A Programmable Aerosol Diluter for Generating Time-Varied Sub-Micrometer Particles

Real-world aerosols often vary over time. A time-varied aerosol generation system is thus needed to evaluate the performance of aerosol sensors for characterizing time-dependent aerosol size distribution. However, all laboratory aerosol generators are designed for the production of aerosols with stable concentrations and steady size distributions. A simple way to produce reliable time-dependent aerosols is to combine a stable aerosol generator with a programmable aerosol diluter. Aerosol diluters are also needed to measure aerosols in high concentrations using existing aerosol instruments. In this study we focused on the design and evaluation of a programmable aerosol diluter. The dilution flow rate of the aerosol diluter was controlled by a programmable mass flow controller with a flow rate of up to 200 L/min. Steady and dynamic dilution processes in the diluter were programmed using Visual Basic. Experiments were carried out to characterize the steady and dynamic dilution performance of the aerosol diluter for DMA-classified particles with sizes ranging from 10 nm to 1.0 μm. The steady dilution result shows that the diluter has a non-size dependent dilution performance, and there is a good linear relationship between the aerosol dilution ratio and dilution flow rate ratio (with a calibrated line slope of 1.03, close to the ideal line slope of 1.0). Our experiments further indicate that efficient aerosol mixing in the diluter can be achieved when operated at a flow Reynolds number above 450. The evaluation of four dynamic dilution modes also provides evidence of the excellent performance of the diluter, which has the capability of continuously producing welldefined and concentration-varied aerosols. A simple empirical model was also proposed to describe the steady and dynamic dilution performance of the diluter.


