Origin of idealized static thermodynamic forces inducing solid particle motion, orientation and related effects in a solute concentration gradient

Abstract

The forces acting on a solid particle in the concentration gradient of a solution or mixture are given for a carefully specified thermodynamic model. From this analysis it is possible to predict the initial nature of any ensuing motion of the particle and, in particular, to give the potential propelling force on a particle at rest as [graphic ommitted] where the integration is over each slice of solid of surface area δA_s, with s denoting different types of surface, and dσ_s/dξ is the variation in the interfacial tension for each s at position ξ. An orientation effect is predicted for certain solids with composite surfaces. The propelling and orientation forces can be related to the surface excess adsorption of a solute at a solid surface. Aspects discussed are the implications for using density-gradient columns, the behaviour of particles at liquid interfaces and a variety of qualitative phenomena possible in special circumstances (some of biological relevance) including two-particle effects, the potential for the complementary movement of liquid over or through a stationary solid and conditions whereby a collection of particles might become separated. Some of the effects might apply to macromolecules to which the concepts of surface area and interfacial tension are not relevant. All predictions are based on static considerations using equilibrium thermodynamics: no attempt is made to describe actual motion.