Effect of nanoparticle clustering on the effective thermal conductivity of concentrated silica colloids

Recent research on nanofluids has offered particle clustering as a possible mechanism for the abnormal enhancement of the effective thermal conductivity $\left(k\right)$ when nanoparticles are dispersed in liquids. This paper was devoted to verify experimentally and theoretically the significance of the effect by altering the cluster structure, size distribution, and thermal conductivity of solid particles in water. Starting with well dispersed ${\text{SiO}}_2$ sols in water as a reference system, we control the aggregation kinetics by adjusting $p\text{H}$. Contrary to previous model predictions, the present experiment showed that clustering did not show any discernable enhancement in the thermal conductivity even at high volume loading. A series of fractal model calculations not only suggested that the conductive benefit due to clustering might be completely compensated by the reduced convective contribution due to particle growth, but also recommended the need for higher thermal conductivity and optimized fractal dimension of particles for maximizing the clustering effect.

Figure 1

(Color online) DLS size distributions for ST-40 silica colloids under controlled aggregation. (a) 3 h 15 min since initial $p\text{H}$ adjustment except for the pristine case. The inset is viscosity evolution of the $p\text{H}$ 8.0 and 7.5 samples. (b) Size evolution of silica clusters under controlled aggregation.

Figure 2

TEM images of Au clusters aggregated through (a) DLCA, (b) RLCA [22], and aggregated ST-40 silica colloid at $p\text{H}=7.5$ after 3 h 15 min.

Figure 3

Thermal conductivity of ST-40 silica colloids under controlled aggregation measured using $3\omega$-wire technique. Monodisperse pristine stock colloid ($p\text{H}=10.1$, $\sim 15\text{nm}$) has a volume fraction of 0.233. Measurements were taken 3 h 15 min since initial $p\text{H}$ adjustment except for the pristine case. Dashed and solid lines indicate results predicted by the M-G model. Typical measurement uncertainty of $k$ is within $\pm 1.5\%$.

Figure 4

(Color online) Influence of particle conductivity and interfacial thermal resistance $R_b$ on the effective thermal conductivity of nanofluids in aggregated system. Set of $k/k_f$ data corresponding to $k_p=1.4$, 14, and $140\text{W}{\text{m}}^{-1}{\text{K}}^{-1}$ are model-predicted values at (a) $R_b=0.77\times {10}^{-8}\text{K}{\text{m}}^2{\text{W}}^{-1}$ and (b) $R_b=0$. The constituent conductive and convective parts of the total thermal conductivity for case (a) are shown in (c) and (d), respectively. Note that the cases with $k_p=14$ and $140\text{W}{\text{m}}^{-1}{\text{K}}^{-1}$ are theoretical materials with all the same properties as ST-40 including aggregation kinetics and solid particle loading $\left(\varphi =0.233\right)$, with the only exception of the inherent thermal conductivity of particle material.

Figure 5

(Color online) Effect of cluster fractal dimension $d_f$ on the effective thermal conductivity of aggregated suspension (initiated from 15 nm monodisperse system) of silica (a) $\left(k_p=1.4\text{W}{\text{m}}^{-1}{\text{K}}^{-1}\right)$ and (b) theoretical material $\left(k_p=140\text{W}{\text{m}}^{-1}{\text{K}}^{-1}\right)$. Interfacial resistance $R_b$ of $0.77e\text{−}8\text{K}{\text{m}}^2{\text{W}}^{-1}$ was used and the numbers in the legends stand for diameters of gyration $\left(2R_g\right)$ of fractals.