to be negligible when the incident velocity close to the critical capture velocity. Table 5 shows the experimental critical capture velocity under four cases. The critical capture
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velocity approximately is 0.85, 1.5, 1.82, and 2.1 m/s under case (Ⅰ), Case (Ⅱ), Case (Ⅲ) and Case (Ⅳ), respectively. The maximum critical capture velocity is about 2.1 m/s under four
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working conditions. Obviously, there is humidity has the significant influence on the critical capture velocity and impact behaviour. The critical capture velocity increases with increasing
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humidity because of viscous damping by humidity increases. Therefore, as in this work, the critical capture velocity with case (Ⅰ) is 0.85 m/s, which increases to 2.1 m/s for the case (Ⅳ).
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Take in Table 5.
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4.4 Analysis of energy loss
To understand the dependence of the normal coefficient of restitution on humidity, it is helpful to analyse the associated energy loss. The dissipated energy can be treated as the sum of two parts:
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the part transferred into the solid body
, and the other part was taken by the humidity
, that
is shown in Eq. (9) and (10), respectively. Fig. 10 shows the plots of adhesion energy versus
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normal incident velocity. From Fig. 10, the surface energy developed over the interfacial contact remains unchanged when
is lower than the
. Rogers and Reed considered that the surface
energy developed over the interfacial contact can be determined by the total projected radius of contact
(
purely elastic compression, and
), where
is the maximum radius of the contact circle under
is the plastic deformation contact circle radius, which forms
at the centre of contact upon further compression once the yield limit is reached. When elastic deformation occurs, Rogers and Reed considered that Rt is the maximum radius of the contact circle under purely elastic compression and has a constant value[6]. Therefore, the surface energy
ACCEPTED MANUSCRIPT developed over the interfacial contact remaining unchanged when
is lower than the
However, the surface energy increases with increasing normal incident velocity when higher than the
. The reason for this is that the total projected radius of contact
. is
increases
when the normal incident velocity is higher than the yield velocity. The changing trends of the mechanical energy associated with the surface contact and adhesion energy due to the contact
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radius are identical. The mechanical energy is several orders of magnitude smaller than the adhesion energy, due to the equilibrium circle of contact and the surface energy developed over
surface energy developed over interfacial contact.
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Take in Figure 10
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interfacial contact. Therefore, the total adhesion energy size is generally the same as that of the
Fig. 11 shows that the energy loss associated with plastic deformation increases rapidly with . The plastic deformation energy loss is several orders of magnitude larger than the
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increasing
adhesion energy, which derived from the equilibrium circle of contact. The plastic deformation
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energy loss plays a dominant role in the high-velocity collision [27]. Take in Figure 11.
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Fig. 12 shows the relative percentages of three different energy loss under humidity 50%.
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The adhesion energy percentage associated with the meniscus relative to the total energy loss basically remains unchanged with the normal incident velocity increase and is close to 1 before plastic deformation occurs. The reason is that other energy loss is small and no plastic deformation
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energy loss occurs before plastic deformation. The percentage of adhesion energy due to the equilibrium circle of contact relative to the total energy loss is less than 0.01 and remains
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unchanged with normal incident velocity. This indicates that adhesion energy due to the meniscus plays the dominant role in energy loss before plastic deformation occurs. As plastic deformation occurs, the percentage of adhesion energy due to the equilibrium circle of contact relative to the total energy loss decreases rapidly with increasing normal incident velocity. The percentage of adhesion energy associated with the meniscus relative to the total energy loss also begins to decrease with incident velocity. However, plastic deformation energy loss relative to the total energy loss increases with normal incident velocity. The plastic deformation energy loss surpasses the adhesion energy due to the meniscus when the normal incident velocity is more than 6.8 m/s. This indicates that the plastic deformation energy loss gradually becomes more dominant in
ACCEPTED MANUSCRIPT energy loss when the collision strength is high. Take in Figure 12.
5. Conclusion In this study, we presented an experimental setup to determine the normal coefficient of restitution using the high-speed digital camera in different humidity condition. The normal
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coefficient of restitution was measured for fly-ash micro-particles with different velocities and humidity, with a focus on small collision velocities. The primary results can be summarized as
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follows.
Firstly, for Vin is larger than the critical capture velocity but close to the critical capture
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velocity, the steep tendencies of normal coefficient of restitution with increasing Vin are most obvious. And then en has a smooth transition. However, with increasing Vin further, the en will
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obviously decrease. The particles with humidity 65% are easily captured than other cases. The results show that the stick process of ash-particle has easily occurred for higher humidity.
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Secondly, the capillary forces between the particle and plate surface are strengthened as the humidity increases. The adhesion energy caused by the meniscus rises steeply at high humidity.
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Therefore, the normal coefficient of restitution decreases and particle rebound weakens with
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increasing humidity.
Thirdly, there is humidity has the significant influence on the critical capture velocity and impact behaviour. The critical capture velocity increases with increasing humidity because of
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viscous damping by humidity increases. Therefore, as in this work, the critical capture velocity with case (Ⅰ) is 0.85 m/s, which increases to 2.1 m/s for the case (Ⅳ).