INTRODUCTION
Real-world aerosols are often time-varied in their physical properties, such as particle concentration and size.Examples of such time-varied aerosols are the nucleation event of particles in the atmosphere (Weber et al., 1995(Weber et al., , 1996;;Mäkelä et al., 1997;Kulmala, 2003Kulmala, , 2004Kulmala, , 2013) ) and the aerosols produced by the combustion processes (Flagan, 1979;Leskinen et al., 1998;Yu et al., 2005;Xu et al., 2011).The performance of aerosol instruments under the challenge of time-varied aerosols needs to be understood in order to properly characterize the transient behavior of aerosols.However, none of the aerosol generators is able to reliably produce well-defined and time-varied aerosols for aerosol instrument calibration.All existed instruments are currently evaluated by stable laboratory aerosols, lack of dynamic performance information for users to properly interpret measured data.With the modern development of aerosol instruments, the investigation of the dynamic response of instruments becomes essential.It is thus desired to develop a time-varied aerosol generation system for evaluating the dynamic performance of aerosol sensors.A simple way to produce time-varied aerosols in the lab is to combine a stable aerosol generator with a programmable aerosol diluter.
Particles in high concentration are often encountered in the measurements of aerosols originating from various particle sources, e.g., combustion.Because of the limitations of aerosol instruments, such as portable Condensation Particle Counter (CPC, TSI Model 3007) having the measurement limit of particle concentration below 10 5 #/cm 3 , they are not suitable for directly characterizing particles in high concentrations.Aerosol dilution is a common technique to deal with this issue.Up to now, a number of different dilution approaches have been developed and commercialized for the study of particle emissions from diesel vehicles (Casati et al., 2007), cigarette smoke aerosols (McCusker et al., 1982) and laboratory-generated aerosols.In an ideal dilution, the dilution ratio of aerosols is directly determined by the ratio of these two flows (i.e., no particle loss during the dilution process).Fuchs and Sutugin (1965), Delattre and Friedlander (1978) and Mikkanen et al. (2001) used porous tube diluters for aerosol dilution, in which the dilution air entered through a tube with a porous wall and was mixed with the particle-free air.The similar design concept can also be found in a "leaky filter" type diluter, which consisted of a glass capillary tube placed in a HEPA Capsule filter (Collins, 2010).Also based on the similar principle, Guichard (1982) designed another new diluter by sending aerosol flow into a cone shape dilution channel which was perforated with rings of blowing holes.Venturi principle was very commonly applied in dilution approach, as well.Koch et al. (1988) developed a Venturi aerosol diluter with a fixed dilution factor of 10, and Abdul-Khalek et al.
(1998) designed a Venturi based aerosol ejector.Both of them can achieve a quick dilution for the entire size range from nanometers up to several micrometers.Helsper et al. (1990) tested a cascade Venturi dilution system with dilution ratio up to 10,000 for particle sizes between 0.1 and 10 µm.Moreover, Koch and Ilgen (1992) developed a particle size selective dilution system based on virtual impaction theory for fine particles (< 1 µm).Differing from the dilution-ratio-fixed designs described above, Hueglin et al. (1997) designed a rotating disk type dilution system for particle sizes between 10 nm and 700 nm.In this diluter, the aerosol dilution ratio showed a linear relationship with the control parameters (e.g., rotating frequency) and can be selected continuously between 10 and 10,000.But for larger particles, the impaction-caused loss in the diluter resulted in a deviation from the ideal condition.And the flow rate of diluted gas was restricted to a few liters per minute (Burtscher, 2005).
During the dilution, passing particles may alter their sizes through many mechanisms such as particle condensation, agglomeration and coagulation.A representative aerosol diluter thus requires a quick and stable dilution process for all particle sizes under consideration.Cheng et al. (2002) investigated the turbulent mixing effect on particle size distribution in an ejector diluter and found no apparent shift on aerosol peak value and distribution spread.Wong et al. (2003) also found an ejector diluter could provide reliable diesel exhaust particle number and size distribution because of negligible coagulation effects in a fast mixing process.Particle losses within the diluters however need to be considered to recover the size distribution of originally sampled aerosols.It is because a significant particle loss in ejector diluters may vary aerosol dilution ratio from the ideal volumetric flow rate ratio, resulting in a particle-sizedependent dilution.Yoon et al. (2005) reported their experimental result of 95% transmission efficiency for particle sizes between 3 nm and 20 nm in a modified Venturi diluter designed by Koch et al. (1988).Collins (2010) also studied the sub-100 nm particle loss within aerosol diluters (TSI 3302, MSP 1100, a laboratory "leaky filter" diluter and an orifice diluter).Particle loss was found to be primarily diffusion driven, and loss within the diluters increased with decreasing particle diameter.And aerosol charge may reduce particle penetration through diluters by as much as 40%.
In this study, we developed a new aerosol diluter for a programmable aerosol generation system to address two issues previously discussed, i.e., dilution of high concentration aerosol to satisfy the detection limit of existed aerosol instruments and generation of time-varied aerosol for evaluating the dynamic response of aerosol sensors.Three design objectives of this new diluter are: (1) the aerosol diluter shall perform a controllable dynamic dilution and have a good repeatability; (2) the aerosol diluter shall have a size-independent dilution performance for particles with sizes less than 1.0 µm; (3) the particle loss in the diluter shall be kept as minimal as possible.To achieve these goals, we designed a new diluter enabling good turbulent flow mixing inside while minimizing the particle loss due to the turbulence flow effect.Experiments were further carried out to evaluate the steady and dynamic performance of the diluter for particles with sizes ranging from 10 nm to 1 µm.Finally we proposed a simple empirical model to describe the dynamic performance of the designed diluter.

