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浙江大学学报(工学版)
浙江大学学报(工学版)  2023, Vol. 57 Issue (5): 967-976    DOI: 10.3785/j.issn.1008-973X.2023.05.013
土木与交通工程     
基于微流控芯片模型的渗流实验与数值模拟
聂绍凯(),刘鹏飞,巴特*(),陈云敏
浙江大学 岩土工程研究所，浙江 杭州，310058
Seepage experiment and numerical simulation based on microfluidic chip model
Shao-kai NIE(),Peng-fei LIU,Te BA*(),Yun-min CHEN
Institute of Geotechnical Engineering, Zhejiang University, Hangzhou 310058, China
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摘要：

基于微流控芯片加工技术，采用显微镜-微观模型实验装置，通过制作准二维微流控芯片模型来模拟多孔介质内部的骨架及孔隙结构，开展多孔介质渗流实验. 通过测量芯片模型两端的压降并进行修正，计算芯片模型的渗透率. 采用计算流体力学方法(CFD)对渗流过程进行数值模拟，并与实验结果进行对比分析. 结果表明：在相同条件下，相对于微柱方形排列的芯片模型，微柱错开排列的芯片模型在微观上表现为迂曲度增大，增大的幅值为5.1%~7.9%；在宏观上表现为流阻和压降更大，渗透率更低，降低的幅值为4.5%~7.4%. 芯片模型渗透率不仅与内部孔隙通道结构和孔隙率有关，还与颗粒直径和颗粒排列方式相关. 当模型孔隙率为0.327~0.900时，数值模拟方法所得的微流控芯片模型的渗透率与实验所测结果接近，误差为9.78%~28.43%. Kozeny-Carman (KC)公式不能准确预测实验结果，并且最大误差为73.97%. 提出修正平行板间导管流（平板流）渗流公式预测准二维微流控芯片模型渗透率，预测渗透率曲线与数值模拟和实验数据具有很好的一致性.
关键词： 多孔介质;  渗透率;  微流控芯片模型;  Kozeny-Carman方程;  平板流    
Abstract:

Based on the microfluidic chip processing technology and using the microscopy-micromodel experimental system, the seepage experiment was performed by fabricating the quasi-two dimensional microfluidic chip model to imitate the internal skeleton and pore structure of porous media. The permeability of chip model was calculated by measuring and modifying the pressure drop of both end of the chip model. Computational fluid dynamics (CFD) method was adopted to make the numerical simulation of the seepage process compared with the results of experiment. Under the same condition, compared with the chip model with the square arrangement micro-pillar, the chip model with staggered micro-pillar showed that the tortuosity increased with an amplitude of 5.1%—7.9% microscopically, the flow resistance and pressure drop increased and the permeability decreased with an amplitude of 4.5%—7.4% macroscopically. The permeability of chip models was not only related to the internal pore structure and porosity, but also related to particle diameter and particle arrangement. When the porosity of model was 0.327—0.900, the permeability of the chip model obtained by the numerical simulation method was closed to the experimental results with the error of 9.78%—28.43%. Kozeny-Carman (KC) equation could not predict the experiment results correctly and the maximum error was 73.97%. A modified parallel plate duct flow equation was proposed to predict the permeability of quasi-two dimensional microfluidic chip model. The curve of predicted permeability was consistent well with the numerical and experimental data.nt well with the numerical and experimental data.
Key words: porous media    permeability    microfluidic chip model    Kozeny-Carman equation    parallel plate duct flow
收稿日期: 2022-05-10 出版日期: 2023-05-09
CLC:  TU 443  
基金资助: 国家自然科学基金资助项目(51988101)
通讯作者: 巴特     E-mail: nsk@zju.edu.cn;ba-te@zju.edu.cn
作者简介: 聂绍凯（1995—），男，博士生，从事多孔介质渗流理论研究. orcid.org/0000-0002-0887-0241. E-mail: nsk@zju.edu.cn
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引用本文:

聂绍凯,刘鹏飞,巴特,陈云敏. 基于微流控芯片模型的渗流实验与数值模拟[J]. 浙江大学学报(工学版), 2023, 57(5): 967-976.

Shao-kai NIE,Peng-fei LIU,Te BA,Yun-min CHEN. Seepage experiment and numerical simulation based on microfluidic chip model. Journal of ZheJiang University (Engineering Science), 2023, 57(5): 967-976.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2023.05.013    或    https://www.zjujournals.com/eng/CN/Y2023/V57/I5/967

图 1  显微镜-微观模型实验装置
芯片模型 $ L $ $ /\mathrm{m}\mathrm{m} $ $W/\mathrm{m}\mathrm{m}$ $D/{\text{μm}}$ $h/{\text{μm}}$ $D/\text{μ}\mathrm{m}$ $ \varepsilon $
1) 注：Sq为方形排列；St为错开排列；Sq 0.60-500的孔隙率为0.60，微柱直径为 $ 500 $ μm的方形排列芯片模型，其他依此类推，O为孔喉直径，ε为孔隙率.
Sq 0.60-500 20 10 500 50 207.0 0.60
Sq 0.60-1000 20 10 1 000 50 414.0 0.60
Sq 0.60-1500 20 10 1 500 50 621.0 0.60
Sq 0.60-2000 20 10 2 000 50 828.0 0.60
St 0.60-500 20 10 500 50 258.5 0.60
St 0.60-1000 20 10 1 000 50 519.7 0.60
St 0.60-1500 20 10 1 500 50 779.5 0.60
St 0.60-2000 20 10 2 000 50 1 039.3 0.60
St 0.54-500 20 10 500 50 207.0 0.54
St 0.54-1000 20 10 1 000 50 414.0 0.54
St 0.54-1500 20 10 1 500 50 621.0 0.54
St 0.54-2000 20 10 2 000 50 828.0 0.54
表 1  实验芯片模型类型及内部结构参数1)
图 2  数值模拟物理模型示意图
图 3  数值模拟物理模型的网格独立性检验和正确性验证
图 4  当孔隙率为 $ 0.60 $时不同微柱直径芯片模型的实验单位压降随流速的变化规律
图 5  当孔隙率 $ \mathbf{为}0.60 $时不同微柱直径和排列方式下实验流阻随流量变化规律
图 6  不同类型芯片模型的渗透率对比
图 7  芯片模型预测渗透率与实验值、模拟值的对比
图 8  芯片模型流线示意图
图 9  不同类型芯片模型平均迂曲度对比
图 10  当流量为10 µL/min、孔隙率为0.60时，旋转角 $ \mathit{\theta } $对芯片模型(D=1 000 µm)速度分布的影响
图 11  旋转角和孔喉直径对微柱错开排列芯片模型渗透率的影响
图 12  不同旋转角下芯片模型的平均迂曲度值
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