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Finally, the percentage of adhesion energy associated with the meniscus relative to the total energy loss is close to 1 and basically remains unchanged before plastic deformation occurs. The percentage of adhesion energy due to the equilibrium circle of contact relative to the total energy loss remains unchanged with Vin. The percentage of plastic deformation energy loss relative to total energy loss increases with increasing Vin. However, the percentage of adhesion energy due to the meniscus relative to the total energy loss reduced with increasing Vin. Acknowledgements The authors acknowledge the National Natural Science Foundation of China (No. 51576030), the National Key Research and Development Program of China (No. 2016YFB0600602),
ACCEPTED MANUSCRIPT and Fundamental Research Funds for the Central Universities (No. DUT16ZD202). References
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[1] B. Crüger, V. Salikov, S. Heinrich, V.S. Sutkar, et al., Coefficient of restitution for particles impacting on wet surfaces: An improved experimental approach, Particuology. 25 (2016) 1-9. [2] K. Washino, Ei L. Chan, T. Matsumoto, S. Hashino, Normal viscous force of pendular liquid bridge between two relatively moving particles, J. Colloid Interf. Sci. 494 (2017) 255-265. [3] D.B. Hastie, Experimental measurement of the coefficient of restitution of irregular shaped particles impacting on horizontal surfaces, Chem. Eng. Sci. 101(2013) 828-836. [4] B. Dahneke, Measurements of bouncing of small latex spheres, J. Colloid Interf. Sci. 45(1973) 584-590. [5] B. Dahneke, Further measurements of the bouncing of small latex spheres J. Colloid Interf. Sci. 51(1975)58-65. [6] L.N. Rogers and J. Reed, The adhesion of particles undergoing an elastic-plastic impact with a surface, J. Phys. D Appl. Phys. 17(1984)677-689. [7] S. Wall, W. John, H.C. Wang, S.L. Goren, Measurements of kinetic energy loss for particles impacting surfaces, Aerosol Sci. Technol. 12(4) (1990)926-946. [8] M. Dong, J. Han, S.F. Li, H. Pu, A dynamic model for the normal impact of fly ash particle with a planar surface, Energies. 6(2013)4288-4307. [9] S.F. Li, J. Xie, M. Dong, L.Y. Bai, Rebound characteristics for the impact of SiO2 particle onto a flat surface at different temperatures, Powder Technol. 284 (2015) 418-428. [10] H. Kuuluvainen, A. Arffman, A. Järvinen, J. Harra, J. Keskinen, The effect of materials and obliquity of the impact on the critical velocity of rebound, Aerosol Sci. Tech. 51(2017)301-310. [11] R.H. Davis, D.A. Rager, B.T. Good, Elastohydrodynamic rebound of spheres from coated surfaces, J. Fluid Mech. 468(2002)107-119. [12] J. Ma, D. Liu, X. Chen, Experimental study of oblique impact between dry spheres and liquid layers, Phys. Rev E. 88 (2013) 033018. [13] J. Ma, D. Liu, X. Chen, Normal and oblique impacts between smooth spheres and liquid layers: Liquid bridge and restitution coefficient, Powder Technol. 301(2016) 747-759. [14] N.V. Zarate, A.J. Harrison, J.D. Litster, S.P. Beaudoin, Effect of relative humidity on onset of capillary forces for rough surfaces, J. Colloid Interf. Sci. 411(2013) 265-272. [15] R. Givehchi and Z. Tan, The effect of capillary force on airborne nanoparticle filtration, J. Aerosol Sci. 83(2015)12-24. [16] O. H. Pakarinen, A.S. Foster, M. Paajanen, T. Kalinainen, et al., Towards an accurate description of the capillary force in nanoparticle-surface interactions, Model. Simul. Mater. Sc. 13(2005) 1175. [17] L. Xu, A. Lio, H. Jun, D.F. Ogletree and M. Salmeron, Wetting and capillary phenomena of water on mica, J. Phys. Chem. B. 102(1997)540-548. [18] D.L. Sedin and K.L. Rowlen, Adhesion forces measured by atomic force microscopy in humid air, Anal. Chem. 72(2000)2183-2189. [19] X. Xiao and L. Qian, Investigation of humidity-dependent capillary force, Langmuir. 16(2012)8153-8158. [20] L. Zitzler, S. Herminghaus and F. Mugele, Capillary forces in tapping mode atomic force
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microscopy, Phys. Rev. B. 66(2002)155436. [21] M. Dörmann and H.J. Schmid, Simulation of capillary bridges between nanoscale particles. Langmuir. 30 (2014)1055-1062. [22] T. Matsunaga, J. Kim, S. Hardcastle and P. Rohatgi, Crystallinity and selected properties of fly ash particles, Mat. Sci. Eng. A-Struct. 325(2002)333-343. [23] J.G.A. Bitter, A study of erosion phenomena: Part II, Wear. 6 (1963)169-190. [24] K. Johnson, K. Kendall, A. Roberts, Surface energy and the contact of elastic solids, in Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, The Royal Society, (1971)301-313. [25] A.P. Bateman, H. Belassein and S.T. Martin, Impactor apparatus for the study of particle rebound: Relative humidity and capillary forces, Aerosol Sci. Tech. 48(2014)42-52. [26] M. Dong, X. Li, Y.K. Mei, S.F. Li, Experimental and theoretical analyses on the effect of physical properties and humidity of fly ash impacting on a flat surface, J. Aerosol Sci. 117 (2018), 85-99. [27] L. Kogut and I. Etsion, Adhesion in elastic–plastic spherical microcontact, J. Colloid Interf. Sci. 261(2003)372-378. [28] H.J. Butt and M. Kappl, Normal capillary forces, Advances in colloid and interface science, 146(2009)48-60. [29] H. Princen, I. Zia, S. Mason, Measurement of interfacial tension from the shape of a rotating drop, J. Colloid Interf. Sci. 23(1967)99-107. [30] N. Cross and R. Picknett, The liquid layer between a sphere and a plane surface, Transactions of the Faraday Society, 59(1963)846-855. [31] R. Coughlin, B. Elbirli, L.V. Edwards, Interparticle force conferred by capillary-condensed liquid at contact points: I. Theoretical considerations, J. Colloid Interf. Sci. 87(1982)18-30. [32] R. Jones, H.M. Pollock, J.A. Cleaver, C.S. Hodges, Adhesion forces between glass and silicon surfaces in air studied by AFM: Effects of relative humidity, particle size, roughness, and surface treatment, Langmuir : the ACS journal of surfaces and colloids, 18(2002)8045-8055.
