High‐Rate Accumulation of Tiny Aqueous Droplets Using a Pyroelectrohydrodynamic Jet System

It is well known how the quantification of tiny amounts of molecular species in biological assays is a crucial issue. Herein, a deep investigation on a pyroelectrohydrodynamic jet system is presented in aim to demonstrate its capability to accumulate a large number of tiny aqueous droplets on the surface of a target slide with high efficiency. It makes use of the pyroelectric effect in a lithium niobate crystal for producing a continuous jetting of tiny droplets, thus reducing drastically the volume of sample required for successive biochemical reactions. The performance of the system in terms of electrical field and crystal size is characterized experimentally as well as numerically. An optimal condition is found that produces the deposition of more than 100 pL‐sized droplets in 14 s. Thus, a possible 70‐fold increase in the analyte concentration in the overlap region with a diameter of less than 40 μm is estimated, compared with an individual droplet deposition. Moreover, in case, an additional increase can be achieved simply by extending the droplet accumulation time. This approach may find application in all of those crucial biological assays where highly diluted analytes could be detected by increasing the density of molecules per unit area.


Introduction
The demand on sensitivity improvement beyond the common limit of detection (LOD) of about 1 pM is always of increasing importance for the detection of biomolecules in highly diluted solutions. [1,2] Moreover, the increasing need for more rapid and noninvasive assays in biomedicine requires the search for biomolecular markers in peripheral body fluids (e.g., saliva, capillary blood, and tears) where their concentration is highly diluted and the available volumes are reduced. Just as an example, in case of the Alzheimer's disease a noninvasive diagnosis that avoids the withdrawal of cerebrospinal fluid is still highly desired. [3] One way to proceed involves the development of techniques able to amplify the number of molecules, whereas another family of strategies, namely preconcentration by solvent removal, regard the ability of reducing the reaction volume to increase the analyte concentration, leading to an amplification of the signal. [4,5] For example, Giordano et al. used a microfluidic-based platform for carrying out an oil-assisted water extraction in trapped microwells, whereas other groups have presented a polarization-based phenomenon. [6][7][8][9] Alternatively, a sessile drop evaporating on a superhydrophobic structure or in presence of Marangoni flow inside can be used for increasing the analyte concentration. [10][11][12] However, microfluidics-based methods need rather large volumes of sample, whereas the methods with sessile drops require the use of challenging techniques for the fabrication of the substrate. Moreover, using oil-based mixing buffers can be highly detrimental for the chemical-physical stability of the biological samples.
Recently, we demonstrated how the pyroelectric effect in lithium niobate (LN) crystals can be used for generating high electric fields in the order of a few kV/mm through an innovative electrode-free configuration. These fields were used for ejecting tiny daughter droplets from the free meniscus of a mother drop with a sub-μL volume. [13][14][15][16] We called it pyroelectrohydrodynamic jet (p-jet) and we demonstrated its usefulness for accumulating protein-based as well as sugar-based molecules, by printing multiple overlapping droplets on a restricted area. [17][18][19][20] Note that there are many methods for generating liquid microdroplets, [21,22] but the key advantage of the p-jet DOI: 10.1002/adem.202100756 It is well known how the quantification of tiny amounts of molecular species in biological assays is a crucial issue. Herein, a deep investigation on a pyroelectrohydrodynamic jet system is presented in aim to demonstrate its capability to accumulate a large number of tiny aqueous droplets on the surface of a target slide with high efficiency. It makes use of the pyroelectric effect in a lithium niobate crystal for producing a continuous jetting of tiny droplets, thus reducing drastically the volume of sample required for successive biochemical reactions. The performance of the system in terms of electrical field and crystal size is characterized experimentally as well as numerically. An optimal condition is found that produces the deposition of more than 100 pL-sized droplets in 14 s. Thus, a possible 70-fold increase in the analyte concentration in the overlap region with a diameter of less than 40 μm is estimated, compared with an individual droplet deposition. Moreover, in case, an additional increase can be achieved simply by extending the droplet accumulation time. This approach may find application in all of those crucial biological assays where highly diluted analytes could be detected by increasing the density of molecules per unit area.
is that it is nozzle-free, thus allowing us to avoid the typical clogging drawbacks encountered in conventional pipetting systems and inkjet printers.
Here, we present a significant step forward in which we produce a much higher number of aqueous tiny droplets in a single thermal stimulation, by applying an appropriate heating ramp on a small piece of LN crystal thus achieving good control of the jetting operation. A quasistatic pyroelectric field is generated that slowly decays due to the attraction of charges from the environment to the crystal surface. The decay of the electric field governs the duration of the p-jet, and therefore being the important feature of the droplet accumulation process. We study this decay experimentally as a function of the LN crystal size. In addition, the influence of the crystal size LN on the distribution of the electric field around the upper surface of the crystal and the meniscus was investigated numerically. We use here a top-down configuration of the p-jet system in which a micro-orifice allows us to load a higher volume of sample, thus being free from the crucial deposition of the sample in the form of a sub-μL mother drop, as occurred in the previous bottom-up arrangements. [15,[17][18][19][20] Finally, we demonstrate the ability of the proposed p-jet configuration to accumulate about 70% of the dispensed aqueous droplets into a limited area with a micrometric cross size, thus opening the perspective for a more affordable concentrator of analytes in aqueous solutions. Thereby, here we aim at further development of the p-jet system for accumulation of microdroplets, which was proposed and applied for biosensors in our previous works. [17][18][19][20] 2. Results and Discussion

