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Depinning of liquid droplets on substrates by flow of a surrounding immiscible fluid is central to applications such as cross-flow microemulsification, oil recovery and waste cleanup. Surface roughness, either natural or engineered, can cause droplet pinning, so it is of both fundamental and practical interest to determine the flow strength of the surrounding fluid required for droplet depinning on rough substrates. Here, we develop a lubrication-theory-based model for droplet depinning on a substrate with topographical defects by flow of a surrounding immiscible fluid. The droplet and surrounding fluid are in a rectangular channel, a pressure gradient is imposed to drive flow and the defects are modelled as Gaussian-shaped bumps. Using a precursor-film/disjoining-pressure approach to capture contact-line motion, a nonlinear evolution equation is derived describing the droplet thickness as a function of distance along the channel and time. Numerical solutions of the evolution equation are used to investigate how the critical pressure gradient for droplet depinning depends on the viscosity ratio, surface wettability and droplet volume. Simple analytical models are able to account for many of the features observed in the numerical simulations. The influence of defect height is also investigated, and it is found that, when the maximum defect slope is larger than the receding contact angle of the droplet, smaller residual droplets are left behind at the defect after the original droplet depins and slides away. The model presented here yields considerably more information than commonly used models based on simple force balances, and provides a framework that can readily be extended to study more complicated situations involving chemical heterogeneity and three-dimensional effects.
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Radiation pressure-induced nonlinearity in a micro-droplet
In recent years, some of the most interesting discoveries in science and engineering emerged from interdisciplinary areas that defy the traditional classification. One recent and extensively studied example is the advent of optomechanics that explores the radiation pressure-induced nonlinearity in a solid micro-resonator. Instead of using a solid resonator, we studied a liquid droplet resonator in which optical pressure could actively interact with the fluid interface. The droplet resonator supported high-quality whispering gallery modes along its equatorial plane, which produced a radiation pressure that counterbalances the interfacial tension, resulting in a droplet with damped harmonic oscillation. A major goal of this study was to demonstrate that such a novel and all-liquid platform could lead to a single-photon-level nonlinearity at room temperature. If successful, such a highly nonlinear system may lead to new research paradigms in photonics, fluid mechanics, as well as quantum information science.
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- Award ID(s):
- 1919753
- PAR ID:
- 10144545
- Publisher / Repository:
- Optical Society of America
- Date Published:
- Journal Name:
- Optics Express
- Volume:
- 28
- Issue:
- 9
- ISSN:
- 1094-4087; OPEXFF
- Format(s):
- Medium: X Size: Article No. 12675
- Size(s):
- Article No. 12675
- Sponsoring Org:
- National Science Foundation
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