Penetration efficiency of nanoparticles in a bend of circular cross-section*

YIN Zhao-qin （尹招琴）, LIN Jian-zhong （林建忠）, LOU Ming （婁明）

Institute of Fluid Measurement and Simulation, China Jiliang University, Hangzhou 310018, China, E-mail: yinzq@cjlu.edu.cn

Penetration efficiency of nanoparticles in a bend of circular cross-section*

YIN Zhao-qin （尹招琴）, LIN Jian-zhong （林建忠）, LOU Ming （婁明）

Institute of Fluid Measurement and Simulation, China Jiliang University, Hangzhou 310018, China, E-mail: yinzq@cjlu.edu.cn

(Received June 23, 2013, Revised August 27, 2013)

In order to quantify the losses of nanoparticles in a bend of circular cross-section, the penetration efficiency of nanoparticles of sizes ranging from 5.6 nm to 560 nm in diameter is determined as a function of the Dean number, the Schmidt number and the bend angle. It is shown that the effect of the Dean number on the penetration efficiency depends on the particle size. The Dean number has a stronger effect on the penetration efficiency for small particles than for large particles. There exists a critical value of the Dean number beyond which the penetration efficiency turns from increasing to decreasing with the increase of the Dean number, and this critical value is dependent on the particle size and the bend length. The penetration efficiency increases abruptly when the Schmidt number changes from 7 500 to 25 000. Finally, a theoretical relation between the penetration efficiency and the Dean number, the Schmidt number and the bend length is derived.

nanoparticle, penetration efficiency, bends, measurement, Dean number, Schmidt number

Introduction

The particle deposition in bends is important in various scenarios ranging from a ventilation system and an aerosol experiment to human circulation systems[1-4]. Nanoparticles are more diffusible and toxic and would suffer greater losses in their number than larger particles[5,6]. Deposited particles can change the particle number distribution, the size distribution, the total mass concentration and the mean particle size within the bends. Better understanding of the deposition process is important to the applications of the nanoparticle technology.

Even though the lengths of the flow paths within the bends are usually short, the strong secondary flow inside the bends affects both the particles and the fluid that transports the particles from the core of the flow toward the walls[7], and redistributes the particles across the bend cross-section, greatly enhancing the particle diffusional deposition inside the bends.

For nanoparticles in bends, the numerical[5]and experimental results[8-10]show that smaller nanoparticles (of diameter less than 50 nm) deposit on the wall surface more easily. Wang et al.[9]studied the nanoparticles of diameters ranging from 5 nm to 15 nm ino 90 bends, and found that the curvature ratio and the Dean number ()De have effects on the nanoparticle penetration efficiency. Yook and Pui[10]studied experimentally the penetration efficiency with particle diameters ranging from 3 nm to 50 nm in coils with the Dean number in the range 211799 De＜＜, and indicated that the penetration efficiency increased with the increase of the Dean number and the particle size. Lin et al.[11]observed that the effects of the Schmidt number, the bending radius and the Reynolds number on the relative deposition efficiency are different.

Several factors can cause particles to deposit[12,13]. For nanoparticles, the diffusion instead of the inertia is the main factor in the particle deposition. The Brownian diffusion is an important factor for particles smaller than 100 nm, while both the Brownian and the turbulence diffusions are important for particles larger than 100 nm[9,14]. Therefore, the particle, flow and bend characteristic parameters must be used to describe the property of the particle deposition. The particleStokes number ()St is an important parameter for the particle motion in the Stokesian regime. For nanoparticles, the particle Stokes number is about 10-5in orders of magnitude. So the Schmidt number was used to describe the particle deposition[8,15]. The Schmidt number is a dimensionless number that characterizes the ratio of the mass diffusion and convection processes of the nanoparticles. The strength of the secondary flow in a bend is characterized by the Dean number. For a bend flow, the Dean number plays a role of the “Reynolds number”, i.e.,De=Re/R/ a where Re=2Ua/ν is the flow Reynolds number, ν is kinematic viscosity of the air, U is the mean axial velocity in the bend, R and a are the radius of the bend and the tube, respectively. So the Schmidt number, the Dean number and the bend angle are the main parameters to describe the nanoparticle deposition.

Even though a large number of results about the particle deposition in bends were obtained, most of them were about micro particles in theo90 bends or coils[16,17]. The effects of the Dean number, the Schmidt number and the bend angle on the penetration efficiency of the nanoparticles in a bend remain an unexplored topic of research. With the bend being always the important part of the corrosion and the jam, it is necessary to understand the mechanism of the nanoparticle deposition in the bend. Therefore, the aim of this paper is to study the effects of above factors on the penetration efficiency of nanoparticles, and to derive a theoretical relation between the penetration efficiency and the Dean number, the Schmidt number and the bend length.

