Particle migration in a flow of nanoparticle suspensions Yulong Ding * , Dongsheng Wen Institute of Particle Science and Engineering, University of Leeds, Leeds LS2 9JT, United Kingdom Received 11 November 2003; received in revised form 22 September 2004; accepted 1 November 2004 Available online 23 December 2004 Abstract This paper is concerned with particle migration in pressure-driven laminar pipe flows of relatively dilute suspensions of nanoparticles (nanofluids), one of the most frequently used configuration in industries. The motivation behind the work is associated with the thermal behaviour of nanofluids, which can greatly exceed the values predicted by currently available macroscopic theories. A theoretical model is formulated to predict particle concentration, and velocity field of nanofluids in the transverse plane of the pipe. The model takes into account the effects of the shear-induced and viscosity gradient-induced particle migrations, as well as self-diffusion due to the Brownian motion. It is shown that particle concentration in the wall region can be much lower than that in the central core region. This indicates a highly non- uniform thermal conductivity profile across the transverse plane of the pipe, and thus has a significant implication to heat transfer intensification using nanofluids. The results also suggest the existence of an optimal particle size whereby the thermal conductivity is enhanced with little penalty due to the effect of pressure drop. D 2004 Elsevier B.V. All rights reserved. Keywords: Particle migration; Nanoparticles; Suspensions; Pipe flow 1. Introduction Recent advances in nanoscience and nanotechnology have allowed creation of a novel type of fluids termed nanofluids. Such fluids are suspensions containing particles significantly smaller than 100 nm, and have been found to have an anomalously higher thermal conductivity than that predicted by the macroscopic theory [1–10]. The excellent thermal conductivity of nanofluids is unique and could provide a basis for an enormous innovation for heat transfer intensification, which is of major importance to a number of industrial sectors including transportation, power genera- tion, micro-manufacturing, chemical and metallurgical industries, as well as heating, cooling, ventilation and air- conditioning industry. Nanofluids are also important for the production of nanostructured materials [11,12], for engi- neering of complex fluids [13], as well as for enhancement of wetting and spreading behaviour [14]. Flow of suspensions has attracted an increased attention over the past decade due to a wide range of industrial applications; see for example Leighton and Acrivos [22], Phillips et al. [15], Morris and Brady [16], and Liu [17]. These studies, however, have been focused on suspensions of micron-sized particles in which the Brownian motion has little effect. Due to the size effect, the results of these previous studies may not be applicable to flows of nano- fluids for which little has been seen in the literature. This constitutes the main motivation of this work. This paper aims at formulating a theoretical model for predicting particle concentration and velocity fields of nanofluids flowing through a pipe, one of the most frequently used configurations in industries. The model takes into account shear-induced and viscosity gradient-induced particle migra- tions, as well as self-diffusion due to the Brownian motion. Focus will be on dilute suspensions, which are expected to have applications in heat transfer intensification. Understanding of the flow behaviour and particle migration in nanofluids is important for future utilisation of nanofluids as potential heat transfer media for process intensification. Recent work by e.g. Choi [2], Eastman et al. 0032-5910/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.powtec.2004.11.012 * Corresponding author. Tel.: +44 113 343 2747; fax: +44 113 243 2405. E-mail address: y.ding@leeds.ac.uk (Y. Ding). Powder Technology 149 (2005) 84 – 92 www.elsevier.com/locate/powtec