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Probing the influence of inertia, viscosity, and initial offset on the hydrodynamic interaction of droplet pairs in confined shear flow
Phys. Rev. Fluids 7, 123603 – Published 22 December, 2022
DOI: https://doi.org/10.1103/PhysRevFluids.7.123603
Abstract
Understanding the hydrodynamics of droplet collision is vitally important due to the inherent small-scale phenomena and various practical applications. The morphology, course trajectory, and final state of the droplets in such a collision are greatly affected by different physical parameters together with system geometry. Yet the collision behavior of droplet pairs at high density and viscosity ratios remains unexplored and unquantified, and therefore the critical density and viscosity ratios for the collision mode of droplets under geometric parameters were unknown. Through computational analyses, we address the interplay between the density ratio (60 to 800), the viscosity ratio (24 to 60), the initial offset, and the confinement on the coalescence of droplet pairs subjected to a confined shear flow. Simulations have been performed using a free-energy-based lattice Boltzmann method, with the aim of determining new regimes compared to the previous study. The results reveal that the coupling effect of density ratios and viscosity ratios contributes to generating inertia and viscous interaction forces that significantly impact the coalescence consequences. On the other hand, the wall confinement and the initial vertical offset of droplets are shown to play a significant role in either promoting or suppressing the collision mode of interacting droplets. Interestingly, we observe unusual trajectory motion of droplets for an intermediate range of density ratios (i.e., 245–600) near the critical initial offset of droplets. Regions of different collision modes are further presented in terms of phase diagrams, which reveal the critical dependency of droplet behavior on the coupling effect of density ratios, viscosity ratios, initial vertical offset, and confinement. The reported results are expected to provide new insights into the collision of pair droplets under confined shear flows in the effect of various parameters and help elucidate the intrinsic nature and the condition of coalescence.
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References (41)
- J. Xu, P. Cheng, and T. Zhao, Gas–liquid two-phase flow regimes in rectangular channels with mini/micro gaps, Int. J. Multiphase Flow 25, 411 (1999).
- T. Zhao and Q. Bi, Co-current air–water two-phase flow patterns in vertical triangular microchannels, Int. J. Multiphase Flow 27, 765 (2001).
- Y. Zhao, H. C. Shum, L. L. Adams, B. Sun, C. Holtze, Z. Gu, and D. A. Weitz, Enhanced encapsulation of actives in self-sealing microcapsules by precipitation in capsule shells, Langmuir 27, 13988 (2011).
- I. Halliday, R. Law, C. M. Care, and A. Hollis, Improved simulation of drop dynamics in a shear flow at low reynolds and capillary number, Phys. Rev. E 73, 056708 (2006).
- A. K. Haghighat, M. G. Olsen, R. D. Vigil, and A. Sarkar, Droplet coalescence and phase separation in a topical ointment: Effects of fluid shear and temperature, Int. J. Pharmaceut. 591, 119872 (2020).
- H. Tokumitsu, H. Ichikawa, Y. Fukumori, and L. H. Block, Preparation of gadopentetic acid-loaded chitosan microparticles for gadolinium neutron-capture therapy of cancer by a novel emulsion-droplet coalescence technique, Chem. Pharm. Bull. 47, 838 (1999).
- Y.-J. Zhao, X.-W. Zhao, J. Hu, J. Li, W.-Y. Xu, and Z.-Z. Gu, Multiplex label-free detection of biomolecules with an imprinted suspension array, Angew. Chem., Int. Ed. 48, 7350 (2009).
- Y. Zhao, Z. Xie, H. Gu, C. Zhu, and Z. Gu, Bio-inspired variable structural color materials, Chem. Soc. Rev. 41, 3297 (2012).
- J.-J. Elmendrop and A.-K. Van Der Vegt, A study on polymer blending microrheology: Part IV. The influence of coalescence on blend morphology origination, Polymer Engineering & Science, 26, 1332 (1986).
- M. Minale, J. Mewis, and P. Moldenaers, Study of the morphological hysteresis in immiscible polymer blends, AIChE J. 44, 943 (1998).
- A. Ramic, S. Hudson, A. Jamieson, and I. Manas-Zloczower, Temporary droplet-size hysteresis in immiscible polymer blends, Polymer 41, 6263 (2000).
- L. Nilsson and B. Bergenståhl, Adsorption of hydrophobically modified starch at oil/water interfaces during emulsification, Langmuir 22, 8770 (2006).
- L. Lobo and A. Svereika, Coalescence during emulsification, J. Colloid Interface Sci. 261, 498 (2003).
- S. M. Jafari, E. Assadpoor, Y. He, and B. Bhandari, Re-coalescence of emulsion droplets during high-energy emulsification, Food Hydrocoll. 22, 1191 (2008).
