Micro-Inertia Effects in Material Flow

Abstract

Abstract The mechanics of understanding a new application of the bracket theory of Non-Equilibrium Thermodynamics that allows for the incorporation of microstructural inertia effects within conformation tensor-based constitutive models of macroscopic material behavior is presented. Introducing inertia effects generally requires the replacement of a first order in time evolution equation for the conformation tensor by a second order one. Through the analysis of a simple damped oscillator we bring forward here the close connection to the structural dissipation brackets present in the two cases, with the weights being inverted as one transitions from the inertialess to the inertial description. Moreover, one may also describe inertial effects in material flow in certain situations through a simple modification of the first order evolution equation for the conformation tensor, which consists of adding a new non-affine term that couples the conformation and the vorticity tensors, as detailed in a recent publication (P. M. Mwasame, N. J. Wagner and A. N. Beris, Phys. Fluids, 30 (2018), 030704). As shown there, when applied to the low particle Reynolds flow of dilute emulsions, this reduced inertial flow model provides predictions consistent with literature-available microscopically based asymptotic results.