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Ban T, Ishii H, Onizuka A, Chatterjee A, Suzuki RX, Nagatsu Y, Mishra M. Momentum transport of morphological instability in fluid displacement with changes in viscosity. Phys Chem Chem Phys 2024; 26:5633-5639. [PMID: 38288549 DOI: 10.1039/d3cp03402j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2024]
Abstract
Saffman-Taylor instability exhibits a stepwise unstable morphology from a stable interface to viscous fingering, eventually leading to tip splitting. The nonlinear dynamics of the destabilized interface depends on various flow properties. However, the physicochemical mechanism that determines the transition point of the flow state is unclear. We studied the interfacial instability transition in miscible displacement from a thermodynamic perspective by calculating the momentum transport and entropy production. Using numerical analysis based on Darcy's law coupled with the convection-diffusion equation, the observed flux-dependent flow state transitions were attributed to the selection of the flow state with a higher entropy production.
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Affiliation(s)
- Takahiko Ban
- Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Machikaneyamacho 1-3, Toyonaka City, Osaka 560-8531, Japan.
| | - Hibiki Ishii
- Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Machikaneyamacho 1-3, Toyonaka City, Osaka 560-8531, Japan.
| | - Atsushi Onizuka
- Division of Chemical Engineering, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Machikaneyamacho 1-3, Toyonaka City, Osaka 560-8531, Japan.
| | - Atanu Chatterjee
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Ryuta X Suzuki
- Department of Chemical Engineering, Tokyo University of Agriculture and Technology, Naka-cho 2-24-16, Koganei, Tokyo 184-8588, Japan
- PRESTO, Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan
| | - Yuichiro Nagatsu
- Department of Chemical Engineering, Tokyo University of Agriculture and Technology, Naka-cho 2-24-16, Koganei, Tokyo 184-8588, Japan
| | - Manoranjan Mishra
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140001, India
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Martyushev LM, Birzina AI. Morphological stability of an interface between two non-Newtonian fluids moving in a Hele-Shaw cell. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:013004. [PMID: 25679705 DOI: 10.1103/physreve.91.013004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2014] [Indexed: 06/04/2023]
Abstract
The problem of the morphological stability of an interface in the case of the displacement of one non-Newtonian fluid by another non-Newtonian fluid in a radial Hele-Shaw cell has been considered. Both fluids have been described by the two-parameter Ostwald-de Waele power-law model. The nonzero viscosity of the displacing fluid has been taken into account. A generalized Darcy's law for the system under consideration, as well as an equation for the determination of the critical size of morphological stability with respect to harmonic perturbations (linear analysis), has been derived. Morphological phase diagrams have been constructed, and the region of the parameters in which nonequilibrium reentrant morphological transitions are possible has been revealed.
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Affiliation(s)
- L M Martyushev
- Ural Federal University, Mira Street 19, Yekaterinburg, 620002 Russia
| | - A I Birzina
- Ural Federal University, Mira Street 19, Yekaterinburg, 620002 Russia and and Institute of Industrial Ecology, S. Kovalevskoi Street 20a, Yekaterinburg, 620219 Russia
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Martyushev LM, Konovalov MS. Thermodynamic model of nonequilibrium phase transitions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:011113. [PMID: 21867119 DOI: 10.1103/physreve.84.011113] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2011] [Indexed: 05/31/2023]
Abstract
Within the scope of a thermodynamic description using the maximum entropy production principle, transitions from one nonequilibrium (kinetic) regime to another are considered. It is shown that in the case when power-law dependencies of thermodynamic flux on force are similar for two regimes, only a transition accompanied by a positive jump of thermodynamic flux is possible between them. It is found that the difference in powers of the dependencies of thermodynamic fluxes on forces results in a number of interesting nonequilibrium transitions between kinetic regimes, including the reentrant one with a negative jump of thermodynamic flux.
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Affiliation(s)
- L M Martyushev
- Institute of Industrial Ecology, Russian Academy of Sciences, 20A Sophy Kovalevskaya Street, 620219 Ekaterinburg, Russia.
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