Imbibition by polygonal spreading on microdecorated surfaces
Original entry: Sung Hoon Kang, APPHY 226, Spring 2009
Authors: Laurent Courbin, Etienne Denieul, Emilie Dressaire, Marcus Roper, Armand Ajdari, and Howard A. Stone.
Nature Materials, Vol 6, September 2007
Softmatter keywords: Wetting, contact angles, droplets, curvature, hydrophobic, hydrophilic, capillary force, Hele-Shaw, Darcy's Law
Review by: Scott Tsai, APPHY 226, Spring 2009
Contents
Abstract
Courbin et al use micropatterned surfaces to create different final shapes for spreading droplets. They show that they can control the final shape by changing the liquid. They describe a model for the velocity of the contact line, and they also show that the radii of the spreading drops scale with Washburn's scaling.
Wetting On Patterened Surfaces
Most studies on the wetting of patterened surfaces is concerned with increasing the hydrophobicity of the surface via increased roughness. In this study, the authors have focused on hydrophilic surfaces, where the increase in solid surface increases wettability. The paper presentated is concerened with the situation where the resultant contact angle is lower than the equilibrium contact angle of a drop sitting on a surface of the same material, but unpatterened. The authors use regularly patterened surfaces like the ones shown in Fig. 1.By varying the liquid used and keeping the size of the drops the same, the authors were able to see seven different macroscopic scenarios. As Fig.2 shows, the seven scenarios are (i) a circle around a reservoir, (ii) an octagon around a reservoir, (iii) a square around a reservoir, (iv) a square, (v) an octagon, (vi) a rounded octagon, and (vii) a circle.
Motion Of The Contact Line
As will be shown, the contact line dynamics of the system are what determines the final shape of the drop.
To see the movement of the contact line, the authors used bright-field microscopy coupled with high-speed imaging. When the contact line reaches a row of posts, a single post is first wet, then a lateral propagation of wetting of the posts in the lateral direction occurs (Fig.3).
The spreading rate in the lateral direction is much higher than the spreading rate in the front of the contact line. The dynamics of spreading are largely controlled by the speed at with the front of the contact line wets the next row of posts. Since the inter-post distance is shorter along the diagonal and longer in the lattice axis direction, it is expected that there will be slower motion in the lattice axis direction.
By decreasing the wettability of the liquid, the authors were able to generate shapes from (i) to (vii), starting with the lowest wettability to the highest wettability. In (i), the low wettability causes the contact lines to pin, where in (ii) and (iii), the contacts lines have room to rearrange such that an octagon and a square can be formed while the reservoir of liquid remains circular. By increasing wettability more, unpinning starts to occur along the diagonals and not the lattice axes, so the square is formed (iv). Increasing the wettability some more unpins the contact line more and results in shapes (v), (vi), and (vii).
V, the velocity of the contact line, is controlled by a balance of capillary driving (<math>\gamma{\cos}{\theta}/{\mathrm d}</math>) and viscous resistance (<math>\eta{\mathrm LV}/{\mathrm d^2}</math>), where <math>{\mathrm L}</math> is the distance to the reservoir (Fig. 4). The velocity V is obtained and has the form <math>\mathrm V {\sim} (\mathrm d\gamma/\mathrm L\eta)\cos\theta</math>.
The authors also show in Fig.4 that they obtain the classical Washburn scaling <math>L \propto (\mathrm d\gamma/\mathrm L\eta)</math>
In Fig.5, the authors show how the seven resultant shapes corrospond to normalized values of diagonal or axis velocities and show that the shapes are deteremined by the ratio of the two velocities.
By Sung Hoon Kang
Imbibition by polygonal spreading on microdecorated surfaces
Reference: LAURENT COURBIN, ETIENNE DENIEUL, EMILIE DRESSAIRE, MARCUS ROPER, ARMAND AJDARI AND HOWARD A. STONE, Nature Mat. 6, 661-664 (2007).
