Low friction droplet transportation on a substrate with a selective Leidenfrost effect

An energy saving Leidenfrost levitation method is introduced to transport micro-droplets with virtually frictionless contact between the liquid and solid substrate. By micro-engineering the heating units, selective areas of the whole substrate can be electro-thermally activated. A droplet can be levitated as a result of the Leidenfrost effect, and further transported when the substrate is tilted slightly. The selective electro-heating produces a uniform temperature distribution on the heating units within 1 s, in response to a triggering voltage. Alongside these experimental observations, finite element simulations are conducted to understand the to understand the role of the substrate thermal conductivity on the temperature profile of the selectively heated substrate,. We also generate phase diagrams to verify the Leidenfrost regime for different substrate materials. Finally, we demonstrate the possibility of controlling low friction high speed droplet transportation (~ 65 mm/s) when the substrate is tilted (~ 7 °) by structurally designing the substrate. This work establishes the basis for an entirely new approach to droplet microfluidics.


INTRODUCTION
Transporting droplets in a controllable and energy efficient manner could have a significant impact on several engineering applications, such as low drag liquid transportation 1,2 , water collection 3,4 , and advanced microfluidic devices 5 . Based on a theoretical understanding of the wetting of surfaces, common approaches usually focus on creating a surface with designed physical/chemical features, e.g. hierarchical micro/nanostructured surfaces 6,7 , chemical gradients 8,9 , or slippery surfaces created by infusing low surface tension lubricant into microstructures that yield directional motion of water droplets when tilted at a low angle [10][11][12] .
Notably, some interesting attempts have demonstrated liquid transportation efficiency using such 3 techniques: for example, Chaudhury and Whitesides achieved an average velocity of 1−2 mm/s for droplet transportation on a silicon wafer possessing a gradient in wettability 13 , Ghosh et al. employed extreme wettability patterns to achieve a flow rate of up to 300 mm/s 14 , and Lv et al.
achieved a maximum speed of 420 mm/s for droplet transportation in a microfluidic system 15 .
Approaches taken to date have been based on the liquid-solid contact, where the droplet motion will more or less be affected by the friction or dragging effect induced by local surface roughness, dimensional confinement, as well as the non-uniformity of the surface wettability.
The Leidenfrost phenomenon (Figure 1a), first discovered in 1756 16 , describes a meta-stable state of a droplet on a substrate heated significantly above the boiling point of the liquid. In this state, the droplet is levitated by an instantaneously generated vapor layer (~ 100-200 µm) caused by the initial contact of the droplet with the substrate [17][18][19][20][21] . The levitation yields a virtually frictionless contact between the droplet and substrate [21][22][23] , therefore playing a key role in drag reduction for the liquid flow 24,25 . Moreover, the vapor layer acts as a thermal insulator preventing rapid droplet evaporation despite the high temperature of the substrate. Recent developments show some attempts to control the droplet motion based on the Leidenfrost effect levitation by employing ratcheted and other patterned substrates 21,[26][27][28][29] , magnetic fields 30 , electric fields 31 and acoustic radiation pressure 32 . However, the actuation of the Leidenfrost effect for a droplet has thus far involved heating the entire substrate, which limits downstream applications due to the extreme substrate temperature condition. Despite recent work to reduce the transition temperature 24,28 , the high energy consumption remains due to heating the substrate globally, rather than the localized area which supports the droplet.
In this study, we trigger Leidenfrost levitation of a droplet by the application of a voltage to micron-scaled serpentine shaped heating arrays, which cover the substrate in a selective manner.
In addition to initializing the levitation of droplets of three different liquids via selective heating of substrate areas, we also show that the droplet transportation can be actuated and controlled by designing heating array patterns, along with tilting of the substrate (5−10 °). The proposed strategy of selective heating could significantly reduce the energy input needed to actuate the Leidenfrost effect, and also offer a control mechanism for droplet motion by locally controlling the designed heating array. By combining our approach with surface relief patterns, precise directional control and self-propulsion can be achieved without the need to tilt a surface 33   Leidenfrost Levitation Activation and Measurements: Each wafer was selectively covered by 4 two dimensional arrays of devices, and electrical contact pads for each array were designed to enable independent control of the heating arrays. A customized rig was assembled with a stainless steel stage on an x y z θ manipulator, to assist the characterization. In order to maintain a uniform temperature within the stage, an mbed-controlled Peltier cooler with cooling pipes and fan was mounted on the underside of the stage to stabilize the ambient condition. Spring loaded electrical contacts were then used to pass a current through each array in turn. To verify the effectiveness of the Leidenfrost Levitation, we tested three different liquids, isopropanol (surface tension  20 mN/m), acetone (surface tension  28 mN/m), and deionized water (surface tension  72 mN/m). All liquids produced similar results, once heated beyond their respective Leidenfrost transition temperatures. In this paper, we present the summarized results for IPA as a typical case for the lowest surface tension liquid, which is the most difficult liquid when attempting to use materials techniques to create a super-liquid-repellent state. A 1000x USB optical microscope was used to observe the arrays, and a FLIR A40 thermal camera was used to observe the temperature profile of the substrate. Different powers were applied to each heated array in turn, and the array was left for 1 minute for the temperature to equalize.

