Interaction between macroparticles in a binary fluid mixture: anomalous effects due to the bulk composition

Abstract

The interaction between macroparticles in a binary fluid mixture has been analysed using the reference hypernetted-chain (RHNC) theory. The mixture is composed of particles interacting through an attractive potential (component 1) and hard spheres (component 2). Particles of different components interact through a hard-sphere potential. Significantly high affinity is assumed between the macroparticle surface and component 1. Two cases have been studied: case 1 where the bulk mixture unavoidably separates into two immiscible phases in the regime x _1p < x ₁ < x _1Q (x ₁ is the mole fraction of component 1, and x _1p and x _1Q denote values at the spinodal points); and case 2 where the bulk mixture is miscible over the entire composition range. As x ₁ increases from x ₁ = 0 or x ₁ decreases from x ₁ = 1 in case 1, the macroparticle interaction always shifts to the more attractive side. As x ₁ → x _1R;1—0 or x ₁ → x _1S;1 + 0 (x _1R;1 and x _1S;1 are threshold values, and x _1R;1 < x _1P and x _1S;1 > x _1Q), the range of the interaction exhibits sudden growth to a scale that is far longer than molecular dimensions, and the interaction becomes strongly attractive. This behaviour is ascribed to a surface-induced phase transition, the partial wetting of one of the components accompanied by the partial drying of the other. Even in case 2, similar behaviour has been observed as x ₁ → x _1R;2—0 or x ₁ → x _1S;2 + 0 (x _1R;2 and x _1S;2 are threshold values). Over the regime x _1R;2 < x ₁ < x _1S;2 the RHNC theory possesses no solutions. The interaction between unlike macroparticles, whose surfaces have high affinity only with component 1 and only with component 2, respectively, has been analysed also. Although the interaction between like macroparticles is strongly attractive except for very small separations, the interaction between unlike macroparticles is strongly repulsive for all separations.