Soft matter keywords
wetting, pinning, hydrophilic, equilibrium contact angle, imbibition
Abstract from the original paper
Micropatterned surfaces have been studied extensively as model systems to understand influences of topographic1 or chemical heterogeneities on wetting phenomena. Such surfaces yield specific wetting or hydrodynamic effects, for example, ultrahydrophobic surfaces, ‘fakir’ droplets, tunable electrowetting6, slip in the presence of surface heterogeneities and so on. In addition, chemical patterns allow control of the locus, size and shape of droplets by pinning the contact lines at predetermined locations. Applications include the design of ‘self-cleaning’ surfaces and hydrophilic spots to automate the deposition of probes on DNA chips. Here, we discuss wetting on topographically patterned but chemically homogeneous surfaces and demonstrate mechanisms of shape selection during imbibition of the texture. We obtain different deterministic final shapes of the spreading droplets, including octagons, squares, hexagons and circles. The shape selection depends on the topographic features and the liquid through its equilibrium contact angle. Considerations of the dynamics provide a ‘shape’ diagram that summarizes our observations and suggest rules for a designer’s tool box.
Soft matter example
When a surface structure is introduced in a material, the roughness of the material changes wetting behavior of the surface. Wenzel derived an expression for a contact angle with the microstructured surface as follows:
cosθ_{W} = rcosθ
(θ: contact angle of a surface without microstructures, θ_{W}: contact angle of a surface with microstructures, r is the ratio of the actual area to the projected area [1])
As a result, a hydrophobic surface (a surface with a contact angle larger than 90°) becomes more hydrophobic, whereas a hydrophilic surface (a surface with a contact angle smaller than 90°) becomes more hydrophilic [2]. In this paper, the authors enhanced the wettability of polydimethylsiloxane (PDMS) surface by using microtextures (Fig. 1) made by soft-lithography technique based on the argument described above [3]. They studied the case when 0< θ_{eq} < θ_{c} < π/2 where θ_{eq} is the equilibrium contact angle and θ_{c} is the threshold which I couldn't understand the exact meaning. In this case, the liquid can penetrate the surface by partial imbibition (See http://en.wikipedia.org/wiki/Imbibition for more information.) by the rough surface whereas the macroscopic droplet does not spread but gradually reduces its size by the loss into the surface texture.
The velocity of the contact line movement described in Fig. 3 is determined by a balance between capillary force (γ cosθ_{eq}/d) and viscous resistance (ηLV/d^{2}), where L is the distance to the reservoir shown in Fig. 4 above. Then, they analyzed the dynamics of spreading summarized as a "shape diagram" shown in the Fig. 5 above. From the shape diagram, they demonstrated control of the locus, size and shape of spreading droplets by varying the fluid, volume of the fluid and the underlying lattice as shown in Fig. 6 below. As authors mentioned, further modifications of the surface geometry can increase the number of possible shapes. For reference, the surface tensions of the pure fluids used in this study are summarized as below [4].
Liquid | Temperature °C | Surface tension, γ |
---|---|---|
Ethanol | 20 | 22.27 |
n-Hexane | 20 | 18.4 |
Isopropanol | 20 | 21.7 |
Table 1. Surface tension (unit: mN/m) of some liquids against air [5].
Fig.6 The design of the microtexture allows for the control of the locus, size and shape of spreading droplets. a. Four droplets of the same fluid coloured with different dyes give identical squares. b. Four different fluids spreading over a given microtextured surface exhibit different shapes (circumscribed square and octagon, square and octagon). The liquids are respectively: (circumscribed octagon) 98 vol% ethanol and 2 vol% isopropanol, (circumscribed square) 75 vol% ethanol and 25 vol% isopropanol, (square) 25 vol% ethanol and 75 vol% isopropanol, and (octagon) isopropanol. c. Two droplets of the same fluid on the same rough surface exhibit the same shapes (squares, octagons on a square lattice and hexagons on a hexagonal array) but with different sizes as the volume of the drop is changed. We used ethanol to form the squares and isopropanol for the octagons and hexagons. Scale bar: 1 mm. The parameters of the surface are d =200 μm, R =50 μm, H =50 μm for a,b and d =100 μm, R =25 μm, H =60 μm for c.
References
[1] R. N. Wenzel, "Resistance of Solid Surfaces to Wetting by Water". Ind. Eng. Chem. 28, 988-994, (1936).
[2] P.-G. de Gennes, F. Brochard-Wyart, D. Quéré, A. Reisinger, Capillarity and Wetting Phenomena (Springer, New York, NY, 2004).
[3] J. C. McDonald, G. M. Whitesides, Acc. Chem. Res. 35, 491-499 (2002).
[4] http://en.wikipedia.org/wiki/Surface_tension
[5] Lange's Handbook of Chemistry, 10th ed. pp 1661–1665.