Design of Aerosol Diluter
In order to build up a size-independent aerosol dilution system, we designed and evaluated a new aerosol diluter which is shown in Fig. 1.The aerosol diluter consists of three sections: fast premixing, full mixing/dilution and aerosol sampling sections.The aluminum-made fast premixing section is the most important part of the diluter.Three inlets are included in the section.The central inlet with the outer diameter (OD) of 1/4" (0.635 cm) and inner diameter (ID) of 0.225" (0.572 cm) is for undiluted aerosol and the other two identical side inlets with OD of 1/2" (1.27 cm) and ID of 0.41" (1.041 cm) are for the injection of particle-free dilution gas flows.Each side inlet forms 45º angles with the central aerosol inlet.In the pre-mixing section, two identical dilution gas flows at controllable flow rates are mixed with aerosol flow in a relatively small tubular space, whose diameter is 0.75" (1.905 cm), length is about 1.2" (30.48 mm) and volume is about 8.71 cm 3 .Once mixed, the entire flow is then transported to the full mixing section, which is a cone shaped space with diameter increasing from 0.75" to 1.85" (4.699 cm), for complete mixing process.The full dilution section of the diluter is a 1foot (30.48 cm) long aluminum tube with OD of 2" (5.08 cm) and ID of 1.85" (4.699 cm).The large space in the full dilution section weakens the flow turbulence effect.Particles continue their mixing with dilution air flow in the full dilution section, and a spatially uniform aerosol distribution across the cross section of the tube will be developed at the end of this section.The metal material was chosen to reduce potential particle loss resulted from the electrostatic effect.A "Y" shaped PVC connector at the downstream of diluted flow forms the sampling section of the diluter, in which only a portion of diluted aerosol flow is sampled via a stainless steel tubing of 0.375" (0.953 cm) OD and 0.305" (0.775 cm) ID for measurement while the majority of flow is exhausted from the side opening.For the operation, aerosol dilution is determined by the setting for the ratio of dilution flow rate to aerosol flow rate.When the undiluted aerosol flow rate is fixed, the concentration of diluted aerosol output from the diluter depends on the dilution gas flow rate.

Experimental Setup
Fig. 2 is the schematic of the experimental setup for testing the new aerosol diluter.As shown, a custom-made Collison atomizer and a diffusion dryer were used to generate dry solid polydisperse particles in a stable concentration and size distribution from liquids, which were prepared by dissolving sodium chloride in DI water for different concentrations (5%, 0.1% and 0.01%, in v/v).To test ultrafine particles, especially particles with diameter down to 10 nm, an aerosol generation system based on the evaporation and condensation technique (Scheibel and Porstendörfer, 1983;Gurav et al., 1994;Li and Chen, 2005) was used in this study to produce particles in the same chemical compound as those generated by the Collison atomizer.This setup mainly consisted of a cylinder of nitrogen gas (Grade 4.8), a Lingerberg tube furnace with a ceramic tube inside (Al 2 O 3 , Coors Ceramics Co), a combustion boat, and a compressed air source.NaCl powder was placed in the combustion boat located in the middle of the ceramic tube.To produce stable polydisperse nanoparticles of desired sizes, the tube furnace temperature was carefully controlled.Filtered N 2 gas was introduced into the ceramic tube to transport NaCl vapor, then mixed with a cold quenching stream of particle-free compressed air at the exit.Thus, the evaporation inside the furnace and condensation outside resulted in nanoparticle generation.In the experimental setup of aerosol generators, 4 laminar flow meters (LFMs) and 4 needle valves were used for flow rate monitoring and control, respectively.
To obtained DMA-classified particles with size up to 1.0 µm, TSI 3081 and 3085 differential mobility analyzers (DMAs) and custom-build DMA with the classification length of 66 cm, combined with TSI 3080 DMA platform, were used as the particle size selectors.The aerosol-to sheath flow rate ratios in all experiments were kept at 1:10 to ensure the consistent size quality of selected particles.Particles with 16 different mobility sizes, covering the range from 10.0 nm to 1.0 µm, were individually chosen and delivered into the aerosol diluter for testing (i.e., 10, 30, 50, 100, 150, 200, 250, 300, 350, 400, 500, 600, 700, 800, 900 and 1000 nm).Another LFM, filter and needle valve in front of the dilution system was used to inject a makeup flow in some cases.Undiluted classified aerosol flow rates were thus controlled from 0.3 L/min to 5.0 L/min, according to the downstream flow rate of DMAs and required flow rate for dilution operation.Meanwhile, two particle-free dilution air flows controlled by a mass flow controller (MFC; MKS type 1559A), which receives control signals from a data acquisition (DAQ) card, were injected into the diluter to achieve the desired dilution effect (see in Fig. 1).In this study, the flow rate of dilution air can be precisely adjusted from 0 to 200 L/min.The performance of MFC showed its quick response and flow rate adjustment within 2-3 seconds.The MFC can also send the flow rate signals back to the DAQ card for feedback control.A computer program developed on Visual Basic (VB) language communicated with the DAQ card and TSI 3025A UCPC, and monitored the entire system by recording the data and operational parameters.
To evaluate aerosol dilution ratio for different sizes and dynamically control particle concentrations, six different dilution modes were developed in the VB program: constant dilution mode (in which the dilution flow rate remains unchanged during dilution), step dilution mode (in which the dilution flow rate changes step by step according to a user-defined step function), linear ramp dilution mode (in which the dilution flow rate is either increased or decreased linearly during the dilution), rectangular wave dilution mode (in which the variation of dilution flow rate is in a rectangular wave pattern), triangular wave dilution mode (in which the real dilution flow rate as a function of time follows a user-defined triangular wave pattern) and half-sine wave dilution mode (in which the real dilution flow rate curve as a function of time follows a user-defined half-sine wave function).The specific dilution process for these 6 modes all can be determined by setting dilution ratio or dilution flow rate, dilution step number and step dilution time or total dilution time.Both the real-time flow rate data of dilution air and the particle number concentration data were recorded and displayed with 1-second time resolution.To evaluate steady and transient dilution performance of aerosol diluter, constant dilution mode and step dilution mode were chosen.For each evaluation case of DMAclassified aerosol (with the sizes ranging from 10 nm to 1.0 µm), at least three different flow rates were chosen to be tested to characterize the features of aerosol diluter, such as dilution ratio and delay time.To investigate dynamic performance of aerosol diluter, linear ramp dilution mode, rectangular wave dilution mode, triangular wave dilution mode and half-sine wave dilution mode were conducted.Aerosol flows with particle size of 30, 300 and 700 nm and flow rate of 1.0 L/min or 0.5 L/min were used in this experiment.For each specific evaluation case, identical testing was done for at least 3 times, and the results proved an excellent repeatability of the studied dilution system.

