Microstructure evolution during liquid–liquid laminar mixing: a kinetic theory approach

Many material forming processes involve liquid–liquid mixing, and in general the induced properties are strongly dependent on the resulting microstructure. Microstructure during liquid–liquid mixing exhibits a morphology characterized by a length scale usually much smaller that the one associated with the macroscopic flow. In this context a microstructure description allowing to characterize the microscopic morphology, its characteristic size, shape and orientation as well as the time evolution of the specific interface area, seems to be necessary in order to qualify and even quantify, the ability of flows to perform mixing, leading to the definition of optimal flows to maximize some desired criteria. The approach based on the definition of area tensor is a promising description of such phenomena, being its main drawback the necessity of introducing a closure relation to derive the equation governing its time evolution, whose impact on the computed solution can be in some cases significant. In this paper we propose a new description which considers the area tensor description as starting point, but defines its evolution in a kinetic theory framework, avoiding the introduction of any closure relation.