The energetics of drop deposition are considered in the capillary-ballistic regime characterized by high Reynolds number and moderate Weber number. Experiments are performed impacting water/glycol drops onto substrates with varying wettability and contact-angle hysteresis. The impacting event is decomposed into three regimes: (i) pre-impact, (ii) inertial spreading and (iii) post contact-line (CL) pinning, conveniently framed using the theory of Dussan & Davis ( J. Fluid Mech. , vol. 173, 1986, pp. 115–130). During fast-time-scale inertial spreading, the only form of dissipation is CL dissipation ( $$\mathcal {D}_{CL}$$ ). High-speed imaging is used to resolve the stick-slip dynamics of the CL with $$\mathcal {D}_{CL}$$ measured directly from experiment using the $$\Delta \alpha$$ - $$R$$ cyclic diagram of Xia & Steen ( J. Fluid Mech. , vol. 841, 2018, pp. 767–783), representing the contact-angle deviation against the CL radius. Energy loss occurs on slip legs, and this observation is used to derive a closed-form expression for the kinetic K and interfacial $$\mathcal{A}$$ post-pinning energy $$\{K+\mathcal {A}\}_p/\mathcal {A}_o$$ independent of viscosity, only depending on the rest angle $$\alpha _p$$ , equilibrium angle $$\bar {\alpha }$$ and hysteresis $$\Delta \alpha$$ , which agrees well with experimental observation over a large range of parameters, and can be used to evaluate contact-line dissipation during inertial spreading. The post-pinning energy is found to be independent of the pre-impact energy, and it is broken into modal components with corresponding energy partitioning approximately constant for low-hysteresis surfaces with fixed pinning angle $$\alpha _p$$ . During slow-time-scale post-pinning, the liquid/gas ( $lg$ ) interface is found to vibrate with the frequencies and mode shapes predicted by Bostwick & Steen ( J. Fluid Mech. , vol. 760, 2014, pp. 5–38), irrespective of the pre-impact energy. Resonant mode decay rates are determined experimentally from fast Fourier transforms of the interface dynamics.
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Dissipation of oscillatory contact lines using resonant mode scanning
Abstract Moving contact-lines (CLs) dissipate. Sessile droplets, mechanically driven into resonance by plane-normal forcing of the contacting substrate, can exhibit oscillatory CL motions with CL losses dominating bulk dissipation. Conventional practice measures CL dissipation based on the rate of mechanical work of the unbalanced Young’s force at the CL. Typical approaches require measurements local to the CL and assumptions about the “equilibrium” contact angle (CA). This paper demonstrates how to use scanning of forcing frequency to characterize CL dissipation without any dependence on measurements from the vicinity of the CL. The results are of immediate relevance to an International Space Station (ISS) experiment and of longer-term relevance to Earth-based wettability applications. Experiments reported here use various concentrations of a water-glycerol mixture on a low-hysteresis non-wetting substrate.
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- Award ID(s):
- 1637960
- PAR ID:
- 10154266
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- npj Microgravity
- Volume:
- 6
- Issue:
- 1
- ISSN:
- 2373-8065
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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