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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Predictive modeling of drop impact force on concave targets
Impacting drops are ubiquitous and the corresponding impact force is their most studied dynamic quantity. However, impact forces arising from collisions with curved surfaces are understudied. In this study, we impact small cups with falling drops across drop Reynolds number 2975–12 800, isolating five dominant parameters influencing impact force: drop height and diameter, surface curvature and wettability, and impact eccentricity. These parameters are effectively continuous in their domain and have stochastic variability. The unpredictable dynamics of the system incentivize the implementation of tools that can unearth relationships between parameters and make predictions about impact force for parameter values for which there is not explicit experimental data. We predict force due to the impacting drop in a concave target using an ensemble learning algorithm comprised of four base algorithms: a random forest regressor, k-nearest neighbor, a gradient boosting regressor, and a multi-layer perceptron. We train and test our algorithm with original experimental data comprising 387 total trials using four cup radii with two wetting conditions each. Our approach permits the determination of relative importance of the input features in producing impact force and force predictions which can be compared to scaling relations modified from those for flat targets. Algorithmic predictions indicate that deformation of the drop and surface wettability, often neglected in scaling for impact force on flat surfaces, are important for concave targets. Finally, our approach provides another opportunity for the application of machine learning to characterize complex systems' fluid mechanics for which experimental variables are numerous and vary independently.
more » « less- NSF-PAR ID:
- 10376734
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- Physics of Fluids
- Volume:
- 34
- Issue:
- 10
- ISSN:
- 1070-6631
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Experimental observations of drops of water with aniline dye softly located or impacting onto balsa wood substrates were used to elucidate the effect of an in-plane electric field (at a high voltage of 10 kV applied) on drop behavior. The top and side views were recorded simultaneously. The short-term recordings (on the scale of a few ms) demonstrated a slight effect of the applied in-plane electric field. In some trials, a greater number of finger-like structures were observed along the drop rim compared to the trials without voltage applied. These fingers developed during the advancing motion of the drop rim. The long-term recording (on the scale of ∼10 s) was used to evaluate the wettability-driven increase in the area-equivalent radius of the wetted area. These substrates had grooves in the inter-electrode or the cross-field directions. The groove directions affected the wettability-driven spreading and imbibition. The wettability-driven spreading in the long term was a much more significant effect than the effect of the electric field, because the imbibition significantly diminished the drop part above the porous surface, which diminished, in turn, the electric Maxwell stresses, which could stretch the drop. A simplified analytical model was developed to measure the moisture transport coefficient responsible for liquid imbibition in these experiments. Furthermore, the phase-field modeling of drops on balsa was used to illustrate how a change in the contact angle from hydrophobic to hydrophilic triggers drop imbibition into balsa wood.more » « less
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