Experimental study of nanoparticle penetration efficiency through coils of circular cross-sections

Nanoparticle penetration efficiencies through five different coils of circular cross-sections were measured as a function of particle size, Dean number, and curvature ratio of coil. Silver particles with diameters ranging from 3 to 50 nm were used, and the Dean number was varied from 21 to 1779. According to the equation of critical Reynolds number for the coil (Ito 1959), all the flows in this study were laminar. The penetration efficiency through coils was found to increase with increasing particle size and also with increasing Dean number. The influence of curvature ratio on penetration efficiency seemed to be negligible when the Dean number was greater than approximately 200. Secondary flow developed due to centrifugal force in the coil is known to increase diffusional particle loss. Boundary layer thickness (δ) of the secondary flow can affect the particle loss in coils, because the average flow velocity of secondary flow within the boundary layer is related to δ. The particle loss in coils is assumed to be a byproduct of secondary flow and Brownian diffusion. As a result, a non-dimensional parameter (ζ) to explain the particle loss in coils was defined as ζ = δ × ξ, where ξ is the dimensionless parameter proposed by Gormley and Kennedy (1949) for describing the particle loss due to Brownian diffusion in a straight cylindrical tube. An empirical equation of the nanoparticle penetration efficiency through coils in laminar flow regime was suggested as a function of the new coil parameter, ζ.