Aerosol Science and Technology, 40:1–10, 2006Copyright c© American Association for Aerosol ResearchISSN: 0278-6826 print / 1521-7388 onlineDOI: 10.1080/02786820600616764

Instruction Manual for the Aerodynamic Lens Calculator

Xiaoliang Wang and Peter H. McMurryDepartment of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota, USA

This is an instruction manual for the aerodynamic lens designtool: the “Aerodynamic Lens Calculator”. We explain how to in-stall and use this software. Examples are provided to use this toolto design or test a lens system. The structures of the source codeprogramming are also provided in this manual. The design tooland its manual mentioned in this article are available in the pub-lisher’s online edition of Aerosol Science and Technology. To accessthis file, click on the link for this issue, then select this article. Inorder to access the full article on-line, you must either have an insti-tutional subscription or a member subscription accessed throughwww.aaar.org.

1. INTRODUCTIONWe have developed an Aerodynamic Lens Calculator that

can be conveniently used to design and evaluate aerodynamiclens systems. This Calculator utilizes empirical relations de-rived from numerical or experimental studies, and hence avoidsthe need to repeat detailed numerical simulations in the designprocess.

The Calculator has two modules: the Design Module and theTest Module. The Design Module takes input from the user anddesigns the lens system dimensions, operating conditions andprovides estimations of the lens performance. The Test Moduletests the performance of a lens system with known dimensions.

The detailed equations and design guidelines have been de-scribed in a companion paper (Wang and McMurry 2006). Thismanual provides instruction on how to use this Calculator. Wefirst describe the Design and Test Modules in more detail, andprovide examples of the design and test processes. We then de-scribe the structure of the background programming of the Cal-culator. This will help users to understand the coding and to mod-ify the Calculator to their specific needs. The lens calculator hasbeen tested by the authors and several other researchers. How-ever, we cannot guarantee that it is bug-free. Therefore, pleasecontact us if you encounter problems. We would also appreciateyour comments or suggestions for improving this AerodynamicLens Calculator.

Received 23 November 2005; accepted 3 February 2006.Address correspondence to X. Wang or P. H. McMurry, 111 Church

St. S.E., Minneapolis, MN 55455, USA. E-mail: wxl@me.umn.edu;mcmurry@me.umn.edu

The tests were mostly carried out in Microsoft Office©R Excel2003 in Windows XP operating systems. It may not work in otherExcel versions or operating systems. For example, the toolbarmay not be loaded in certain versions of Excel for Macintosh.But the Macintosh users can still use this Calculator. Detailedinstruction on setting up the program is given in the next section.

2. SETTING UP THE PROGRAMThe Aerodynamic Lens Calculator and its manual can be

downloaded from the website of Aerosol Science and Technol-ogy (http://www.taylorandfrancis.com). Create a new folder andstore the Excel file (AeroLensCalculator 060201 vl.0.xls) andPDF manual file (Manual.pdf) in the same directory. Doubleclick the Excel file to open the Calculator. If the file opens with-out a warning message, you are ready to play with the Calculator.If a warning message similar to Figure 1 pops up, try to lowerthe Macro security Level.

1. Select the Tools menu option and then select Macro andSecurity;

2. In the resulting Security dialog, set the security level toMedium by clicking the Medium radio button;

3. Close the file, Open the file again and click the Enable buttonwhen prompted to allow for the macro to run.

If you get an error message warning that “Visual Basic for Ap-plications (VBA) is not installed on your computer,” install VBAusing the following steps.

1. Run the Microsoft Office Installer;2. Choose Custom Install;3. In the list of applications, expand Office Tools and select

Visual Basic for Applications;4. Install VBA.

After these steps, close Excel and open the Calculator fileagain. A security warning message will appear. Choose the “En-able Macros” option.

For certain Macintosh Excel versions, an error message asshown in Figure 2 may popup. Click the “End” button. In thatcase, the user will not be able to use the custom toolbar of theLens Calculator. But equivalent buttons are available for calcu-lations. See next section for detailed instructions.

1

2 X. WANG AND P. H. McMURRY

FIG. 1. Security warning message for Macros.

