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Liquid under tension “breaks” by cavitation, forming a vapor bubble. It occurs in engineering (ultrasonic cleaning, erosion of ship propellers...) as well as in the natural sciences (gas embolism in trees, pistol shrimp...). In the cavities of a saturated porous material, the liquid is also under tension when it evaporates. In this case, it was long considered that evaporation occurs by recession of the menisci delimiting the saturated region but it is now recognized that evaporation can also be due to cavitation [Thommes 2006, Rasmussen 2010, Doebele 2020]. However, there are only few experimental data on the impact of the confinement on the cavitation threshold so that theoretical approaches [Rasmussen 2020, Morishige 2021] cannot be accurately tested.
In this work, we focus on evaporation of nitrogen in ordered mesoporous silica (SBA-16). We have designed a capacitive setup in order to perfom continuous measurement of the fraction $f$ of the pores filled with liquid, while decreasing the vapor pressure $P _V$ outside the pores at controlled rate $A$. This technique has two major advantages compared to usual volumetry. First, comparing the dependence of $f$ with $P_V$ at different rate $A$ provides a direct signature that cavitation is sensitive or not to the fluid confinement. Second, the pressure cavitation threshold $P^*$ can be unambiguously defined and precisely measured as a function of the rate $A$. This allows to determine the dependence $\alpha=dE_B/dP_V$ of the energy barrier $E_B$ with the pressure.
We have performed systematic measurements of $\alpha$ for temperatures ranging from 70 K up to $T_h$ at which adsorption hysteresis disappears, for a serie of SBA-16 with cage diameter in the range 5 – 9 nm. For the largest pores and the lower temperatures, that is when the critical nucleation radius is the smallest, we recover $\alpha$ values which are close to those obtained for bulk cavitation [Bossert 2023]. The departure from the bulk case increases when the critical bubble radius becomes closer to the cage radius.
In contrast with $P^*$ measurements, the determination of $\alpha$ can be easily compared with theoretical predictions, since neither the knowledge of the attempt frequency nor the number of nucleation sites is required. Following the semi-macrosopic approach of Bonnet and Wolf [B&W 2018] and Morishige [Morishige 2021], we have calculated the energy barrier for bubble nucleation in the sharp interface limit, taking into account the curvature dependence of the surface tension [Bossert 2023]. Whatever the type of the wall-fluid interaction potential (whose amplitude is fixed by the measured value of $T_h$), we find this simple model underestimates the observed effect of confinement. More sophisticated approaches such as Density Functional Theory could possibly yield a better agreement with measurements. However, the semi-macrosopic model can still be improved by breaking the spherical symmetry, that is taking into account the probability that nucleation does not occur at the center of the cage, as observed in Molecular Dynamics simulations.
| References | [Thommes 2006] M. Thommes et al., Langmuir 2006, 22, 756-764 [Rasmussen 2010] C.J. Rasmussen , Langmuir 2010, 26(12), 10147–10157, [Doebele 2020] Phys. Rev. Lett., 125, 255701 (2020), [Morishige 2021] ACS Omega 2021, 6, 15964−15974, [Bossert 2023] PNAS 2023, 120, e2300499120, [B&W 2018] J. Phys. Chem. C 2019, 123, 1335−1347 |
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| Country | France |
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