A Gibbs formulation for reactive materials with phase change

Abstract

Abstract. Energetic material condensed phase constituents come into contact, chemically react and simultaneously undergo phase change. Phase change in a given molecular material is often considered separately from chemical reaction. Continuum phase field models often use a indicator function to change the phase in different regions according to an evolutionary (Ginzburg-Landau) equation. But chemical kinetic descriptions of change (according to physical chemistry formulations) count species or component concentrations and derive kinetic evolution equations based on component mass transport. We argue the latter is fundamental and that all components, designated by both phase and chemical characters are treated as distinct chemical species. We pose a self-consistent continuum, thermo-mechanical model based on specified Gibbs potentials for all relevant species/components that are present in a single material. Therefore a single stress tensor, and a single temperature is assumed for the material for all relevant component-species, for all equilibrium potentials, interaction energies and material properties. We discuss recent examples where we have applied the Gibbs formulation to model behavior of complex reactive materials.

Modeling ignition of HMX with the Gibbs formulation

“…Each component has a rate of reaction and is subject to mass diffusion. A summary of the formulation is found in Stewart, [1]. The calculations described here extend those recently carried out for a constant volume, constant energy thermal explosion for RDX, that used the Gibbs formulation to mirror the transients predicted by a reactive molecular dynamic simulation, [2].…”

“…The corresponding infinitesimal normal strain component is 11 . The stress-strain-temperature relation, derived from taking thermodynamic derivatives of the mixture Gibbs free energy, [1]…”

“…The Gibbs formulation, [1] is used to model an ignition event for a nano-sized, one-dimensional slab of the explosive HMX. One side of an initially solid, β-HMX slab is rapidly heated.…”

Modeling the Thermo‐Mechanical‐Chemical Behavior of Condensed Phase Reactive Materials

“…We have developed [1], a non-equilibrium thermodynamic theory that can be used to describe a distributed mixture of components that allow for solids, liquids, and gases that can change phase and undergo a chemical reaction. It is based on the same classical formulations found in physical chemistry and has a formulation that is parallel to that used in combustion theory for multicomponent mixtures of gases.…”

“…Here, we present a high-level overview of a modeling approach based on a non-equilibrium, multicomponent thermodynamic formulation, we have dubbed the Gibbs formulation [1]. The Gibbs formulation can be thought of as a generalization of the classical non-equilibrium formulations used in gaseous, multicomponent combustion theory [2], but expanded to mixtures with simultaneously present concentrations of solids, liquids, and gases.…”