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Two-dimensional Janus drops in shear: deformation, rotation and their coupling

Published online by Cambridge University Press:  06 December 2023

Chun-Yu Zhang Open the ORCID record for Chun-Yu Zhang [Opens in a new window] ,
Jia-Lei Chen ,
Li-Juan Qian  and
Hang Ding Open the ORCID record for Hang Ding [Opens in a new window]
Chun-Yu Zhang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027,PR China
Jia-Lei Chen
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027,PR China
Li-Juan Qian
Affiliation:
College of Mechanical and Electrical Engineering, China Jiliang University, Hangzhou 310018, PR China
Hang Ding*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027,PR China
*
†Email address for correspondence: hding@ustc.edu.cn
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Abstract

In this work, the dynamics of two-dimensional rotating Janus drops in shear flow is studied numerically using a ternary-fluid diffuse interface method. The rotation of Janus drops is found to be closely related to their deformation. A new deformation parameter $D$ is proposed to assess the significance of the drop deformation. According to the maximum value of $D$ ($D_{max}$), the deformation of rotating Janus drops can be classified into linear deformation ($D_{max}\le 0.2$) and nonlinear deformation ($D_{max}> 0.2$). In particular, $D_{max}$ in the former depends linearly on the Reynolds and capillary numbers, which can be interpreted by a mass–spring model. Furthermore, the rotation period $t_R$ of a Janus drop is found to be more sensitive to the drop deformation than to the aspect ratio of the drop at equilibrium. By introducing a corrected shear rate and an aspect ratio of drop deformation, a rotation model for Janus drops is established based on Jeffery's theory for rigid particles, and it agrees well with our numerical results.

JFM classification

Complex Fluids: Suspensions Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 976 , 10 December 2023 , A29
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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Footnotes

‡

Present address: Microsoft Azure AI.

