Reconsidering Adhesion and Bounce of Submicron Particles Upon High-Velocity Impact

Abstract

Adhesion and bounce of liquid and solid particles upon high-velocity impact with a surface has been investigated using semi-empirical and explicit hydrodynamic simulations. Ammonium nitrate (AN) and sodium chloride (NaCl) were selected as test compounds for the liquid and solid particles, respectively, and tungsten (W) as the target surface. Changes in the shape, temperature, strain, and rebound velocity of these particles upon high-velocity impact are investigated assuming operational conditions (particle diameter, and velocity) of Aerodyne aerosol mass spectrometer (AMS). The simulations show that the AN particles adhere to the W surface, which is consistent with previous experimental studies. In the case of NaCl, the collection efficiencies depend significantly on the stress–strain characteristics of the crystal. Our results suggest that, in addition to particle phase and impact velocity, anisotropy of the elastic properties and brittleness are key factors in controlling the adhesion and bounce of solid particles.

Copyright 2013 American Association for Aerosol Research

1. INTRODUCTION

Particle bounce is an important and problematic phenomenon in aerosol sampling methods that are based on high-velocity impact (Rao and Whitby 1978a,b; Jayne et al. 2000). Previous studies (Cheng and Yeh 1979) have suggested that particles above a certain threshold velocity (or kinetic energy) can bounce off the surface. Furthermore, recent experimental studies using Aerodyne aerosol mass spectrometers (AMS) and low-pressure impactors (LPI) have suggested that the collection efficiency of solid particles is substantially lower than 100% and is dependent on factors such as the relative humidity (RH) of the sampled air, the chemical composition of the particles, and the particle mixing state (Matthew et al. 2008; Virtanen et al. 2010; Chen et al. 2011). These studies have assumed that the adhesion and bounce of particles from a surface can be characterized solely by the phase (liquid or solid) and mixing state of the aerosol particles. Nonzero collection efficiencies for solid particles (e.g., Figure 7 of Tsai and Cheng 1995) have not yet been fully discussed in previous studies.

FIG. 1 Relationships between impact velocities (V_i ) and particle sizes (D_a or D _va) for various particle impact phenomena (based on the paradigm originally proposed by Klinkov et al. [2005]). Extreme regimes include erosion, cold spray, and hypervelocity impacts (Klinkov et al. 2005). Particle geometric diameters for each phenomena given in Klinkov et al. (2005) are converted to D_a by assuming that particle density is 1.5 g cm⁻³. The impact velocity-size relationships in AMS (black circles), MOUDI (open circles), and ELPI (gray circles) systems are shown as examples. Data for AMS, MOUDI, and ELPI were taken from Takegawa et al. (2005), Marple et al. (1991), and Keskinen et al. (1992), respectively. For MOUDI and ELPI, particle diameters correspond to the 50% cut point D_a at each stage in MOUDI and ELPI. The area enclosed by thick dashed black lines corresponds to the regime of the aerosol sampling techniques (e.g., Aerodyne AMS).

In order to minimize particle bounce from a surface following impact, the collection surface has been coated with a sticky material such as oil or grease, thus increasing the adhesion energy (McFarland and Zeller 1963; Pak et al. 1992). This coating method, however, is not suitable for off- and on-line chemical analyses of collected samples. The development of a reliable method for chemical analyses that minimizes particle bounce from a surface will require a more detailed understanding the physical fundamentals of high-velocity solid particles bouncing and adhering to a surface.

Particle impact with surfaces has been extensively studied over a wide range of impact velocities (V_i ) and particle sizes (Klinkov et al. 2005, and references therein). Klinkov et al. (2005) summarizes the ranges of impact velocities and particle sizes for several categories of particle impact phenomena (Figure 1, based on the paradigm originally proposed by Klinkov et al. [2005]). Particle size is based on the aerodynamic (D_a ) or vacuum aerodynamic diameters (D _va), which is equivalent to D_a at high vacuum. Phenomena occurring at the extreme values of V_i and D_a include erosion (V_i = 50 to 300 m s⁻¹ and D_a = 120 to 2 mm), cold spray (V_i = 300 to 1200 m s⁻¹ and D_a = 20 to 0.6 mm), and hypervelocity impacts (V_i > 2 to 3 km s⁻¹) (see Klinkov et al. (2005) for details of these processes). Because of the very high incident kinetic energies of particles in these regimes, the particles very likely deform and break apart upon impact with a surface, regardless of their phase. On the other hand, high-velocity impacts of aerosol particles observed in aerosol sampling regimes using instrumentation such as AMS and LPI appear at values of V_i < ∼300 m s⁻¹ and D_a or D _va < ∼10 μm and can exhibit different behaviors such as adhesion or bounce. The relationship between V_i and D _va of our Aerodyne AMS (Takegawa et al. 2005), which incorporates an aerodynamic lens (ADL) (Liu et al. 1995), is plotted in Figure 1. For comparison, that for a MOUDI (micro-orifice uniform deposit impactor) and ELPI (electrical LPI) is also shown.

