Numerical investigation of viscous fingering in Hele-Shaw cell with spatially periodic variation of depth

doi:10.1007/s10483-016-2017-9

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (1): 45-58.doi: https://doi.org/10.1007/s10483-016-2017-9

Numerical investigation of viscous fingering in Hele-Shaw cell with spatially periodic variation of depth

Jiangping HU¹, Bofu WANG², Dejun SUN¹

1. Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China;
2. School of Power and Mechanical Engineering, Wuhan University, Wuhan 430071, China

收稿日期:2015-03-25 修回日期:2015-06-17 出版日期:2016-01-01 发布日期:2016-01-01
通讯作者: Bofu WANG E-mail:dsun@ustc.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 11232011) and the 111 Project of China (No. B07033)

Numerical investigation of viscous fingering in Hele-Shaw cell with spatially periodic variation of depth

Jiangping HU¹, Bofu WANG², Dejun SUN¹

1. Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China;
2. School of Power and Mechanical Engineering, Wuhan University, Wuhan 430071, China

Received:2015-03-25 Revised:2015-06-17 Online:2016-01-01 Published:2016-01-01
Contact: Bofu WANG E-mail:dsun@ustc.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11232011) and the 111 Project of China (No. B07033)

摘要/Abstract

摘要：

Viscous fingering in a modified Hele-Shaw cell is numerically investigated. The cell allows periodic variation of depth in the lateral direction. The wavenumber n of the depth perturbation has great influence on fingering patterns. For n=1, the fingering pattern due to the interface instability remains the same as that in the conventional HeleShaw cell, while the depth variation causes the steady finger to be a little narrower. For n=2, four different fingering patterns are captured, similar to the available experimental observations in a modified Hele-Shaw cell containing a centered step-like occlusion. It is found that new fingering patterns appear as n further increases, among which, two patterns with spatial oscillation along both edges of the finger are particularly interesting. One is a symmetric oscillatory finger for n=3, and the other is an asymmetric one for n=4. The influence of capillary number on fingering patterns is studied for n=3 and 4. We find that spatial oscillation of the finger nearly ceases at moderate capillary numbers and occurs again as the capillary number increases further. Meanwhile, the wide finger shifts to the narrow one. It is accompanied by a sudden decrease in the finger width which otherwise decreases continuously as the capillary number increases. The wavenumber and the amplitude of depth perturbation have little effect on the finger width.

关键词: pattern formation, interfacial instability, viscous fingering, Hele-Shaw cell

Abstract:

Key words: Hele-Shaw cell, interfacial instability, pattern formation, viscous fingering

中图分类号:

Jiangping HU, Bofu WANG, Dejun SUN. Numerical investigation of viscous fingering in Hele-Shaw cell with spatially periodic variation of depth[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(1): 45-58.

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Numerical investigation of viscous fingering in Hele-Shaw cell with spatially periodic variation of depth

Numerical investigation of viscous fingering in Hele-Shaw cell with spatially periodic variation of depth

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