2.3.10. Hydrodynamic Instability

Another relevant feature of the pool-boiling-induced nanoparticle deposition is the hydrodynamic instability alteration [71]. The vapor bubble dynamics during the poolboiling process are affected by the deposition of nanoparticles onto the heating surface, which reduces the distance between the vapor bubble departure points. This distance is commonly designated by the Rayleigh–Taylor wavelength instability wavelength or hydrodynamic instability wavelength, which can be easily identified in the film boiling regime. The alteration of this wavelength is linked to the nanoparticle-deposited layer on the heating surface during boiling, given that the deposited layer will alter the spacing between nucleating bubbles (or vapor columns) and, consequently, the Rayleigh–Taylor instability wavelength. In addition, the hydrodynamic instability approach or hydrodynamic fluid-choking limit connects the characteristic wavelength of the hydrodynamic instability with the CHF enhancement of the nanoparticle-deposited porous layer. The hydrodynamic limit theory is based on the Rayleigh–Taylor instability wavelength and was introduced by Zuber [72] for a plain surface and can be broadened to a coated heating surface having capillary limit. Regarding the hydrodynamic limit, the CHF is generally caused by the vapor columns' instability. The deposited layer can modify the distance between vapor columns on the surface and, consequently, alter the critical instability wavelength. The researchers Liter and Kaviany [73] interpreted the impact of the modulated wavelength on the CHF of a modulated porous layer of nanoparticles (having periodic variations in the layer thickness) using the following expression:

$$Q''\_{prous} = \frac{\pi}{8} \Delta h\_{lv} \sqrt{\frac{\sigma \Delta \rho\_{lv}}{\lambda\_m}}$$

where *λ<sup>m</sup>* is the modulated wavelength or the length scale that defines the vapor escape locations in the working pool-boiling fluid from the porous structure of the heating surface, ∆*hlv* is the enthalpy gradient between liquid and vapor phases, ∆*ρlv* is the density gradient between the liquid and vapor phases, and σ represents the fluid surface tension. For a smooth surface, the *λ<sup>m</sup>* parameter is influenced by the balance between the buoyancy force and surface tension, being a function of the thermal characteristics of the working fluid. In the case of a surface coated with a porous layer, the parameter *λ<sup>m</sup>* depends on the vapor escape pathways and, consequently, is a function of the porous structure of the deposition layer. In the experimental work performed by Park et al. [74], the wavelength alteration corresponded to the employed pool-boiling alumina and graphene/graphene oxide nanofluids CHF amelioration trend. As already stated by Liter and Kaviany, the wavelength can be taken as a well-defined geometrical parameter that depends on the surface conditions. As a consequence, the research team found that the change in the wavelength extends the wetting of the heating surface by enabling the working fluid to break through, resulting in the CHF improvement. Nevertheless, the researchers recognized that the recent published CHF enhancement and wavelengths are not consistent with the prediction of the Liter and Kaviany equation. Accordingly with the findings of the aforementioned authors, Park and Bang [71] stated that the onset of the CHF based on the hydrodynamic limit is due to the instability of vapor columns. The nanoparticle porous layer of the deposited nanoparticles during the boiling process could change the critical distance between vapor columns rising from the heating surface and, consequently, alter the critical instability wavelength. Moreover, a similar situation was observed in the droplet formation on the nanoparticle layer, which is closely linked with the detachment of the bubbles from the heating surface. The authors prepared different nanofluids and the used

pool-boiling apparatus was designed to enable the direct observation of the Rayleigh–Taylor instability wavelengths. The authors reported that the distance between the bubbles was different for each nanoparticle-coated surface, which revealed a shorter distance between the bubbles than that of the bare heating surface. Moreover, the nanofluids that promoted a higher CHF enhancement exhibited shorter Rayleigh–Taylor instability wavelengths. A short wavelength allows the vapor to prevent the formation of a bulk of vapor by venting the vapor evenly across the heating surface. Furthermore, it was demonstrated that the shorter wavelengths also improved the wettability by allowing the liquid to break through the developing vapor film, which also increases the CHF.
