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Width effect on contact angle hysteresis in a patterned heterogeneous microchannel

Published online by Cambridge University Press:  23 September 2022

Xiangting Chang Open the ORCID record for Xiangting Chang [Opens in a new window] ,
Haibo Huang Open the ORCID record for Haibo Huang [Opens in a new window] ,
Xi-Yun Lu Open the ORCID record for Xi-Yun Lu [Opens in a new window]  and
Jian Hou
Xiangting Chang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Haibo Huang*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Xi-Yun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, PR China
Jian Hou
Affiliation:
School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, PR China
*
†Email address for correspondence: huanghb@ustc.edu.cn
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Abstract

The width effect on contact angle hysteresis in a microchannel with patterned heterogeneous surfaces is systematically investigated. In the model, identical defects periodically appear on the background surface. To this end, a droplet's evaporation and condensation processes inside the microchannel are studied by theoretical analysis and numerical simulation based on a diffuse-interface lattice Boltzmann method. The microchannel width effect on the system's equilibrium properties is studied. The results demonstrate that the number of equilibrium configurations increases linearly with the microchannel width ($b$), and has a quadratic relationship with the cosine of the reference contact angle and the heterogeneity strength ($\varepsilon$). The average most stable contact angle is independent of $b$ and is always equal to the contact angle predicted by the Cassie–Baxter equation. For contact angle hysteresis ($H$), when the microchannels are narrow and wide, there are individual-effect-dominated hysteresis (IDH) and collective-effect-dominated hysteresis (CDH), respectively. The IDH and CDH are hysteresis modes corresponding to the jumping behaviour of contact lines affected by individual defects and two neighbouring defects, respectively. Based on the graphical force balance approach, we establish a scaling law to quantify the connection between $H$, $b$ and $\varepsilon$. Specifically, in the IDH mode, $H\sim b \varepsilon ^2$, while in the CDH mode, $H$ increases linearly with $\varepsilon$ but nonlinearly with $b$.

JFM classification

Interfacial Flows (free surface): Contact lines Phase change: Condensation/evaporation Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 949 , 25 October 2022 , A15
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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