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Recent developments in liquid technology have created a new class of fluids called “nanofluids” which are two-phase mixtures of a non-metal-liquid matrix and addon particles usually less than 100 nm in size. It is reputed that such liquids have a great potential for application. Indeed, many tests have shown that their thermal conductivity can be increased by almost 20% compared to that of the base fluids for a relatively low particle loading (of 1 up to 5% in volume). It is confirmed by experimental data and simulation results. In this study, the author considers an effect of impurity clustering by liquid density fluctuations as a natural mechanism for stabilizing microstructure of the colloidal solution and estimates the effect of fractal structure of colloidal particles on thermal conductivity of water. The results of this study may be useful for motivating choosing the composition of heat-transfer suspension and developing technology for making the appropriate nanofluid.

Nanofluids are composite materials consisting of solid small particles or fibers with sizes typically of 10 to 100 nm suspended in nonmetal liquids. These liquids are characterized by enhanced thermal properties (up to 40%) due to a small amount (<1% vol.) of such particles in liquids [

Presently, nanofluids are produced by two techniques [_{2}O_{3}, CuO, and TiO_{2}), nitrides (AlN and SiN), and carbides (SiC and TiC) are produced by the two-step process, and the ones containing metals (Ag, Au, Cu, and Fe) are produced by the single-step process.

Obviously, it is necessary to study any water nanofluid composition [

Furthermore, the observed enhancement of thermal nanofluid conductivity is larger than predicted by well-established theories. Other perplexing results in this rapidly evolving field include a surprisingly strong temperature dependence of the thermal conductivity and a threefold higher critical heat flux compared with the base fluids [

At the same time, it is known [

The last as a two-phase state for impurity is the very interesting way for stabilizing the nanofluid structure and to improve its thermal properties. For this, an effect of ramified fractal clusters as a solid-state part of the addition solution is considered within the framework of the heat-transfer theory. A subject of investigations in the given work is the thermal conductivity correction for such the fractal particles in the liquid.

It is found [^{+}(H_{2}O)_{100}, Na^{+}(H_{2}O)_{100}, Na^{+}(H_{2}O)_{20}, and Cl^{−}(H_{2}O)_{17} below the cluster melting temperature, but they are solvated into the interior of the cluster above the melting temperature. It should be noted that the exclusion of the Cl^{−} ion from the cluster surface was far less dramatic than that for the Na^{+} clusters studied. In increasing temperature, the Cl^{−} maxima transitions occur gradually from near surface to interior displaying a significant interior bias only at the highest temperatures considered.

On the other hand, impurity atoms (at a low concentration) are placed on the external faces of tetrahedral clusters of the dense liquid part not changing its microstructure, that is forming the introduction solution [

In two-structured water, the low-density tetrahedral-ordered ice-regions are divided by higher density clusters with an asymmetrical structure [

Dense-part cluster in MD model of water at 300 K and its frame (broken red line); blue points are the molecules and red points are the centers of the cluster tetrahedrons.

Typical tetrahedral cluster in MD model of the dense part of liquid potassium and the frame connecting the centers of tetrahedrons (broken red line with its three projections as blue lines).

At the same time, a parameterization of the energy functional cannot be arbitrary since the condensate structure at the fixed density weakly depends on temperature for a wide class of matter: metals and ionic melts, liquid semiconductors, and nonconductors [

Logarithm of correlation radius,

One can see a sharp falling

This impurity clustering differs from the first-order phase transition in the solution when the excessive phase of an impurity compound precipitates. It may be considered as an analogue of such transition only in microregions of liquid which has continuous character without a singularity and concerns only to change the impurity form in the solution.

As illustration of such density fluctuations clustering of any impurity, Figure _{2}O)_{n} received by molecular-dynamic simulation of nonsaturated alloy K–O [

The quasioxide cluster in oxygen-nonsaturated melt of potassium, Big circles are oxygen anions and small circles are potassium cations.

As one can see in Figure

Thus, in order to prepare stable nanofluids, it is important to form nanoparticles in water directly from the dissolved impurity. Such ramified fractal cluster is shown in Figure

The cluster [Al(OH)_{3}]_{n} of aluminum hydroxide in water.

The scheme of percolation fractal cluster of solid-like filaments.

The fractal cluster as a solid-like micelle.

Here, is assumed that fractal-cluster mass,

In real objects, the fractal structure is observed on scales,

It is evident that thermal and physical properties of fiber (filaments) composites are locally anisotropic. However, these properties are isotropic in a clew of filaments as a whole.

Many theoretical and numerical studies exist about thermal conductivity of nanometer-sized particles in liquids [

A thermal conductivity,

Now, for well-dispersed fractal particles, we can use the potential theory of Maxwell [

The function (

Many of the obtained experimental data for a high fraction of particles can be understood if one allows clustering particles into fractal aggregates (see Figure

The estimates of water thermal conductivity enhancement

Al_{2}O_{3} | Carbon fiber | |||||
---|---|---|---|---|---|---|

3.0 | 2.7 | 2.5 | 3.0 | 2.7 | 2.5 | |

— | 0.02 | 0.1 | — | 0.02 | 0.02 | |

0.015 | 0.015 | 0.015 | ||||

2.87 | 8.35 | 7.56 | 3.0 | 8.73 | 17.7 |

We discuss the case of spherical fractal particles in which Hausdorff’s dimension is equal to

In the limit of the small volume fraction of particles and the high thermal conductivity of particles, our version of the effective medium theory converges to the prediction that the thermal conductivity of colloidal solution can enhance up to

Thus, the significant property of fractal colloidal particles is an explanation of observed enhancement obtained by several research groups of nanofluids.

At the same time, it is important to understand that the fractal particles can be produced in water solution as a result of complex chemical reactions between a chosen impurity and the liquid. Therefore, it is necessary to develop a special technology for getting them in the medium directly.

The theoretical studies show how one can provide the stable formation of particles in water solution. It is important to form clusters in water directly from impurities which are dissolved there. Then, ramified fractal clusters as natural solid-state part of addition solution can be stable constituents of nanofluid on water base, and its thermal conductivity can be enhanced up to

The results of microscopic investigation may be useful for motivating choosing a composition of a heat-transfer suspension and developing technology for making the appropriate nanofluid.

Thus, the fractal structure of colloidal particles can give the sixfold enhancement of usual nanofluid contribution to the thermal conductivity of water.

The author is pleased to acknowledge Dr. A. S. Kolokol for giving some data on molecular-dynamic simulation of water structure and discussing this work, which is supported by the Russian Foundation of Basic Researches (Grant no. 10-08-00217).