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Capillary self-transport action is based on the assumption of aspersing apparent activity of aqueous droplets. The self-transport action has been numerically advised application Apparent Evolver. Figure 2 shows a simulation of a baptize atom affective on a hydrophilic/superhydrophobic blooming surface, breadth allotment of the atom is on the hydrophilic receptor armpit and added allotment is on the superhydrophobic substrate. Due to the apparent activity gradient, the atom moves appear the added hydrophilic breadth until it alcove its calm state.



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Simulation of a baptize atom (1 nL) affective on a 200 μm × 200 μm hydrophilic/superhydrophobic (50°/170°) blooming surface: (a) a baptize atom is placed on a blooming surface, breadth bisected of the atom rests on the hydrophilic receptor armpit and added bisected is on the beneath wettable substrate; (b,c) the atom moves appear added hydrophilic area; (d) the atom alcove its calm state.

To accept the self-transport process, three elements were taken into application in the simulation: a hydrophilic receptor armpit with berserk substrate, a atom of baptize and a dent placed at a specific ambit from the receptor site. The ambit of the dent and the receptor armpit are both 200 μm (L) × 200 μm (W) and both the gravitational force and abrasion are advised negligible. The gravitational force of the dent can be alone because the admeasurement of the dent (200 μm) is abundant abate than the capillary breadth (2.7 mm) for baptize at accepted temperature and pressure19. The abrasion force amid the dent and the substrate can be affected application the blueprint Ff = μ  FN, breadth μ is the accessory of abrasion and FNis the accustomed force. Bhushan et al.20 abstinent the accessory of abrasion on surfaces with altered wetting backdrop application diminutive force microscopy and showed that abrasion force on a berserk apparent is abundant abate than the abrasion force abstinent on a hydrophilic surface, e.g. the accessory of abrasion on a lotus blade (contact bend with water: 150°) is 0.05, admitting the accessory of abrasion on a hydrophilic magnolia blade (contact bend with water: 80°) is 0.1. In our simulation, FN is artlessly the weight of the chip, which is about 0.014 μN. Assuming that the accessory of the abrasion of a berserk apparent is about 0.0520, the estimated abrasion force should be beneath than 1 nN, which is about 1,000 times abate compared to the abating force (several micro-newton) acting on a atom with aggregate of 0.9 nL appear in our antecedent work21. Therefore, the abrasion force can be cautiously alone in the simulation.



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In adjustment to acquisition abuttals altitude for self-transport and investigate how far a dent can be placed alfresco a receptor site, we apish the action by adjusting the aggregate of the droplet. The acquaintance angles of the receptor armpit and the substrate are 50° and 170°, respectively. Figure 3(a) shows the accord amid the gap and absolute apparent activity with account to the aggregate of liquid. The breach point in the activity ambit (highlighted with a red mark) indicates that the baptize meniscus starts to breach up back the gap alcove its limit. The aggregate has bright access on the best gap amid the dent and receptor site. The above the aggregate of the aqueous is, the greater the accustomed gap. With an access of aggregate to 6 nL, the dent can be confused up to 100 μm abroad the receptor site. On the added hand, as the aggregate decreases to 1 nL, the best gap amid the dent and the receptor armpit is bargain admitting still a admirable 25 μm. Figures 3(b,c) represent appropriately acknowledged and bootless self-transport with the aforementioned aggregate of liquid, the high one shows a dent placed aural the gap absolute and there is abundant aqueous to affix the dent and the receptor site; the added case represents a dent placed above the gap absolute and a baptize arch cannot be established.



(a) Apparent activity as action of gap admeasurement with account to the aggregate (red marks represent breach credibility breadth the meniscus starts to breach up and atramentous mark on the blooming ambit represents case (b,c), respectively); (b,c) simulation of self-transport with a dent placed 30 μm and 70 μm abroad from a receptor site; (d) apparent activity as action of gap admeasurement with account to the wetting contrast.

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To accept the access of the wetting adverse on capillary self-transport process, 6 sets of wetting adverse were simulated. The aggregate of the atom was kept as 1 nL for all the simulations. The acquaintance bend of baptize on the receptor armpit was anchored at 50° and the acquaintance bend on the substrate assorted from 60° to 170°. Figure 3(d) shows the affiliation amid the apparent activity and the gap with account to the wetting contrast. The apparent activity decreases as the gap narrows. Therefore, in theory, back a atom is placed on a blooming surface, breadth allotment of the atom is sitting on the hydrophilic receptor armpit and allotment of it is on the beneath wettable substrate, alike with actual baby wetting contrast, e.g. 50° on receptor armpit and 60° on substrate, the atom will move appear added hydrophilic area, provided that the gap is aural the best acceptable ambit for the accurate configuration. However, back the substrate is hydrophilic and the wetting adverse is small, the self-transport best acceptable cannot be accomplished due to (1) the accretion abrasion force amid the dent and hydrophilic apparent compared to the abrasion force amid a dent and a superhydrophobic surface; (2) the lower the wetting adverse is, the added collapsed the activity ambit becomes and the collapsed activity ambit leads to low abating force. A case of bootless self-alignment is approved application hydrophilic/hydrophobic blooming apparent (Supplementary Figure S1), which consists of hydrophilic silicon receptor armpit (water acquaintance angle: 50°) and berserk fluoropolymer coated silicon substrate (water acquaintance angle: 100°). Despite the ample wetting adverse amid the receptor armpit and the substrate and the hydrophobicity of the substrate, the self-alignment bootless back the abrasion force amid the dent and the substrate becomes abundant above and stops dent from moving. Therefore, the key factors to accomplish reliable capillary self-transport are ample wetting adverse amid the receptor armpit and the substrate and the superhydrophobicity of the substrate.

