Stability and flow fields structure for interfacial dynamics with interfacial mass flux

We analyze from a far field the evolution of an interface that separates ideal incompressible fluids of different densities and has an interfacial mass flux. We develop and apply the general matrix method to rigorously solve the boundary value problem involving the governing equations in the fluid bulk and the boundary conditions at the interface and at the outside boundaries of the domain. We find the fundamental solutions for the linearized system of equations, and analyze the interplay of interface stability with flow fields structure, by directly linking rigorous mathematical attributes to physical observables. New mechanisms are identified of the interface stabilization and destabilization. We find that interfacial dynamics is stable when it conserves the fluxes of mass, momentum and energy. The stabilization is due to inertial effects causing small oscillations of the interface velocity. In the classic Landau dynamics, the postulate of perfect constancy of the interface velocity leads to the development of the Landau-Darrieus instability. This destabilization is also associated with the imbalance of the perturbed energy at the interface, in full consistency with the classic results. We identify extreme sensitivity of the interface dynamics to the interfacial boundary conditions, including formal properties of fundamental solutions and qualitative and quantitative properties of the flow fields. This provides new opportunities for studies, diagnostics, and control of multiphase flows in a broad range of processes in nature and technology

Inertial dynamics of an interface with interfacial mass flux: Stability and flow fields’ structure, inertial stabilization mechanism, degeneracy of Landau’s solution, effect of energy fluctuations, and chemistry-induced instabilities

This work focuses on the long-standing problem of inertial dynamics of an interface with interfacial mass flux and reports new mechanisms for the interface stabilization and destabilization. The interface is a phase boundary separating fluids of different densities and having interfacial mass flux. To analyze the interface dynamics from a far field, we develop and apply the general matrix method to rigorously solve the boundary value problem involving the governing equations in the fluid bulk and the boundary conditions at the interface and at the outside boundaries of the domain. We find the fundamental solutions for the linearized system of equations and analyze the interplay of interface stability with flow fields’ structure by directly linking rigorous mathematical attributes to physical observables. We find that the interface is stable when the dynamics conserves the fluxes of mass, momentum, and energy; the stabilization is due to an inertial mechanism causing small oscillations of the interface velocity. In the classic Landau’s dynamics, the postulate of perfect constancy of the interface velocity leads to the development of Landau–Darrieus instability. This destabilization is also linked to the imbalance of the perturbed energy at the interface. The classic Landau’s solution is found to have degeneracy; lifting of the degeneracy may lead to singularity and self-similar dynamics. Our results compare well with traditional theories of combustion and propose new experiments to study the dynamics of the interface and the flow fields in combustible systems. We further conduct reactive molecular dynamics simulations to elucidate the complexity of chemical processes, to study the destabilizing effect of energy fluctuations on the interface stability, and to illustrate the chemistry-induced instabilities. In summary, we identify the extreme sensitivity of the interface dynamics to the interfacial boundary conditions, including the formal properties of fundamental solutions and the qualitative and quantitative properties of the flow fields. This provides new opportunities for studies, diagnostics, and control of multiphase flows in a broad range of processes in nature and technology

First principles-based multiscale atomistic methods for input into first principles nonequilibrium transport across interfaces

This issue of PNAS features “nonequilibrium transport and mixing across interfaces,” with several papers describing the nonequilibrium coupling of transport at interfaces, including mesoscopic and macroscopic dynamics in fluids, plasma, and other materials over scales from microscale to celestial. Most such descriptions describe the materials in terms of the density and equations of state rather than specific atomic structures and chemical processes. It is at interfacial boundaries where such atomistic information is most relevant. However, there is not yet a practical way to couple these phenomena with the atomistic description of chemistry. The starting point for including such information is the quantum mechanics (QM). However, practical QM calculations are limited to a hundred atoms for dozens of picoseconds, far from the scales required to inform the continuum level with the proper atomistic description. To bridge this enormous gap, we need to develop practical methods to extend the scale of the atomistic simulation by several orders of magnitude while retaining the level of QM accuracy in describing the chemical process. These developments would enable continuum modeling of turbulent transport at interfaces to incorporate the relevant chemistry. In this perspective, we will focus on recent progress in accomplishing these extensions in first principles-based atomistic simulations and the strategies being pursued to increase the accuracy of very large scales while dramatically decreasing the computational effort

Interface dynamics: Mechanisms of stabilization and destabilization and structure of flow fields

