Hydrodynamic dispensing and electrical manipulation of attolitre droplets

Abstract

Dispensing and manipulation of small droplets is important in bioassays, chemical analysis and patterning of functional inks. So far, dispensing of small droplets has been achieved by squeezing the liquid out of a small orifice similar in size to the droplets. Here we report that instead of squeezing the liquid out, small droplets can also be dispensed advantageously from large orifices by draining the liquid out of a drop suspended from a nozzle. The droplet volume is adjustable from attolitre to microlitre. More importantly, the method can handle suspensions and liquids with viscosities as high as thousands mPa s markedly increasing the range of applicable liquids for controlled dispensing. Furthermore, the movement of the dispensed droplets is controllable by the direction and the strength of an electric field potentially allowing the use of the droplet for extracting analytes from small sample volume or placing a droplet onto a pre-patterned surface.

Introduction

Dispensing and manipulation of small droplets is central to inkjet printing1,2, bioassays3,4,5, drug delivery6,7, microcapsules8,9,10, microreactors11,12 and fabrication of micromechanical13,14,15, -electrical16,17 and even -biological18,19,20 devices. Over the past decades, scientific and industrial communities have aimed for dispensing smaller and smaller drops. So far, small droplets have been produced by methods based on micro-orifices (or channels) or by orifice-free methods. Examples for micro-orifice-based methods comprise the piezo-driven injection21, and the heat bubble ejection22 widely used in the field of inkjet printing. The T-junction23 and flow focusing24methods stand for channel-based methods used in microfluidics. Despite the effectiveness of the micro-orifice (or channel)-based droplet-producing devices, their typically confined geometry poses several challenges, such as high flow resistance and propensity to clogging. For the micro-orifice (or channel)-based methods, droplets were generated by squeezing the liquid out of the orifice, and this is the main reason why the size of the droplets depends largely on the size of the orifice. The currently existing micro-orifice (or channel)-based techniques (for example, inkjet printing) still encounter problems to generate droplets that are substantially smaller than the orifice from which they are ejected25. The size parameter χ=Rd/Ro is the ratio of the droplet radius Rd and the inner radius of the orifice Ro. Typically χ lies between 0.5 and 3 (ref. 25), and, consequently, ultra-small orifices would be needed for the generation of sub-micrometer-sized droplets26. Although the electrohydrodynamic jet (e-jet) printing27 can produce droplets much smaller than the orifice in the micrometre scale, it still meets constrains when aiming for small values of χ when Rdis in the sub-micrometre range. The coupling of drop and orifice sizes translates into challenges for fabrication of fragile micronozzles and handling them, for example, prevention of clogging when dispensing highly viscous liquids or suspensions.

Besides the orifice-based techniques, small droplets can also be produced by orifice-free techniques, such as droplets splitting based on surface-wetting properties28,29, pyroelectrodynamic-driven techniques30 and nanowire liquid pump techniques31. However, those techniques evoke a number of complex technical problems that require locally tuning of wetting properties of the substrate surface28,29, manipulation of a hot tip or an infrared laser beam30 or nanowires31 on a substrate.

Here we present a novel approach to dispense ultra-small droplets with controllable size. Instead of squeezing the liquid out of the nozzles, the droplets are formed by sucking back the liquid from a sessile drop initially suspended from the nozzles. In this way the size parameter χcan be decreased to 0.025 enabling the dispensing of picolitre to microlitre volumes even from a millimetre-sized orifice that is rather immune against clogging when dispensing highly viscous liquids or suspensions. Furthermore, the use of orifices with diameters of several micrometres shows the capacity of dispensing sub-micrometre sized droplets.

Results

Daughter droplet pinch-off regimes

We investigate this phenomenon with a sessile surfactant-stabilized water droplet suspended from surface-treated nozzles, which are connected to a computer-controlled syringe pump for extruding droplets or draining the liquid from the droplets back into the nozzle.Figure 1 shows that by draining the liquid with different drainage ratesQ, the droplet size Vd can be controlled and pinch-off regimes can be switched. Figure 1a and Supplementary Movie 1 show that the whole pinch-off process can be divided into two stages: first, the sphere-shaped sessile drop evolves into a cylindrical column with the height being much larger than its radius due to the drainage of the liquid. Second, the liquid column breaks up due to Rayleigh–Plateau instability after the stop of the drainage and pinches off one main daughter droplet with Rd much smaller than the radius of the mother droplet Rm. In addition, several ultra-fine satellite droplets are formed due to break-up of the liquid neck. Image analysis showed that the main droplet contains more than 99% of the total volume of the daughter droplets (last amplified panel of Fig. 1a). The presence of satellites proves that the neck was indeed broken up due to the Rayleigh–Plateau instability. The extension factor ɛ of the liquid column, defined as the ratio of its length to circumference, is very important for the subsequent break-up. In fact, we observed that the liquid columns always break-up if ɛ>1. In contrast, they never break-up when ɛ<1 consistent with the classical theory of Rayleigh–Plateau instability (Fig. 1c). This regime occurs when using small Q. Between pinch-off regime (Fig. 1a) and no pinch-off regime (Fig. 1c), there is a transition regime in which several drops of similar sizes are formed (Fig. 1b). Supplementary Movies 2 and 3 show the dynamic process of the transition regime and no pinch-off regime.

Figure 1: Three regimes of droplet formation.

Droplet formation at various Q (a) 7.2 nl s−1 (regime A, one main droplet), (b) 2.46 nl s−1(regime B, multiple droplets of similar sizes) and (c) 1.96 nl s−1 (regime C, no droplet formation). The outer and inner radii of the nozzle are 23 and 15 μm, respectively, Vm=0.52 nl, σ12=9 mN m−1. Scale bar, 50 μm.