Steady Performance of Aerosol Dilution (Evaluation of Aerosol Dilution Ratio)
To evaluate the steady performance of the prototype aerosol diluter, particles of different sizes smaller than 1 µm were tested.For each run, the same stepping dilution mode was chosen and operated to provide a series of dilution levels from the low flow rate ratio of 5 to the high flow rate ratio of 200.Here, we defined flow rate ratio (FR) and aerosol dilution ratio (AR) as: , , , where i indicates test particle size; Q dilu,i and Q aero,i are particle-free dilution flow rate and non-diluted aerosol flow rate, respectively; N non-dilu,i and N dilu,i are the aerosol concentrations of non-diluted and diluted aerosol measured at the downstream of aerosol diluter, respectively; ƞ i is the particle penetration efficiency through the diluter, defined as N non-dilu,i /N upstream,i .Particle penetration efficiency test was conducted prior to all experimental runs for programmable dilution experiments.The result showed that in general all particles (10 nm to 1.0 µm) have more than 88% penetration efficiencies for test dilutor.The 99% penetration efficiency for the diluter has been achieved for particles with the diameters larger than 60 nm.Fig. 3 shows the plot of experimentally obtained aerosol dilution ratio as a function of flow rate ratio.Also included in the above plot is the straight line assuming the ideal dilution (i.e., FR = DR) for the reference.As evidenced in Fig. 3, the dilution result for test aerosols with sizes from 10 nm to 1 µm in the studied aerosol diluter were all very close to the line for the ideal case, indicating the excellent performance of the studied diluter.In general, the characteristics of aerosol dynamics in an aerosol diluter are sensitive to the turbulent flow condition in the dilution tunnel/chamber.Gas flow introduced into the turbulent region of a diluter is transported and dispersed across it by the fluid eddy motion (from the largest eddies to the smallest ones).Such eddy motion of gas flow permits the flow mixing to proceed effectively (Dimotakis, 2005).However, aerosol particles under such a turbulent mixing process are easily lost, resulting in that the real dilution data AR i would be larger than the flow rate ratio FR i .The more particles loss, the further real dilution data deviated from the ideal.The aerosol loss in the turbulent mixing should thus be minimized in order to achieve an ideal aerosol dilution (i.e., no particle loss).Through curve fitting of all dilution ratio data in this experiment, the result of a straight line with slope of 1.03 demonstrates that particle loss in the studied diluter is overall negligible.The dilution strategy applied to the design of the studied aerosol diluter seems to work reasonably well in the particle size range of interest.In the studied aerosol diluter, the fast premixing was first achieved by impinging a highly concentrated aerosol stream with two particle-free dilution gas flows in a relatively small space.The resultant stream was quickly transported to a large space to reach a stable mixing with minimal loss.The curve-fitted line can then be used as the calibration curve of the studied aerosol diluter for particles with sizes smaller than 1.0 µm.
Detailed examination of the experimental data given in Fig. 3 further reveals that for the studied prototype the aerosol dilution in some cases noticeably deviates from the ideal condition.To analyze those cases, the value of AR/FR for all the dilution cases (shown in Fig. 3) is given in Fig. 4 as the function of flow Reynolds number (Re = ρ v D/µ, where ρ is the air density, v is flow velocity, D is the inner diameter of the fast premixing section of diluter and µ is the kinetic viscosity of the air).Two parallel dash lines are also included in Fig. 4 as the ± 15% deviation from the reference value (i.e., 1.03).As shown in Fig. 4, the scattering of dilution data was reduced as the flow Reynolds number increased and was within ± 15% when the flow Reynolds number was higher than 450, and up to ~10 4 (maximum case in this study).The above observation is comparable with that reported by Dimotakis (1993)   diluter, the critical Reynolds number for fully turbulent flows is expected to be less than that reported by Dimotakis (1993).The primary mixing of aerosol stream with particle-free flows in the studied diluter obviously resulted from the turbulent flow mixing.Note that the total flow rate for the Reynolds number of 450 in the studied diluter can be calculated as 6.0 L/min.

