Mechano-regulated surface for manipulating liquid droplets

The effective transfer of tiny liquid droplets is vital for a number of processes such as chemical and biological microassays. Inspired by the tarsi of meniscus-climbing insects, which can climb menisci by deforming the water/air interface, we developed a mechano-regulated surface consisting of a background mesh and a movable microfibre array with contrastive wettability. The adhesion of this mechano-regulated surface to liquid droplets can be reversibly switched through mechanical reconfiguration of the microfibre array. The adhesive force can be tuned by varying the number and surface chemistry of the microfibres. The in situ adhesion of the mechano-regulated surface can be used to manoeuvre micro-/nanolitre liquid droplets in a nearly loss-free manner. The mechano-regulated surface can be scaled up to handle multiple droplets in parallel. Our approach offers a miniaturized mechano-device with switchable adhesion for handling micro-/nanolitre droplets, either in air or in a fluid that is immiscible with the droplets.


Supplementary Note 1-The assembly of mechano-regulated surfaces
To fabricate the MRS, a polyester mesh coated with superhydrophobic graphene nanoplatelets-based mixture and peeled optical microfibres were used. As illustrated in Supplementary Fig. 1, after coating, the mesh had a thread diameter of roughly 65 m, and a square mesh pore length of about 200 m. The quartz optical fibre had a diameter of 125 m with its lower part wrapped in protective jackets. By tightly bounding the protective jackets of the fibres, the inter-fibre distance was about the same as the interpore distance of the mesh. Therefore, the matched size facilitates the protrusion and retraction of the fibre array.

Supplementary Note 2-The superhydrophobic background mesh
To pin the water droplet firmly on the MRS, the mesh should be sufficiently hydrophobic to prevent the wetting and wicking of the water droplet through the mesh.
We can deduce the hydrophobic requirement of the mesh by considering a column of liquid inside the droplet as illustrated in Supplementary Fig. 2a. The force balance among the surface tension, Laplace pressure and gravitational force is as following: where  is the surface tension of water;  is the angle indicating the position of the contact line on the mesh threads; a(WM)  is the advancing water contact angle on the mesh surface; r is the radius of the mesh threads; a is the inter-thread distance; r(WF)  is the receding water contact angle on the quartz fibre surface; d is the diameter of the quartz fibres;  is the density of water; g is the gravitational acceleration; R is the radius of the water droplet.
Thus, using the parameters in our case  is calculated to be about 122.59°.

Supplementary Note 3-The measurement of adhesive forces
The adhesive forces of MRS were measured by deforming water droplets and analysing their deformed shapes as describe in ref. 1 1 . In details, as shown in Supplementary Fig. 3, a pendant water droplet with volume of 3 l on micro-syringe tip was brought to contact with MRS and then pulled away. By increasing the pulling distance, the droplet gradually deformed. Right before the droplet detached from the MRS, the outline of the deformed droplet was recorded and analysed to obtain the adhesive force.
Considering the force balance of lower part of water droplets, we have:  (3).

Supplementary Note 4-Peripheries of the capillary bridges
For hydrophobic fibres, the capillary bridges formed at top of each fibre as shown in Supplementary Fig. 4a. LG SG LG SL (1 cos ) 0 ( 180 ) where indices L, G, and S of interfacial energies  represent liquid, gas, and solid, respectively. Therefore, the adhesion between the hydrophobic microfibres and water is always larger than zero. Such adhesion is sufficient to pin tiny droplets.
To demonstrate the solid-liquid adhesive force between hydrophobic surfaces and water droplets, we made a pendant water droplet in contact with a hydrophobic substrate which has a water contact angle of 108 ( Supplementary Fig. 5a). During the retreating of the microsyringe tip, the pinning force acted on the water droplet caused the pinch-off of the droplet. For a superhydrophobic substrate, a water droplet readily detached from the surface (Supplementary Fig. 5b).

Supplementary Note 6-Nearly-loss-free release of water droplets
For the 3-hydrophobic-fibre MRS, during the withdrawing of the microfibres, the water contact line easily receded on sides of the fibres. Once the contact line moved to the edge of the fibres, it was pinned initially. According to Gibbs criterion, the three phase contact line started to recede again when the receding angle was reached on the top facet during detaching. As a result, we observed the remaining water with volume of roughly 0.07 nl on the top of a hydrophobic fibre, as shown in Supplementary Fig. 6a.
For the 3-hydrophilic-fibre MRS, the superhydrophobic mesh repelled water and the receding contact angle was reached on sidewalls of the fibres during the withdrawing of the microfibres. The water contact line receded, leaving no trace of water behind.
Right before the detachment of the water droplet from the 3-fibre MRS, the liquid column was split into three small capillary bridges on each fibre facet. After the pinch-off of the three capillary bridges, there was roughly 0.15 nl water residue on the top of each fibre, as shown in Supplementary Fig. 6b.

Supplementary Note 7-Assisting detection of highly-diluted chemicals
The detection of highly-diluted chemicals bears great interest in fields such as medical diagnostics, pollution detection and biomedicine synthesis. To detect traces of chemicals, the evaporation of sample droplets on a superhydrophobic detection substrate is proved to be an effective method; however, the requirement for the superhydrophobicity of the detection substrates impairs generality of the method because most of detection substrates such as lots of surface-enhanced Raman spectroscopy (SERS) substrates are difficult to be made highly water-repellent.
The capability of the MRS for capturing and releasing both micro-and nano-litre droplets with nearly no loss shows potential for assisting the detection of highly-diluted chemicals or biomarkers 3,4 . As shown in Supplementary Fig. 7, we used the MRS to capture a 9 l droplet, which contained a fluorescent dye with an undetectable concentration, 66.7 nM rhodamine 6G (R6G). The droplet was evaporated under room temperature for 115 min. The volume of the droplet drastically shrank 225 times to 40 nl; consequently the concentration of the dye increased to roughly 15 M, which is clearly detectable under a fluorescence microscope. Such application of assisting the detection of low-concentration substances cannot be easily achieved by using a microsyringe or micropipette.

Supplementary Note 8-Mixing between droplets for micro-reactors
The mixing process of a coalesced droplet was recorded by a high speed camera ( Supplementary Fig. 8a). Once merged, extra surface energy was released which converted into inertial energy causing the coalesced droplet oscillated violently 5  The size distribution of silver nanoparticles synthesized in Fig. 6b was determined based on the TEM image ( Supplementary Fig. 8b). The synthesized silver nanoparticles have an average diameter of 7.87 nm with a standard deviation (SD) of 3.54 nm ( Supplementary Fig. 8c). The size distribution is in agreement with the UV-vis absorption spectrum which has a peak at 389 nm with full width at half maximum (FWHM) of 70 nm ( Supplementary Fig. 8d) 6 .