Liquid spreading along nanostructured superhydrophilic lanes

A liquid hanging from a liquid-filled tube can spread spontaneously on rough hydrophilic surfaces while it cannot on smooth hydrophilic surfaces, a difference resulting from the competition between the capillary suction pressures provided by the tube and by the surface roughness. In order to pattern liquids on solid surfaces utilizing such wetting characteristics, we investigate the dynamics of a spontaneous liquid spreading from a tube onto a nanostructured superhydrophilic microlane surrounded by a superhydrophobic background. We find distinct regimes of liquid film propagation dynamics to arise depending on the lane width and the liquid column height in the tube. We theoretically analyze the spreading rates of films, which change power laws in the course of spreading, and corroborate the theory with experiments. The spontaneous liquid patterning process reported in this work can provide a viable venue for such applications as electronic circuit printing and biochip fabrication.

Figure 1

(a) Scanning electron microscopy image of nanograsses formed on a Si wafer. The inset shows a side view of the nanograsses. (b) A schematic of a capillary tube with a hanging drop that touches a superhydrophilic microlane of the width $w$. The initial height of the liquid column in the tube is denoted by $h_L$. (c) A tilted tube to imbibe liquid more than Jurin's height $h_J$.

Figure 2

Spreading of water films from a tube (loaded with the same height of the liquid column, $h_L=38$ mm) onto superhydrophilic microlanes of different widths. The lane widths are (a) $w=0.2$ mm and (b) $w=0.6$ mm. Insets in panels (a) and (b) respectively show the magnified views of the zigzag front of the fringe film and of the fringe film preceding the bulk. (c) A schematic of the longitudinal cross section of the fringe film on the narrow lane. (d) A schematic of the longitudinal cross section of the bulk film on the wide lane. (e) Experimentally measured spreading distances of the fringe film ($x_f$) and the bulk film ($x_b$) versus time. (f) The log-log plot of the spreading distances versus time. (g) Experimental conditions for the symbols.

Figure 3

(a) Sequential images of a propagating fringe film of water emerging from a bulk beneath a capillary tube when $[w,h_L]=[2,10]$ mm. (b) Schematic of the cross-sectional view of the wetted nanograsses. (c) Measurement results of $x_f$ versus time for different liquids, lane widths, and initial liquid column heights. Inset: The log-log plot of the main graph. (d) The fringe extension $x_f$ plotted according to scaling law (1). The slope of the best fitting line is 0.21. Inset: The magnified plot for the initial time period. (e) Experimental conditions for the symbols.

Figure 4

(a) Types of liquid spreading depending on the width of the lane, $w$, and the height of the liquid column, $h_L$. The solid and empty symbols correspond to the fringe and the bulk spreading, respectively. (b) Experimental data in panel (a) are replotted according to scaling law (2). The slope of the best fitting line, $c$, is 0.36. (c) Experimental conditions for the symbols.

Figure 5

(a) Images of a propagating bulk water film in the early stages for $[w,h_L]=[1.0,38]$ mm. (b) Schematic of bulk spreading in the early stages. (c) Experimentally measured temporal evolution of bulk film, $x_b$, under different experimental conditions. (d) The experimental data of $x_b$ plotted according to scaling law (3). (e) Experimental conditions for the symbols.

Figure 6

(a) Sequential images of a propagating bulk film of water in the middle stages for $[w,h_L]=[0.8,33]$ mm. (b) A schematic of bulk spreading in the middle stages. (c) Experimentally measured temporal evolution of the bulk film extension, $x_b$, under different experimental conditions. Inset: The log-log plot of $x_b$ versus $t$. (d) The experimental data of $x_b$ plotted according to scaling law (4). The slope of the best fitting line is 1.0. (e) Experimental conditions for the symbols.

Figure 7

(a) Sequential images of a propagating bulk film of water in the late stages for $[w,h_L]=[0.8,33]$ mm. (b) A schematic of bulk spreading in the late stages. The inset shows the cross-sectional shape change of the bulk along the longitudinal direction, where the central thickness of the bulk, $h_f$, decreases with $x$. (c) Experimentally measured temporal evolution of the bulk film, $x_b$, under different experimental conditions. Inset: The log-log plot of $x_b$ versus $t$. (d) The experimental data of $x_b$ plotted according to scaling law (5). (e) Experimental conditions for the symbols.