Fig.1 Schematic diagram of the experimental setup

1. Experimental method

Measurements of the size and number distributions of nanoparticles are usually made by using instruments such as the electrical low pressure impactors (ELPI), the scanning mobility particle sizers (SMPS), the ultrafine particle condensation counters (UPCC). Most of these instruments have low sampling frequencies relative to that required to characterize the nanoparticle transmission in bends[18]. For example, for the SMPS, it takes 30 s to 180 s to analyze a single scan. In this paper, therefore, the fast mobility particle sizer (FMPS, Model3091, TSI Inc.) system is chosen to measure the size and number distributions of nanoparticles. A sampling frequency of 1 Hz is taken in each measurement. The particles of sizes ranging from 5.6 nm to 560 nm can be measured in 32 channels[19].

Fig.2 Particle size distribution

A schematic diagram of the experimental setup is shown in Fig.1. Particles and compressed air are mixed in a pressure chamber. The flow required for the bend is regulated using a valve downstream of the mixing chamber. In order to obtain a fully developed flow profile, each bend has an inlet straight section of a sufficient length. The valves 2, 3, 4 are three way valves used to regulate the fluid flow. When the fluid flows through the valves 1, 2, 4 and FMPS3091, the entrance parameters are measured. While the fluid flows through the valves 1, 2, the bend, the valve 4 and FMPS3091, the exit parameters are measured. The inner radius of the bend ()a is 0.006 m. The sample flow rate is 0.01 m3/min, corresponding to themean velocity of 1.47 m/s .The sampling time of the experiment is 1 min for each measurement. The material of the pipe is polyvinyl chloride.

The LaVision Aerosol Generator generates polydisperse particles by atomizing vegetable oil into particles. The particles larger than 560 nm are filtered out by the FMPS. The particle Schmidt number varies from 51 to 172 574. To ensure accurate measurements, these experiments are repeated at least three times with essentially the same results. Figure 2 shows the size distributions of the nanoparticles under the air supplied pressure of 0.7 MPa.

2. Results and discussions

2.1 Nanoparticle penetration efficiency

The nanoparticle penetration efficiency ()p in a bend is defined as the ratio of the particle number concentrations at the exit (exit) and the entrance of the test section(entrance)

The measured penetration efficiencies are shown in Fig.3, where the results given by Yook et al.[10]are also displayed. The data points with error bars are the present results, which are shown to be in agreement with previous results. It can be seen that the penetration efficiency increases with the increase of the Dean number. According to the definition of the Dean number, the penetration efficiency increases with the increase of the Reynolds number or the decrease of the curvature ratio.

Fig.3 Penetration efficiency compared with previous results

2.2 Effect of Dean number on the penetration efficiency

Figures 4 and 5 show the penetration efficiency as a function of the Dean number for different particle sizes. For small and intermediate Dean numbers, the flow can be considered as a laminar flow. As the Dean number increases, the flow turns into a turbulent one. The turn point is 370.

Fig.4 Penetration efficiency as a function of Dean number for different particle sizes (l/ a=500)

Fig.5 Penetration efficiency as a function of Dean number for different particle sizes (l/ a=666.7)

From Fig.4 and 5, it can be seen that the penetration efficiencies increase with the increase of the Dean number when De＜400. As the Dean number increases, the penetration efficiency also increases and tends to remain at a constant level for Dp=10.8 nm , while decreases slightly for Dp=107.5 nm and 254.8 nm when De＞400, where Dpis the nanoparticle size. This indicates that the effect of the Dean number on the penetration efficiency is dependent on the particles size.

The penetration efficiency for Dp=8.6 nm increases 20% when De increases from 144.3 to 922.1 for l/ a=500, while the penetration efficiency for Dp>100 nm only increases less than 10% under the same condition. So the Dean number has a stronger effect on the penetration efficiency for small particles (Dp<100 nm)than for large particles (100 nm< Dp<560 nm).

In the previous studies, only the results for De＜370 were obtained, as shown in Fig.3, where the penetration efficiency increases with the increase of the Dean number because the flow is laminar and theBrownian motion dominates the particle diffusion. For De＞370, the flow is turbulent and both Brownian and turbulent motions are responsible for the particle diffusion. The turbulent motion has a main effect on the particle diffusion when Dp>100 nm , which would result in an enhancement of the particle deposition and a reduction of the penetration efficiency. There exists a critical value of the Dean number beyond which the penetration efficiency turns from increasing to decreasing with the increase of the Dean number, and this critical value is dependent on the particle size and the bend length. Comparing Fig.4 and Fig.5 it is obvious that the penetration efficiency is larger for a long bend than for a short bend.

