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Viscoelastic effects on the deformation and breakup of a droplet on a solid wall in Couette flow

Published online by Cambridge University Press:  16 May 2023

Ningning Wang ,
Sheng Li ,
Liang Shi ,
Xuefeng Yuan  and
Haihu Liu Open the ORCID record for Haihu Liu [Opens in a new window]
Ningning Wang
Affiliation:
School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, PR China
Sheng Li
Affiliation:
School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, PR China
Liang Shi
Affiliation:
Heilongjiang Provincial Key Laboratory of Reservoir Physics and Fluid Mechanics in Porous Medium, Daqing 163712, PR China
Xuefeng Yuan
Affiliation:
Institute for Systems Rheology, Guangzhou University, 230 West Outer Ring Road, Guangzhou 510006, PR China
Haihu Liu*
Affiliation:
School of Energy and Power Engineering, Xi'an Jiaotong University, 28 West Xianning Road, Xi'an 710049, PR China Heilongjiang Provincial Key Laboratory of Reservoir Physics and Fluid Mechanics in Porous Medium, Daqing 163712, PR China
*
†Email address for correspondence: [email protected]
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Abstract

The deformation, movement and breakup of a wall-attached droplet subject to Couette flow are systematically investigated using an enhanced lattice Boltzmann colour-gradient model, which accounts for not only the viscoelasticity (described by the Oldroyd-B constitutive equation) of either droplet (V/N) or matrix fluid (N/V) but also the surface wettability. We first focus on the steady-state deformation of a sliding droplet for varying values of capillary number ($Ca$), Weissenberg number ($Wi$) and solvent viscosity ratio ($\beta$). Results show that the relative wetting area $A_r$ in the N/V system is increased by either increasing $Ca$, or by increasing $Wi$ or decreasing $\beta$, where the former is attributed to the increased viscous force and the latter to the enhanced elastic effects. In the V/N system, however, $A_r$ is restrained by the droplet elasticity, especially at higher $Wi$ or lower $\beta$, and the inhibiting effect strengthens with an increase of $Ca$. Decreasing $\beta$ always reduces droplet deformation when either fluid is viscoelastic. The steady-state droplet motion is quantified by the contact-line capillary number $Ca_{cl}$, and a force balance is established to successfully predict the variations of $Ca_{cl}/Ca$ with $\beta$ for each two-phase viscosity ratio in both N/V and V/N systems. The droplet breakup is then studied for varying $Wi$. The critical capillary number of droplet breakup monotonically increases with $Wi$ in the N/V system, while it first increases, then decreases and finally reaches a plateau in the V/N system.

JFM classification

Non-Newtonian Flows: Viscoelasticity Multiphase and Particle-laden Flows: Multiphase flow Interfacial Flows (free surface): Contact lines
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 963 , 25 May 2023 , A18
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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