By Paul Roman

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Small particles are held by the capillary force, large particles fall down due to the dominating gravitational force. Beyond which particle radius is gravity strong enough to separate the two spheres? For quartz (SiO2 ) we assume a density of ρ = 3000 kgm−3 . 14: Two particles with rough surfaces in contact. In reality the capillary force is often much smaller than the calculated value. This can be explained by the roughness of the surfaces. The particle surfaces are usually rough and touch only at some points.

2 Fundamental thermodynamic relations 31 Hence, in equilibrium the chemical potentials are the same everywhere in the system. With this, we can further simplify Eq. 21) T,V,V β ,Ni The surface tension tells us how the Helmholtz free energy of the system changes when increasing the surface area while keeping the temperature, the total volume, the volume of phase β and the total numbers of all components constant. Is this a useful equation? It is not so difﬁcult to control T , V , and Ni but V β might be difﬁcult to keep constant.

Physics professor at the University of Glasgow. 16 2 Liquid surfaces due to the Laplace pressure. In general, any change in the Gibbs free energy is given by the fundamental equation dG = V dP − SdT . 19) We have assumed that the molar volume remains constant, which is certainly a reasonable assumption because most liquids are practically incompressible for the pressures considered. For a spherical drop in its vapor, we simply have ΔGm = 2γVm /r. 22) Since the liquid and vapor are supposed to be in equilibrium, the two expressions must be equal.