The microphysical behavior (e.g., particle-surface interactions) of high-velocity impacts of aerosol particles related to aerosol sampling was originally investigated by theoretical and experimental approaches (Dahneke 1971, 1973, 1975). A number of additional studies have since verified, and improved the bounce studies given by Dahneke (Paw U 1983; Rogers and Reed 1984; Derjaguin et al. 1987; Tsai et al. 1990). According to energy conservation upon particle impact which was quantitatively investigated by Tsai et al. (1990), two important features have been identified.

1.	For low-velocity impacts (lower than ∼5 m s−1), elastic flattening and surface roughness are key factors for enhancing adhesion energy in determining the collection efficiency of solid particles.
2.	For high-velocity impacts (higher than 20 to 30 m s−1), solid particles impacting upon the surface can plastically deform, resulting in substantial loss of the incident kinetic energy.

Although these studies revealed key factors that affect adhesion and bounce of a particle upon impact, there are other processes, such as energy loss due to thermodynamic works and fracturing process resulting from large deformations that were not considered in previous studies. Thermodynamic work, however, can lead to substantial increases in temperature inside particles.

Our primary goal of this study was to understand the particle bounce phenomenon in the Aerodyne AMS, which is now widely used in aerosol researches. Key parameters are therefore set to match the typical operating condition of an AMS. We also aimed to investigate, in general, the important factors that may play an important role when a particle impacts with a surface. For this purpose, we adopted two approaches: the semi-empirical particle bounce model (T1990 model) by Tsai et al. (1990) and explicit hydrodynamic simulations. The T1990 model is used to assess the importance of plastic deformation of solid particles and the effect of anisotropy of their elastic properties upon particle impact, but it cannot be used for simulating adhesion and bounce of the liquid particles. Hydrodynamic simulations are employed to explicitly investigate changes in the physical properties of the liquid and solid particles during the course of high-velocity impact with a surface. We chose ANSYS AUTODYN for these simulations. AUTODYN has been commonly used for the study of a wide variety of explosion and impact processes (Katayama et al. 1997). It should be noted that both simulations do not account for interactions between air molecules and particles.

2. CONCEPTUAL DESCRIPTION

We investigated the high-velocity impact of liquid and solid particles on a flat Tungsten (W) surface in high vacuum (no interaction between gas molecules and particles). W is a representative hard metal and has been used for the material of the vaporizer of Aerodyne AMS (Jayne et al. 2000). The impact velocity of the submicron particles was chosen based on the typical performance of an ADL (Liu et al. 1995; Zhang et al. 2004). The temperature of both the submicron particles and W surface was assumed to be room temperature (300 K) in order to investigate impact-induced changes in temperature within the submicron particles. Ammonium nitrate (AN) and sodium chloride (NaCl) were selected as the materials of the liquid and solid particles, respectively. The reasons why we have chosen these compounds are these are ubiquitously found in atmosphere and also the material properties necessary for our simulations, including shock wave data, elastic property, and stress-strain characteristics, are available for these compounds. Previous studies have suggested that once AN deliquesces at the deliquescence relative humidity (DRH), it can exist as a metastable liquid droplet at a lower RH than its DRH (Tang 1980; Richardson and Hightower 1987; Lightstone et al. 2000). We therefore assumed that the AN particles exist as liquid droplets. NaCl is one of the most ubiquitous inorganic aerosols in the atmosphere and is in the form of a solid particle at a lower RH than its crystallization RH (Tang 1980). It is important to note that the elastic properties of NaCl crystals are anisotropic (Murri and Anderson 1970), allowing the investigation of the effects of elastic anisotropy of crystalline particles during the high-velocity impact.

