Geometric dispersion of unattached particles in foams

Abstract

A sound understanding of the phenomena affecting the flow of unattached particles through the Plateau border network of a foam is essential for the accurate modelling of industrial flotation processes. One such phenomenon is the dispersion of liquid and particles perpendicular to the overall direction of flow, known as geometric dispersion. This dispersion is due to the interconnected nature of the Plateau border network within the foam, which causes the flow to split and disperse through the foam at every vertex encountered. Given the structure of the foam, the flow through the Plateau border network can be calculated and from this a geometric dispersion coefficient can be obtained. This coefficient quantifies the geometric dispersion within the foam for all flow conditions and is used as an input variable in fundamentally based flotation models. Previously the geometric dispersion coefficient has been calculated using a two-dimensional regular structure. This method has been extended here to enable the calculation of the coefficient from simulations of unattached particle flow through a three-dimensional random, monodisperse foam. The flow within the foam is modelled through the coupling of descriptions of flow on both the bulk foam and Plateau border scales. These descriptions are then combined with realistic Plateau border network structures to allow the simulation of unattached particle motion through the foam. Additionally, a geometric dispersion coefficient was predicted for the three-dimensional random, monodisperse foam, solely based on the structural properties of the network used in the particle simulations. The coefficient calculated from the simulations compares well with this predicted value, further confirming the dependence of geometric dispersion on foam structure. Specifically it is dependent on the average Plateau border length of the structure, as this varies in relation to the bubble diameter, according to the structure chosen.