Nonadditive penetrable mixtures in nanopores: surface-induced population inversion

When does Wenzel's extension of Young's equation for the contact angle of droplets apply? A density functional study

The contact angle of a liquid droplet on a surface under partial wetting conditions differs for a nanoscopically rough or periodically corrugated surface from its value for a perfectly flat surface. Wenzel's relation attributes this difference simply to the geometric magnification of the surface area (by a factor r_w), but the validity of this idea is controversial. We elucidate this problem by model calculations for a sinusoidal corrugation of the form z_wall(y) = Δ cos(2πy/λ), for a potential of short range σ_w acting from the wall on the fluid particles. When the vapor phase is an ideal gas, the change in the wall-vapor surface tension can be computed exactly, and corrections to Wenzel's equation are typically of the order σ_wΔ/λ². For fixed r_w and fixed σ_w, the approach to Wenzel's result with increasing λ may be nonmonotonic and this limit often is only reached for λ/σ_w > 30. For a non-additive binary mixture, density functional theory is used to work out the density profiles of both coexisting phases for planar and corrugated walls as well as the corresponding surface tensions. Again, deviations from Wenzel's results of similar magnitude as in the above ideal gas case are predicted. Finally, a crudely simplified description based on the interface Hamiltonian concept is used to interpret the corresponding simulation results along similar lines. Wenzel's approach is found to generally hold when λ/σ_w ≫ 1 and Δ/λ < 1 and under conditions avoiding proximity of wetting or filling transitions.

Dynamics of field-driven population inversion in a confined colloidal mixture

We study, using Langevin dynamics simulations, the change in composition of a binary colloidal mixture confined in a finite-length channel, induced by an external field. The field-induced transition from a near-bulk composition to an inverted population is studied as a function of time, for different field strengths and system parameters. For state points corresponding to reversible field cycles, the cyclic filling and emptying of the channel by the minority species are compared. Extrapolation of the physical relaxation times to the colloidal regime is performed through a series of simulations at increasing value of the damping parameter. For state points at which the mixture is unstable at zero field, reproducible irreversible cycles are illustrated. For reversible field cycles, the scaling with the particles size of the characteristic cycling time is discussed.