3. USING THE AERODYNAMIC LENS CALCULATORThe Aerodynamic Lens Calculator has a user interface in Mi-

crosoft Excel, while programming is done through Visual Basicfor Applications (VBA). The Calculator consists of three spread-sheets: “Design,” “Test,” and “Gases.” The Design sheet is theDesign Module, with which one calculates the dimensions ofthe lens system and estimates the performance. The Test sheet isthe Test Module, which is used to evaluate the lens performancewhen the lens dimensions are known. The Gas sheet is a databaseof gas properties. The user can copy these properties to the De-sign or Test sheet.

In the remainder of this section, we will explain the input andoutput of each module, and provide examples of designing ortesting lens systems.

3.1. The Design Module3.1.1. Inputs of the Design Module

Figure 3 shows an example of the input data required to designan aerodynamic lens system. There are three categories of inputs:gas properties, lens conditions, and particle properties.

The properties of the carrier gas used in lens design are:molecular weight (g/mol), specific heat ratio, viscosity (Pa-s),Sutherland’s constant (K), and mean free path (nm). These vari-ables are specified at one atmospheric pressure and 296.15 K

FIG. 2. Toolbar loading error in Macintosh.

(Rader 1990). Data for some carrier gases are listed in the spread-sheet “Gas.” The user can put in any values pertinent to his/herspecific application.

The inputs for lens conditions are: number of focusing lenses(inlet orifice and accelerating nozzle are not counted), pressurebefore inlet orifice (Pa), pressure before the nozzle (Pa), pres-sure after the nozzle (Pa), volumetric flowrate through the lenssystem (slm), operating temperature (K), and the distance (mm)from the nozzle exit to the target where the beam width is ofinterest. Although the pressure before the nozzle is normallydifficult or impossible to measure, this parameter is chosen asan input to make sure the nozzle is choked, and to make the de-sign programming easier. If the input of the pressure before thenozzle is left blank, the Calculator will find a maximum oper-ating pressure. This feature is especially useful when designinglenses for nanoparticles (Wang et al. 2005a, b). The user shouldmake sure the Reynolds number is at least below 200 when usingthis feature.

The input particle properties are: particle density (kg/m3)and the focusing size range defined by the maximum diam-eter dpl (nm) and minimum diameter dpn (nm). The pro-gram designs a lens system so that the first lens focusesdp1, the last lens focuses dpn , and lens i focuses sizedpi = dpl − dp1−dpn

n−1 (i − 1)(i = 1 to n). We assume that then

AERODYNAMIC LENS CALCULATOR 3

FIG. 3. Example of the input data for the Design Module (A lens for focusing 50–500 nm unit density particles in air).

lenses are responsible for all focusing. In this Calculator, thepressure limiting orifice is denoted as lens 0 (i = 0), the ac-celerating nozzle is denoted as lens n + 1 (Please refer to theschematic near the title of the Design or Test Module, or Figure 1in Wang and McMurry (2006)).

The design module has an optional input of user defined par-ticle diameter and corresponding Stokes number for lens 1 to n(not including the inlet orifice or the accelerating nozzle). Thisoption will overwrite the size input in the “particle properties”section, and it will force the program to design lenses with theuser defined Stokes numbers instead of the optimal Stokes num-bers. This option is very useful when the user wants to designlenses operating at Stokes numbers other than optimal values,for example, when designing nanoparticle lenses where optimalSt’s are not possible, and when designing lenses for focusingover a range of sizes that exceeds a decade.

Figure 3 shows an example of the input used to design anaerodynamic lens system that focused 50–500 nm particles ofunit density using air as the carrier gas. Five lenses are usedin the system. A sample of 0.1 slm aerosol flow is drawn fromatmospheric pressure (101325 Pa), and the pressure before thenozzle is specified to be 150 Pa. The detector is located 100 mmdownstream of the nozzle exit. The user defined Stokes numbersof each stage is left blank, so optimal Stokes numbers will beused in calculating the orifice diameters.

