*4.2.2 Solid-liquid balance*

*Textile Industry and Environment*

Two n-alkanes are only miscible if they have the same crystal structure. This prerequisite, which was first formulated by Kitajgorodskij, is necessary but not

Kravchenko defines a criterion that predicts the mutual solid state solubility of

*n* − *n*'

With n and n′ denoting the number of carbon atoms contained in each molecule. Thus, the total solubility is obtained for τ < 0.06, it is partial when 0.06 < τ < 0.15,

However, the latter rule is insufficient since the symmetry rule implies that n-alkanes below C36 whose chain length differs from one unit cannot have total solubility since they are not isomorphic. Thus, many authors present phase diagrams in the literature where this rule is not respected. Also, Agafonov et al. [30], and He and Setterwall [31], also reported that the mixture of two isomorphic

Therefore, synthetic paraffin has many advantages (no or low subcooling, perfect thermal reversibility) but remain relatively expensive and have a very low

K<sup>−</sup><sup>1</sup>

from 91 to 388°K depending on the number of carbon atoms, which potentially

and reduces the available powers accordingly. Their latent heat and density increase as the number of carbon atoms increases from C1 to C40 and stabilizes around 280 J

Inorganic PCMs, and more specifically saline hydrates, represent an interesting alternative to paraffin because of their low cost, high storage density (between 250

main problem encountered when using these materials is phase segregation during melting [33]. Indeed, many of them have an incongruous fusion, making the system

The realization of energy storage by latent heat is related to the physico-chemical

properties of the materials used, that is, (i) subcooling, (ii) crystallization rate, (ii) and the melting. A rapid rate of crystallization is generally required to allow the energy absorbed by the material to be released within a reasonable time. However, latent heat storage systems, because of their operation under a low-temperature difference, require a low crystallization rate. Acceleration of crystallization kinetics can be achieved by introducing solvents with high polarity and a high dielectric constant in order to improve ion mobility. Hydrated salt can be classified according

to their type of melting into four categories, that is, (i) congruent melting, (ii) semi-congruent melting hydrates, (iii) non-congruent melting, and

), and relatively good thermal conductivity [32]. However, the

, respectively. The melting temperature also varies very gradually

*<sup>n</sup>* (4)

), which inhibits phase change kinetics

sufficient [21], concerns n-alkanes of neighboring chain lengths.

components in the solid state forms a continuous solid solution.

makes the use of this family of materials very flexible.

*4.2.1 Physico-chemical properties of materials*

*4.1.7.2 Symmetry rule*

*4.1.7.3 Kravchenko rule*

and almost null for τ > 0.15.

two n-alkanes in the form (Eq. (4)) [29]:

thermal conductivity (λ = 0.24 W m<sup>−</sup><sup>1</sup>

τ = \_\_\_\_

**78**

g<sup>−</sup><sup>1</sup>

and 820 J m3

**4.2 Inorganic PCMs**

and 400 MJ m<sup>−</sup><sup>3</sup>

irreversible.

During its fusion, the salt, noted X(Y)n·mH2O, is likely to undergo one of the following two reactions (Eqs. (5) and (6)).

$$X \, (Y)\_n \mathfrak{m} H\_2O \quad \text{+} \quad X \, (Y)\_n \, kH\_2O \text{+} \text{(}m\text{ -}k\text{)} \, H\_2O \tag{5}$$

$$X\,(Y)\_n \mathfrak{m}H\_2O \quad \to \, X\,(Y)\_n \star mH\_2O \tag{6}$$

Hydrated salt tends to separate into two phases, no longer maintaining the salt/ water ratio in suitable proportions. A salt-rich liquid (denser) tends to accumulate it at the bottom of the container, and a water-rich salt solution floats over the whole. When repeating fusion/crystallization cycles, less and less salt and water can come together and react to form a hydrate with the desired melting temperature. Part of the solid cannot be melted, and part of the liquid cannot be crystallized. The effect is a gradual loss of phase change enthalpy and latent heat storage capacity [35]. The most effective method to overcome this problem remains the suspension or agitation of the system. Suspension requires the introduction of clay or the formation of a gel that traps the hydrate so that when it crystallizes, salt and water are in contact to allow the system to recombine. The dimensions of the storage container can also be adjusted by minimizing them to limit phase separation.

### *4.2.3 Anhydrous rearrangement*

The effectiveness of these materials is related to the amount of water and salt that can react to form the hydrated form. In the case of sodium sulfate, it appears that the salt settles very quickly, and rearranges [36]. As a result, it only partially hydrates, generating a low storage material. The addition of a continuous quantity of water up to the crystallization point makes it possible to overcome this problem. Nevertheless, shaking the system is strongly required to optimize the formulation of the PCM.

Therefore, among inorganic compounds, only saline hydrates and their eutectics have acceptable properties, including high latent heat and relatively low prices. Nevertheless, these materials have some limitations for latent heat energy storage including subcooling and their tendency to melt incongruently. This phenomenon is all the more embarrassing as it leads to the non-reversibility of the change of state. This problem can be eliminated by adding a clay-based gelling mixture that inhibits the settling effect of the lower hydrate [37]. Reversibility is thus restored within a reasonable time. The final limitation for these compounds is their low crystallization rate, which limits the thermal storage capacity. Some solvents or additives with high polarity and high dielectric constant accelerate the kinetics [38]. Indeed, better mobility of ions and therefore a high dielectric constant leads to a decrease in liquid-solid interfacial energies.

The performance of a latent heat storage system is based on the thermal properties of the compounds selected according to their melting and crystallization temperature, which must be in adequacy with the intended application, but also the enthalpy of phase change, and their stability during their implementation. The choice of one family over another is generally a function of the application and the initial cost of the products.
