High-resolution liquid patterns via three-dimensional droplet shape control

Abstract

Understanding liquid dynamics on surfaces can provide insight into nature's design and enable fine manipulation capability in biological, manufacturing, microfluidic and thermal management applications. Of particular interest is the ability to control the shape of the droplet contact area on the surface, which is typically circular on a smooth homogeneous surface. Here, we show the ability to tailor various droplet contact area shapes ranging from squares, rectangles, hexagons, octagons, to dodecagons via the design of the structure or chemical heterogeneity on the surface. We simultaneously obtain the necessary physical insights to develop a universal model for the three-dimensional droplet shape by characterizing the droplet side and top profiles. Furthermore, arrays of droplets with controlled shapes and high spatial resolution can be achieved using this approach. This liquid-based patterning strategy promises low-cost fabrication of integrated circuits, conductive patterns and bio-microarrays for high-density information storage and miniaturized biochips and biosensors, among others.

Dynamic polygonal spreading of a droplet on a lyophilic pillar-arrayed surface

“…Later, by varying the geometry of the surface array and the liquid, Courbin et al [20] found a diversity of final wetted shapes, including polygons and circles, of droplets on pillar-arrayed surfaces. Raj et al [23] then showed complete control of polygonal wetted shapes via the design of topographic or chemical heterogeneity on the surface. Jokinen et al [24] developed a method of fabricating irregular pillars on a square array surface, and found directional wetting property of droplets on this surface, where droplets spread to irregular square-like shapes.…”

Well-defined porous membranes for robust omniphobic surfaces via microfluidic emulsion templating

“…The reversible Cassie–Wenzel transition would then benefit applications involving liquid immersion such as anti-fouling and drag reduction for fluidic systems and ship hull coatings. The sustained Cassie state during droplet evaporation makes the omniphobic surfaces suitable for surface patterning in various materials43 and biosensing44. Moreover, the enclosed micro-cavity prevents sideways propagation of the wetting transition, which is quite useful in isolating localized damages and defects of the surface.…”

A Free Boundary Problem with Facets

“…While it is easy enough to construct a problem of the form (1.1) with facets in the free boundary, we are able to derive such a problem as a scaling limit of a simple microscopic model for the liquid droplet problem. Furthermore we find solutions which can be reliably obtained by a natural flow at the level of the microscopic problem, advancing the contact line from a small initial wetted set as was done in the experiments [16]. among the functions u ∈ H 1 loc (R d ) satisfying u = 1 on R d \ U .…”

“…As mentioned earlier in the introduction, the first motivation for our work was to explain the formation of facets in the effective contact line of liquid drops wetting a patterned solid surface. In a series of physical experiments, Raj-Adera-Enright-Wang [16] control the shape of a liquid droplet by creating a surface patterned with periodic arrays of micro-pillars. For an expanding droplet the contact line is pinned sooner when it is parallel to a lattice direction.…”

“…While the scaling limit of our problem is of the same form as the homogenized limit of (1.6), a significant part our our work is devoted to proving convexity and facet formation of the free boundary of the limiting minimal supersolution of the natural boundary value problem (1.5). The difficulties with the continuum models, and the appealing similarity between the finite solutions in Figure 1 and the droplets observed in [16], were one motivation for our study of (1.5).…”