3.1.2 Tool Bar of the Design ModuleWhen the Excel spreadsheet “Design” is activated, a floating

tool bar “Lenses Design” as shown in Figure 4 will popup onthe spreadsheet. This tool bar contains the following clickablecontrols: Design, More, Reset, and Help.

The Design ( ) button activates design of the aerody-namic lens system based on the user’s input described in theprevious section. The More ( ) button allows the user toexamine the focusing effects of a given particle size once a lenssystem is designed. This button is only valid when the Design

FIG. 4. Design tool bar.

button has been clicked and the spreadsheet has not been de-activated; otherwise a warning message as shown in Figure 5will pop up. If the More button is clicked after a lens system isdesigned, then a popup window as shown in Figure 6 will appearto ask the user to input a particle diameter (nm). After the userinputs a diameter and clicks “OK,” a row will be added to eachsection of Particle Results. The user can examine up to 20 par-ticle sizes. The Reset ( ) button resets the spreadsheet ofthe Design Module to a default format. This is useful if the useraccidentally deleted some critical cells in the spreadsheet andmade an error with the format. When the Help ( ) buttonis clicked, this manual will be opened.

Besides the floating tool bar, there are four fix buttons:, , , and . These

four buttons are equivalent to the buttons in the toolbar. Both theWindows and Macintosh users can use these buttons.

3.1.3. Results of the Design ModuleThe design results are expressed in two categories: flow and

particle results (Figure 7).The flow results first provide the minimum pumping speed

required for the nozzle to operate at choked condition. The fol-lowing results are then listed at each column: the lens num-bers (0 to n + 1), the calculated aperture diameter of each lens(mm), the pressure upstream of each orifice (Pa), the gas den-sity upstream of each orifice (kg/m3), the volumetric flowrateat each stage (cm3/s), the mass flowrate through the lens sys-tem (constant at each stage, kg/s), the pressure drop across eachorifice (Pa), the average gas velocity at each orifice (m/s), theflow Mach, Reynolds, and Knudsen numbers at each orifice,

FIG. 5. Warning message of clicking “More” button before the lens was de-signed.

4 X. WANG AND P. H. McMURRY

FIG. 6. Input for an particle diameter to examine its focusing effect.

and the length and inner diameter of spacers after each orifice(mm).

The listed particle results include the following parameters ateach lens stage for each particle size: Stokes number, contractionfactor, root mean square (RMS) displacement due to diffusion(mm), particle beam diameter (mm) and transmission efficiency.Also listed is the estimated particle terminal axial velocity (m/s).

FIG. 7. Example of the result data for the Design Module (A lens for focusing 50–500 nm unit density particles in air).

Figure 7 shows an example of the results when the Designbutton is clicked with the input data shown in Figure 3.

3.2. The Test Module3.2.1. Inputs of the Test Module

Figure 8 shows the inputs when using Test Module to evaluatethe lens system e described by Liu et al. (1995b). Note that the

AERODYNAMIC LENS CALCULATOR 5

FIG. 8. Example of the input data for the Test Module (Lens system e described in Liu et al. 1995b).

gas and particle properties inputs of the Test Module are exactlythe same as the Design Module. However, there are two optionsin the lens condition input. The first option is to specify thepressure before lens 1 (i.e., in the relaxation chamber) and toleave the flowrate input blank. The other option is to specifythe flowrate and to leave the pressure before lens 1 blank. Theprogram will solve for the value of the parameter that is leftblank. If both the pressure and the flowrate are specified, theprogram will take the pressure as input by default.

The lens dimensions need to be specified in the Test Module.These inputs include the aperture diameter of each lens and thenozzle exit, the length and inner diameter (mm) of spacers. Thediameter of the inlet orifice should be left blank; the programwill calculate its value. The diameter and length of the relaxationchamber (spacer 0) need also be provided. It is assumed that thereis no spacer after the nozzle.

