Abstract We have developed a continuum modeling approach, grounded in classical physical chemistry, based on the following assumptions: (1) That the states in the material can be represented by local stationary averages of the pressure (stress), temperature, and mass fractions computed from atomistic simulation, (2) and that the mixture has well-defined molecular components, each with a complete equation of state. The continuum model, “Gibbs formulation”, applies to near-atomic length and time scales, which we identify as the scales where the high frequency, high energy phonons equilibrate in molecular mixtures, (about six atomic radii and six to ten vibrational periods). Phase changes and chemical changes due to reaction are not in (asymptotically, long-time) equilibrium, and changes are assumed to occur on much longer time scales than those required for stress and temperature equilibration. The Gibbs formulation can be thought of as a generalization of the classical non-equilibrium formulations used in gaseous, multicomponent combustion theory, but expanded to mixtures with simultaneously present concentrations of solids, liquids and gases. We present an example of this approach applied to the ignition and burning of a nano-sized aluminum flake, modeled as a slab of aluminum coated with a thin alumina layer. The model considers up to six components: solid, liquid and gaseous aluminum, solid and liquid aluminum oxide (alumina), and oxygen. We discuss the many different behaviors and possible regimes of combustion, that depend on what is assumed for the thermal and mass transport and reaction rates.

中文翻译：

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用 Gibbs 公式模拟氧化环境中的铝燃烧

摘要 我们开发了一种以经典物理化学为基础的连续介质建模方法，基于以下假设：(1) 材料中的状态可以由计算的压力（应力）、温度和质量分数的局部平稳平均值表示根据原子模拟，(2) 并且混合物具有明确定义的分子成分，每个成分都有完整的状态方程。连续模型“吉布斯公式”适用于近原子长度和时间尺度，我们将其确定为分子混合物中高频、高能声子平衡的尺度（大约六个原子半径和六到十个振动周期） . 由于反应引起的相变和化学变化不处于（渐近，长时间）平衡状态，并且假定变化发生的时间尺度比应力和温度平衡所需的时间尺度要长得多。Gibbs 公式可以被认为是气体、多组分燃烧理论中使用的经典非平衡公式的推广，但扩展到具有同时存在的固体、液体和气体浓度的混合物。我们展示了该方法应用于纳米尺寸铝片的点火和燃烧的示例，模拟为涂有薄氧化铝层的铝板。该模型最多考虑六种成分：固体、液体和气体铝、固体和液体氧化铝（氧化铝）和氧。我们讨论了许多不同的行为和可能的燃烧方式，这取决于对热和质量传输和反应速率的假设。