Dispersion induced by unsteady diffusion-driven flow in a parallel-plate channel
Dispersion induced by unsteady diffusion-driven flow in a parallel-plate channel
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DOI：
10.1103/physrevfluids.8.084501
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发表时间：
2023-04
影响因子：
2.7
通讯作者：
Lingyun Ding;R. McLaughlin
中科院分区：
文献类型：
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作者：
Lingyun Ding;R. McLaughlin
我们调查扩散驱动的流动在平行板通道域与线性密度分层，这是由于重力和扩散的密度分层流体的综合影响。在Boussinesq近似下，我们用本征函数展开法计算了含时扩散驱动流和扰动密度场。在槽道域中，非定常流根据施密特数和无量纲化的分层标量扩散系数之间的关系单调或非单调（高度振荡）地收敛到定常解，而半空间斜面问题中的流对所有参数都表现出振荡收敛。为了验证Boussinesq近似，我们提出了准Boussinesq近似，其中包括横向密度变化的惯性项。数值解表明，Boussinesq和准Boussinesq近似之间的相对差异是一致的小。我们还研究了由非定常扩散驱动流的平流引起的被动示踪剂的混合，并给出了随时间变化的有效扩散系数的级数表示。对于小的施密特数，诱导的非定常流的解决方案的有效扩散系数可以振荡的振幅大于诱导的长时间限制的稳态流的有效扩散系数。有趣的是，在某些参数范围内，非稳态流解可以暂时降低与时间相关的有效扩散系数，甚至低于没有流动时纯分子扩散产生的系数。然而，在长时间内，有效扩散显着增强大的P'eclet数。
We investigate diffusion-driven flows in a parallel-plate channel domain with linear density stratification, which arise from the combined influence of gravity and diffusion in density-stratified fluids. We compute the time-dependent diffusion-driven flows and perturbed density field using eigenfunction expansions under the Boussinesq approximation. In channel domain, the unsteady flow converges to a steady-state solution either monotonically or non-monotonically (highly oscillatory), depending on the relation between the Schmidt number and the non-dimensionalized stratified scalar diffusivity, while the flow in the half-space inclined plane problem exhibits oscillatory convergence for all parameters. To validate the Boussinesq approximation, we propose the quasi-Boussinesq approximation, which includes transverse density variation in the inertial term. Numerical solutions show that the relative difference between the Boussinesq and quasi-Boussinesq approximations is uniformly small. We also study the mixing of a passive tracer induced by the advection of the unsteady diffusion-driven flow and present the series representation of the time-dependent effective diffusion coefficient. For small Schmidt numbers, the effective diffusion coefficient induced by the unsteady flow solution can oscillate with an amplitude larger than the effective diffusion coefficient induced by the long-time-limiting steady-state flow. Interestingly, the unsteady flow solution can reduce the time-dependent effective diffusion coefficient temporally in some parameter regimes, below even that produced by pure molecular diffusion in the absence of a flow. However, at long times, the effective diffusion is significantly enhanced for large P\'eclet numbers.