Motion of nanodroplets near chemical heterogeneities

Instabilities of Layers of Deposited Molecules on Chemically Stripe Patterned Substrates: Ridges versus Drops

A mesoscopic continuum model is employed to analyze the transport mechanisms and structure formation during the redistribution stage of deposition experiments where organic molecules are deposited on a solid substrate with periodic stripe-like wettability patterns. Transversally invariant ridges located on the more wettable stripes are identified as very important transient states and their linear stability is analyzed accompanied by direct numerical simulations of the fully nonlinear evolution equation for two-dimensional substrates. It is found that there exist two different instability modes that lead to different nonlinear evolutions that result (i) at large ridge volume in the formation of bulges that spill from the more wettable stripes onto the less wettable bare substrate and (ii) at small ridge volume in the formation of small droplets located on the more wettable stripes. In addition, the influence of different transport mechanisms during redistribution is investigated focusing on the cases of convective transport with no-slip at the substrate, transport via diffusion in the film bulk and via diffusion at the film surface. In particular, it is shown that the transport process does neither influence the linear stability thresholds nor the sequence of morphologies observed in the time simulation, but only the ratio of the time scales of the different process phases.

Interaction of 3D dewetting nanodroplets on homogeneous and chemically heterogeneous substrates

Long-time interaction of dewetting nanodroplets is investigated using a long-wave approximation method. Although three-dimensional (3D) droplets evolution dynamics exhibits qualitative behavior analogous to two-dimensional (2D) dynamics, there is an extensive quantitative difference between them. 3D dynamics is substantially faster than 2D dynamics. This can be related to the larger curvature and, as a consequence, the larger Laplace pressure difference between the droplets in 3D systems. The influence of various chemical heterogeneities on the behavior of droplets has also been studied. In the case of gradient surfaces, it is shown how the gradient direction could change the dynamics. For a chemical step located between the droplets, the dynamics is enhanced or weakened depending on the initial configuration of the system.

Nanochannel with uniform and Janus surfaces: shear thinning and thickening in surfactant solution

On basis of molecular simulation of confined surfactant solutions, we show that by adding chemical patterns on the inner surface of nanochannels dynamical properties of the confined surfactant solutions could be modified from shear thinning to shear thickening. To this end, we select uniformly hydrophobic and hydrophilic surfaces as well as a stripe-patterned Janus surface as three prototype confining surfaces of nanochannels. In all three nanochannels, when the surfactant solution is under relatively low shear rates, it shears thin. Under moderate shear rates, a sharp decrease in the shear viscosity could occur due to surfactant morphology transition. Under relatively high shear rates, a shear-thinning-to-thickening transition can emerge due to the tendency of stratification normal to the confining surface. Our simulation study offers a guide to steering dynamic properties of surfactant fluids in nanofluidic devices through engineering surfaces of nanochannels by design.

Dynamics of nanodroplets on wettability gradient surfaces

A lubrication model is used to study the dynamics of nanoscale droplets on wettability gradient surfaces. The effects of the gradient size, size of the nanodroplets and the slip on the dynamics have been studied. Our results indicate that the position of the center of mass of the droplets can be well described in terms of a third-order polynomial function of the time of the motion for all the cases considered. By increasing the size of the droplets the dynamics increases. It is also shown that the slip can considerably enhance the dynamics. The results have been compared with the results obtained using theoretical models and molecular dynamics simulations.

Spreading and retraction as a function of drop size

We simulate the spreading and retraction of a two-dimensional drop over a thin film in the small slope limit for drop heights ranging from a few nanometers to hundreds of nanometers. Drop motion is initiated by an impulsive change in surface wettability expressed in terms of disjoining pressure. Owing to the presence of the film, these simulations require no closure condition at the 'apparent' contact line. Rather, we study the relationships that emerge between the apparent contact line velocity and dynamic contact angles. The disjoining pressure that we study includes stabilizing van der Waals interactions and destabilizing acid-base interactions. Changes in wetting conditions that promote spreading place the thin film surrounding the drop out of equilibrium; the drop spreads as the film thickens to its new equilibrium value. Changes in wetting conditions that promote retraction can either place the thin film out of equilibrium in a stable regime, or they can place the thin film in a spinodally unstable regime. We study drop rearrangement as a function of drop scale for these three cases. Small drops, with heights on the same order as the film thickness, are strongly influenced by disjoining pressure gradients everywhere beneath them. Larger drops, with heights at least an order of magnitude greater than the film thickness, have disjoining pressure gradients isolated near the apparent contact line at all times. For these larger drops, after initial dynamics, macroscopic behavior is recovered; drops move in agreement with Tanner's law. However, dynamics associated with the thin film can play a leading role in the ensuing drop response even after Tanner's law emerges. In particular, when drops retract over spinodally unstable films, retraction occurs in three regimes. Rims form near the apparent contact line over time scales comparable to the time scale for the instability. The rim geometry can be characterized in terms of spinodal film thicknesses. The rims then propagate toward the bulk drop. Finally, the rim disappears and the drop assumes a cap-like shape. Tanner's law is obeyed during the latter two regimes. Attempts to simulate drop rearrangements disregarding the thin film dynamics before Tanner's law manifests can lead to erroneous outcomes, as shown in simulations of drop retraction on a solid surface with an imposed Navier slip length.

