News Release

Great progress in interfacial hydrodynamics combined with chemical thermodynamics

A new study has succeeded in numerically reproducing the topological change of interfacial hydrodynamics caused by partial miscibility

Peer-Reviewed Publication

Tokyo University of Agriculture and Technology

Numerical simulation results (time evolution of concentration field (c))

image: Fig. Numerical simulation results (time evolution of concentration field (c)). (a) Fully miscible system, (b) Partially miscible system (phase separation effect : weak), (c) Partially miscible system (phase separation effect: medium), (d) Partially miscible system (phase separation effect: strong) at successive dimensionless times t = 1000, 2000, 3000, 4000, from top to bottom. The scale bar is shown at the right. (a) In the fully miscible system, typical viscous fingering is formed. (b ~ d) In the partially miscible system, as the strength of phase separation increases, the viscous fingering changes to a droplet formation pattern. view more 

Credit: Yuichiro Nagatsu/TUAT, Takahiko Ban/Osaka University, Manoranjan Mishra/IIT Ropar

The international collaborative team of Tokyo University of Agriculture and Technology (TUAT) in Japan, Osaka University in Japan, and Indian Institute of Technology Ropar (IIT Ropar) in India has succeeded for the first time in numerically reproducing a topological change of viscous fingering (one of classical interfacial hydrodynamics), which is driven by a partial miscibility, where the two liquids do not mix completely with finite solubility. This is obtained by designing a new mathematical model that incorporates the phase separation resulting from partial miscibility and the effect of the spontaneously generated liquid flow during the phase separation into a set of equations of fluid dynamics that describes conventional viscous fingering.

The researchers published their results in the Journal of Fluid Mechanics on March 15th, 2022.

Viscous fingering (VF) is a classical interfacial hydrodynamic problem, in which a finger-like interfacial pattern is formed when a more viscous fluid is displaced by a less viscous fluid in a porous medium. This problem has been studied since the 1950s. Until very recently, it is widely accepted that the properties can be classified according to whether the two fluids are fully miscible or immiscible. “It is very recently (in 2017) that studies of partially miscible VFs were first reported by numerical simulations. This is because chemical thermodynamics is necessary to describe partial miscibility. In these numerical studies, the characteristics of partial miscibility induced some quantitative differences, but did not induce qualitative differences among fully miscible and immiscible VF dynamics.” said Dr. Nagatsu, one of the corresponding authors on the paper, Professor in the Department of Chemical Engineering at TUAT. “In 2020, for the first time, our research group succeeded in experimental research on partially miscible VF. We discovered that the fingering interface changes topologically in a partially miscible system, that is, the fingering interface is torn and forms droplets, which is qualitatively different from that of a fully miscible system or an immiscible system. For complete elucidation of this mechanism, a mathematical model and its numerical simulation to reproduce the experimental results are required.” add Dr. Nagatsu.

“The research team, for the first time, has succeeded in providing a mathematical model and numerical simulation that can reproduce the experimental results of topological change in a partially miscible VF pattern induced by a phase separation.” Dr. Mishra, one of the corresponding authors on the paper, Professor in the Department of Mathematics, IIT Ropar, explains. “This was achieved by incorporating spinodal decomposition effects and the so-called Korteweg force (a body force originating during spinodal decomposition) as chemical thermodynamic effects into the classical miscible VF model; these factors were not considered in previous numerical studies,” said Dr. Ban, one of the corresponding authors on the paper, Associate Professor in the Department of Chemical Engineering at Osaka University.

“This model and simulation will be useful in elucidating the mechanism of the experimental results currently under investigation, such as the effect of the flow rate on the dynamics. In turn, an approach will be possible in which we find new dynamics of VF with a phase separation through numerical experiments with this model, which we will verify experimentally. Therefore, this study enables us to collaborate on this subject through experimentation and numerical simulations, thus paving the way for a comprehensive understanding of partially miscible VF with a phase separation, which is still a new discipline.” Nagatsu said. In addition, the VF in partially miscible systems is strongly relevant to high-pressure and/or high-temperature processes, such as enhanced oil recovery and CO2 sequestration. Therefore, this study can contribute to establishing highly efficient processes involving VF with phase separation in such processes.


This work was supported by JSPS KAKENHI Grant nos 19J12553 and 19K04189. M.M. gratefully acknowledge the JSPS Invitation Fellowships for Research in Japan (no. L19548).

For more information about the Nagatsu laboratory, please visit


Original publication

Numerical study on topological change of viscous fingering induced by a phase separation with Korteweg force

Shoji Seya, Ryuta X. Suzuki, Yuichiro Nagatsu, Takahiko Ban, and Manoranjan Mishra

Journal of Fluid Mechanics 938 A18


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


About Osaka University  

Osaka University was founded in 1931 as one of the seven imperial universities of Japan and is now one of Japan's leading comprehensive universities with a broad disciplinary spectrum. This strength is coupled with a singular drive for innovation that extends throughout the scientific process, from fundamental research to the creation of applied technology with positive economic impacts. Its commitment to innovation has been recognized in Japan and around the world, being named Japan's most innovative university in 2015 (Reuters 2015 Top 100) and one of the most innovative institutions in the world in 2017 (Innovative Universities and the Nature Index Innovation 2017). Now, Osaka University is leveraging its role as a Designated National University Corporation selected by the Ministry of Education, Culture, Sports, Science and Technology to contribute to innovation for human welfare, sustainable development of society, and social transformation.  



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



Yuichiro Nagatsu, Ph.D.

Professor, Department of Chemical Engineering, TUAT, Japan


Takahiko Ban, Ph.D.

Associate Professor, Graduate School of Engineering Science, Osaka University, Japan


Manoranjan Mishra, Ph.D.

Professor, Department of Mathematics, Indian Institute of Technology Ropar, India

Disclaimer: AAAS and EurekAlert! are not responsible for the accuracy of news releases posted to EurekAlert! by contributing institutions or for the use of any information through the EurekAlert system.