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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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Tsushima K, Itatani M, Fang Q, Nabika H. Role of Stochasticity in Helical Self-Organization during Precipitation. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2023; 39:249-255. [PMID: 36541612 DOI: 10.1021/acs.langmuir.2c02441] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
Spontaneous pattern formation with a well-defined periodicity is ubiquitous in nature. The Liesegang phenomenon is a chemical model of such a spontaneous pattern formation. In this study, we investigated the role of stochasticity in reaction-diffusion precipitation processes by demonstrating the temperature dependence of spontaneous symmetry breaking and helix formation in the Liesegang pattern with CuCrO4 precipitates; experimental analysis and numerical simulations based on reaction-diffusion equations were used. At high temperatures, helices with no, single, and double branches appeared in addition to the discrete parallel band characteristic of the Liesegang phenomenon. The probability of helix formation increased drastically when the experimental temperature during the pattern formation exceeded 20 °C. Moreover, the spacing coefficient, quantitatively representing the periodicity of obtained patterns, increased at high temperatures. Numerical simulations were performed to investigate the temperature dependence of the probability of helix formation and spacing coefficients. The stochasticity of the initial chemical reaction, which can trigger consequent nucleation and crystal growth, critically affected the probability of helix formation and the spacing coefficient. These features were explained in the framework of the prenucleation model by considering the degree of stochasticity in the initial chemical reaction step.
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Affiliation(s)
- Kotori Tsushima
- Graduate School of Science and Engineering, Yamagata University, 1-4-12, Kojirakawa, Yamagata990-8560, Japan
| | - Masaki Itatani
- Graduate School of Science and Engineering, Yamagata University, 1-4-12, Kojirakawa, Yamagata990-8560, Japan
| | - Qing Fang
- Faculty of Science, Yamagata University, 1-4-12, Kojirakawa, Yamagata990-8560, Japan
| | - Hideki Nabika
- Faculty of Science, Yamagata University, 1-4-12, Kojirakawa, Yamagata990-8560, Japan
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