The T1990 model considers the relationship between contact deformation and contact surface energy. It uses the material density, Young's modulus, Poisson's ratio, Hamakar constant, and stress strain curve as input parameters. Through solving a simple energy conservation equation for a particle with an empirically derived critical velocity for bulk plastic deformation, the T1990 model can calculate the velocity of a particle rebounding from the surface. In contrast, the AUTODYN is a finite volume method-based analysis tool for simulating the nonlinear dynamics of solids, fluids, gases, and their interactions. The AUTODYN considers the equation of state (EOS), material constitutive law, and failure law for each cell of the particle and surface (see Section 4.1 and the online supplementary information for details). While some detailed physical properties (e.g., shock wave data) are needed for the simulations, the AUTODYN can provide information on the time-dependent changes in shape, temperature, pressure, and internal and kinetic energies of particles. The ANSYS AUTODYN cannot deal with molecular interactions between particles and the surface, indicating that this model is not recommended to be used for analyzing the particle impact with lower impact velocities (<∼5 m s⁻¹).

3. SIGNIFICANCE OF PLASTIC DEFORMATION AND ANISOTROPY OF ELASTICITY OF SOLID PARTICLES

Using the T1990 model, it is possible to calculate the velocity of rebounding particles (V_r ) and coefficient of restitution (COR) for a wide range of impact velocities (V_i ). In this section, we describe the deformation processes taking place upon the particle impact using the T1990 model.

The minimum V_i at which bulk plastic deformation can occur, V_iy , is calculated using the method given by Tsai et al. (1990) (see the online supplementary information for details). The predicted values of V_iy are strongly dependent on the yield stress of the material, σ_y , where the material yielding processes occur (Figure 2). Estimated values of σ_y of NaCl ranged from ∼0.01 to ∼1 GPa (see the following for details) and the predicted values of V_iy for NaCl particles were lower than 100 m s⁻¹. V_i of submicron particles in all devices are generally greater than ∼30 m s⁻¹ as shown in Figure 2. The predicted V_iy here using the T1990 model are comparable to or greater than V_i in the impactors and ADL systems. We may need to consider possible influence of the plastic deformation of submicron particles on the impact process for those devices.

FIG. 2 V _iy calculated for the impact of NaCl particles on the W surface as a function of their yield stresses.

The T1990 model can also simulate V_r and COR using the physical properties of the materials (e.g., Young's modulus) and was thus used to calculate COR for the NaCl particles. The incident and rebound kinetic energies are defined as KE_i and KE_r , respectively. The COR of the particles upon the impact is defined as the ratio of V_r to V_i . The total energy after impact is the sum of KE_r , the energy loss breaking contact surface (EL _cs), plastic strain energy (IE_p ), and the energy loss due to local asperity deformation (EL _asp). Note that IE_P is the internal energy stored inside the particles throughout the impact. The following conservation of energy equation is derived:

EL _asp is assumed to be zero for perfectly smooth surfaces. Details for calculating IE _P and EL _cs were elsewhere (Tsai et al. 1990).

The failure of the particle structure caused by significant deformation and thermodynamic work done inside the particle are not taken into account in the T1990 model. The T1990 model, therefore, cannot accurately simulate the energy budget for cases involving large deformations which can lead to significant changes in the internal energy comparable to KE_i . Despite this limitation, the model can be used for investigating the effect of mechanical properties such as σ_y during solid particle impact and predicting particle bounce.

The particle diameter was assumed to be 250 nm in all simulations. Values of V_i were determined based on the typical particle velocity-D _va relationship in the ADL (Figure 1). The values of D _va (≡ (ρ_p /χ)·D_p , where ρ_p is the particle density, χ is the dynamic shape factor (χ ≡ 1 for spherical shape), and D_p is the geometric diameter, DeCarlo et al. [2004]) for the 250-nm AN and NaCl particles were calculated to be 433 and 540 nm, respectively, using those particle densities (1.73 and 2.16 g cm⁻³, respectively). Spherical morphology of the particle was also assumed. Intermediate V_i values of 90 m s⁻¹ were estimated using data in Figure 1.