3.2.2. Tool Bar of the Test ModuleWhen the Excel spreadsheet “Test” is activated, a floating

tool bar “Lenses Test” as shown in Figure 9 will popup on thespreadsheet in Windows based Excel. This tool bar is very simi-lar to the design tool bar, except that the Design ( ) buttonis replaced by the Test ( ) button. Once the Test button isclicked, the Calculator carries out evaluation of the lens system.The More ( ) and Help ( ) buttons have the samefunctions as those in the design tool bar. The Reset ( )button, however, resets the spreadsheet of the Test Module to adefault test of lenses e by Liu et al. (1995). Similar to the DesignModule, the Test spreadsheet has four fix buttons ,

, , and , which are equivalentto the , , and buttons in the toolbar,respectively.

3.2.3. Results of the Test ModuleThe content of the Test Module results is exactly the same as

that of the Design Module. An example of the test results corre-

FIG. 9. Test tool bar.

sponding to the inputs in Figure 8 is shown in Figure 10. Notethat the spacer length and inner diameter listed in the resultsare the suggested values instead of the user input value. How-ever, the beam width and transport efficiencies are calculatedaccording to the user input spacer dimensions.

Note that the performance estimations might be slightly dif-ferent between Design Module and the Test Module even for thesame inputs. These differences arise mainly from small errorswhen iteratively solving for pressure or flowrate and when inter-polating the parameterized equations for the contraction factorsand losses. Small differences also exit in some cases betweenthe two input methods (pressure or flowrate) of the Test Modulefor the same reasons.

3.3. Warning Messages and Error HandlingThe Calculator provides the following warning messages

when the input is not valid or the Calculator cannot find asolution.

1. Flow is supersonic.Flow through lenses (except the inlet orifice and the nozzle)is constrained to be subsonic. However, when the user spec-ified flowrate or operating pressure is too high, supersonicflow may happen. In this case, the error message shown inFigure 11 will pop up, and the calculation is suspended. Thefollowing adjustments can be made to solve this problem:• Reduce flowrate;• Reduce operating pressure (pressure before the nozzle

for Design Module and pressure before lens 1 for TestModule);

• Increase the minimum particle diameter to be focuseddpn;

• Increase particle density;• Use lighter carrier gas or gas mixtures;• Use smaller user defined Stokes number if in the De-

sign Module.2. Flow is not laminar.

Flow through lenses (except the inlet orifice) needs to belaminar to prevent turbulent dispersion of the particle beam.In this calculator, the non-laminar flow error message asshown in Figure 12 will pop up when the flow Reynoldsnumber at any of the orifices (except the inlet orifice) is

6 X. WANG AND P. H. McMURRY

FIG. 10. Example of the result data for the Test Module corresponding to input data in Figure 8.

greater than 200. Although the Calculator will continue thecalculation, the user should be aware of the potential dete-rioration of the beam quality. One can use the same meth-ods as those in overcoming supersonic flow to make flowlaminar.

FIG. 11. Warning message of supersonic flow.

3. Flow is not continuum.It is required that flow through the lens system (upstreamof the vacuum chamber) is continuum. Non-continuum flowwill occur when the operating pressure is too low. The non-continuum flow warning message shown in Figure 13 will

FIG. 12. Warning message of turbulent flow.

AERODYNAMIC LENS CALCULATOR 7

FIG. 13. Warning message of non-continuum flow.

pop up when the flow Knudsen number at any orifices is largerthan 0.1. The solutions to this continuum flow violation are:• Increase operating pressure;• Increase the minimum particle diameter to be focused

dpn;• Increase particle density;• Use lighter carrier gas or gas mixtures;• Use smaller user defined Stokes number if in the De-

sign Module.4. Solution cannot be found.

When an operating pressure cannot be found because themolecular weight of the carrier gas is too high or the particlesize is too small (e.g., to optimally focus 5 nm in air, as shownin Figure 3b in Wang et al. (2005a), a no-solution warningmessage as shown in Figure 14 will pop up. The solutions tothis problem are:• Increase the minimum particle diameter to be focused

dpn;• Increase particle density;• Use lighter carrier gas or gas mixtures;• Use smaller user defined Stokes number if in the De-

sign Module.5. Nozzle is not choked.

