Microfluidics and Nanofluidics

, Volume 5, Issue 2, pp 215–224 | Cite as

Aerosol flow through a long micro-capillary: collimated aerosol beam

  • I. S. Akhatov
  • J. M. Hoey
  • O. F. Swenson
  • D. L. Schulz
Research Paper


A micro-capillary system capable of generating a focused collimated aerosol beam (CAB) is demonstrated both theoretically and experimentally. The approach is based on a manifestation of the Saffman force where high velocity (∼100 m/s) aerosol particles, flowing through a micro-capillary (d ∼ 100 μm and l ∼ 1 cm), migrate perpendicular to the centerline of the capillary. Upon exiting the micro-capillary system, the particles maintain momentum, and when the aerosol is comprised of solid-in-liquid dispersions such as Ag nanoparticle ink, the CAB approach enables printing of advanced materials features with linewidth ≤ 10 μm.


Aerosol Focusing Beam collimation Micro-capillary Saffman force Direct-write fabrication 


  1. Akhatov IS, Hoey JM, Swenson OF, Schulz DL (2007) Aerosol focusing in micro-capillaries: theory and experiment. J Aerosol Sci (submitted)Google Scholar
  2. Batchelor GK (2000) An introduction to fluid dynamics. Cambridge University Press, CambridgeGoogle Scholar
  3. Bracht K, Merzkirch W (1979) Dust entrainment in a shock-induced, turbulent air flow. Int J Multiphase Flow 15(5):301CrossRefGoogle Scholar
  4. Carlson DJ, Hoglund RF (1964) Particle drag and heat transfer in rocket nozzles. AIAA J 2(11):1980CrossRefGoogle Scholar
  5. Cunningham E (1910) On the velocity of steady fall of spherical particles through fluid medium. Proc Soc Lond Ser A 83:357–365CrossRefGoogle Scholar
  6. Dahneke B, Friedlander SK (1970) Velocity characteristics of beams of spherical polystyrene particles. J Aerosol Sci 1:325–339CrossRefGoogle Scholar
  7. Dandy DS, Dwyer HA (1990) A sphere in a shear flow at finite Reynolds number: effect of shear on particle lift, drag, and heat transfer. J Fluid Mech 216:381–410CrossRefGoogle Scholar
  8. Di Fonzo F, Gidwani A, Fan MH, Neumann D, Iordanoglu DI, Heberlein JVR, McMurry PH, Girshick SL, Tymiak N, Gerberich WW, Rao NP (2000) Focused nanoparticles-beam deposition of patterned microstructures. Appl Phys Lett 77(6):910–912CrossRefGoogle Scholar
  9. Fernandez de la Mora J, Riesco-Chueca P (1988) Aerodynamic focusing of particles in a carrier gas. J Fluid Mech 195:1–21CrossRefGoogle Scholar
  10. Fletcher B (1976) The interaction of a shock with a dust deposit. J Phys D Appl Phys 9(2):197–202CrossRefMathSciNetGoogle Scholar
  11. Fuerstenau S, Gomez A, Fernandez de la Mora J (1994) Visualization of aerodynamically focused subsonic aerosol jets. J Aerosol Sci 25:165–173CrossRefGoogle Scholar
  12. Gerrard JH (1963) An experimental investigation of the initial stages of the dispersion of dust by shock waves. Br J Appl Phys 14:186–192CrossRefGoogle Scholar
  13. Hishida M, Hayashi AK (1989) Numerical simulation of a shock wave–solid particle interaction. In: Proceedings of international symposium on computational fluid dynamics, Nagoya, Japan, pp 1055–1060Google Scholar
  14. Hoey JM, Akhatov IS, Swenson OF, Schulz DL (2007) Focusing of aerosol particles. US Provisional Patent Application # 60/956,493Google Scholar
  15. Hwang CC (1986) Initial stages of the interaction of a shock wave with a dust deposit. Int J Multiphase Flow 12(4):655–666CrossRefGoogle Scholar
  16. Israel GW, Friedlander SK (1967) High-speed beams of small particles. J Colloid Interface Sci 24:330–337CrossRefGoogle Scholar
  17. Israel GW, Wang JS (1971) Dynamical properties of aerosol beams. Technical note BN-709. Institute for Fluid Dynamics and Applied Mathematics, University of MarylandGoogle Scholar
  18. Karniadakis G, Beskok A, Aluru N (2005) Microflows and Nanoflows: fundamentals and simulation. Springer, BerlinMATHGoogle Scholar