Dynamic study of nanodroplet nucleation and growth on self-supported nanothick liquid films

The dynamics of water condensation on self-supported thin films was studied at the nanoscale using transmitted electrons in an environmental scanning electron microscope. The initial stages of nucleation and growth over nanothick water films have been investigated. Irregularities at the water-film boundaries constituted nucleation sites for asymmetric dropwise and filmwise condensation. Nanodroplet growth was associated with center of mass movement, and the dynamic growth power law dependence was explored for the nanoscale.

Dynamics of nanodroplets on topographically structured substrates

Mesoscopic hydrodynamic equations are solved to investigate the dynamics of nanodroplets positioned near a topographic step of the supporting substrate. Our results show that the dynamics depends on the characteristic length scales of the system given by the height of the step and the size of the nanodroplets as well as on the constituting substances of both the nanodroplets and the substrate. The lateral motion of nanodroplets far from the step can be described well in terms of a power law of the distance from the step. In general the direction of motion depends on the details of the effective laterally varying intermolecular forces. But for nanodroplets positioned far from the step it is solely given by the sign of the Hamaker constant of the system. Moreover, our study reveals that the steps always act as a barrier for transporting liquid droplets from one side of the step to the other.

Ultrasmall liquid droplets on solid surfaces: production, imaging, and relevance for current wetting research

The investigation of micro- and nanoscale droplets on solid surfaces offers a wide range of research opportunities both at a fundamental and an applied level. On the fundamental side, advances in the techniques for production and imaging of such ultrasmall droplets will allow wetting theories to be tested down to the nanometer scale, where they predict the significant influence of phenomena such as the contact line tension or evaporation, which can be neglected in the case of macroscopic droplets. On the applied side, these advances will pave the way for characterizing a diverse set of industrially important materials such as textile or biomedical micro- and nanofibers, powdered solids, and topographically or chemically nanopatterned surfaces, as well as micro-and nanoscale devices, with relevance in diverse industries from biomedical to petroleum engineering. Here, the basic principles of wetting at the micro- and nanoscales are presented, and the essential characteristics of the main experimental techniques available for producing and imaging these droplets are described. In addition, the main fundamental and applied results are reviewed. The most problematic aspects of studying such ultrasmall droplets, and the developments that are in progress that are thought to circumvent them in the coming years, are highlighted.

Disjoining pressure for nonuniform thin films

The effect of the attractive forces originating from van der Waals interactions on the dynamics of thin films (<or= approximately 100 nm) is often approximated in fluid dynamics as the disjoining pressure between two unbounded parallel interfaces. However, it is known that this concept of the disjoining pressure, as a force per unit area between parallel interfaces, cannot generally be extended to films of nonuniform thickness. In this paper, we derive a formula for the disjoining pressure for a film of nonuniform thickness by minimizing the total Helmholtz free energy for a thin film residing on a solid substrate. Comparing to the augmented Young-Laplace equation, the disjoining pressure for a thin film of small slope on a flat substrate is shown to take the form Pi=-A_{123}(4-3h_{x};{2}+3hh_{xx})/24pih;{3} , where A123 is the Hamaker constant for phases 1 and 3 interacting through phase 2; h , h_{x} , and h_{xx} are the local film thickness, slope and second order derivative, respectively. For the limiting case of parallel interfaces (e.g., h_{x}=h_{xx} identical with 0 ), the disjoining pressure reduces to Pi=-A_{123}/6pih;{3} in agreement with the classical Lifshitz expression for the van der Waals force. The derivation can be readily extended to more general nonuniform films by constructing tangential planes at both interfaces of the films. Because of steric effects that prevent molecules from overlapping each other, the molecular size cannot be neglected when applying the mesoscopic concept of the disjoining pressure to films of thickness comparable to molecular scales.