386420 A Model to Predict Thermal Conductivity in Colloidal Dispersions
The presence of nanoparticles with high thermal conductivity in a fluid seems to be a simple way of improving the poor thermal conductivity of the fluids used in many cooling processes. Maxwell's mean field theory is the standard theory for predicting the thermal conductivity of a dispersion and consist of two limiting bounds. The theory predicts two limit: a lower limit that corresponds to a fully dispersed colloid, and an upper limit, which is taken to represent the conductivity of a colloidal gel. It is understood that the conductivity of aggregated colloids falls somewhere in between the two limits, but no theory exists to calculate conductivity of partially aggregated colloids.
Here we present a model, based on Maxwell's theory, that is capable of describing the thermal conductivity of finite-size clusters. We employ a two-level model. First, we calculate the thermal conductivity of clusters using the upper bound of Maxwell's theory, then we obtain the conductivity of a dispersion of such clusters using the lower limit. We put the theory to test against numerical simulations. We generate fractal clusters in a base fluid and evaluate the thermal conductivity of the system using a Monte Carlo algorithm. We find that theory provides excellent agreement with the simulations using one adjustable parameter that corrects for the fact that clusters form a bicontinuous structure, whereas theory assumes clusters to form a continuous solid phase with the liquid pockets dispersed within. We present results for various types of clusters and show that the adjustable parameter is rather insensitive to the details of the structure of the aggregate.