  19. Knudsen M, Weber S (1911) Luftwiderstand gegen die langsame Bewegung kleiner Kugeln. Amm Physics 36:981–994Google Scholar
  20. Lauga E, Brenner MP, Stone HA (2005) Microfluidics: the no-slip boundary condition. In: Foss J, Tropea C, Yarin A (eds) Springer handbook of experimental fluid dynamics. Springer, BerlinGoogle Scholar
  21. Li Z, Wang H (2003) Drag force diffusion coefficient, and electric mobility of small particles. I. Theory applicable to the free-molecule regime. Phys Rev 68:061206Google Scholar
  22. Lipatov GN, Grinshpun SA, Semenyuk TI (1989) Properties of crosswise migration of particles in ducts and inner aerosol deposition. J Aerosol Sci 20(8):935–938CrossRefGoogle Scholar
  23. Liu P, Ziemann PJ, Kittelson DB, McMurry PH (1995a) Generating particle beams of controlled dimensions and divergence: I. Theory of particle motion in aerodynamic lenses and nozzle expansions Aerosol Sci Technol 22(3):293–313CrossRefGoogle Scholar
  24. Liu P, Ziemann PJ, Kittelson DB, McMurry PH (1995b) Generating particle beams of controlled dimensions and divergence: II. Experimental evaluation of particle motion in aerodynamic lenses and nozzle expansions. Aerosol Sci Technol 22(3):314–324CrossRefGoogle Scholar
  25. Mei R (1992) An approximate expression for the shear lift force on a spherical particle at finite Reynolds number. Int J Multiphase Flow 18(1):145–147CrossRefMATHGoogle Scholar
  26. Merzkirch W, Bracht K (1978) The erosion of dust by a shock wave in air: initial stages with laminar flow. Int J Multiphase Flow 4(1):89–95CrossRefGoogle Scholar
  27. Millikan RA (1923) Coefficients of slip in gases and the law of reflection of molecules from the surface of solids and liquids. Phys Rev 21(3):217–238CrossRefGoogle Scholar
  28. Osiptsov AN (1988) Motion of dusty gas at the entrance to a flat channel and a circular pipe. Fluid Dyn 23(6):867–874MATHCrossRefMathSciNetGoogle Scholar
  29. Osiptsov AN (1997) Mathematical modeling of dusty-gas boundary layers. Appl Mech Rev 50(6):357–370CrossRefGoogle Scholar
  30. Pique A, Chrisey DB (eds) (2002) Direct write technologies for rapid prototyping applications. Academic, San DiegoGoogle Scholar
  31. Rao NP, Navascues J, Fernandez de la Mora J (1993) Aerodynamic focusing of particles in viscous jets. J Aerosol Sci 24(7):879–892CrossRefGoogle Scholar
  32. Renn MJ, Marquez G, King BH, Essien M, Miller WD (2002) Flow- and laser-guided direct write of electronic and biological components. Direct write technologies for rapid prototyping applications. In: Pique A, Chrisey DB (eds) Academic, San Diego, pp 475–492Google Scholar
  33. Saffman PG (1965) The lift on a small sphere in a slow shear flow. J Fluid Mech 22:385–400MATHCrossRefGoogle Scholar
  34. Saffman PG (1968) Corrigendum. J Fluid Mech 31:624Google Scholar
  35. Wang B, Xiong Y, Osiptov AN (2005a) Two-way coupling model for shock-induced laminar boundary-layer flows of a dusty gas. Acta Mech Sin 21:557–563CrossRefGoogle Scholar
  36. Wang X, Gidvani A, Girshick SL, McMurry PH (2005b) Aerodynamic focusing of nanoparticles: II. Numerical simulation of particle motion through aerodynamic lenses. Aerosol Sci Technol 39:624–636CrossRefGoogle Scholar
  37. Wang X, Kruis FE, McMurry PH (2005c) Aerodynamic focusing of nanoparticles: I. Guidelines for designing aerodynamic lenses for nanoparticles. Aerosol Sci Technol 39:611–623CrossRefGoogle Scholar
  38. Wang X, McMurry PH (2006) A design tool for aerodynamic lens systems. Aerosol Sci Technol 40:320–334CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • I. S. Akhatov
    • 1
    • 3
  • J. M. Hoey
    • 1
    • 3
  • O. F. Swenson
    • 2
    • 3
  • D. L. Schulz
    • 1
    • 3
  1. 1.Department of Mechanical EngineeringNorth Dakota State UniversityFargoUSA
  2. 2.Department of PhysicsNorth Dakota State UniversityFargoUSA
  3. 3.Center for Nanoscale Science and EngineeringNorth Dakota State UniversityFargoUSA

Personalised recommendations