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A DESIGN TOOL FOR AERODYNAMIC LENS SYSTEMS 333 p1 pressure upstream of an orifice p2 fully recovered pressure downstream of an orifice pfocusing pressure upstream of a lens for focusing particles of a given size pMa minimum pressure for flow to be subsonic pmax maximum operating pressure of an aerodynamic lens pKn minimum pressure for flow to be continuum Q volumetric flowrate Qi volumetric flowrate at stage i R universal gas constant Re flow Reynolds number based on orifice diameter Res flow Reynolds number based on spacer diameter ri critical initial particle radial position r pi particle initial radial location in an aerodynamic lens S Sutherland constant Sa particle axial stopping distance Sr particle radial stopping distance St Stokes number based on orifice diameter Sto Sts Sts50 optimum Stokes number Stokes number based on spacer diameter Spacer Stokes number corresponding to a 50% impaction loss stage i includes lens i and the downstream spacer t T1 TpF particle residence time temperate upstream of the lens particle frozen temperature in the jet expansion Tr u reference temperature in Sutherland’s Law average flow velocity at orifice entrance based on upstream flow conditions u p particle axial velocity Us va vpr average flow velocity in the spacer axial jet flow velocity particle terminal radial velocity in the vacuum chamber vr xc ≈ 1 − radial jet flow velocity � �p pressure drop across an orifice ηc particle contraction factor ηc,i contraction factor at lens i ηt particle transmission efficiency ηt, diffusion, i penetration after diffusional loss at stage i ηt, GK, i penetration after loss at stage i estimated by Gormley-Kennedy equation ηt, orifice, i transmission efficiency after impaction losses on the orifice plate i ηt, spacer, i transmission efficiency after impaction loss to spacer i θ jet opening angle λ1 mean free path of the gas molecules upstream of the orifice µ carrier gas viscosity ξ = � γ 2 γ −1 γ +1 xrms particle root mean square displacement due to diffusion xrms,i root mean square displacement between lenses i and i+1 Y β = d f /ds γ orifice flow expansion factor constriction ratio specific heat ratio of the carrier gas Dils,i Qi dimensionless diffusion deposition parameter ρ1 carrier gas density upstream of the aerodynamic lens ρp particle material density τ particle relaxation time REFERENCES Back, L. H., and Roschke, E. J. (1972). Shear-Layer Flow Regimes and Wave Instabilities and Reattachment Lengths Downstream of an Abrupt Circular Channel Expansion, J. App. Mech. 94:677–681. Bean, H. S. (1971). Fluid Meters: Their Theory and Applications (Report of ASME research committee on fluid meters). New York, ASME. Cheng, Y. S., and Dahneke, B. E. (1979). Properties of Continuum Source Particle Beam. II. Beams Generated in Capillary Expansions, J. Aerosol Sci. 10:363–368. Dahneke, B. E., and Cheng, Y. S. (1979). Properties of Continuum Source Particle Beam. I. Calculation Methods and Results, J. Aerosol Sci. 10:257– 274. Di Fonzo, F., Gidwani, A., Fan, M. H., Neumann, A., Iordanoglou, D. I., Heberlein, J. V. R., McMurry, P. H., Girshick, S. L., Tymiak, N., Gerberich, W. W., and Rao, N. P. (2000). Focused Nanoparticle-Beam Deposition of Patterned Microstructures, Appl. Phys. Lett. 77(6):910–912. Dong, Y., Bapat, A., Hilchie, S., Kortshagen, U., and Campbell, S. A. (2004). Generation of Nano-Sized Free Standing Single Crystal Silicon Particles, J. Vacuum Sci. & Technol. B: Microelectronics and Nanometer Structures 22(4):1923–1930. Drewnick, F., Hings, S. S., DeCarlo, P., Jayne, J. T., Gonin, M., Fuhrer, K., Weimer, S., Jimenez, J. L., Demerjian, K. L., Borrmann, S., and Worsnop, D. R. (2005). A New Time-of-Flight Aerosol Mass Spectrometer(TOF-AMS)— Instrument Description and First Field Deployment, Aerosol Sci. Technol. 39(7):637–658. Eichler, T., de Juan, L., and Fernández de la Mora, J. (1998). Improvement of the Resolution of TSI’s 3071 DMA via Redesigned Sheath Air and Aerosol Inlets, Aerosol Sci. Technol. 29(1):39–49. Fernández de la Mora, J., and Riesco-Chueca, P. (1988). Aerodynamic Focusing of Particles in a Carrier Gas, J. Fluid Mech. 195:1–21. Fernández de la Mora, J., Rosell-Llompart, J., and Riesco-Chueca, P. (1989). Aerodynamic Focusing of Particles and Molecules in Seeded Supersonic Jets. in Rarefied Gas Dynamics: Physical Phenomena, Progress in Astronautics & Aeronautics. E. P. Muntz, D. P. Weaver, and D. H. Campbell, eds., Washington, DC, AIAA. 117:247–277.
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