The international collaborative team of Tokyo University of Agriculture and Technology (TUAT) in Japan and Indian Institute of Technology Ropar (IIT Ropar) in India has explored, for the first time, viscous fingering (VF, one of classical interfacial hydrodynamics) of annular ring where VF in fluid of finite volume grow radially through combination of experiment and numerical simulation. They demonstrate that the VF of an annular ring is a persistent phenomenon in contrast to the transient nature of VF of a slice where VF in fluid of finite volume grow rectilinearly.
The researchers published their results in the Journal of Fluid Mechanics on Apr 6th, 2021.
When a less viscous fluid moves in a more viscous fluid in porous media, the interface between the two fluids becomes unstable and deforms in a finger shape. This phenomenon is technically called "Viscous fingering (VF)". Since the 1950s, the VF has been studied as one fluid dynamics issue. VF can be classified according to whether the less viscous fluid displace the more viscous one rectilinearly or radially.
"Classically, VF formed at an interface between two semi-infinite domains of different viscosity have been studied. However, recently, VF formed at either the front or the rear interface of the fluid of finite volume has attracted attention because such VF is relevant to chromatography, spreading of groundwater contamination, and enhanced-oil-recovery. So far, VFs formed in finite volume fluids in linear geometry have been mainly studied only by numerical simulation. However, VFs formed in finite volume fluids in radial geometry have been rarely studied experimentally or numerically." said Dr. Nagatsu, one of the corresponding authors on the paper, Associate Professor in the Department of Chemical Engineering at Tokyo University of Agriculture and Technology (TUAT). "This is because of the complexity of creating finiteness in experiments and difficulties in numerically solving the governing equations."
The research team succeeded in integrated analysis experiments and numerical simulation on VF formed in finite volume fluids in radial geometry (see Figure). The experiments are carried out using a water- glycerol miscible system in a Hele-Shaw cell which is an experimental apparatus to mimic the porous medium flows. The simulation is done using the two-phase Darcy law (TPDL) module of COMSOL (COMSOL Multiphysics®).
"Our team found that the VF of an annular ring is a persistent phenomenon in contrast to the transient nature of VF of a slice (see Figure). Although new fingers cease to appear after some time but due to the radial spreading of the area available for VF, a finite number of fingers always remain at a later time. Furthermore, we clearly showed that VF was observed only if the width of the finite layer exceeds some value," Dr. Mishra, one of the corresponding authors on the paper, Associate Professor in Department of Mathematics, Indian Institute of Technology Ropar, explains.
"Apparently our results shows that the dynamic of VF in annular ring is dramatically different from those classical radial VF and rectilinear VF with one fluid sandwiched between layers of another. VF in annular actually takes place in spreading of groundwater contamination, and enhanced-oil-recovery. Thus, our finding is expected to enable us to make highly accurate prediction of such processes," adds Nagatsu.
For more information about the Nagatsu laboratory, please visit http://web.tuat.ac.jp/~nagatsu/en/index.html
For more information about the Mishra laboratory, please visit http://www.iitrpr.ac.in/FD/Home.html
Viscous fingering of miscible annular ring
Vandita Sharma, Hamirul Bin Othman, Yuichiro Nagatsu and Manoranjan Mishra
Journal of Fluid Mechanics, 916, A14.
Acknowledgements. M.M. gratefully acknowledge the JSPS Invitation Fellowships for Research in Japan (no. L19548). M.M. and V.S. thank Global innovation research, Tokyo University of Agriculture and Technology (TUAT) and Y. Nagatsu for providing the local support during the research stays at TUAT. M.M. acknowledges the financial support from SERB, Government of India through project grant number MTR/2017/000283.
About Tokyo University of Agriculture and Technology (TUAT)
TUAT is a distinguished university in Japan dedicated to science and technology. TUAT focuses on agriculture and engineering that form the foundation of industry, and promotes education and research fields that incorporate them. Boasting a history of over 140 years since our founding in 1874, TUAT continues to boldly take on new challenges and steadily promote fields. With high ethics, TUAT fulfills social responsibility in the capacity of transmitting science and technology information towards the construction of a sustainable society where both human beings and nature can thrive in a symbiotic relationship. For more information, please visit http://www.tuat.ac.jp/en/.
About Indian Institute of Technology Ropar (IIT Ropar)
Indian Institute of Technology Ropar (IIT Ropar) is a premier engineering, science, and technology institute in India established in 2008 by the Ministry of Education, Govt. of India (formerly: Ministry of Human Resource Development (MHRD), Govt. of India). IIT Ropar has initiated research on socially relevant problems like water and air pollution, affordable point-of-care healthcare technologies, and artificial intelligence applied to solve future engineering challenges. IIT Ropar has made active research collaborations with the likes of MIT, SUNY, Cardiff University, Cambridge University to name a few. Department of Science of Technology (DST), Govt of India, has established a Technology Innovation Hub (TIH) in the application domain of Agriculture & Water, named as Agriculture and Water Technology Development Hub (AWaDH), at IIT Ropar in the framework of National Mission on Interdisciplinary Cyber-Physical Systems (NM-ICPS). The high standard of research has ensured that year-after-year IIT Ropar has the best research performance amongst newer IITs, in India and in world rankings like the QS Asia rankings (205th) and Times Higher Education World University rankings (301-350). The institute has made significant research investment in Industry 4.0 in partnership with the Government of Taiwan by setting up the Indo-Taiwan Joint Research Centre on Artificial Intelligence and Machine Learning, a one of its kind in India. For more information, please visit http://www.iitrpr.ac.in
Yuichiro Nagatsu, Ph.D.
Associate Professor, Department of Chemical Engineering, TUAT, Japan
Manoranjan Mishra, Ph.D.
Associate Professor, Department of Mathematics, Indian Institute of Technology Ropar, India
Journal of Fluid Mechanics