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Simulation of drop deformation and breakup in simple shear flow

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Abstract

The behavior of drops in the emulsion is significant in transport phenomena and the oil and the petrochemical industry. In this study, the behavior of drops that are close to each other was investigated. These drops were studied at two viscosity ratios (0.5 and 0.9, which are the viscosity ratio of drops to fluid) and six capillary numbers (0.05, 0.11, 0.17, 0.42, 0.28, and 0.36). The results demonstrate the effect of drops on each other at a range of volume fractions. Also, at capillary numbers of 0.42, 0.82, and 0.36, there were volume fractions at which drops stuck to each other and broke after combining. In contrast, the single drop at these new capillary numbers after merging was not broken. At the capillary number of 0.84, and volume fraction of 0.001495, the drops did not stick to each other, but they were broken under the influence of each other. For each capillary number, a specified volume fraction was achieved, at which the drops behave as a single drop. Therefore, in each capillary number, a volume fraction can be found so that in volume fractions less than that, drops behave individually and do not interact with each other.

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References

  1. Xu Z, Wang T, Che Z (2020) Droplet deformation and breakup in shear flow of air. Phys Fluids 32(5):052109

    Article  ADS  CAS  Google Scholar 

  2. Liang C et al (2018) Three-dimensional simulations of drop deformation and breakup in air flow and comparisons with experimental observations. Atom Sprays 28(7):621–641

    Article  Google Scholar 

  3. Amani A et al (2019) Numerical study of droplet deformation in shear flow using a conservative level-set method. Chem Eng Sci 207:153–171

    Article  CAS  Google Scholar 

  4. Wang D et al (2020) A lattice Boltzmann modeling of viscoelastic drops’ deformation and breakup in simple shear flows. Phys Fluids 32(12):123101

    Article  ADS  CAS  Google Scholar 

  5. Krzeczkowski SA (1980) Measurement of liquid droplet disintegration mechanisms. Int J Multiph Flow 6(3):227–239

    Article  CAS  Google Scholar 

  6. Faeth G, Hsiang L-P, Wu P-K (1995) Structure and breakup properties of sprays. Int J Multiph Flow 21:99–127

    Article  CAS  Google Scholar 

  7. Han J, Tryggvason G (1999) Secondary breakup of axisymmetric liquid drops. I. Acceleration by a constant body force. Phys Fluids 11(12):3650–3667

    Article  ADS  CAS  Google Scholar 

  8. Dai Z, Faeth G (2001) Temporal properties of secondary drop breakup in the multimode breakup regime. Int J Multiph Flow 27(2):217–236

    Article  CAS  Google Scholar 

  9. Helenbrook B, Edwards C (2002) Quasi-steady deformation and drag of uncontaminated liquid drops. Int J Multiph Flow 28(10):1631–1657

    Article  CAS  Google Scholar 

  10. Cao X-K et al (2007) A new breakup regime of liquid drops identified in a continuous and uniform air jet flow. Phys Fluids 19(5):057103

    Article  ADS  Google Scholar 

  11. Grace HP (1982) Dispersion phenomena in high viscosity immiscible fluid systems and application of static mixers as dispersion devices in such systems. Chem Eng Commun 14(3–6):225–277

    Article  CAS  Google Scholar 

  12. Rumscheidt F-D, Mason S (1961) Particle motions in sheared suspensions XII. Deformation and burst of fluid drops in shear and hyperbolic flow. J Colloid Sci 16(3):238–261

    Article  CAS  Google Scholar 

  13. Marks CR (1998) Drop breakup and deformation in sudden onset strong flows. University of Maryland, College Park

    Google Scholar 

  14. Taylor GI (1932) The viscosity of a fluid containing small drops of another fluid. Proc R Soc Lond Ser A, Contain Pap Math Phys Charact 138(834):41–48

    ADS  CAS  Google Scholar 

  15. Taylor GI (1934) The formation of emulsions in definable fields of flow. Proc R Soc Lond Ser A, Contain Pap Math Phys Charact 146(858):501–523

    ADS  CAS  Google Scholar 

  16. Li J, Renardy YY, Renardy M (2000) Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method. Phys Fluids 12(2):269–282