References

Aidun, C.K., Lu, Y.N. & Ding, E.J. 1998 Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. J. Fluid Mech. 373, 287–311.CrossRefGoogle Scholar
Bartok, W. & Mason, S.G. 1958 Particle motions in sheared suspensions: VII. Internal circulation in fluid droplets (theoretical). J. Colloid Sci. 13, 293–307.CrossRefGoogle Scholar
Brandt, L. & Coletti, F. 2022 Particle-laden turbulence: progress and perspectives. Annu. Rev. Fluid Mech. 54, 159–189.CrossRefGoogle Scholar
Cox, R.G. 1971 The motion of long slender bodies in a viscous fluid. Part 2. Shear flow. J. Fluid Mech. 45, 625–657.CrossRefGoogle Scholar
Cox, R.G. & Mason, S.G. 1971 Suspended particles in fluid flow through tubes. Annu. Rev. Fluid Mech. 3, 291–316.CrossRefGoogle Scholar
Dabade, V., Marath, N.K. & Subramanian, G. 2016 The effect of inertia on the orientation dynamics of anisotropic particles in simple shear flow. J. Fluid Mech. 791, 631–703.CrossRefGoogle Scholar
Díaz-Maldonado, M. & Córdova-Figueroa, M. 2015 On the anisotropic response of a Janus drop in a shearing viscous fluid. J. Fluid Mech. 770, R2.CrossRefGoogle Scholar
Ding, E.J. & Aidun, C.K. 2000 The dynamics and scaling law for particles suspended in shear flow with inertia. J. Fluid Mech. 423, 317–344.CrossRefGoogle Scholar
Ding, H., Spelt, P.D.M. & Shu, C. 2007 Diffuse interface model for incompressible two-phase flows with large density ratios. J. Comput. Phys. 226, 2078–2095.CrossRefGoogle Scholar
Hao, X., Du, T., He, H., Yang, F., Wang, Y., Liu, G. & Wang, Y. 2022 Microfluidic particle reactors: from interface characteristics to cells and drugs related biomedical applications. Adv. Mater. Interfaces 9, 2102184.CrossRefGoogle Scholar
Hu, X.Y. & Adams, N.A. 2007 An incompressible multi-phase SPH method. J. Comput. Phys. 227, 264–278.CrossRefGoogle Scholar
James, C.B.G., Mingotti, N. & Woods, A.W. 2022 On particle separation from turbulent particle plumes in a cross-flow. J. Fluid Mech. 932, A45.CrossRefGoogle Scholar
Jeffery, G. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 161–179.Google Scholar
Leal, L.G. 1980 Particle motions in a viscous-fluid. Annu. Rev. Fluid Mech. 12, 435–476.CrossRefGoogle Scholar
Li, C., Lim, K., Berk, T., Abraham, A., Heisel, M., Guala, M., Coletti, F. & Hong, J. 2022 Settling and clustering of snow particles in atmospheric turbulence. J. Fluid Mech. 912, A49.CrossRefGoogle Scholar
Li, C.G., Ye, M. & Liu, Z.M. 2016 On the rotation of a circular porous particle in 2D simple shear flow with fluid inertia. J. Fluid Mech. 808, R3.CrossRefGoogle Scholar
Liu, H.-R., Ng, C.S., Chong, K.L., Lohse, D. & Verzicco, R. 2021 An efficient phase-field method for turbulent multiphase flows. J. Comput. Phys. 446, 110659.CrossRefGoogle Scholar
Liu, H.-R., Zhang, C.-Y., Gao, P., Lu, X.-Y. & Ding, H. 2018 On the maximal spreading of impacting compound drops. J. Fluid Mech. 854, R6.CrossRefGoogle Scholar
Liu, W.K. & Park, J.M. 2022 Ternary modeling of the interaction between immiscible droplets in a confined shear flow. Phys. Rev. Fluids 7, 013604.CrossRefGoogle Scholar
Luo, J., Hu, X.Y. & Adams, A. 2015 A conservative sharp interface method for incompressible multiphase flows. J. Comput. Phys. 284, 547–565.CrossRefGoogle Scholar
Magaletti, F., Picano, F., Chinappi, M., Marino, L. & Casciola, C.M. 2013 The sharp-interface limit of the Cahn–Hilliard/Navier–Stokes model for binary fluids. J. Fluid Mech. 714, 95–126.CrossRefGoogle Scholar
Mao, W. & Alexeev, A. 2014 Motion of spheroid particles in shear flow with inertia. J. Fluid Mech. 749, 145–166.CrossRefGoogle Scholar
Marath, N.K. & Subramanian, G. 2017 The effect of inertia on the time period of rotation of an anisotropic particle in simple shear flow. J. Fluid Mech. 830, 165–210.CrossRefGoogle Scholar
Shklyaev, S., Ivantsov, A.O., Díaz-Maldonado, M. & Córdova-Figueroa, U.M. 2013 Dynamics of a Janus drop in an external flow. Phys. Fluids 25, 082105.CrossRefGoogle Scholar
Singeetham, P.K., Chaithanya, K.V.S. & Thampi, S.P. 2021 Dilute dispersion of compound particles: deformation dynamics and rheology. J. Fluid Mech. 917, A2.CrossRefGoogle Scholar
Singh, R.K. & Sarkar, K. 2011 Inertial effects on the dynamics, streamline topology and interfacial stresses due to a drop in shear. J. Fluid Mech. 683, 149–171.CrossRefGoogle Scholar
Song, Q., Chao, Y., Zhang, Y. & Shum, H.C. 2021 Controlled formation of all-aqueous Janus droplets by liquid–liquid phase separation of an aqueous three-phase system. J. Phys. Chem. B 125, 562–570.CrossRefGoogle ScholarPubMed
Stone, H.A. 1994 Dynamics of drop deformation and breakup in viscous fluids. Annu. Rev. Fluid Mech. 26, 65–102.CrossRefGoogle Scholar
Taylor, G.I. 1932 The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. A 138, 41–48.Google Scholar
Tsai, S.T. 2022 Sedimentation motion of sand particles in moving water (i): the resistance on a small sphere moving in non-uniform flow. Theor. Appl. Mech. Lett. 12 (6), 100392.CrossRefGoogle Scholar
Voth, G.A. & Soldati, A. 2017 Anisotropic particles in turbulence. Annu. Rev. Fluid Mech. 49, 249–276.CrossRefGoogle Scholar
Wei, W.S., Jeong, J., Collings, P.J. & Todh, A.G. 2022 Focal conic flowers, dislocation rings, and undulation textures in smectic liquid crystal Janus droplets. Soft Matt. 18, 4360–4371.CrossRefGoogle ScholarPubMed
Yi, L., Wang, C., van Vuren, T., Lohse, D., Risso, F., Toschi, F. & Sun, C. 2022 Physical mechanisms for droplet size and effective viscosity asymmetries in turbulent emulsions. J. Fluid Mech. 951, A39.CrossRefGoogle Scholar
Yue, P.T., Feng, J.J., Liu, C. & Shen, J. 2004 A diffuse-interface method for simulating two-phase flows of complex fluids. J. Fluid Mech. 515, 293–317.CrossRefGoogle Scholar
Zettner, C.M. & Yoda, M. 2001 Moderate-aspect-ratio elliptical cylinders in simple shear with inertia. J. Fluid Mech. 442, 241–266.CrossRefGoogle Scholar
Zhang, C.Y., Ding, H., Gao, P. & Wu, Y.L. 2016 Diffuse interface simulation of ternary fluids in contact with solid. J. Comput. Phys. 309, 37–51.CrossRefGoogle Scholar
Zhang, C.-Y., Gao, P., Li, E.-Q. & Ding, H. 2021 On the compound sessile drops: configuration boundaries and transitions. J. Fluid Mech. 917, A37.CrossRefGoogle Scholar
Supplementary material: File

Zhang et al. supplementary movie 1

Rotation dynamics of a Janus drop with linear deformation (at Ca=0.07 and Re=0.2)
Download Zhang et al. supplementary movie 1(File)
File 7.8 MB
Supplementary material: File

Zhang et al. supplementary movie 2

Rotation dynamics of a Janus drop with nonlinear deformation (at Ca=0.35 and Re=0.2)
Download Zhang et al. supplementary movie 2(File)
File 15.1 MB