Session BF: Drops and Bubbles II: Wetting and Splashing

Splashing and bouncing on dry, spinning surfaces

We investigate splashing and bouncing of drops on a hydrophilic rotating surface. Experiments were performed where we systematically varied the impact velocity and the rotation speed of the substrate for several different fluids. We identify distinct transitions where there is complete wetting, bouncing, or splashing. For the case where there is splashing, there is an asymmetry of the impact that leads to an azimuthal variation of the ejected rim. A model for the azimuthal splash threshold is compared both with the data and with existing splash criteria.   

Liquid drop splashing on a textured surface

We have studied splashing of a liquid drop impacting on a dry solid surface. Previously we discovered that air causes the ``corona'' splashes seen on smooth surfaces and that surface roughness causes ``prompt'' splashing$^{ }$[1]. We can further control surface roughness by making textured surfaces of regular patterns. We manufactured arrays of pillars in a square lattice configuration on a flat surface. Surprisingly, the splashing on these surfaces shows four-fold symmetry -- splashing predominantly along the diagonal. By varying the horizontal and vertical sizes of the pattern, we also found that the pillar height and the spacing between pillars are crucial factors for creating a splash. These discoveries could have practical applications in controlling the amount and direction of splashing. \newline \newline [1] L. Xu, W. W. Zhang, and S. R. Nagel, Phys. Rev. Lett. \textbf{94}, 184505 1-4 (2005); L. Xu, L. Barcos, and S. R. Nagel to be published.   

The effect of drop size on splash

Recently Xu, et. al \footnote{L. Xu, W. W. Zhang, and S. R. Nagel, Phys. Rev. Lett. 94, 184505 1-4 (2005)} discovered that the splash created when a liquid drop hits a smooth, dry substrate disappears if the surrounding air pressure is lowered below a certain threshold value. In the same experiment, the dependence of this threshold pressure on the liquid drop's velocity, fluid viscosity and molecular weight of the surrounding gas, was measured. Those measurements suggest a criterion for the onset of splashing that includes a certain dependence on the drop size. Here we investigate this dependence of the threshold pressure on drop size. It is shown that the proposed scaling relations work well for the regime of high velocity impact. There is another regime at low impact velocity with different dependence on the control parameters. We see that the crossover velocity between the two regimes shifts as the drop size and fluid viscosity are varied.   

Driven Coalescence of Sessile Drops on PDMS Surfaces

Knowledge of the dynamic behavior of droplets on a surface is important in numerous technological processes including spray cooling, ink-jet printing, and solder jet technology. Although spreading and deposition of drops on surfaces have been studied in detail, most studies on coalescence focus on spherical drops in bulk. In studies of coalescence on surfaces, drops merged due to natural spreading, with little control over drop size or velocity of approach. In this study, we utilize a microfluidic device to inject volume into two approaching sessile drops at a controlled rate, while controlling their separation and thus the initial drop size at coalescence. We simultaneously acquire high-speed images of the side and top views of the coalescence event through use of a prism. Through measurements in both viscous and inertial regimes, we investigate the influence of surface wettability, initial drop size at coalescence, and velocity of approach on the coalescence dynamics. We compare with available theory and propose new scaling arguments with respect to the injected volume flow rate.   

Diffuse-interface simulations of inertial effects in droplet spreading and in 3D shear-driven droplet motion on a wall

A diffuse interface method is developed to simulate 3D two-phase flows with moving contact lines. The method is first used to study axisymmetric spreading of a droplet on a solid surface. The results are shown to agree well with those obtained from a level-set method, and also to agree well with lubrication theory at low capillary numbers. At sufficiently large Reynolds numbers (Re$>$20), in an inertial spreading regime, a capillary wave is observed to travel away from the contact line, in qualitative agreement with experiments. In the second part of this presentation, the method is made to account for effects of contact-line hysteresis, and is used to study of 3D shear flow past a droplet on an adhering channel wall. Results are presented for cases at different capillary and Reynolds numbers. These include results in which part of a moving droplet is sheared off.   

Wetting droplet spread into porous medium: A micro-force balance capillary network solution

An accurate solution of a droplet spread into a porous medium with fluid/solid wetting interaction becomes more important, as application scales shift toward micro- and nano-level. In the capillary network models, an actual porous medium is represented as a network of connected pores, where the rule(s) for droplet spread can be set in different ways. We have developed a general capillary network model with the progression rule based on the setting the micro-force balance at each pore, and the pressure jump condition (capillary pressure) at the phase interface. Using micro-force balance, the local flow due to the capillary force is accounted for. Therefore, in some pores, the flow may retreat rather than only advance throughout the medium. This approach is neither limited by process rate nor interaction type (force balance changes for wetting or non-wetting interaction). From the solution, the phase content (saturation) and the phase pressure are calculated. The parameters as phase permeability, capillary pressure and flow front thickness can be determined. It is also shown how the rate of phase spread changes due to the influence of the local heterogeneities of porous medium. Finally, in order to compare the influence of capillary and viscous forces, the analysis of fluid radial spread into a porous medium with the different inlet pressures is carried out.   

Detection of the precursor layer in front of the moving contact line using fluorescence microscopy

For wetting fluids a microscopic film, which is known as the precursor film, exists at the front of the moving contact line. The structure of this thin film has been studied theoretically, but previous experimental investigations were limited by the resolution of the measurement system (lateral or vertical) required to capture the complete scope of this feature. We studied the evolution of the profile of a spreading droplet near the moving contact line using a total internal reflection fluorescence microscope (TIR-FM). The TIR-FM system can detect nano-particles and fluorescence materials approximately 100 nm from the substrate with high spatial resolution. The dynamic characteristics of the precursor films have a good agreement with the available theoretical results.   

Theory of slope-dependent disjoining pressure with application to Lennard-Jones liquid films.

A liquid film of thickness h $<$ 100 nm is subject to additional intermolecular forces, which are collectively called disjoining pressure $\Pi $. Since $\Pi $ dominates at small film thicknesses, it determines the stability and wettability of thin films. Current theory derived for uniform films gives $\Pi =\Pi $(h). This solution has been applied recently to non-uniform films and becomes unbounded near a contact line as h $\to $ 0. Consequently, many different effects have been considered to eliminate or circumvent this singularity. We present a mean-field theory of $\Pi $ that depends on the slope $h_x $ as well as the height h of the film.[1] When this theory is implemented for Lennard-Jones liquid films, the new $\Pi $ = $\Pi $(h, $h_x )$ is bounded near a contact line as h $\to $ 0. Thus, the singularity in $\Pi $(h) is artificial because it results from extending a theory beyond its range of validity. We also show that the new $\Pi $ can capture all three regimes of drop behavior (complete wetting, partial wetting, and pseudo partial wetting) without altering the signs of the long and short-range interactions. We find that a drop with an unbounded precursor film is linearly stable. \newline [1] Wu {\&} Wong, J. Fluid Mech. \underline {506}, 157 (2004)