Avalanches and Extreme Value Statistics of a Mesoscale Moving Contact Line

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Avalanches and Extreme Value Statistics of a Mesoscale Moving Contact Line

Caishan Yan, Dongshi Guan, Yin Wang, Pik-Yin Lai, Hsuan-Yi Chen, and Penger Tong

Phys. Rev. Lett. 132, 084003 – Published 23 February 2024

Abstract

We report direct atomic force microscopy measurements of pinning-depinning dynamics of a circular moving contact line (CL) over the rough surface of a micron-sized vertical hanging glass fiber, which intersects a liquid-air interface. The measured capillary force acting on the CL exhibits sawtoothlike fluctuations, with a linear accumulation of force of slope $k$ (stick) followed by a sharp release of force $δ f$ , which is proportional to the CL slip length. From a thorough analysis of a large volume of the stick-slip events, we find that the local maximal force $F_{c}$ needed for CL depinning follows the extreme value statistics and the measured $δ f$ follows the avalanche dynamics with a power law distribution in good agreement with the Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model. The experiment provides an accurate statistical description of the CL dynamics at mesoscale, which has important implications to a common class of problems involving stick-slip motion in a random defect or roughness landscape.

Received 21 June 2023
Revised 13 November 2023
Accepted 16 January 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.084003

Physics Subject Headings (PhySH)

Capillary interactions Collective behavior Contact line dynamics Interfacial flows Slip boundary effects Wetting

Liquid-solid interfaces Porous materials

Atomic force microscopy

Polymers & Soft MatterFluid Dynamics

Authors & Affiliations

Caishan Yan ¹, Dongshi Guan ^2,3, Yin Wang ¹, Pik-Yin Lai ^4,5,*, Hsuan-Yi Chen ^4,5,†, and Penger Tong ^1,‡

¹Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
²State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
³School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China
⁴Department of Physics and Center for Complex Systems, National Central University, Taoyuan City 320, Taiwan
⁵Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan

^*Corresponding author: hschen@phy.ncu.edu.tw
^†Corresponding author: pylai@phy.ncu.edu.tw
^‡Corresponding author: penger@ust.hk

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Issue

Vol. 132, Iss. 8 — 23 February 2024

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Images

Figure 1
Schematic of the long-needle AFM probe made of a vertical glass fiber of diameter $d ≃ 3 μ m$ and length $\sim 600 μ m$ . The glass fiber penetrates a liquid-air interface and a circular contact line is formed on the fiber surface. The inset shows a magnified AFM topographic image of a portion of the fiber covered by a variety of PTS clusters.
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Figure 2
(a) Measured capillary force $F (z)$ as a function of vertical displacement $z$ of the fiber, when it is pushed downward (advancing) and is pulled upward (receding) through a liquid interface. The red curve is obtained for a water-air interface and the black curve is obtained with the same fiber segment in contact with an ethylene-glycol-air interface. All the measurements are made when the fiber moves at a constant speed $u = 0.62 μ m / s$ . (b) A magnified view of the black curve marked in the blue box in (a). The blue downward and red upward triangles mark, respectively, the beginning and end of each slip event of the CL.
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Figure 3
Measured PDFs $P (f_{c})$ of the normalized maximal force $f_{c}$ . The black symbols are obtained using the same PTS-coated fiber with three different liquids: water (upward triangles), 66 wt.% glycerol aqueous solution (downward triangles) and ethylene glycol (circles). The red circles are obtained using a different PTS-coated fiber with ethylene glycol. The four sets of data are all obtained in the advancing direction at $u = 0.62 μ m / s$ . For each set of data, the measured $F (z)$ recorded approximately 2500 slip events over a traveling distance $z ≃ 500 μ m$ . The black and red solid lines show the fits of Eq. (2) to the black and red circles, respectively, with $ξ = - 0.17 \pm 0.04$ (black line) and $ξ = - 0.06 \pm 0.04$ (red line). Insets show the AFM topographic images of the two PTS-coated fiber surfaces used and the vertical gray-scale bar applies to both AFM images.
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Figure 4
Log-log plot of the measured PDFs $P (Δ z_{slip})$ of the slip length $Δ z_{slip}$ . The four sets of data are obtained using the same force trajectories and with the same symbols as those used in Fig. 3. The solid line shows a fit of Eq. (4) to the data points with the power-law exponent $ε = 1.45 \pm 0.10$ . The inset shows a sketch of a local slip of the CL, with the blue solid line and black dashed line indicating, respectively, the CL positions before and after the slip. The red solid and dashed lines show the corresponding center-of-mass positions of the CL.
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Figure 5
Measured PDF $P (k^{'})$ of the local gradient $k^{'}$ of the pinning force field. In the plot, the value of $k^{'}$ is normalized by $k_{0}$ . The solid line shows a fit of Eq. (6) to the black symbols with $b = 0.165 \pm 0.015$ . Inset shows the measured PDF $P (k)$ of the dynamic spring constant $k$ normalized by $k_{0}$ . The four sets of data in the main figure and inset are all obtained from the same force trajectories and with the same symbols as those used in Fig. 3. The error bars show the experimental uncertainties of the measurements.
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