In the simulation, the Hugoniot elastic limit (P _HEL) was used to estimate the order of σ_y for NaCl through the following equation:

where ν is the Poisson's ratio of the material (NaCl in this case). The crystal direction-dependence (anisotropy) of elastic properties is an important feature of ionic crystalline materials (not peculiar to NaCl). P _HEL of single crystal NaCl were experimentally determined to be 0.017–0.028, 0.069–0.085, and 0.59–0.78 GPa for [100], [110], and [111] directions, respectively (Murri and Anderson 1970). It should be noted that values of P _HEL depends on the experimental conditions, specimen thickness, porosity, and grain size (Davison and Shahinpoor 1997). Here, we assumed σ_y values to be 0.02 (represents [100] direction), 0.1 ([110] direction), 0.5 ([111] direction), and 1.0 ([111] direction) GPa by using the above P _HEL. These values were also used in the hydrodynamic simulations (Section 4).

TABLE 1 COR predicted by the T1990 model as a function of σ_y

Yield stress	Predicted
σy (GPa)	COR
0.02	0
0.1	0
0.5	0.015
1.0	0.154

TABLE 2 Summary of the hydrodynamic simulations of liquid and solid particle impact

	Conditions			Results
	Vi	σy			ΔT max	Fracture ^b
Run ID	(m s^–1)	(GPa)		COR	(°C)	(%)	Note ^a
AN_case1	90	–	–	0	∼0	–	Liquid particles
NaCl_case1	90	1.0	0.2	0.516	124	0.4	Anisotropic elasticity
NaCl_case2	90	0.5	0.2	0.112	64	1.1	Anisotropic elasticity
NaCl_case3	90	0.1	0.2	0	12	3.8	Anisotropic elasticity
NaCl_case4	90	0.02	0.2	0	2	26.8	Anisotropic elasticity
NaCl_case5	180	1.0	0.2	0.018	128	3.0	Incident velocity
NaCl_case6	90	1.0	0.01	0.004	10	2.3	Brittleness
NaCl_case7	90	0.5	0.01	0.039	20	4.6	Brittleness

The values of COR predicted by T1990 model as a function of σ_y were listed in Table 1. For higher σ_y values (0.5 and 1.0 GPa), predicted values of COR were larger than zero, indicating that the NaCl particles bounced off the W surface under these conditions. COR at σ_y = 1.0 GPa was 0.154, so the particle bounce was not only elastic but also plastic. COR was close to zero at σ_y = 0.5 GPa, suggesting almost all of KE_i was converted to be IE_P . For lower values of σ_y (0.02 and 0.1 GPa), predicted values of COR were zero, indicating that the NaCl particles adhered to the W surface. According to these simulation results, significant plastic deformation during impact leads to a large loss of kinetic energy (98% loss with σ_y = 1.0 GPa and 100% loss with the lower σ_y ). Therefore, the collection efficiency for solid particles was strongly dependent not only on their elasticity (e.g., Young's modulus) but also on their material yield strength, σ_y .

FIG. 3 A qualitative description of the stress-strain characteristics (von Mises model) used in the AUTODYN simulations.

FIG. 4 Simulation results of the AN particle impact for the case of AN_case1. (a) The temporal evolutions of KE (black line) and IE (gray line) of the AN particle. (b) Pressure and temperature distributions of the AN particle and W surface at t = 1.0 ns.

4. HYDRODYNAMIC SIMULATIONS

4.1. Simulation Details

Two-dimensional axisymmetry, completely flat surface, in high vacuum, and spherical shape of particles before impact were assumed in order to simplify the model system. The detail of the coordinate system of the AUTODYN simulation is given in the online supplementary information. A Lagrange solver was used for the particles and the W surface to clearly delineate their boundary.

FIG. 5 Simulation results of the impact of NaCl particles. (a; left panel) Temporal evolutions of fractional contribution of KE (thick solid lines) and IE (thin dashed lines) for the cases NaCl_case1 (σ_y = 1.0 GPa). (a; right panel) Temporal evolutions of fractional contribution of ThW (thick solid lines) and IE_P (thin dashed lines) for the cases NaCl_case1. (b; left panel) Temporal evolutions of fractional contribution of KE (solid lines) and IE (dashed lines) of the NaCl particle for the cases NaCl_case3 (σ_y = 0.1 GPa) (black) and NaCl_case4 (σ_y = 0.02 GPa) (shaded). (b; right panel) Temporal evolutions of fractional contribution of ThW (thick solid lines) and IE_P (thin dashed lines) for the cases NaCl_case3 (black) and NaCl_case4 (gray).

