Session H36: Drops: Wetting and Moving Contact Line Effects

Homogeneous deposition of particles on hydrogels by absorption

A drying drop containing solid particles, such as coffee, leaves a ring stain resulting from the accumulation of the particles near a contact line. In many industrial applications such as printing, coating or biological microtechnologies, these inhomogeneities must be avoided. To suppress the coffee stain effect, different strategies have been developed.In the present work, we propose to substitute the drying by absorption in hydrogels to extract the solvent of a colloidal drop. We study the deposition mechanisms of micrometer-sized particles on the surface of swelling hydrogels. To the best of our knowledge, we show for the first time that the particle deposition on these gels is homogeneous. Using fluorescence microscopy coupled with particle tracking techniques, we record the flow field inside the droplet and analyze the particle deposition mechanism. We rationalize our findings with a theoretical model for the absorption and the particle deposition dynamics that enables the measurement of the diffusion coefficient in the gels.   

A scale-dependent model for direct computation of dynamic contact lines

When using numerical schemes for the simulation of moving contact lines with the classical ``no-slip'' boundary condition, the numerical solutions become dependent on grid spacing. Numerical approaches that account for the slip of the contact line avoid this difficulty; a numerically feasible slip length however can often be much larger than the physically ``true'' one. Afkhami et al.~[J.~Comp.~Phys., 228:5370--5389, 2009] addressed this issue, where they proposed a numerical model for the implementation of contact angle based on the mesh size that resulted in mesh independent solutions. Here we refine and apply their numerical observation by studying the problem of coating a plate withdrawn from a viscous liquid reservoir. We consider a partially wetting liquid and show that depending on the capillary number, either a stationary meniscus is formed or a liquid film is deposited on the substrate, known as the transition to a Landau--Levich--Derjaguin film. We derive an effective numerical boundary condition model for the computation of the transition capillary number. The model can be thought of as a large scale solution in an asymptotic matching procedure.   

Interfacial transport alone accounts for coffee-ring deposition

When a colloidal sessile droplet dries on a substrate, the suspended particles usually deposit on the surface in a ring-like pattern. The phenomenon is commonly known as the ``coffee-ring'' effect and it is widely believed to stem from the transport of solutes towards the pinned contact line by the evaporation-induced flow inside the drop. It is, therefore, assumed that the liquid-gas interface does not play an active role in shaping the deposition pattern. Here, we propose an alternative mechanism for the coffee-ring deposition, in which the particles first intersect the receding free surface and then are transported along the interface until they deposit at the edge. That the interface ``captures'' the solutes as the evaporation proceeds is supported by a Lagrangian tracking of particles advected by the flow field within the droplet. We model the interfacial adsorption and transport of particles by a one-dimensional advection-generation equation in a toroidal coordinate system and show that the theory adequately accounts for the coffee-ring effect. Using this model, we study the final deposition pattern on hydrophilic and hydrophobic surfaces under diffusive and uniform evaporation fluxes.   

Passive bloodstains: from an impact energy to a final dried pattern

Tracking down the origin of a blood droplet present on a crime scene has become of major importance in bloodstain pattern analysis. Passive bloodstains are not yet well understood. Accordingly the purpose of this research is to provide new tools to forensic investigators in the analysis of bloodstains arising from blood droplets dripping naturally. The study aims to understand the link between the final dried pattern of a passive bloodstain and its impact energy. Currently no such tool exists, and no correlation has yet been proven. This research was therefore focusing on a new parameter, the thicker outer rim observed on the dried final pattern. To do so, we created several passive bloodstains with different impact energies. A correlation was highlighted between the inner diameter, the maximum spreading diameter, the initial diameter of a blood droplet and its impact energy. This correlation shows how the drying mechanism of a blood droplet is influenced by its impact energy as it alters the red blood cells dispersion inside the droplet. The biological deposit and the final dried pattern are subsequently modified.   

Active depinning of bacterial droplets: the collective surfing of Bacillus subtilis

How systems are endowed with migration capacity is a fascinating question with implications ranging from the design of novel active systems to the control of microbial populations. Bacteria, which can be found in a variety of environments, have developed among the richest set of locomotion mechanisms both at the microscopic and collective levels. Here, we uncover experimentally a new mode of collective bacterial motility in humid environment through the depinning of bacterial droplets. While capillary forces are notoriously enormous at the bacterial scale, even capable of pinning water droplets of millimetric size on inclined surfaces, we show that bacteria are able to harness a variety of mechanisms to unpin contact lines, hence inducing a collective sliding of the colony. Contrary to flagella-dependent migration modes like swarming we show that this much faster colony surfing still occurs in mutant strains of \textit{Bacillus subtilis} lacking flagella. The diversity of mechanisms involved in the active unpinning seen in our experiments suggests that collective surfing should be a generic mode of migration of microorganisms in humid environments.   

