Wetting behavior of a colloidal particle trapped at a composite liquid-vapor interface of a binary liquid mixture

A partially miscible binary liquid mixture, composed of A and B particles, is considered theoretically under conditions for which a stable A-rich liquid phase is in thermal equilibrium with the vapor phase. The B-rich liquid is metastable. The liquids and the thermodynamic conditions are chosen such that the interface between the A-rich liquid and the vapor contains an intervening wetting film of the B-rich phase. In order to obtain information about the large-scale fluid structure around a colloidal particle, which is trapped at such a composite liquid-vapor interface, three related and linked wetting phenomena at planar liquid-vapor, wall-liquid, and wall-vapor interfaces are studied analytically, using classical density functional theory in conjunction with the sharp-kink approximation for the number density profiles of the A and B particles. If in accordance with the so-called mixing rule the strength of the A-B interaction is given by the geometric mean of the strengths of the A-A and the B-B interactions, and similarly the ratio between the wall-A and the wall-B interaction, the scenario, in which the colloid is enclosed by a film of the B-rich liquid, can be excluded. Up to six distinct wetting scenarios are possible, if the above mixing rules for the fluid-wall and for the fluid-fluid interactions are relaxed. The way the space of system parameters is divided into domains corresponding to the six scenarios, and which of the domains actually appear, depends on the signs of the deviations from the mixing rule prescriptions. Relevant domains, corresponding, e.g., to the scenario in which the colloid is enclosed by a film of the B-rich liquid, emerge, if the ratio between the strengths of the wall-A and the wall-B interactions is reduced as compared to the mixing rule prescription, or if the strength of the A-B interaction is increased to values above the one from the mixing rule prescription. The range, within which the contact angle may vary inside the various domains, is also studied.