Experimental tests accept been agitated out to investigate the proposed self-transport action with diminutive rain (Fig. 4(a)). The analysis sample consists of silicon receptor sites and atramentous silicon substrate coated with fluorocarbon polymer. Acquaintance bend hysteresis is an important agency for self-transport. As the baptize atom on the hydrophilic receptor armpit alcove the dent that was placed on the superhydrophobic substrate, the baptize acquaintance bend on one ancillary of the atom is the abbreviating acquaintance bend on the superhydrophobic substrate and the acquaintance bend on the added ancillary of the atom is the advancing acquaintance bend on the receptor site. To accomplish self-transport, the abbreviating acquaintance bend on the substrate needs to be decidedly above than the advancing acquaintance bend on the receptor site. In our experiments, the abstinent advancing/receding acquaintance bend on the substrate and the silicon receptor armpit are 174°/168° and 52°/28°, appropriately (Supplementary Figure S2). The abbreviating acquaintance bend on the substrate is abundant greater than the advancing acquaintance bend on the receptor site, which is the key for acknowledged self-transport. Due to the ample wetting adverse and the superhydrophobicity of the substrate, the baptize aerosol can be bedfast central the hydrophilic silicon receptor sites as apparent in the Fig. 4(b). Scanning cyberbanking micrographs of a silicon receptor armpit on atramentous silicon substrate coated with fluorocarbon polymer are apparent in Fig. 4(c,d). The aggregate of the atramentous silicon nanostructures and the low apparent activity fluoropolymer contributes to the superhydrophobicity of the substrate. Diminutive rain was produced application an accelerated humidifier, which contains a backlog of baptize and an aquiver plate. The degradation action was recorded with a accelerated video camera and the aerosol were detected and aggregate of the aerosol was affected with a machine-vision algorithm. The algorithm was implemented in MATLAB. The bore of the aerosol is in the ambit of 1–5 μm. Due to the superhydrophobicity of the surface, the aerosol can be affected as spheres and the aggregate can be affected based on the bore empiric from the video camera. Figure 4(e) shows the aggregate of the microdroplets per assemblage breadth and the allotment of the breadth covered by microdroplets as action of the degradation time. The after-effects announce that both the aggregate per assemblage breadth and the advantage breadth access linearly with degradation time.

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Experimental accoutrement and analysis sample: (a) Automatic micro-handling apparatus with diminutive rain; (b) microdroplets deposited on a hydrophilic/superhydrophobic blooming surface; (c) scanning electron micrograph of a silicon receptor armpit on atramentous silicon coated with fluorocarbon polymer; (d) cross-sectional appearance of a blooming apparent (planar silicon receptor armpit on larboard and annoying fluoropolymer coated atramentous silicon on right); (e) aggregate per assemblage breadth and advantage breadth as action of microdroplet degradation time.

In the tests, a 200 μm × 200 μm × 30 μm SU-8 dent is coarsely placed on the superhydrophobic substrate abutting to a analogous sized hydrophilic receptor armpit application a automatic micro-handling apparatus as apparent in Fig. 4(a). Diminutive rain was alien to the accumulation armpit to actualize the diminutive aerosol for the capillary self-transport. Examples of the tests are apparent in Fig. 5(a–f). The gap amid the dent and the receptor armpit is about 25 μm. The diminutive aerosol were accumulating on both the top of the chip, the receptor armpit and the substrate. The diminutive rain was delivered for about 18 seconds and the bulk of the aerosol basic a baptize arch amid the dent and the receptor armpit was estimated as 1.5 nL. Once the baptize arch was formed, the self-transport was acutely fast and took alone about 0.5 seconds for the dent to move from its antecedent position to breadth it is altogether accumbent with the receptor armpit (Fig. 5(c,d)). After the self-alignment occurred, it took tens of abnormal for the aerosol to be evaporated, abrogation the apparent dry (Fig. 5(d–f)). Capillary self-transport is additionally accessible back the dent was placed abutting to a receptor armpit with both beeline accession absurdity and rotational accession absurdity (Supplementary Figure S3). The capillary self-transport tests accept been again for 15 times with gap sizes alignment from 10 μm up to 90 μm. Among the tests, 14/15 tests resulted in acknowledged self-alignment. One barring was due to bereft atom deposition, arch to too fast atom dehydration (Supplementary Figure S4). This aftereffect is in aciculate adverse to cases breadth the substrate is not superhydrophobic (Supplementary Figure S1) and self-alignment of a dent placed alfresco its receptor armpit is not possible. We begin two analytical ambit to acquiesce acknowledged self-transport. Firstly, it is important to accumulation acceptable aqueous during the self-transport process. In case of bereft aqueous degradation during the final date of the self-transport, the dent accumbent alone partially (Supplementary Figure S4). The additional analytical constant is the gap size. Back the minimum gap was 90 μm, the ample aerosol on the receptor armpit and the dent led to a flip-chip apparatus in the self-transport (Supplementary Figure S5). The aerosol contacted anniversary added and aerial the dent up-side-down afore dehydration and adjustment it on the receptor site. This sets a acute absolute for a abiding self-transport that drags the dent appear the receptor site.

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Self-transport of a 200 μm × 200 μm × 30 μm SU-8 dent on a analogous sized silicon receptor armpit with superhydrophobic substrate application diminutive rain: (a) a dent is placed abutting to a receptor armpit with a gap of 25 μm; (b) diminutive rain is delivered to the accumulation site; (c) a aqueous meniscus forms amid the receptor armpit and the chip; (d) the dent aligns with the receptor armpit due to the capillary force; (e) aerosol are evaporating; (f) baptize has evaporated abrogation the apparent dry. The images are snapshots from Supplementary Movie S2.

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