Interfacial mixing and transport are nonequilibrium processes coupling kinetic to macroscopic scales. They occur in fluids, plasmas, and materials over celestial events to atoms. Grasping their fundamentals can advance a broad range of disciplines in science, mathematics, and engineering. This paper focuses on the long-standing classic problem of stability of a phase boundary—a fluid interface that has a mass flow across it. We briefly review the recent advances in theoretical and experimental studies, develop the general theoretical framework directly linking the microscopic interfacial transport to the macroscopic flow fields, discover mechanisms of interface stabilization and destabilization that have not been discussed before for both inertial and accelerated dynamics, and chart perspectives for future research

Interface dynamics: Mechanisms of stabilization and destabilization and structure of flow fields

Interfacial mixing and transport are nonequilibrium processes coupling kinetic to macroscopic scales. They occur in fluids, plasmas, and materials over celestial events to atoms. Grasping their fundamentals can advance a broad range of disciplines in science, mathematics, and engineering. This paper focuses on the long-standing classic problem of stability of a phase boundary—a fluid interface that has a mass flow across it. We briefly review the recent advances in theoretical and experimental studies, develop the general theoretical framework directly linking the microscopic interfacial transport to the macroscopic flow fields, discover mechanisms of interface stabilization and destabilization that have not been discussed before for both inertial and accelerated dynamics, and chart perspectives for future research

Stability and flow fields structure for interfacial dynamics with interfacial mass flux

We analyze from a far field the evolution of an interface that separates ideal incompressible fluids of different densities and has an interfacial mass flux. We develop and apply the general matrix method to rigorously solve the boundary value problem involving the governing equations in the fluid bulk and the boundary conditions at the interface and at the outside boundaries of the domain. We find the fundamental solutions for the linearized system of equations, and analyze the interplay of interface stability with flow fields structure, by directly linking rigorous mathematical attributes to physical observables. New mechanisms are identified of the interface stabilization and destabilization. We find that interfacial dynamics is stable when it conserves the fluxes of mass, momentum and energy. The stabilization is due to inertial effects causing small oscillations of the interface velocity. In the classic Landau dynamics, the postulate of perfect constancy of the interface velocity leads to the development of the Landau-Darrieus instability. This destabilization is also associated with the imbalance of the perturbed energy at the interface, in full consistency with the classic results. We identify extreme sensitivity of the interface dynamics to the interfacial boundary conditions, including formal properties of fundamental solutions and qualitative and quantitative properties of the flow fields. This provides new opportunities for studies, diagnostics, and control of multiphase flows in a broad range of processes in nature and technology

First principles-based multiscale atomistic methods for input into first principles nonequilibrium transport across interfaces

This issue of PNAS features “nonequilibrium transport and mixing across interfaces,” with several papers describing the nonequilibrium coupling of transport at interfaces, including mesoscopic and macroscopic dynamics in fluids, plasma, and other materials over scales from microscale to celestial. Most such descriptions describe the materials in terms of the density and equations of state rather than specific atomic structures and chemical processes. It is at interfacial boundaries where such atomistic information is most relevant. However, there is not yet a practical way to couple these phenomena with the atomistic description of chemistry. The starting point for including such information is the quantum mechanics (QM). However, practical QM calculations are limited to a hundred atoms for dozens of picoseconds, far from the scales required to inform the continuum level with the proper atomistic description. To bridge this enormous gap, we need to develop practical methods to extend the scale of the atomistic simulation by several orders of magnitude while retaining the level of QM accuracy in describing the chemical process. These developments would enable continuum modeling of turbulent transport at interfaces to incorporate the relevant chemistry. In this perspective, we will focus on recent progress in accomplishing these extensions in first principles-based atomistic simulations and the strategies being pursued to increase the accuracy of very large scales while dramatically decreasing the computational effort

First principles-based multiscale atomistic methods for input into first principles nonequilibrium transport across interfaces

This issue of PNAS features “nonequilibrium transport and mixing across interfaces,” with several papers describing the nonequilibrium coupling of transport at interfaces, including mesoscopic and macroscopic dynamics in fluids, plasma, and other materials over scales from microscale to celestial. Most such descriptions describe the materials in terms of the density and equations of state rather than specific atomic structures and chemical processes. It is at interfacial boundaries where such atomistic information is most relevant. However, there is not yet a practical way to couple these phenomena with the atomistic description of chemistry. The starting point for including such information is the quantum mechanics (QM). However, practical QM calculations are limited to a hundred atoms for dozens of picoseconds, far from the scales required to inform the continuum level with the proper atomistic description. To bridge this enormous gap, we need to develop practical methods to extend the scale of the atomistic simulation by several orders of magnitude while retaining the level of QM accuracy in describing the chemical process. These developments would enable continuum modeling of turbulent transport at interfaces to incorporate the relevant chemistry. In this perspective, we will focus on recent progress in accomplishing these extensions in first principles-based atomistic simulations and the strategies being pursued to increase the accuracy of very large scales while dramatically decreasing the computational effort