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.

中文翻译：

---

界面质量通量界面的惯性动力学：稳定性和流场结构、惯性稳定机制、Landau 解的简并性、能量波动的影响和化学诱导的不稳定性

这项工作侧重于具有界面质量通量的界面惯性动力学的长期问题，并报告了界面稳定和不稳定的新机制。界面是分隔不同密度流体并具有界面质量通量的相边界。为了从远场分析界面动力学，我们开发并应用通用矩阵方法来严格求解边界值问题，该问题涉及流体体中的控制方程以及界面处和域外边界处的边界条件。我们找到了线性方程组的基本解，并通过将严格的数学属性与物理可观察量直接联系起来，分析了界面稳定性与流场结构的相互作用。我们发现，当动力学守恒质量、动量和能量通量时，界面是稳定的；稳定是由于惯性机制导致界面速度的小幅振荡。在经典的朗道动力学中，界面速度完全恒定的假设导致朗道-达里厄斯不稳定性的发展。这种不稳定也与界面处扰动能量的不平衡有关。发现经典的 Landau 解具有退化性；退化的解除可能导致奇异性和自相似动力学。我们的结果与传统的燃烧理论进行了很好的比较，并提出了新的实验来研究可燃系统中界面和流场的动力学。我们进一步进行反应性分子动力学模拟以阐明化学过程的复杂性，研究能量波动对界面稳定性的破坏作用，并说明化学引起的不稳定性。总之，我们确定了界面动力学对界面边界条件的极端敏感性，包括基本解的形式特性以及流场的定性和定量特性。这为研究、诊断和控制各种自然和技术过程中的多相流提供了新的机会。我们确定了界面动力学对界面边界条件的极端敏感性，包括基本解的形式特性以及流场的定性和定量特性。这为研究、诊断和控制各种自然和技术过程中的多相流提供了新的机会。我们确定了界面动力学对界面边界条件的极端敏感性，包括基本解的形式特性以及流场的定性和定量特性。这为研究、诊断和控制各种自然和技术过程中的多相流提供了新的机会。