小密度差，大理查德森数：浮力决定石膏在离心微流控汇流单元中的沉积位置
Small density differences, large Richardson numbers: buoyancy decides where gypsum deposits in a centifluidic confluence cell
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中文总结 AI 辅助
本文发现，即使密度差很小，浮力效应仍可通过大理查德森数显著影响石膏沉积位置，提出了沉积距离与理查德森数的标度关系，并强调仅小密度差不足以忽略浮力。
中文摘要 AI 辅助
在小通道中混合两种水溶液时，当两种溶液之间的密度差异仅为几个百分点或更小时，通常采用恒定密度模型进行模拟。本文研究了在氯化钙与硫酸钠相遇并形成石膏的汇流单元中，这一假设是否成立。对反应流的恒定密度模拟预测沉积发生在通道中心线沿线的底部。然而，在实验中，石膏却在两侧壁上形成带状沉积，且随着流速降低，沉积带起始位置向上游移动。染料实验采用了密度差为0.14%至2.1%的两种溶液、三种通道高度和32种流速，结果表明染料流到达对侧壁的距离由整体理查德森数Ri=g'H/U^2控制，并在Ri的四个数量级范围内遵循L/H=3.31Ri^{-0.66}（R^2=0.89）。当两种溶液的密度相等时，在大多数条件下染料流不再到达对侧壁，并且在密度匹配的反应实验中，石膏沉积在底部，正如恒定密度模拟所预测的那样。因此，较小的相对密度差并不是忽略浮力的充分条件：理查德森数也必须较小。对于离心微流控设备中典型的流速而言，理查德森数往往并不小。
英文摘要
The mixing of two aqueous streams in small channels is usually modeled with constant density when the difference in density between the streams is only a few percent or less. In this paper, we investigate whether this holds in a confluence cell where calcium chloride and sodium sulfate meet and form gypsum. A constant density simulation of the reacting flow results in deposition on the floor along the channel centreline. However, in the experiment, gypsum instead forms bands on both side walls, and the deposition bands start further upstream as the flow rate decreases. Dye experiments with density differences between the streams of 0.14 to 2.1\,\%, three channel heights, and 32 flow rates show that the distance at which the dyed stream reaches the opposite side wall is governed by the bulk Richardson number, $Ri=g'H/U^2$, and follows $L/H = 3.31\,Ri^{-0.66}$ over four decades of $Ri$ ($R^2=0.89$). When the two streams' densities match, the dyed stream no longer reaches the opposite wall under most conditions, and in a density-matched reacting experiment, gypsum deposits on the floor, as the constant-density simulation predicts. A small relative density difference is thus not a sufficient condition for neglecting buoyancy: the Richardson number must also be small. For the flow rates typical of centifluidic devices, it often is not.
发表机构
- Norwegian University of Science and Technology (NTNU)（挪威科技大学）
- Technical University of Denmark（丹麦技术大学）
- Universidad Autónoma de Madrid (UAM)（马德里自治大学）
- Eindhoven University of Technology（埃因霍温理工大学）
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