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Orbit dynamics of Janus drop in shear flow

Published online by Cambridge University Press:  19 December 2025

Jia-Qi Cheng ,
Chun-Yu Zhang Open the ORCID record for Chun-Yu Zhang [Opens in a new window] ,
Jing-Wei Chen ,
Hao-Ran Liu ,
Li-Juan Qian ,
Peng Gao Open the ORCID record for Peng Gao [Opens in a new window]  and
Hang Ding Open the ORCID record for Hang Ding [Opens in a new window]
Jia-Qi Cheng
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
Chun-Yu Zhang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China College of Mechanical and Electrical Engineering, China Jiliang University, Hangzhou 310018, PR China
Jing-Wei Chen
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
Hao-Ran Liu
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
Peng Gao
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
Hang Ding*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
*
Corresponding authors: Hang Ding, hding@ustc.edu.cn; Li-Juan Qian qianlj@cjlu.edu.cn
Corresponding authors: Hang Ding, hding@ustc.edu.cn; Li-Juan Qian qianlj@cjlu.edu.cn
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Abstract

In this paper, we numerically investigate the orbit dynamics of three-dimensional symmetric Janus drops in shear flow using an improved ternary-fluids phase field method, focusing on how drop deformation and initial orientation affect the orbit drift of two configurations of Janus drops: dumbbell-shaped and near-spherical. We find that the motion of dumbbell-shaped drops eventually evolves into tumbling, while near-spherical drops attain stable spinning. We attribute this bifurcation in orbit drift to contrasting deformation dynamics and shape-dependent hydrodynamics of the two configurations. Specifically, the drift bifurcation is closely related to the aspect ratio of Janus drops at equilibrium, giving rise to two distinct mechanisms: (1) coupling between outer interface deformation and the surrounding flow field; and (2) interplay between inner interface deformation and vortices enclosed within the drop. In addition, we observe that for the dumbbell-shaped Janus drops with different aspect ratios, their tumbling dynamics resembles ellipsoids in shear flow. Moreover, the trajectories of the dumbbell-shaped Janus drops during orbit drift collapse onto a universal curve, independent of their initial orientations, and significant deformation and inertia accelerate the orbit transition. To quantitatively evaluate the effect of drop deformation on the orbit drift of the dumbbell-shaped Janus drops, we propose an effective aspect ratio model based on the drop shapes at equilibrium and at the maximum elongation. By incorporating the effective aspect ratio into Jeffery’s theory for solid particles, we accurately predict the rotation period and angular velocity of Janus drops in the tumbling regime and during the orbit drift, especially for drops with linear deformation. Moreover, the orbit parameter $C$ is found to vary exponentially with time for drops with linear deformation, while the time variation of $C$ transits from one exponential function to another for drops with nonlinear deformation.

JFM classification

Drops and Bubbles: Drops Interfacial Flows (free surface): Capillary flows

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1025 , 25 December 2025 , A32
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Footnotes

†

The authors contributed equally to the article.

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Supplementary material: File

Cheng et al. supplementary movie 1

Tumbling mode of a dumbbell-shaped Janus droplet at θ0=π/6, Re=0.5 and Ca=0.05
Download Cheng et al. supplementary movie 1(File)
File 1.3 MB
Supplementary material: File

Cheng et al. supplementary movie 2

Tumbling mode of a dumbbell-shaped Janus droplet at θ0=π/6, Re=0.5 and Ca=0.2
Download Cheng et al. supplementary movie 2(File)
File 1.4 MB
Supplementary material: File

Cheng et al. supplementary movie 3

Spinning mode of a near-spherical Janus droplet at θ0=π/6, Re=1 and Ca=0.05
Download Cheng et al. supplementary movie 3(File)
File 1.2 MB