Choice of appropriate aggregation radius for the descriptions of different properties of the nanofluids

Nanofluids with suspensions containing nanoparticles, have been considered to have great potential in the application of energy conversion, chemical technology or heat transfer enhancement. Due to the high surface energy, nanoparticles in nanofluid tend to form large secondary aggregates. The aggregation and the size increase could lead to significant change in various physical properties of the suspension. It is well known that many kinds of equivalent radii can be potentially employed in the description of the particle aggregates, such as hydrodynamic radius (R_h), gyration radius (R_g) and smallest sphere enclosing radius (R_s) etc. However, in most of previous study, only hydrodynamic radius was used to study the effect of the aggregation on the properties of the nanofluids. Systematic study on the appropriate choice of the equivalent radii for the description of the different properties of the nanofluids, is rare. In this study, the three representative equivalent radii of nanoparticle aggregates, R_h, R_g and R_s, were studied. It was found that for both diffusion limited cluster-cluster aggregation (DLCA) and reaction limited cluster-cluster aggregation (RLCA), the general sequence is R_h < R_g < R_s. The three equivalent radii were correlated with each other by Monte Carlo method using an off-lattice cluster-cluster aggregation algorithm. The relationship is useful because hydrodynamic radius can be obtained experimentally from light scattering technique, while the other two are difficult to obtain experimentally. In our study, based on hydrodynamic radius obtained by DLS method, the other two equivalent radii were successfully obtained based on the proposed relationship. By comparing the experimental results with theoretical prediction, it was found that R_h, R_g and R_s showed the better accuracy when predicting viscosity, thermal conductivity and absorption coefficient, respectively. Based on these findings, in the last part, we propose a criterion for the choice of appropriate aggregation radii in predicting different physical properties of nanofluid. Our study is expected to provide a valuable guidance for the study of the effect of particle aggregation on the various properties of the nanofluids.