is usually greater than 1 mm. This results in a relatively low interfacial area and a low probability of particle–bubble contact. Consequently, several cells in series are required to increase the particle residence time, thus increasing the probability of particle–bubble contact. Selective adhesion Froth flotation depends on the selective adhesion of air bubbles to mineral surfaces in a mineral/water slurry. The air bubbles attach to more hydrophobic particles, as determined by the interfacial energies between the solid, liquid, and gas phases. This energy is determined by the Young–Dupré equation: where: γlv is the surface energy of the liquid/vapor interface γsv is the surface energy of the solid/vapor interface γsl is the surface energy of the solid/liquid interface, θ is the contact angle, the angle formed at the junction between vapor, solid, and liquid phases. Minerals targeted for separation may be chemically surface-modified with collectors so that they are more hydrophobic. Collectors are a type of surfactant that increase the natural hydrophobicity of the surface, increasing the separability of the hydrophobic and hydrophilic particles. Collectors either chemically bond via chemisorption to the mineral or adsorb onto the surface via physisorption. IMFs and surface forces in bubble-particle interactions Collision The collision rates for fine particles (50 - 80 μm) can be accurately modeled, but there is no current theory that accurately models bubble-particle collision for particles as large as 300 μm, which are commonly used in flotation processes. For fine particles, Stokes law underestimates collision probability while the potential equation based on surface charge overestimates collision probability so an intermediate equation is used. It is important to know the collision rates in the system since this step precedes the adsorption where a three phase system is formed. Adsorption (attachment) The effectiveness of a medium to adsorb to a particle is influenced by the relationship between the surfaces of both materials. There are multiple factors that affect the efficiency of adsorption in chemical, thermodynamic, and physical domains. These factors can range from surface energy and polarity to the shape, size, and roughness of the particle. In froth flotation, adsorption is a strong consequence of surface energy, since the small particles have a high surface area to size ratio, resulting in higher energy surfaces to form attractions with adsorbates. The air bubbles must selectively adhere to the desired minerals to elevate them to the surface of the slurry while wetting the other minerals and