Theory for solvent, momentum, and energy transfer between a surfactant solution and a vapor atmosphere

We develop a complete set of equations governing the evolution of a sharp interface separating a volatile-solvent/nonvolatile-surfactant solution from a vapor atmosphere. In addition to a sorption isotherm equation and the conventional balances for mass, linear momentum, and energy, these equations include a counterpart of the Hertz???Knudsen???Langmuir equation familiar from conventional theories of evaporation-condensation. This additional equation arises from a consideration of configurational forces within a thermodynamical framework. While the notion of configurational forces is well-developed and understood for the description of materials, like crystalline solids, that possess natural reference configurations, very little has been done regarding their role in materials, such as viscous fluids, that do not possess preferred reference states. We therefore provide a comprehensive discussion of configurational forces, the balance of configurational momentum, and configurational thermodynamics that does not require a choice of reference configuration. The general evolution equations arising from our theory account for the thermodynamic structure of the solution and the interface and for sources of dissipation related to the transport of surfactant, momentum, and heat in the solution, the transport of surfactant and momentum within the interface, and the transport of solute, momentum, kinetic energy, and heat across the interface. Due to the complexity of these equations, we provide approximate equations which we compare to relations that appear in the literature.published or submitted for publicationis peer reviewe

The Stored Energy of Cold Work, Thermal Annealing, and Other Thermodynamic Issues in Single Crystal Plasticity at Small Length Scales

This paper develops a thermodynamically consistent gradient theory of single-crystal plasticity using the principle of virtual power as a paradigm to develop appropriate balance laws for forces and energy. The resulting theory leads to a system of microscopic force balances, one balance for each slip system, and to an energy balance that accounts for power expended during plastic flow via microscopic forces acting in concert with slip-rates and slip-rate gradients. Central to the theory are an internal energy and entropy, plastic in nature, dependent on densities that account for the accumulation of glide dislocations as well as geometrically necessary dislocations – and that, consequently, represent quantities associated with cold work. Our theory allows us to discuss – within the framework of a gradient theory – the fraction of plastic stress-power that goes into heating, as well as the reduction of the dislocation density in a cold-worked material upon subsequent (or concurrent) thermal annealing.National Science Foundation (U.S.) (NSF CMMI Award No.1063626)National Research Foundation (South Africa

Thermodynamics of non-local materials: extra fluxes and internal powers

The most usual formulation of the Laws of Thermodynamics turns out to be suitable for local or simple materials, while for non-local systems there are two different ways: either modify this usual formulation by introducing suitable extra fluxes or express the Laws of Thermodynamics in terms of internal powers directly, as we propose in this paper. The first choice is subject to the criticism that the vector fluxes must be introduced a posteriori in order to obtain the compatibility with the Laws of Thermodynamics. On the contrary, the formulation in terms of internal powers is more general, because it is a priori defined on the basis of the constitutive equations. Besides it allows to highlight, without ambiguity, the contribution of the internal powers in the variation of the thermodynamic potentials. Finally, in this paper, we consider some examples of non-local materials and derive the proper expressions of their internal powers from the power balance laws.Comment: 16 pages, in press on Continuum Mechanics and Thermodynamic

Numerical approach to a model for quasistatic damage with spatial BV-regularization

We address a model for rate-independent, partial, isotropic damage in quasistatic small strain linear elasticity, featuring a damage variable with spatial BV-regularization. Discrete solutions are obtained using an alternate time-discrete scheme and the Variable-ADMM algorithm to solve the constrained nonsmooth optimization problem that determines the damage variable at each time step. We prove convergence of the method and show that discrete solutions approximate a semistable energetic solution of the rate-independent system. Moreover, we present our numerical results for two benchmark problems

The unifying nature of the configurational force balance

(1) Introduction: some conditions for nonmaterial interfaces; (2) The need for a configurational force balance; (3) A framework for the study of evolving nonmaterial interfaces; (4) The normal configurational force balance and the dissipation inequality; (5) Relation of the normal configurational force balance to the classical equations; (6) A final remark.published or submitted for publicationis peer reviewe

Cosserat fluids and the continuum mechanics of turbulence: A generalized Navier-Stokes-alpha equation with complete boundary conditions

We here develop a continuum-mechanical formulation and generalization of the Navier???Stokes-alpha equation based on a general framework for fluid-dynamical theories involving gradient dependencies (Fried & Gurtin 2005). That generalization entails two additional material length scales: one of energetic origin, the other of dissipative origin. In contrast to Lagrangian averaging, our formulation delivers boundary conditions???involving yet another material length scale???and a complete framework based on thermodynamics applied to an isothermal system. As an application, we consider the classical problem of turbulent flow in a plane, rectangular channel with fixed, impermeable, slip-free walls and make comparisons with results obtained from direct numerical simulations. For this problem, only one of the material length scales involved in the flow equation enters the final solution. When the additional material length scale associated with the boundary conditions is signed to ensure satisfaction of the second law at the channel walls the theory delivers solutions that agree neither quantitatively nor qualitatively with observed features of plane channel flow. On the contrary, we find excellent agreement when the sign of the additional material parameter associated with the boundary conditions violates the second law. We discuss the implication of this result.published or submitted for publicationis not peer reviewe

A unified treatment of evolving interfaces accounting for small deformations and atomic transport: grain-boundaries, phase transitions, epitaxy

This review presents a unified treatment of several topics at the intersection of continuum mechanics and materials science; the thrust concerns processes involving evolving interfaces, focusing on grain-boundaries, solid-vapor interfaces (with emphasis on epitaxy), and coherent phase-transitions. Central to our discussion is the interaction of deformation, atomic transport, and accretion within a dissipative, dynamical framework, but as our interest is crystalline materials, we restrict our attention to small deformations. To avoid geometrical complications associated with surfaces in R^3, we work in two space-dimensions when discussing interfaces, but in R^3 when discussing the theory in bulk.published or submitted for publicationis peer reviewe