FIG. 6 Simulated profiles of (a) pressure, (b) temperature, (c) effective plastic strain, and (d) material status at t = 0.25 and 1.0 ns for the case of NaCl_case1 (σ_y = 1.0 GPa). The black area in the material status map is defined as the region that underwent failure due to large deformations.

An EOS is needed to describe the relationship between hydrostatic pressure, local density, and local specific energy (i.e., temperature). We chose the Mie-Grüneisen form of EOS based on the shock Hugoniot for the particle and the W surface. The Steinberg–Guinan model was used as the material constitutive law for the W surface (Steinberg et al. 1980). We assume that the W surface does not fail from the particle impact. Details of the Mie-Grüneisen EOS and Steinberg–Guinan model are shown in the online supplementary information. For the NaCl particles, the elastic-perfectly-plastic (von Mises) model was used as the material constitutive law. We did not apply the material constitutive and failure laws for simulating the AN particles, because they are assumed to be liquid. In the von Mises model, changes in the stress, σ, are regulated by σ_y and maximum plastic strain, (Figure 3). Effects of a work hardening after the yielding point are neglected, because those are not important for ionic crystals like NaCl (Black and Kohser 2007). The linear relationship between σ and the strain, ϵ, where σ < σ_y follows the Hooke's law, and the slope of the stress–strain relationship is the Young's modulus. When ϵ of the particle exceeds during the impact process, the particle undergoes failure (Figure 3).

The conditions assumed in the hydrodynamic simulations were summarized in Table 2. Values of σ_y used in the cases from NaCl_case1 to NaCl_case4 were 1.0, 0.5, 0.1, and 0.02 GPa, respectively, for the same reason presented in Section 2. The effects of anisotropy of elastic property on the particle impact were investigated under these conditions. The sensitivity of the incident velocity was also tested by doubling incident velocity to 180 m s⁻¹ (NaCl_case5 in Table 2). It should be noted that changes in strain rates caused by changes in V_i can affect the stress–strain characteristics (Tanimura et al. 2006). Here, we assumed that the stress-strain characteristics of NaCl were not altered by changes in V_i . Furthermore, a lower value of , was used to investigate the importance of bulk failure of the solid particles, which can mimic the brittle fracture of solid particles upon impact (NaCl_case6 and _case7 in Table 2).

4.2. Simulation Results

4.2.1. AN Particle (Liquid Particle)

Simulation results from the case AN_case1 in Table 2 are discussed in this section. We show the temporal evolution of the energy budget (i.e., breakdown of energies of particles) of an AN particle during the course of the high-velocity impact, which is helpful for interpreting the particle impact (Figure 4a). The AN particle did not immediately lose kinetic energy (KE) and the internal energy (IE) of AN particle slowly increased. Such evolutions are typically associated with the fluidic motion of materials. The AN particle continued in the fluidic motion along the W surface during the entire simulation period of 1 ns, and did not bounce off the W surface within 1 ns. Although simulations were not performed after 1 ns, the AN particle will very likely spread over the W surface and never bounce off. The AN particle showed no elastic deformation and there was little conversion of KE to IE. Owing to this negligible conversion to IE, no large increase in pressure and temperature inside the AN particle (Figure 4b) was observed (Table 2).

