Session G19: Dynamic Surface Interactions II

Unusual damping behaviour in nonlinear shape oscillations of surfactant-laden drops

Drop shape oscillations have received considerable attention in the literature since the earliest works of Lord Rayleigh, Sir Horace Lamb, and Chandrasekhar. It is widely understood that surfactants lower the restoring force due to surface tension and enhance the damping of such oscillations. As we show here, for the first time, via three-dimensional direct numerical simulations, however, however, the nonlinearity in the coupled surfactant-laden Marangoni stress, diminishes the damping of such oscillations over a range of system parameters. We also demonstrate via a scaling analysis the dependence of the oscillatory dynamics on the surfactant elasticity parameter in which we contrast the surfactant-free and surfactant-laden cases. This analysis captures the trends obtained from the numerical predictions.   

Self-sustained droplet motion on gradient substrates

Gradient substrates can cause the motion of droplets without providing an external energy source. Here, various substrate designs will be presented, which are studied by means of extensive molecular dynamics simulations, with motion taking place in the direction of the gradient, as well as in the opposite direction. The influence of various system parameters for each system will be presented and the underlying mechanisms will be explained, anticipating that this will provide valuable information for relevant experimental designs.   

Drops spreading and retracting and forming a rim

Surfactant laden droplets spreading on a solid may spontaneously retract due to interfacial energy gradients at the solid surface. We explain this retraction by considering fluctuations near the triple line, along with an instability due to these fluctuations and the surface gradients. We provide a theoretical description of this phenomenon along with experimental evidence.

The spreading of the drop is modelled by lubrication theory followed by scaling analysis. At low surfactant concentrations, spreading conforms to Tanner’s law whereby the base radius scales as r_B~t^1/10. Surfactant adsorption is modelled by Langmuir kinetics and the dynamic solid-vapor surface energy, γ_SV, and solid-liquid interfacial energy, γ_SL, are both modelled in accordance with the dynamic adsorption coupled with spreading of the drop.

The retraction process is then considered qualitatively, where fluctuations near the triple line are propagated by hydrodynamic instability. At low surfactant concentrations, this instability is also responsible for a noticeable rim which is left behind after retraction. We also show that the width of the rim increases with decreasing surfactant concentration.

We provide experimental support to the theoretical explanation with octadecylamine-laden tetradecane drops on mica. The drops are filmed with a high-speed camera and then analyzed via frame-by-frame software. For all concentrations tested, we find good agreement with both the analytical and qualitative portions of the theory.   

Oscillations of a sessile drop driven by oblique substrate vibrations

Surface waves are formed on the surface of a sessile drop with pinned contact line when subjected to mechanical vibration, which are characterized by the mode number pair (l,m). Prior experiments by Chang et al. 2015, JFM, have shown that when the vibration is plane-normal (vertically oriented) the wave dynamics can be complex, with zonal modes (m=0) responding harmonically and non-zonal modes (m≠0) subharmonically. Particularly important are the (1,1) rocking mode and (2,0) pumping mode, as these motions are associated with the dominant horizontal and vertical center-of-mass motions, respectively, and often associated with climbing drops. We report on experiments of oblique substrate vibrations focusing on the dynamic response of the rocking mode, which can either i) respond harmonically at its resonance frequency f_r or ii) respond subharmonically and mix with the harmonic pumping mode at f_p =2f_r. We measure the instability tongues in the driving acceleration-frequency space and show how the dominant dynamic response depends upon the orientation of the mechanical vibration. To better understand these experimental observations, we develop a theoretical model by detuning the driving acceleration, which results in an inhomogeneous Mathieu equation governing the drop oscillations. We use a perturbation method to compute the stability tongues showing qualitative agreement with both prior and current experimental results.   

Capillary flow in open microchannels with rectangular cross-sections: a numerical study

Liquids in microchannels are driven by capillary force and spontaneously penetrate into the channels. Predicting and controlling such capillary-driven flow is important in various industrial fields (e.g., high-performance heat exchangers).

It is known that capillary flow is well described by the Lucas-Washburn theory. However, for open microchannels, the applicability of the Lucas-Washburn theory is not yet explored due to the existence of free liquid-gas interfaces, and remains as a challenge.

In this study, numerical simulations of capillary flow in open microchannels with rectangular cross-sections are performed to analyze the structures of liquid-gas interfaces and liquid flow. It is shown that the present simulation results fairly agree with the existing experimental observations and theoretical predictions.