- D. Wasan, S. Shah, N. Aderangi, M. Chan, and J. McNamara, Observations on the coalescence behavior of oil droplets and emulsion stability in enhanced oil recovery, Soc. Pet. Eng. J. 18, 409 (1978).
- D. Wasan, J. McNamara, S. Shah, K. Sampath, and N. Aderangi, The role of coalescence phenomena and interfacial rheological properties in enhanced oil recovery: An overview, J. Rheol. 23, 181 (1979).
- A.-K. Chesters, The modeling of coalescence processes in fluid-liquid dispersions: A review of current understanding, Chemical Engineering Research and Design: transactions of the Institution of Chemical Engineers: Part A 69, 259 (1991).
- P. De Bruyn, R. Cardinaels, and P. Moldenaers, The effect of geometrical confinement on coalescence efficiency of droplet pairs in shear flow, J. Colloid Interface Sci. 409, 183 (2013).
- P. De Bruyn, D. Chen, P. Moldenaers, and R. Cardinaels, The effects of geometrical confinement and viscosity ratio on the coalescence of droplet pairs in shear flow, J. Rheol. 58, 1955 (2014).
- S. Guido and M. Simeone, Binary collision of drops in simple shear flow by computer-assisted video optical microscopy, J. Fluid Mech. 357, 1 (1998).
- O. Shardt, J. Derksen, and S. K. Mitra, Simulations of droplet coalescence in simple shear flow, Langmuir 29, 6201 (2013).
- B. Huang, H. Liang, and J. Xu, Lattice Boltzmann simulation of binary three-dimensional droplet coalescence in a confined shear flow, Phys. Fluids 34, 032101 (2022).
- D. Chen, R. Cardinaels, and P. Moldenaers, Effect of confinement on droplet coalescence in shear flow, Langmuir 25, 12885 (2009).
- Y. Chen and C. Wang, Hydrodynamic interaction of two deformable drops in confined shear flow, Phys. Rev. E 90, 033010 (2014).
- K. Sarkar and R. K. Singh, Spatial ordering due to hydrodynamic interactions between a pair of colliding drops in a confined shear, Phys. Fluids 25, 051702 (2013).
- M. Bayareh and S. Mortazavi, Binary collision of drops in simple shear flow at finite reynolds numbers: Geometry and viscosity ratio effects, Adv. Eng. Softw. 42, 604 (2011).
- M. Loewenberg and E. Hinch, Collision of two deformable drops in shear flow, J. Fluid Mech. 338, 299 (1997).
- T. Lee and L. Liu, Lattice Boltzmann simulations of micron-scale drop impact on dry surfaces, J. Comput. Phys. 229, 8045 (2010).
- T. Lee, Effects of incompressibility on the elimination of parasitic currents in the lattice Boltzmann equation method for binary fluids, Comput. Math. Appl. 58, 987 (2009).
- S. Farokhirad, J. F. Morris, and T. Lee, Coalescence-induced jumping of droplet: Inertia and viscosity effects, Phys. Fluids 27, 102102 (2015).
- R. Zhang, S. Farokhirad, T. Lee, and J. Koplik, Multiscale liquid drop impact on wettable and textured surfaces, Phys. Fluids 26, 082003 (2014).
- S. Farokhirad and T. Lee, Computational study of microparticle effect on self-propelled jumping of droplets from superhydrophobic substrates, Int. J. Multiphase Flow 95, 220 (2017).
- S. Farokhirad, M. Mohammadi Shad, and T. Lee, Coalescence-induced jumping of immersed and suspended droplets on microstructured substrates, Eur. J. Comput. Mech. 26, 205 (2017).
- A. Mohamad, Lattice Boltzmann Method, Vol. 70 (Springer, Berlin, 2011).
- P. L. Bhatnagar, E. P. Gross, and M. Krook, A model for collision processes in gases. i. small amplitude processes in charged and neutral one-component systems, Phys. Rev. 94, 511 (1954).
- X. He, X. Shan, and G. D. Doolen, Discrete Boltzmann equation model for nonideal gases, Phys. Rev. E 57, R13(R) (1998).
- D. Lee, J.-Y. Huh, D. Jeong, J. Shin, A. Yun, and J. Kim, Physical, mathematical, and numerical derivations of the cahn–hilliard equation, Comput. Mater. Sci. 81, 216 (2014).
- P. Yue, C. Zhou, and J. Feng, Sharp-interface limit of the cahn–hilliard model for moving contact lines, J. Fluid Mech. 645, 279 (2010).
- P. Yue and J. Feng, Can diffuse-interface models quantitatively describe moving contact lines? Eur. Phys. J. Spec. Top. 197, 37 (2011).
- D. Jacqmin, Calculation of two-phase navier–stokes flows using phase-field modeling, J. Comput. Phys. 155, 96 (1999).
- S. Frijters, F. Günther, and J. Harting, Effects of nanoparticles and surfactant on droplets in shear flow, Soft Matter 8, 6542 (2012).
