Thursday, September 28, 2017
2:30 - 3:30 pm
Speaker: Dr. Antony Beris, University of Delaware
Particulate flows are encountered in a number of industrially important applications ranging from fluidized bed catalytic reactors to biochemical fermenters. As the size of the particles increases microinertia effects start becoming important. So far those have been studied only based on microscopic calculations providing a wealth of information about the detailed characteristics of the flow and particle dynamics. So far though this information has not been utilized in the construction of macroscopic flow models, despite the fact that significant macroscopic flow phenomena are demonstrated to arise in the presence of microinertia. In this presentation, a new approach is outlined that allows for this transfer of information to take place in the particular example of dilute emulsions. The model is based on an internal contravariant conformation tensor structural variable which is physically identified with the deformed ellipsoidal geometry of the dispersed phase. Most importantly, micro-inertia effects are introduced by a new non-affine term that couples the conformation and the vorticity tensors in the evolution equation for the conformation tensor. This derivation and resultant constitutive equation provide a new pathway to rigorously incorporate micro-inertia into general, conformation tensor-based, macroscopic models for multiphase systems. The model is consistent with previously developed in the literature asymptotic theories in the limit of small capillary, Ca, as well as small particle Reynolds, Re, numbers. These asymptotic solutions are also used to uniquely determine all the model parameters. Additional, more recent, applications to concentrated suspensions are also going to be outlined.