Prediction of aerodynamic diameter of particles with rough sur P. Tang a,b , H.-K. Chan a, * , J.A. Raper b,1 a Faculty of Pharmacy, University of Sydney, NSW 2006, Australia b Department of Chemical Engineering, University of Sydney, NSW 2006, Australia Received 20 September 2004; accepted 22 September 2004 Available online 5 November 2004 Abstract This work demonstrates a simple means of predicting aerodynamic diameter of particles having fractal surfaces. A number of drag coefficient expressions were employed for the calculation of aerodynamic diameter. A set of model objects having surfac varying from 2.00 to 2.55 was constructed, from which all the parameters required to compute shape and surface rough obtained. Drag coefficients (C D ) formulated by Ro and Neethling, Haider and Levenspiel, Thompson and Clark, Ganser, and Tra were shown to perform similarly within the specified criteria. The aerodynamic diameters calculated follow the expected diameter with increasing surface roughness. Comparisons with literature data show that the C D expressions by Ro and Neethling, Haider and Levenspiel, and Ganser, on average, agree to within 17–23% of the measured values. D 2004 Elsevier B.V. All rights reserved. Keywords: Fractal; Aerodynamic diameter; Drag coefficients 1. Introduction Reportshave shown that surfacesofmostmaterials, including natural and synthetic, porousand non-porous, amorphous and crystalline are fractal on a molecular scale [1– 4]. Since two-thirds of drag on particles is friction drag (related to the total surface area) and one-third is the form drag (related to projected area in the settling direction), the effect of surface roughness is crucial [5]. Surface roughness increases the drag force of a particle as it settles and therefore reduces the settling velocity. Accurate prediction of settling velocity is crucial in many processes in various engineering fields,e.g.,flotation, thickening, and purification. In phar- maceutical applications, a precise determination of aerody- namic diameter is required for assessing the performance of aerosol particles widely used for inhalation therapy [6,7]. The difference in aerosol performance between smooth and rough surfaced objects (Fig. 1) was reported [8], where rough particles showed better dispersion coupled with m fine particles of less than 5 Am generated in the aerosol cloud. The surface roughness of these particles was successf characterized by gas adsorption and light scattering and found to be fractal [9]. Smooth particles (Fig. 1a) were found to have a surface fractal dimension ( D S ) of 2.06 while the rough particles (Fig. 1b) possess a higher D S of 2.45. The improved dispersion and increased fine particles in t aerosol could be due to two factors, namely the contact between particles and their aerodynamic behaviour. Rough particles are less cohesive than smooth particles becaus lesssurfacecontactarea.Oncethey aredispersed into individual particles, it is their aerodynamic behaviour that determines the extent of fine particles generation. Howe determination of aerodynamicdiameterof individual particles is not simple.It is recognized that complete dispersion of dry particulate solids, especially in the size range below 20 Am, is difficult due to strong cohesive fo between the particles. Particlesizing equipment thatmeasures aerodynamic diameter of individual particle is widely available, but the are a number of biases associated with the use of these 0032-5910/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2004.09.036 * Corresponding author. Tel.: +61 29351 6072; fax: +61 29351 4391. E-mail address: kimc@pharm.usyd.edu.au (H.K. Chan). 1 Current affiliation: Department of Chemical Engineering, University of Missouri-Rolla, MO 65409-1230, USA. Powder Technology 147 (2004) 64 – 78 www.elsevier.com/locate/powtec