Under typical operating conditions, the accelerating nozzleof a lens system needs to be choked. This restriction is tomake sure that particles are accelerated to high velocitiesand that the pressure downstream of the nozzle is kept low sothat particles have long enough stopping distances to reachthe downstream destination (a skimmer, substrate or detec-tion chamber, etc.). This warning message is given when the

FIG. 14. Warning message of no solution found.

FIG. 15. Warning message of non-choked the nozzle.

nozzle is not choked (see Figure 15). The user must changethe pressure drop across the nozzle to create a choked flow.

6. Inlet pressure is too low.In the Design Module, when the user specified inlet pressureis lower than the pressure before the nozzle plus the pressuredrop at each stage, this warning message will pop up, asshown in Figure 16. The user has to increase the inlet pressureto a high enough value.There are other warning messages which are mainly relatedto a non-numerical input in a cell where a number is required.It is straightforward to fix these errors and we will not explainin detail.

4. PROGRAM LOGIC OF THE LENS CALCULATORFigure 17 shows the flow chart of the lens Design Module.

The design process starts with reading in the user input informa-tion of carrier gas, several operating parameters, particle densityand the focusing size range. Then the program calculates theoperating pressure and dimensions of the lens system: orificediameters and the length and inner diameter of spacers. Finally,the program estimates the three major performance parameters:size dependent particle terminal axial velocity, beam width, andtransmission efficiency. The flow through lenses is always forcedto be laminar, continuum, and subsonic.

The lens test module is very similar to the design moduleexcept that the lens dimensions are specified by the user as well.The flow diagram of the program logic and the correspondingmain subroutines are shown in Figure 18.

5. OTHER COMMENTSIn this manual we described how to use the Aerodynamic

Lens Calculator and its program logic. More detailed expla-nation of variables and subroutines can be found the program

FIG. 16. Warning message of too low inlet pressure.

8 X. WANG AND P. H. McMURRY

FIG. 17. Flow diagram and main subroutines of the Design Module program.

AERODYNAMIC LENS CALCULATOR 9

FIG. 18. Flow diagram and main subroutines of the Test Module program.

10 X. WANG AND P. H. McMURRY

source code itself. The Visual Basic source code can be accessedfrom Excel Menu Tools\Macro\Visual Basic Editor or by sim-ply use keyboard shortcut Alt + F 11. Find the Project Explorein the Visual Basic Editor. Locate the VBAProject correspond-ing to your Excel file name corresponding to the design tool,and double click “ThisWorkbook.” The source code will nowappear on the screen. Users are welcome to modify the sourcecode to meet their needs. We would appreciate learning aboutsuch changes so that we can incorporate them in the “Calculator”for others to use.

This software is free to the public. Because only a few lensdesigns have actually been built and carefully tested in the lab-oratory, we recognize that not all lenses designed using this cal-culator might function as predicted. Of course, we cannot takeresponsibility for such failures of this design tool. However, wewould like to learn about them so that we can incorporate what

has been learned from the work of others when preparing up-dated versions of this software.

REFERENCESLiu, P., Ziemann, P. J., Kittelson, D. B., and McMurry, P. H. (1995b). Generating

Particle Beams of Controlled Dimensions and Divergence: II. ExperimentalEvaluation of Particle Motion in Aerodynamic Lenses and Nozzle Expan-sions. Aerosol Sci. Technol. 22(3):314–324.

Rader, D. J. (1990). Momentum Slip Correction Factor for Small Particles inNine Common Gases, J. Aerosol Sci. 21(2):161–168.

Wang, X., Kruis, F. E., and McMurry, P. H. (2005a). Aerodynamic Focusing ofNanoparticles: I. Guidelines for Designing Aerodynamic Lenses for Nanopar-ticles, Aerosol Sci. Technol. 39(7):611–623.

Wang, X., Gidwani, A., Girshick, S. L., and McMurry, P. H. (2005b). Aerody-namic Focusing of Nanoparticles: II. Numerical Simulation of Particle Motionthrough Aerodynamic Lenses, Aerosol Sci. Technol. 39(7):624–636.

Wang, X., and McMurry, P. H. (2006). A Design Tool for Aerodynamic LensSystems, Aerosol Sci. Technol. Accepted.