Sessile nanodroplets on elliptical patches of enhanced lyophilicity

We theoretically investigate how nanodroplets wet lyophilic elliptical patches in a lyophobic surrounding on a flat substrate. To do so, we minimize the interfacial energy of the nanodroplet using Surface evolver and Monte Carlo calculations, finding decent agreement between the two methods. We can observe four different wetting phases, which are controlled by the aspect ratio of the ellipse and the Young's contact angles. Of particular interest is the behavior of the contact angle of the nanodroplet along the contact line, with which we can explain why the wetting phase transitions occur. We find that the contact angle of the nanodroplet can only change along the rim of the elliptical patch, while the nanodroplet satisfy Young's equation once the contact line is either inside or outside of the patch. The contact line of the nanodroplet, depending on Young's angles and the aspect ratio of the elliptical patch, may be completely pinned to the rim of the elliptical patch, while for some cases we find that the nanodroplet starts to expand to lyophobic surrounding, although there still is lyophilic surrounding available to wet.   

Diffuse-interface modeling of three-phase interactions

In this work, a numerical model is developed to study the three-phase interactions which take place when two immiscible drops suspended in a third immiscible liquid are brought together. The diffuse-interface model coupled with the hydrodynamic equations are solved by a standard finite element method. Partial and complete engulfing between two immiscible drops are studied, and the effects of several parameters are discussed. In the partial-engulfing case, two stages of wetting and pulling are identified, which qualitatively agrees with experiment. In the complete-engulfing case, three stages of wetting and/or penetration, pulling and spreading are identified.   

Analysis of subphase gas/fluid effects on longitudinal flow over unidirectional superhydrophobic surfaces

An analysis of the slip properties associated with longitudinal shear flow over a unidirectional superhydrophobic surface comprising periodic rectangular grooves of arbitrary geometry is described. We produce analytical expressions for the hydrodynamic slip lengths (in various perturbative limits) when the effects of a subphase viscous fluid occupying the grooves is taken into account.   

Singular effective slip length for longitudinal flow over a dense bubble mattress

We derive accurate asymptotic expansions in the small-solid-fraction limit $\epsilon\ll1$ for the effective slip length characterising unidirectional liquid flow over a `bubble mattress' --- a periodically grooved surface, with trapped bubbles protruding between solid ridges. The slip length diverges in this limit: inversely with $\sqrt{\epsilon}$ for contact angles $\theta$ near $\pi/2$, and logarithmically for $0\le\theta<\pi/2$. The analysis of the velocity field entails matching `inner' expansions valid close to the solid segments with `outer' expansions valid on the scale of the periodicity, where the protruding bubbles appear to touch. For $\theta$ close to $\pi/2$, the inner-region geometry is narrow and the analysis there resembles lubrication theory; for smaller contact angles the inner region is resolved using a Schwarz-Christoffel mapping. In both cases the outer problem is solved using a mapping from a degenerate curvilinear triangle to an auxiliary half plane. The asymptotic analysis explicitly illustrates the logarithmic-to-algebraic transition, and yields a uniformly valid approximation for the slip length for arbitrary contact angles $0\le \theta\le\pi/2$. We demonstrate good agreement with a numerical solution (courtesy of Ms Elena Luca).   

Dewetting on microstructured substrates

A thin liquid film has an equilibrium thickness in such a way as to minimize the free energy. When a liquid film thickness is out of its equilibrium, the film seeks its equilibrium state, resulting in dynamics of liquid film, which are referred to as wetting and dewetting, depending on the flow direction. We here present a combined experimental and theoretical investigation of dewetting on a substrate with parallel microstructures. Our experiments show that residue may remain on the substrate after dewetting, and residue morphologies can be classified into three modes. Based on our experimental observations, we elucidate how the modes depend on the pattern morphology and contact angle, and develop a model for the contact line motion. Our results provide a basis for controlling the thickness film, which is important for many practical applications such as oil recovery, detergency, lithography, and cleaning.