The use of transported probability density function (TPDF) models to predict soot has the strong advantage that the effects of turbulent fluctuations on soot source terms can be rigorously accounted for. However, soot processes are closely coupled to gas-phase composition. Among the open issues for gas-phase micro-mixing is the species-dependence of mixing timescales. The objective is to carry out an evaluation on the effect of incorporating differential mixing timescales among gas-phase species in a TPDF simulation for soot prediction. A DNS having the configuration of a temporally evolving, non-premixed ethylene flame with a four-step, three-moment soot model is considered as the target for evaluation. The DNS dataset is applied to provide key inputs for TPDF simulations to limit the sources of error to micro-mixing. TPDF simulations with the interaction by exchange with the mean (IEM) and modified Curl (MC) models, which impose the same mixing timescale to all species, underpredict soot mass fraction and overpredict extinction levels regardless of the prescribed mixing frequency. By incorporating differential mixing timescales among gas-phase species, IEM-DD and MC-DD models yield notable improvement in predictions of the overall extinction and soot levels, highlighting the benefit of accounting for differential mixing timescales. A TPDF simulation with the Euclidean minimum spanning tree (EMST) model yields even better predictions, illustrating that the localness in composition space remains a critical issue. The indicated species mixing frequencies by the EMST model are shown to follow the DNS results qualitatively, illustrating that the micro-mixing process based on the Euclidean distance in composition space reproduces to a certain extent the differential mixing timescales due to reaction. Finally, it is shown that incorporating differential mixing timescales of soot moments is expected to have limited value as the mixing timescales of soot moments are sufficiently large to safely neglect soot mixing.

使用传输概率密度函数（TPDF）模型来预测烟尘具有强大的优势，可以严格考虑湍流波动对烟尘源项的影响。但是，烟灰过程与气相组成紧密相关。气相微混合的开放问题之一是混合时间尺度的物种依赖性。目的是评估在TPDF模拟中将气相中不同混合时间尺度纳入烟尘预测的效果。具有四步三矩烟灰模型的，具有随时间变化的非预混合乙烯火焰构型的DNS被视为评估的目标。DNS数据集用于为TPDF模拟提供关键输入，以将错误源限制为微混合。通过与均值（IEM）和改良的Curl（MC）模型进行交互来进行交互作用的TPDF模拟，这对所有物种施加了相同的混合时间尺度，低估了烟灰质量分数，而高估了灭绝水平，而与规定的混合频率无关。通过在气相物质中纳入不同的混合时间尺度，IEM-DD和MC-DD模型在总体灭绝和烟灰水平的预测方面取得了显着改善，突出了考虑不同的混合时间尺度的好处。用欧几里得最小生成树（EMST）模型进行的TPDF仿真得出了更好的预测，说明合成空间中的局部性仍然是一个关键问题。EMST模型指示的物种混合频率显示出定性地遵循DNS结果，这说明基于组成空间中欧几里得距离的微混合过程在一定程度上再现了由于反应引起的混合时间尺度的差异。最终，表明，由于烟灰矩的混合时间尺度足够大以安全地忽略了烟灰混合，因此预期掺入烟灰矩的不同混合时间尺度将具有有限的价值。