By Matt Pullen, B.Sc.Reviewed by Matt Pullen, B.Sc.Jun 8 2022
An international collaborative group, for the first time, has been successful in reproducing a topological change of viscous fingering in a numeric manner.
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. Image Credit: Yuichiro Nagatsu/TUAT, Takahiko Ban/Osaka University, Manoranjan Mishra/IIT Ropar.
The group included researchers from the Tokyo University of Agriculture and Technology (TUAT) in Japan, Osaka University in Japan, and the Indian Institute of Technology Ropar (IIT Ropar) in India.
Viscous fingering (known to be one of classical interfacial hydrodynamics) is forced by partial miscibility, where the two liquids do not get mixed entirely with finite solubility.
This has been achieved by developing a new mathematical model that integrates the phase separation leading to partial miscibility and the impact of the freely produced liquid flow at the time of the phase separation into a set of equations of fluid dynamics that explains traditional viscous fingering.
The scientists reported their outcomes in the Journal of Fluid Mechanics on March 15th, 2022.
Viscous fingering (VF) is known to be a classical interfacial hydrodynamic issue, in which a finger-like interfacial pattern has been developed while a highly viscous fluid has been shifted by a less viscous fluid in a porous medium.
Since the 1950s, this issue has been researched. Until recently, it was widely assumed that the properties of two fluids could be classified based on whether they were wholly 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.
Dr Yuichiro Nagatsu, Study Corresponding Author and Professor, Department of Chemical Engineering, Tokyo University of Agriculture and Technology
Dr. Nagatsu added, “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.”
Dr. Nagatsu continued, “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,” concluded 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,” stated Dr. Mishra, one of the corresponding authors on the paper, and Professor in the Department of Mathematics, IIT Ropar.
“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,” stated Dr. Ban, one of the corresponding authors on the paper and 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.
Dr Yuichiro Nagatsu, Study Corresponding Author and Professor, Department of Chemical Engineering, Tokyo University of Agriculture and Technology
Nagatsu added, “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.”
Besides, the VF in partially miscible systems has been strongly relevant to high-pressure and/or high-temperature processes, such as improved oil recovery and CO2 sequestration. Thus, this study could add to establishing greatly efficient processes such as VF with phase separation performed in such processes.
Journal Reference:
Seya, S., et al. (2022) Numerical study on topological change of viscous fingering induced by a phase separation with Korteweg force. Journal of Fluid Mechanics. doi.org/10.1017/jfm.2022.158