Simulation:
A 'unit cell' device was also modelled in COMSOL Multiphysics software, which also included the substrate, stage and effects of the Peltier cooling as a boundary condition. The  In contrast to heating a substrate globally, selective heating to create discontinuously heated fields across the in-plane area of the substrate should reduce the energy input. To understand how the thermal energy distributes across the substrate, we performed surface thermal analysis using COMSOL Multiphysics. The qualitative analysis (Figure 3a) first considers a serpentine 'unit cell' resistor (0.2 heated ratio) on a borosilicate glass substrate with a voltage applied to show the temperature profile of the single unit cell above the Leidenfrost transition temperature.
The heat created as a result is then dissipated through the substrate, the stage underneath and also the air above the resistor. As can be seen in Figure 3a, the temperature difference across a distance of 100 μm, from the center of the heat to half way between two unit cells (or a heated ratio of 0.2) is as high as 20 °C for the borosilicate glass substrate.
As a result of this temperature difference, it would be expected that the resistors with a lower heated ratio (or a larger gap between them) would have to be heated to a higher temperature than required, in order to get the coolest part of the array to still be hot enough for the Leidenfrost effect to occur. To prove this, we further simulate the unit cells, with three adjacent serpentine units shown here on the same substrate ( Figure 3b) with a voltage applied on each unit cell (heated ratio = 0.5), and demonstrate a more uniform distribution of the temperature (the difference of temperature is less than 5 °C). In this case, the voltage required is lower than for the unit cell shown in Figure 3a. We note that the current flow through the serpentine-shaped unit cell is non-uniform as a result of the structure's geometry, as can be seen in Figure S As the selectivity of the Leidenfrost effect is via voltage actuated heating units on the substrate, the thermal conductivity of the latter will have a direct influence on the results. Two substrate materials with a large difference on thermal conductivity were employed to verify this impact, i.e. borosilicate glass (1.14 W/mK) and silicon (1480 W/mK) at 300 K 32 . As can be seen in Figure 3d, the results for a silicon substrate still follow the decreasing trend with increasing heated ratio. However, a greater power per line is required than for the borosilicate substrates to achieve the Leidenfrost effect, because the heat is dissipated through the substrate more readily, rather than remaining in the vicinity of the serpentine-shaped unit cells to form the uniform inplane temperature profile. Therefore, borosilicate is a more preferable substrate material for this experiment, as it could create a uniform temperature profile more effectively on the surface of the substrate, owing to its low thermal conductivity.
Finally, we demonstrate the possibility of controlling droplet transportation by taking advantage of using a selectively heated substrate (Figure S-3). A substrate with four separate blocks of 0.5 ratio heating arrays, each of which could be individually switched in sequence was created, as seen in Figure 4a and 4b. The first, second and fourth arrays were switched on for 0.1 s in turn, with a 0.1 s time gap between each one being switched on. Therefore, the substrate was selectively heated in the micro-scale (due to the heated ratio), the macro scale (the four arrays being heated individually) and in time (the arrays being sequenced individually). Each array was activated for an eighth of a cycle. The third array was left disconnected. A schematic of the controlled droplet transportation shows the droplet to the target zone (un-activated region) possessing the disconnected heating array in a short time. Experimental images (Figure 4c and 4d) indicate rapid droplet movements from both directions to region #3, at a comparable speed to that witnessed in Figure 1c, thus implying rapid, virtually frictionless transport. This concept also enables a new strategy of targeted delivery of a droplet by configuring the substrate to form, on demand, localized frictionless levitation layers, which could be of considerable interest to scientists and researchers in micro-fluidic systems, chemical engineering, biological engineering and other related areas.

CONCLUSION
In conclusion, we have demonstrated the electro-heating actuation of the Leidenfrost effect for three different liquids by applying voltages to heating units which selectively cover a substrate.
This approach provides rapidly switchable and highly targeted transportation of droplet, according to the design of the geometry and layout of the heating array on the substrate. By selectively heating a sample to produce the Leidenfrost effect in a small area where needed, rather than using a hot plate to heat the entire surface, the same effect can be achieved but with a much lower energy requirement. It also provides the potential for easy integration to be part of an on-chip device with an electrical triggering mechanism. Moreover, further energy efficiency could be achieved by using a feedback control system to drive and control the direction of