    Article  ADS  CAS  Google Scholar 

  17. Zhao X (2007) Drop breakup in dilute Newtonian emulsions in simple shear flow: new drop breakup mechanisms. J Rheol 51(3):367–392

    Article  ADS  CAS  Google Scholar 

  18. Vela-Martín A, Avila M (2021) Deformation of drops by outer eddies in turbulence. J Fluid Mech 929:A38

    Article  ADS  MathSciNet  Google Scholar 

  19. Müller-Fischer N et al (2008) Single bubble deformation and breakup in simple shear flow. Exp Fluids 45(5):917–926

    Article  Google Scholar 

  20. Komrakova A et al (2015) Effects of dispersed phase viscosity on drop deformation and breakup in inertial shear flow. Chem Eng Sci 126:150–159

    Article  CAS  Google Scholar 

  21. Kekesi T, Amberg G, Wittberg LP (2016) Drop deformation and breakup in flows with shear. Chem Eng Sci 140:319–329

    Article  CAS  Google Scholar 

  22. Shardt O, Mitra SK, Derksen J (2016) Simulations of charged droplet collisions in shear flow. Chem Eng J 302:314–322

    Article  CAS  Google Scholar 

  23. Wang D, Wang N, Liu H (2022) Droplet deformation and breakup in shear-thinning viscoelastic fluid under simple shear flow. J Rheol 66(3):585–603

    Article  ADS  CAS  Google Scholar 

  24. Renardy Y (2008) Effect of startup conditions on drop breakup under shear with inertia. Int J Multiph Flow 34(12):1185

    Article  CAS  Google Scholar 

  25. Renardy YY, Cristini V (2001) Effect of inertia on drop breakup under shear. Phys Fluids 13(1):7–13

    Article  ADS  MathSciNet  CAS  Google Scholar 

  26. Renardy Y, Cristini V, Li J (2002) Drop fragment distributions under shear with inertia. Int J Multiph Flow 28(7):1125–1147

    Article  CAS  Google Scholar 

  27. Khismatullin DB, Renardy Y, Cristini V (2003) Inertia-induced breakup of highly viscous drops subjected to simple shear. Phys Fluids 15(5):1351–1354

    Article  ADS  MathSciNet  CAS  Google Scholar 

  28. Håkansson A et al (2022) A criterion for when an emulsion drop undergoing turbulent deformation has reached a critically deformed state. Colloids Surf, A 648:129213

    Article  Google Scholar 

  29. Goldsmith H, Mason S (1962) The flow of suspensions through tubes. I. Single spheres, rods, and discs. J Colloid Sci 17(5):448–476

    Article  Google Scholar 

  30. Karnis A, Goldsmith H, Mason S (1963) Axial migration of particles in Poiseuille flow. Nature 200(4902):159–160

    Article  ADS  Google Scholar 

  31. Karnis A (1966) The flow of suspensions through tubes

  32. Hiller W, Kowalewski T (1986) An experimental study of the lateral migration of a droplet in a creeping flow. Exp Fluids 5(1):43–48

    Article  Google Scholar 

  33. Zhou H, Pozrikidis C (1993) The flow of suspensions in channels: single files of drops. Phys Fluids A 5(2):311–324

    Article  ADS  CAS  Google Scholar 

  34. Zhou H, Pozrikidis C (1994) Pressure-driven flow of suspensions of liquid drops. Phys Fluids 6(1):80–94

    Article  ADS  CAS  Google Scholar 

  35. Kamyabi A, Ahmad RSA, Kamyabi M (2015) Surfactant effects on the efficiency of oil sweeping from the dead ends: numerical simulation and experimental investigation. Chem Eng Res Des 94:173–181

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Department of Chemical Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

    Saeed Derakhshan, Ata Allah Kamyabi & Ali Mohebbi

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  1. Saeed Derakhshan
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  2. Ata Allah Kamyabi
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  3. Ali Mohebbi
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Correspondence to Ata Allah Kamyabi.

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Derakhshan, S., Kamyabi, A.A. & Mohebbi, A. Simulation of drop deformation and breakup in simple shear flow. Korea-Aust. Rheol. J. (2024). https://doi.org/10.1007/s13367-023-00085-8

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  • DOI: https://doi.org/10.1007/s13367-023-00085-8

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