We investigate the drying dynamics of porous media with two pore diameters separated by several orders of magnitude. Nanometer-sized pores at the edge of our samples prevent air entry, while drying proceeds by heterogeneous nucleation of vapor bubbles -cavitation -in the liquid in micrometer-sized voids within the sample. We show that the dynamics of cavitation and drying are set by the interplay of the deterministic poroelastic mass transport in the porous medium and the stochastic nucleation process. Spatio-temporal patterns emerge in this unusual reaction-diffusion system, with temporal oscillations in the drying rate and variable roughness of the drying front.The desorption, or drying, of liquids from porous media is important in a variety of contexts, both in nature (e.g., the movement of water in plants [1]) and in technology (e.g., the synthesis [2] and characterization [3] of advanced materials). Studies of desorption have focused on the dynamics and pattern formation associated with drying [4-6] and the thermodynamics that define the shapes of desorption isotherms [7,8]. Despite this attention, uncertainties remain regarding the physical processes that govern desorption. It has been proposed that, rather than by receding of the liquid phase from the edges of the material, drying from porous media could occur by cavitation, i.e. the spontaneous formation of vapor bubbles either when the liquid tensile strength is attained [9] or by thermally activated nucleation in the metastable pore liquid (Fig. 1a) [10]. This process has been observed in simulations [8,11] and has been proposed on several occasions to explain the shape of desorption isotherms in nano-scale porous media [8,12,13], or the apparent emergence of drying events far from the evaporation front [14,15]. Yet, we are unaware of direct optical observation of desorption by cavitation or of an investigation of its effect on drying dynamics.In this Letter, we present a tailored porous medium formed of microfabricated voids coupled to each other and the outside via a nanoporous substrate (Figs. 1b-1c). This extreme ink-bottle structure -large pore bodies connected via narrow throats [16] -has allowed us to observe the nucleation and growth of cavitation bubbles during drying (Fig. 1d) and to show that this process gives rise to interesting coupled drying dynamics that is tunable with geometry.Drying occurs when a saturated porous medium is placed in a sub-saturated atmosphere (relative humidity p v /p sat < 1, where p v and p sat are the vapor pressure and its saturation value). At high relative humidity, evaporation results in the formation of menisci in the pores at the surface of the material, until local mechanical and andarXiv:1402.6776v2 [cond-mat.soft]

We discuss the notion of nonequilibrium chemical potential in gases of non-interacting active particles filling two compartments separated by a potential energy barrier. Different types of active particles are considered: run-and-tumble particles, active Brownian particles, and active Brownian particles with a stochastic reorientation along an external field. After recalling some analytical results for run-and-rumble particles in one dimension, we focus on the two-dimensional case and obtain a perturbative expression of the density profile in the limit of a fast reorientation dynamics, for the three models of active particles mentioned above. Computing the chemical potentials of the non-equilibrium systems in contact from the knowledge of the stationary probability distribution of the whole system -which agrees with a recently proposed general definition of the chemical potential in non-equilibrium systems in contact-we generically find that the chemical potential lacks an equation of state, in the sense that it depends on the detailed shape of the potential energy barrier separating the compartments and not only on bulk properties, at odds with equilibrium. This situation is reminiscent of the properties of the mechanical pressure in active systems. We also argue that the Maxwell relation is no longer valid and cannot be used to infer the nonequilibrium chemical potential from the knowledge of the mechanical pressure.