Transient Performance of Aerosol Diluter
As previously mentioned, particle-free gas flow in the studied dilution system can be quickly changed by the control program (usually less than 3 seconds).However, the additional time is required for the diluter to achieve its steady dilution state (i.e., delay time) once the dilution flow rate is changed.It is because of the finite dilution volume and mixing process in the studied diluter.The delay time is thus one of the primary parameters in describing the transient performance of an aerosol diluter.The determination of the delay time can be done by comparing the timedependent dilution flow rate data with the time-dependent CPC readouts for diluted aerosol concentration.The delay time in general depends on many parameters such as dilution flow rate, dilution volume, particle size, CPC residence time, etc.
To simplify the data analysis, the sampling tubing from the diluter exit to the UCPC inlet was reduced to the minimum, neglecting the time needed to transport the diluted aerosol to UCPC.The time resolution of UCPC data readout from its RS-232 communication protocol is 1.0 s, resulting in the same time resolution for the transient performance characterization of the studied aerosol diluter.Since the CPC response time for a change of aerosol concentration is estimated at 0.3 second when operated at the high flow rate mode, the delay time attributed by the CPC response can also be neglected (i.e., much less than 1.0 second).So, the factors contributing to the observed delay time in the studied aerosol dilution system are limited to the particle size (D p ), total flow rate (Q tot = Q aero + Q dilu ) and dilution volume (V) in the studied diluter.
The dilution delay time is expected to increase when the tested particle size increases.It is because small particles having less inertial effect in flows could easily follow the change of gas flows when compared with that for large particles, resulting in a quicker dilution response for small particles as compared with that of large particles.The particle inertial effect can be characterized by the particle relaxation time (τ), defined as the characteristic time for particles to change from one state to another state.Obviously, the time of particles residing in the diluter (t r ) will directly affect the response of the studied dilution system.Thus, the particle residence time in the diluter shall be included in the analysis of the delay time for the studied diluter, as well.The values of t r and τ can be calculated by the following equations: where the particle terminal velocity is which S is the cross section area of fully developed dilution zone; the drag force F D is a function of the particle size, density and terminal velocity and can be calculated as ; and ρ p is the particle density.A set of 3D curve fitting functions were tested to find out the bestfitted curve of the dilution delay time t delay as a function of particle resident time t r and particle relaxation time τ.Because of its simple mathematic expression and unit uniformity between two sides of equation, we proposed to fit the experimental delay time t d (t r , τ) as: Fig. 5 shows the delay time deducted from the experiment runs and the curve for the proposed best-fitted equation.The delay time for particles of different sizes under various dilution conditions can thus be calculated by Eq. ( 5).

