Friction coefficient and mass of silver agglomerates in the transition regime

W. G. Shin, G. W. Mulholland, S. C. Kim, J. Wang, M. S. Emery, D. Y.H. Pui

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27 Scopus citations


The dynamic shape factor and the exponents, η and Dfm, which characterize the power law dependence of friction coefficient on the number of primary spheres and the mass on the mobility diameter, have been determined for silver agglomerates using the differential mobility-aerosol particle mass (DMA-APM) analyzer method. This method provides characterization of nearly monodisperse agglomerates and is able to analyze thousands of particles over a 10 min period. A quantitative uncertainty analysis finds that the calibration of the APM is the major source of uncertainty and that the combined uncertainties are about 6-7% for the dynamic shape factor and about 3% for the exponents η and Dfm. The dynamic shape factor obtained based on free molecular analysis is larger than the measured results. The observed decrease in η by about 15% with increasing agglomerate size compared to almost constant values for the model predictions suggests a flow interaction between the primary particles not included in the models which are based on free molecular dynamics. An empirical equation is given for the N dependence of the ratio of the measured friction coefficient to a free molecular expression based on a computer simulation. Model predictions indicate that η is independent of agglomerate size while Dfm is sensitive to agglomerate size. Experimentally, it appears the opposite is true: the dependence of η on particle size is greater than for Dfm. The near constancy for the measured Dfm results from the decreasing value in η being compensated by the slip correction term in the expression relating dm to the friction coefficient.

Original languageEnglish (US)
Pages (from-to)573-587
Number of pages15
JournalJournal of Aerosol Science
Issue number7
StatePublished - Jul 2009

Bibliographical note

Funding Information:
Parts of this work were carried out in the University of Minnesota I.T. Characterization Facility, which receives partial support from NSF through the NNIN program. Authors acknowledge Dr. Peter McMurry at the University of Minnesota for allowing us to use APM for our experiments. Authors also acknowledge Graduate School at the University of Minnesota for the Doctoral Dissertation Fellowship awarded to Weon Gyu Shin.


  • Aerosol particle mass (APM) analyzer
  • Agglomerate
  • DMA
  • Dynamic shape factor
  • Friction coefficient


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