Taming contact line instability for pattern formation

Introduction

Coating surfaces with Newtonian fluids and complex fluids is essential in numerous industrial processes such as making functional or flexible thin films with applications spanning microfluidics, sensor arrays1, electronics and biomedical devices2. Different coating techniques exist, such as dip and spin coating, rigid or flexible blade coating. The stability of the contact line between the fluid and the surface plays a key role in the control of the final deposit3,4. An example of an instability that occurs for advancing contact lines is the fingering instability, which takes place when a thin liquid film flows down an inclined plane. Previous work has shed light on this instability both experimentally5,6and theoretically7,8, whereas others offer different interesting ways to control the fingering9 and thus the coating patterns.

While much work has focused on understanding the instability of an advancing contact line driven by gravity10,11 or temperature gradients12, less work has focused on the case of receding contact lines, as in the case of dip or blade coating, which are supposedly stable for Newtonian liquids13. Despite this stability with respect to undulations and formation of fingers, receding contact lines can show the formation of particular patterns as they are prone to cusp formation producing triangular-like films with properties set by the receding velocity of the front. This has been demonstrated in dip-coating experiments14, as well as in experiments using drops flowing down an inclined plane where the rear of the drop produces cusps15. These cusps give rise to the formation of rivulets breaking up into even smaller droplets16. The conditions for the formation of such structures have been studied in detail and are understood15,16,17,18, at least partially.

Here, we show that the instability of a receding contact line towards cusp and droplet formation can be tamed through the use of viscoelastic fluids to produce linear patterns of variable spacings. These patterns can then be used to embed different colloidal particles, stretch long DNA molecules and filter particles by size. The preparation of tunable patterns of oriented well-spaced lines with different embedded objects can be useful in many applications.

Results

Filament formation

Here, and by using a viscoelastic polymer solution, a non-Newtonian fluid, the receding contact line obtained in blade-coating experiments shows the formation of cusp-like patterns, resembling their Newtonian counterparts, but which give rise to long slender filaments instead of droplets. Figure 1 illustrates the patterns obtained with a high-molecular-weight polymer solution in coating experiments using a flexible blade (polyacrylamide (PAM), see Methods and Supplementary Figs 1 and 2). Long, slender and spatially organized filaments are obtained over large extended areas of the surface and for a wide range of velocities. The typical spacing between the filaments is an increasing function of the coating velocity, Fig. 1, in stark contrast with the fingering instability of advancing contact lines where the spacing between fingers is a decreasing function of this velocity.

Figure 1: Deposition of a polymer solution.

(a) Schematic of the flexible blade set-up. A glass surface is translated below the blade, which is fixed to entrain fluid underneath the blade. The meniscus between the fluid and the surface resists wetting the latter and recedes as it is dragged by the bottom surface. (b) Photographs of filaments near the blade for different velocities (V=0.2, 0.5, 10 mm s−1). Note the change in scale as the velocity is increased. (c) Wavelength versus deposition velocity for two different concentrations (3,000 and 10,000 p.p.m.) of PAM of molecular weight 18 M. The error bars in c represent the s.d. More details are shown in Supplementary Fig. 1.