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Maximum droplet volume on cylindrical surfaces

Yi Zhang, Apurav Tambe, Zhao Pan

Abstract

The maximum volume ($Ω$) of a droplet that can remain attached to a horizontal fiber defines the stability limit of droplet-fiber interactions, phenomena common in nature and critical to diverse engineering applications. Existing predictive models for $Ω$ show limitations in accurately capturing the dependence of $Ω$ on fiber size and wettability. To address this gap, we systematically investigate $Ω$ on a horizontal fiber through numerical simulations and experiments. A comprehensive semi-empirical model for $Ω$ is developed and validated against both experimental measurements and reference simulations. This model establishes a new scaling under which the normalized maximum droplet volume depends solely on the contact angle and remains valid across a wide spectrum from a sub-millimeter thin fiber to the flat-surface limit, regardless of the diverse morphologies that droplets exhibit.

Maximum droplet volume on cylindrical surfaces

Abstract

The maximum volume () of a droplet that can remain attached to a horizontal fiber defines the stability limit of droplet-fiber interactions, phenomena common in nature and critical to diverse engineering applications. Existing predictive models for show limitations in accurately capturing the dependence of on fiber size and wettability. To address this gap, we systematically investigate on a horizontal fiber through numerical simulations and experiments. A comprehensive semi-empirical model for is developed and validated against both experimental measurements and reference simulations. This model establishes a new scaling under which the normalized maximum droplet volume depends solely on the contact angle and remains valid across a wide spectrum from a sub-millimeter thin fiber to the flat-surface limit, regardless of the diverse morphologies that droplets exhibit.
Paper Structure (8 sections, 7 equations, 3 figures)

This paper contains 8 sections, 7 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Simulation by surface evolver
  4. Experimental validation
  5. Results and discussion
  6. Simulation results and semi-empirical model development
  7. Validation and discussion
  8. Conclusion

Figures (3)

  • Figure 1: (A) Simulation results of the normalized maximum droplet volume ($\Omega_*=\Omega/\lambda^2r$) as a function of the normalized fiber radius ($r_*=r/\lambda$) for various contact angles ($\theta$). Power-law fits of $\Omega_*$ follow eq \ref{['eq:power-law correlation']}. (B) Fitted values of parameter $a$ corresponding to (A).
  • Figure 2: (A) Validation of the developed semi-empirical model, given by eq \ref{['eq:comp model2']}, for predicting the maximum droplet volume on a horizontal fiber. The legend on the right specifies the liquid type, fiber radius, and fiber material. Error bars represent the standard deviation from three to five repeated measurements. (B) Photos of maximum-volume droplets suspended beneath fibers and flat surfaces for $\theta\approx0^\circ$ and $\theta\approx 60^\circ$, corresponding to the marked data points in (A). Scale bar indicates 0.5mm.
  • Figure 3: Degree of droplet symmetry, characterized by the ratio of the wetting width $W$ across the fiber to the wetting length $L$ along the fiber. (A) $\Omega/\bar{\Omega}$, the ratio between the maximum droplet volume on a fiber ($\Omega$) and that beneath a flat surface ($\bar{\Omega}$) under the same $\lambda$ and $\theta$, as a function of $\left(W/L\right)^b$, where $b=0.5\sin\theta+0.9$. (B) $\left(W/L\right)^b$ as a function of $r_*$. Point symbols correspond to those in (A).