4.2.2. NaCl Particle (Solid Particle)

The temporal evolution of the energy budget of NaCl particles for the case of NaCl_case1 is given in Figure 5a. NaCl particles under this condition bounced off the W surface, namely COR > 0 as shown in Table 2. After contact with the W surface, the KE of the NaCl particle immediately decreased and was converted to its IE. At t = 0.2 ns, almost all of the KE were converted into IE. Subsequently, IE was reconverted into KE. The value of COR in the case NaCl_case1 was ∼0.5 (Table 2), indicating that the bounce was not only elastic and but also plastic. For solid particles, the IE can be separated into two contributions: plastic strain energy (IE_P ) and thermodynamic work (ThW). Here, ThW can be calculated by integrating ∫Pdv inside the particle. The fractional contribution of IE_P and ThW to the total energy for the case of NaCl_case1 indicates that elastic and plastic deformation occurred inside the NaCl particle (Figure 5b). The IE_P of the particle contributed to ∼70% of the total energy at t = 1 ns. The value of COR in the case of NaCl_case2 was 0.112 (Table 2) reflecting the plastic deformation of the particle and significant loss (∼99%) of the KE. Note that the NaCl particle did not bounce off the W surface during the simulation period (2 ns) in spite of the positive value of COR. As discussed in Section 2, the T1990 model estimated COR for the case of NaCl_case2 to be 0.015 (Table 1), thus the T1990 model overestimated the loss of IE_P . This discrepancy is likely the result of differences in the energy loss processes considered by both models (details in Section 2). Profiles of P and T on the particle and surface were calculated at t = 0.25 and 1.0 ns for the case NaCl_case1 (Figure 6a and b, respectively). The maximum IE, which occurred at t = 0.25 ns, led to a significant increase in the P and T inside the NaCl particle. The largest increases in the P and T (ΔT _max) were greater than ∼1.0 GPa and ∼120°C, respectively. The largest P increase was higher than the σ_y (1.0 GPa) assumed in the simulation, resulting in significant plastic strain in the high-P region inside the NaCl particle (Figure 6c). The rebounding NaCl particle at t = 1.0 ns had a plastically deformed region, corresponding to the increased T region (Figure 6b). The effective plastic strain of zero was found in the NaCl particle (indicated by a white wedge-shape area in Figure 6c), which was caused by bulk fail associated with a deformation exceeding . In order to better understand the bulk fail inside the particles, material status maps for t = 0.25 and 1.0 ns are also shown in Figure 6d. The bulk failed region at t = 1.0 ns corresponds to 0.4% of mass of the NaCl particle (Table 2).

FIG. 7 Simulated profiles of (a) pressure and temperature, and (b) effective plastic strain and material status at t = 1.0 ns for the case NaCl_case4 (σ_y = 0.02 GPa). The black area in the material status map is defined as the region that underwent failure due to large deformations.

The behavior of the NaCl particles with lower σ_y (the cases of NaCl_case3 and NaCl_case4) were notably different from those for the cases with higher σ_y (NaCl_case1). NaCl particles were captured by the W surface in the cases with lower σ_y . Gradual decreasing trends of KE for these cases indicated that NaCl particles continued moving for the 2 ns duration of calculation (Figure 5b). The remaining KE could be attributed to motions associated with the impact and in the horizontal direction (parallel to the W surface). Since there was no notable conversion of KE to IE, little change in T was observed. Figure 7a depicts the profiles of P and T inside the NaCl particle at t = 1 ns for the case of NaCl_case4. Bulk fail occurred inside the NaCl particles under these cases. Effective plastic strain and material status map were given in Figure 7b. Significant portions (27% by mass at t = 1 ns) of the NaCl particles were failed due to large deformations, compared to other cases (Table 2). The fracturing resulting from high-velocity impacts is expected to be an important process hindering the reconversion of IE to KE and subsequent loss of KE in the rebound direction. Even though the assumed particle phase of NaCl was solid, particles with a lower σ_y (especially, σ_y = 0.02 GPa) can adhere to the W surface upon the high-velocity impact, similar to what is observed for liquid particles (Section 4.2.1).

4.2.3. Sensitivity of Incident Velocity and to the High-Velocity Impact of Solid Particles

Results from doubling the incident velocity (NaCl_case5) were similar to those for the case of NaCl_case2 (Table 2). The NaCl particle having two times higher velocity lost almost all of its kinetic energy (COR ∼ 0.02) and kept been captured by the W surface during the simulation period. Significant plastic deformations (maximum effective plastic strain exceeded ) were observed inside the particle, which resulted in a notable increase in T (ΔT _max ∼130°C). The degree of kinetic energy loss of the solid particles seems to be dependent on the incident kinetic energies for high-velocity impact: The higher the incident velocity of solid particles, the lower the COR values. These simulations confirm this point, which was also suggested in Dahneke (1975) and Tsai et al. (1990) and emphasize the importance of defining the incident velocity and diameter of solid particles when studying the particle bounce and adhesion.

FIG. 8 Dependence of COR on σ_y calculated using AUTODYN and T1990 model. Filled markers indicate the AUTODYN simulation results assuming 0.2 of

(circles for 90 m s⁻¹ of V_i and a square for 180 m s⁻¹ of V_i ). Open circles indicate the AUTODYN simulation results assuming 0.01 of 

. Triangle and inverse triangle makers indicate the T1990 simulation results assuming 90 and 180 m s⁻¹ of V_i , respectively. The number in square brackets indicates the crystal surface direction approximately corresponding to the values of σ_y assumed in the simulations.