Fig.6 Penetration efficiency as a function of bend angle for different particle sizes

2.3 Effect of Bend angle on the penetration efficiency The penetration efficiency as a function of bend angle for different particle sizes and Dean numbers are shown in Fig.6, where the dimensionless bend angle θ is defined as

when R keeps constant, θ is directly proportional to the bend length l. Therefore, a large θ means that the particles stay longer in the bend and have more opportunities to deposit on the surface. On the other hand, when l keeps constant, the decrease of R will enhance the strength of the secondary flow and promote the particle deposition. As shown in Fig.6, the penetration efficiency decreases with the increase of θ, and is obviously larger for large particles than for small particles. The penetration efficiency increases 16% for Dp=10.8 nm , and 10% for Dp=124.1 nm and 254.8 nm when θ increases from 2 to 10.

2.4 Effect of Schmidt number on the penetration efficiency

According to the definition of the Schmidt number, =/ScDν, it is inversely proportional to the diffusion coefficient D which is in the range from 8.0× 10-11m2/s to 2.67×10-7m2/s when the particle size changes from 523.3 nm to 6.04 nm. D=kTCc/ 3pDμπ,, where k is the Boltzmann’s constant,cC is the slip correction factor, λ is the particle mean free path, μ is dynamic viscosity of air, and T is the temperature. In the experiment, the Schmidt number changes from 51.7 to 172573 with the increase of the particle size. Figure 7 shows the penetration efficiency as a function of the Schmidt number for different De and θ. In the laminar flow (De=144 and θ=8.3), the results are in agreement with the theory of Friendlander[12]and the experimental results given by Malet[8]. The penetration efficiency is larger in the turbulent flow (=De630 and 554) than in the laminar flow (De=144). The difference of the penetration efficiency in the turbulent and laminar flows becomes small when the Schmidt number is larger than 10 000. There exists a range of the Schmidt number within which the penetration efficiency increases abruptly. The range is from 7 500 to 25 000 in the present study.

Fig.7 Variation of penetration efficiency with Sc for different De and θ

2.5 Analytical relation between the penetration efficiency and De, Sc and bend length

For nanoparticles, the diffusion is the main factor for the particle deposition, including the Brownian diffusion and the turbulence diffusion. Therefore, the particle, flow and bend characteristic parameters must be used to describe the particle deposition. So the Schmidt number, the Dean number and the bend length are used to construct a function of the deposition.

Based on the experimental data, an empirical relation between the penetration efficiency and the Dean number, the Schmidt number and the bend length is derived as

Figure 8 shows the comparison between the ana-lytical relation predicted by Eq.(3) and the experimental data. The results of Yook et al.[10]are expressed as the parameters of the Dean number, the Schmidt number, and the bend length to validate the analytical relation.

Fig.8 Comparison between Eq.(3) and experimental data

2.6 Comparison of penetration efficiencies between straight and bend tubes

The relative penetration efficiency ()η is defined as the ratio of the penetration efficiency in a bend to that in a straight tube with the same length

Figure 9 shows the penetration efficiency as a function of the particle size with De=142.9. The penetration efficiency in the bend is lower than that in the straight tube because η is less than 1. The values of η are low when Dp<100 nm because fine particles can easily follow the secondary flow and deviate from the core of the flow toward the walls. The values of η keep a slight variation in the range 100 nm< Dp<523.3nm.

Fig.9 Relative penetration efficiency as a function of particle size

3. Conclusion

In order to quantify the losses of nanoparticles in a bend of circular cross-section, the penetration efficiency of the nanoparticles of sizes ranging from 5.6 nm to 560 nm in diameter is determined as a function of the Dean number, the Schmidt number and the bend angle. It is shown that the effect of the Dean number on the penetration efficiency depends on the sizes of the particles. The Dean number has a stronger effect on the penetration efficiency for small particles than for large particles. The turbulent motion has a main effect on particles of diameters larger than 100 nm, resulting in an enhancement of the particle deposition and reduction in the penetration efficiency. There exists a critical value of the Dean number beyond which the penetration efficiency turns from increasing to decreasing with the increase of the Dean number, and this critical value is dependent on the particle size and the bend length. The penetration efficiency decreases with the increase of the tube length. The penetration efficiency is obviously larger for large particles than for small particles, and is larger in the turbulent flow than in the laminar flow. The difference of the penetration efficiency in the turbulent and laminar flows becomes small when the Schmidt number is larger than 10 000. The penetration efficiency increases abruptly when the Schmidt number changes from 7 500 to 25 000. Finally, an analytical relation between the penetration efficiency and the Dean number, the Schmidt number and the bend length is derived.

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10.1016/S1001-6058(15)60460-7

* Project supported by the Major Program of the National Natural Science Foundation of China (Grant No. 11132008).

Biography: YIN Zhao-qin (1976-), Female, Ph. D., Associate Professor

LIN Jian-zhong, E-mail: mecjzlin@zju.edu.cn