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FIGURE CAPTIONS Figure 1. Schematic of the experimental system
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Figure 2. Surface roughness using FlatMaster200
Figure 3. Typical recorded image for the impact of a fly ash on a flat surface.
Figure 5. Fly ash X-ray diffraction patterns
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Figure 4. Particle size distribution of fly ash
Figure 6. Diagram of particle bounce process as energy balance for normal collision, showing (a)
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process of particle impacting surface, (b) particle at full compression before rebound, and (c) rebound process
Figure 7. The normal coefficient of restitution versus normal incident velocity Figure 8. The normal coefficient of restitution versus the Stokes number
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Figure 9. Adhesion energy caused by meniscus versus humidity
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Figure 10. Energy loss versus normal incident velocity: (a) mechanical energy due to surface contact and surface energy developed over interfacial contact versus the normal incident velocity; and (b) adhesion energy loss derived from the equilibrium circle of contact versus normal incident
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velocity
Figure11. Plastic deformation energy loss versus normal incident velocity
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Figure12. Percentage of total energy loss associated with different mechanisms
TABLE CAPTIONS Table 1. The total elemental analysis of fly ash particles Table 2. Crystalline volume fractions Table 3. Experimental data for XRD experiment of fly ash particles.
ACCEPTED MANUSCRIPT Table 4. Physical parameters of fly ash particles
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Table 5. Critical impact velocity at different conditions by experiment
ACCEPTED MANUSCRIPT Tables Table 1. The total elemental analysis of fly ash particles. SiO2 Al2O3 CaO MgO TiO2 SO3 P2O5 36.4
2.39
0.629
2.84
2.08
1.42
Na2O
SrO
NiO
0.921
0.564
0.137
0.113
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52.3
K2O
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Table 2. Crystalline volume fractions. Crystalline phase (vol%) Fly ash CaSO4
Al2O3
18.43
-
12.57
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SiO2
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Amorphous phase (vol%)
ACCEPTED MANUSCRIPT Table 3. Experimental data for XRD experiment of fly ash particles. Integral intensities of the strongest peak of SiO2
Integral intensities of the strongest peak of CaSO4
Integral intensities of the strongest peak of Al2O3
68.77
2654
-
572
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Mass fraction of crystallization Phase
ACCEPTED MANUSCRIPT Table 4. Physical parameters of fly ash particles. Volume fraction SiO2（%） CaSO4（%） Fly ash
Density
（%）
（kg/m3）
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12.57
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18.43
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Glass phase
Young's modulus （GPa） 116.72
ACCEPTED MANUSCRIPT Table 5. Critical capture velocity at different conditions by experiment. 35% humidity (Yes/
(Yes/ vi,n
rebound)
No
vi,n
rebound)
0.71 2
1.48
1.80
1.49
0.84
1.49
7
No 8
0.85
1.50 5
0.86
1.52
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Yes
3
2.13 Yes
5
Yes 1
Yes 6
1.83
Yes
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3
2.10
Yes
4
Yes
1
Yes
6
1.82
Yes
2.09
No
9
No
7
1.81 No
2
1.93
No 8
No 6
No
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0.80
1.86 3
No 6
No rebound)
No 6
No 8
vi,n
1.79 No
0.76
No rebound)
1.48 No
4
(Yes/
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No
65% humidity
(Yes/
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vi,n
50% humidity
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Dry
Yes 8
1.90
2.20 Yes
Yes 7
ACCEPTED MANUSCRIPT Highlights
(i) The normal coefficient of restitution decreases with increasing humidity. (ii) The critical capture velocity increases with increasing humidity.
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(iii) Systematically analysis of energy dissipation is conducted.
Figure 1
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Figure 12