The simulation having a smaller (NaCl_case6 and _case7) showed the similar result as the case NaCl_case2 (Table 2). According to the von Mises model, solid particles with smaller are inhibited from undergoing significant plastic deformation. The region with large strain inside the particle was failed for the case of NaCl_case6 and _case7. The predicted failure of the NaCl particle resulted in large losses of the KE in the rebound motion and a lower COR (<∼0.04) than that (∼0.5) for NaCl_case1. This result further illustrates the importance of the fracturing process in kinetic energy loss through the high-velocity impact process.

5. WHAT IS THE CONTROLLING FACTOR AFFECTING THE PARTICLE BOUNCE?

The relationship between COR and σ_y for NaCl particles is summarized in Figure 8. As described in section 4.2.2 (NaCl_case1–case4), the COR values were strongly dependent on the assumed σ_y values, which represent the importance of the anisotropy of elasticity. Even though the COR-σ_y relationship in T1990 model was quantitatively different from that in AUTODYN, both simulations showed a similar tendency of the COR-σ_y relationships. The crystal surface direction-dependent σ_y for ionic crystals can be an essential factor to largely affect the solid particle impact, that is, adhesion (zero-COR) or bounce (nonzero-COR). We conducted additional simulations to investigate the influence of V_i and brittleness (i.e., ), and found that both parameters are important for kinetic energy loss processes. Large changes in these parameters can definitively affect the solid particle bounce as indicated by the vertical two-way arrow of Figure 8.

Common features found in two models are that NaCl particles never bounce off the W surface for lower σ_y cases (0.02, 0.1 GPa) and that they tend to bounce off the W surface for higher σ_y cases (0.5, 1.0 GPa) under various simulation conditions. The difference in the model and changes in V_i and brittleness can alter the absolute values of COR in the latter case. These analyses lead to a hypothesis that σ_y of solid particles is a primary important factor affecting the solid particle bounce at least under the conditions assumed in this study. Further studies are needed to draw more general conclusions under a wide variety of particle materials and impact conditions.

6. CONCLUSIONS

Bounce of high-velocity particles impacting upon a surface are an important process in particle sampling including Aerodyn AMS and other LPIs, and was investigated in detail using the T1990 model and AUTODYN. AN and NaCl were selected as test compounds for the liquid and solid particles, respectively. A semi-empirical model, the T1990 model was used to assess the significance of the plastic deformation of solid particles during the high-velocity impacts. Furthermore, hydrodynamic simulations using AUTODYN were employed to explicitly analyze changes in the shape, temperature, strain, and velocity of these particles upon the high-velocity impact. The AN particle were shown to collapse during impact, as have been suggested by a number of previous studies. Pressure and temperature inside the AN particle did not increase significantly because no elastic deformation occurred. For the NaCl particles, anisotropy of the elastic properties affected the particle adhesion and bounce due to variations in the stress–strain characteristics. For higher σ_y values, the NaCl particles bounced off the W surface (COR > 0) and rebound velocities were lowered by plastic deformation and fracture inside the particles. ΔT _max for these cases reached higher than ∼100°C and were dependent upon the values of σ_y and V_i used for the simulations. NaCl particles with lower σ_y adhered to the W surface (COR ∼ 0) because of large kinetic energy losses inside the particles. These results suggest that a single impact process is not sufficient for breaking and capturing all of solid crystalline particles. Furthermore, the effect of elastic anisotropy and brittleness could be a significant consideration for impact process involving other atmospherically important particles. When particles impact upon a surface, values of σ_y at the contact area can be stochastically different among particles because of their anisotropic elasticity. Our simulation results show for the first time that anisotropy of the elastic properties of ionic crystalline materials is a possible cause for nonzero collection efficiencies of solid particles. It is difficult to investigate material properties of solid particles (e.g., elasticity, brittleness, and crystal state) only by measuring COR or collection efficiencies.

Acknowledgments

This study was funded by the SENTAN program of the Japan Science and Technology Agency (JST). The authors would like to thank the editor and two anonymous reviewers for their valuable comments and suggestions to improve the quality of this article.

[Supplementary materials are available for this article. Go to the publisher's online edition of Aerosol Science and Technology to view the free supplementary files.]

Notes

^a“Note” depicts general features for each simulation run.

^bThe unit of “Fracture” is the percent by mass of fractured fraction of particles.