Dynamic Performance of Aerosol Diluter at Designated Dilution Modes
The unique feature of the studied aerosol dilution system is its capability of continuous variation of aerosol dilution according to commands signaled by the control program developed using Visual Basic.The program worked as the platform to carry out six dilution modes described in the diluter design section and to register the concentrations of diluted aerosol and operational parameters during the process.For this part of the experiment, undiluted aerosol flow rate was fixed at 1.0 L/min.Particles of 30, 300 and 700 nm were individually selected for the evaluation.
Fig. 6 shows the dynamic dilution results of the prototype aerosol diluter operated at four dilution modes (i.e., linearly increased dilution mode (a); triangular wave mode (b); half-sine wave mode (c); and rectangular wave mode (d)) for the particles with the sizes of 30, 300 and 700 nm.For comparison, the changes of dilution flow rate ratio as the time proceeded in the process are also given in the corresponding figures.Note that, as mentioned previously, the real dilution flow rate in the studied diluter can be quickly changed after the change command is signaled by the control program, reaching its set flow rate in the duration of 2-3 s.The same observation was obtained in this part of the experiment for these four dilution modes.
Fig. 6(a) shows the dilution result when the diluter was operated at the linearly increased dilution mode.In this case, the dilution flow rate ratio was kept at 10 for the initial 5 s and increased to 150 in the latter 290 s.During the same period of time, the measured aerosol dilution ratios for test particles initially increased to the corresponding dilution flow rate ratio and kept steady for a few seconds.The aerosol dilution ratio then linearly increased as the dilution flow rate ratio continuously increased.Eventually the aerosol dilution ratio matched the dilution flow rate ratio.Only slight time delay in aerosol dilution was observed in this operational mode.
The dilution results when the diluter was operated at the triangular and half-sine wave dilution modes are given in Figs.6(b) and 6(c), respectively.For both tested cases, the dilution process started from a dilution flow rate ratio of 50, and then gradually increased to 100 within 60 s.After reaching the peak, dilution immediately went to decreasing mode and finally got back to 50 within 60 s.Such an operation formed a symmetric triangular wave and half-sine Fig. 5.The dilution delay time as a function of particle residence time (V/Q total ) and particle relaxation time (τ).
wave dilution function.The system can be controlled to repeat a series of the same waved dilution pattern until a stop command is send.In both modes, the testing results showed the aerosol dilution ratio had similar patterns as the corresponding dilution flow rate ratio.A constant time delay between the aerosol dilution and flow rate ratio was observed during these two dilution processes.The difference in the delay between the case (a

Fig. 6 (continued).
two different dilution flow rate ratios (60 s for dilution flow rate ratio of 10 and 60 s for dilution flow rate ratio of 50).Different from the three continuous dilution modes discussed above, a bigger time delay in aerosol dilution was observed after the dilution flows were injected in the diluter.Once the aerosol dilution started, the dilution ratio quickly ascended to reach the set maximal dilution flow rate ratio.However, the time rate of aerosol dilution increase was not as high as that of the dilution flow rate increase in this operation mode.Further, the larger the particle size, the slower the aerosol dilution ratio increased.However, once the dilution flow was turned off, the aerosol dilution ratio dropped at a much faster pace when compared with that in the dilution increase phase.No particle size effect in aerosol dilution was found during the dilution descending phase.

