We investigate the effect of Taylor dispersion on the thermo-diffusive instabilities of premixed flames. This is a physically interesting and analytically tractable problem within a relatively unexplored class of problems pertaining to the interaction between Taylor dispersion (or flow-enhanced diffusion) and Turing-like instabilities in reaction–diffusion systems. The analysis is carried out in the Hele–Shaw burner configuration and adopts a constant density and negligible heat-loss assumptions. These simplifying assumptions allow to isolate the effect of Taylor dispersion on flame stability (by switching off the Darrieus–Landau instability and experimentally challenging extinction phenomena) while keeping the problem analytically tractable. Starting from a 3D formulation, depth-averaged equations are first obtained leading to a 2D model which accounts for enhanced diffusion in the flow direction and shows that diffusion is effectively anisotropic. A linear stability analysis of the travelling wave solutions of the 2D problem leads to a simple dispersion relation which generalises a classical one obtained by Sivashinsky to incorporate the effect of the flow Peclet number coupled to that of the mixture's Lewis number. Based on the new dispersion relation, stability-bifurcation diagrams are drawn in terms of the Peclet and Lewis numbers and their physical implications are discussed. In particular, the study clearly demonstrates the ability of Taylor dispersion to significantly affect the flame thermo-diffusive instabilities, whether these are of the cellular or oscillatory types, with the effect on the latter being more pronounced. It is found that Taylor dispersion typically promotes the cellular instability and hampers the oscillatory instability. This is the first stability analysis accounting for Taylor dispersion in the context of combustion and has thus a fundamental value, both in combustion and in other reaction–diffusion areas, independent of the fact that the phenomena predicted may well be difficult to reproduce experimentally.

我们研究了泰勒色散对预混火焰热扩散不稳定性的影响。在与泰勒色散（或流动增强扩散）和反应扩散系统中的图灵样不稳定性之间的相互作用相关的一类相对未探索的问题中，这是一个物理上有趣且分析上易于处理的问题。分析在 Hele-Shaw 燃烧器配置中进行，并采用恒定密度和可忽略的热损失假设。这些简化的假设允许隔离泰勒色散对火焰稳定性的影响（通过关闭 Darrieus-Landau 不稳定性和实验上具有挑战性的消光现象），同时保持问题在分析上易于处理。从 3D 公式开始，首先获得深度平均方程，得到一个二维模型，该模型解释了流动方向上的增强扩散，并表明扩散实际上是各向异性的。二维问题的行波解的线性稳定性分析导致了一个简单的色散关系，该关系概括了 Sivashinsky 获得的经典色散关系，以结合流动 Peclet 数的影响与混合物的 Lewis 数的影响相结合。基于新的色散关系，根据 Peclet 和 Lewis 数绘制了稳定性-分岔图，并讨论了它们的物理含义。特别是，该研究清楚地证明了泰勒色散显着影响火焰热扩散不稳定性的能力，无论这些不稳定性是细胞型还是振荡型，对后者的影响更为明显。发现泰勒色散通常会促进细胞不稳定性并阻碍振荡不稳定性。这是在燃烧环境中考虑泰勒色散的第一个稳定性分析，因此在燃烧和其他反应扩散领域都具有基本价值，与预测的现象可能很难通过实验重现这一事实无关。