Drag Force and Slip Correction of Aggregate Aerosols

Abstract

The drag force on aggregate particles of uniform spheres was measured in a Millikan apparatus as a function of Knudsen number. Our experiment was designed to study the effect of particle orientation on the slip correction factor of nonspherical particles. The velocities of charged particles in a gravitational field with and without an applied electrical field were measured. An electrical field strength of 2000 V/cm was used to align doublet and triplet particles. Results showed that an aggregate particle moved in random orientation while in the gravitational field. The same particle moved with its polar axis parallel to the electric field (doublets) or with its plane of centers parallel to the electrical field (triangular triplets). Using a nonlinear regression method, both the dynamic shape factor and slip correction factor could be determined separately from the data. The dynamic shape factors at different orientations were in good agreement with those obtained previously in a sedimentation tank. The slip correction factor of singlet particles agreed with results previously obtained by Allen and Raabe for latex particles. Slip correction factors of doublets and triangular triplets can also be expressed in the Knudsen-Weber form: 1 + 2λ/d _a [1.142 + 0.558 exp(−0.999 d _a/2λ)]. The adjusted sphere diameter d _a was 1.21 d ₁ (primary diameter) for doublets moving parallel to the flow and 1.31 d ₁ for doublets randomly oriented. These results show that the slip correction factor of a nonspherical particle depends on the orientation and confirm the theory proposed by Dahneke.