MODEL TO PREDICT THE PERFORMANCE OF STUDIED AEROSOL DILUTER
In the steady state operation (i.e., fixed aerosol dilution), the dilution ratio for particles with sizes ranging from 10 nm to 1 µm was measured as 1.0306 times the dilution flow rate ratio.A time delay between the onset flow rate ratio and output diluted aerosol ratio was also found in our study.In such cases one can simply apply the following equation to describe the time relationship between the aerosol dilution ratio and dilution flow rate ratio: where both aerosol dilution and dilution flow rate ratios are the functions of time t, and delay time t d can be calculated by Eq. ( 5).The same equation can also be applied to the cases for continuous dilution modes of linear increase/decrease, triangular wave and half-sine wave modes.
For step and rectangular wave dilution modes, a different set of equations is proposed to describe the change of aerosol dilution ratio between two adjacent settings of dilution flow rate ratio: For the ascending case And for the descending case where the dilution flow rate ratio is assumed in the functional format of

FR t t t t
One can easily use the Eq. ( 6) to predict the diluted aerosol concentration at any time t under the designated aerosol dilution modes developed in the studied aerosol dilution system, when un-diluted aerosol concentration, aerosol flow rate, particle-free dilution flow rate and the diluter geometry are known.The model can also assist in finding the resultant aerosol dilution under specific dilution flow rate curves defined by users.
To verify the above proposed model, the comparison of calculated aerosol dilution ratios and experimental results is shown in Fig. 7.In this verification part of the experiment, four dilution modes were tested, and the particle size tested in each mode was randomly selected for each mode examination.For the case of linearly increased dilution mode (shown in Fig. 7(a)), a 300 nm particle stream at the flow rate of 1.0 L/min was used.As expected, the trend of all experimental data for the aerosol dilution ratios varying from 10 to 150 in general follows the calculated line for aerosol dilution and falls in the domain bounded by the two predicted limited lines (± 10% deviation from the calculated line).The same verification was also done for the cases of triangular wave, half-sine wave and rectangular wave dilution modes (shown in Figs.7(b), 7(c) and 7(d), respectively).A 30 nm particle stream of 1.0 L/min flow rate was selected in the verification of triangular wave dilution mode with the dilution flow rate ratio varying from 50 to 180.For the half-sine wave dilution mode, a 700 nm aerosol stream of 0.5 L/min flow rate was applied.A 30 nm particle flow at the rate of 1.0 L/min was used in the verification for the rectangular wave dilution mode.Two different operational settings were applied in this mode verification: one is for case of flow rate ratio setting from 0 to 100 and the other is for the case from 10 to 50.For all these cases, predicted results from the model can match the experimental data very well.

Fig. 2 .
Fig. 2. Schematic diagram of the experimental setup for the performance evaluation of proposed diluter.

Fig. 3 .
Fig. 3. Steady state aerosol dilution result of studied aerosol diluter for DMA-classified particles in various sizes.
for fully developed turbulent flows.Dimotakis shows that the fully developed turbulent flow requires a minimum local Reynolds number of 10 4 , or a Taylor Reynolds number (Re T = ρ u' λ T /µ, where u' is the rms streamwise velocity fluctuation level, and λ T is the Taylor microscale) of 10 2 to be sustained.Due to the flow impingement in the studied

Fig. 4 .
Fig. 4. The ratio of aerosol dilution ratio (AR) to dilution flow rate ratio (FR) as a function of flow Reynolds number for the studied aerosol diluter.
Fig. 6.Dilution result of aerosol diluter when operated at four different dilution modes (a.linear increasing dilution; b. triangular wave patterned dilution; c. half-sine wave dilution; d. rectangular wave dilution).

Fig. 7 .
Fig. 7. Comparison of calculated aerosol dilution ratio with experimental ratios for four continuous dilution modes in aerosol diluter (a.linearly increase dilution mode; b. triangular wave dilution mode; c. half-sine wave dilution mode; d. rectangular wave dilution mode).