Pyroelectrohydrodynamic Jet System
The operation of p-jet system is based on the phenomenon of electrohydrodynamic (EHD) emission of microdroplets from the surface of an electrified liquid. The meniscus of the mother liquid reservoir charges under the action of the electric field and therefore a repulsive Coulomb force arises between these charges of the same sign and deforms the meniscus into the so-called Taylor cone, whose apex breaks up into jets or droplets. [23,24] The break process of the meniscus depends on various parameters such as physical properties of the fluid, flow rate, electric field strength, system geometry, etc., which lead to different modes of EHD atomization, classified, for example, by Cloupeau and Brunet-Foch. [25] At low flow rate, the so called microdripping mode is possible, which is characterized by emission of monodisperse microdroplets whose diameter is considerably smaller than the diameter of the capillary tube holding the meniscus. [26] We consider this mode to be beneficial for the p-jet system. Figure 1a shows the schematic view of the top-down configuration of the p-jet used here for achieving a high-rate accumulation of tiny aqueous droplets ejected from the liquid's meniscus.
The aqueous sample (around 10 μL) is loaded manually by a standard pipette into the micro-orifice of an innovative slide that we call here "loading support." See the Supporting Information for more details. Once the micro-orifice is filled with the sample liquid, a stable meniscus emerges, as described in the Supporting Information. A standard XYZ micrometric manual translation stage is used for aligning the micro-orifice aperture with the central point of a square piece of LN crystal, whose size is described later. LN is a pyroelectric material, meaning that is able to generate a non-negligible surface potential upon an appropriate variation of its temperature (see Experimental Section for details). The target slide, namely the slide where accumulating the tiny droplets, is a commercial SuperAmine 2 slide usually used for binding biomolecules (SMM2, ArrayIt) and is inserted between the orifice and the LN crystal. The slide is 75 Â 25 mm 2 sized and 1 mm thick. The heating element underneath the crystal belongs to a commercial heating plate (Linkam) or to a standard Peltier element 15 Â 15 mm 2 sized (see Experimental Section for details). As described in Experimental Section, a thin metal wire is inserted into the orifice, which put in contact the liquid and a thin metal sheet between the crystal and the heating element, to ensure electrical neutralization of the meniscus after emission of a charged droplet and to enhance the electric field strength.
It is important to note the step forward developed here compared with our previous papers where we used a bottomup configuration (see Figure 1b). Two options were used there for the thermal stimulation: 1) CO 2 laser radiation and 2) Joule effect from a titanium coil integrated on the back face of the crystal. [17][18][19][20] The laser-based system was extremely bulky, whereas the coil-based heater needed expensive and www.advancedsciencenews.com www.aem-journal.com time-consuming microfabrication. The common disadvantage was the need for a sub-μL mother drop to produce tiny droplets, thus producing a reduced number of ejected droplets in a single thermal stimulation.

Simulation of the Electric Field
Prior the application of the p-jet for dispensing tiny droplets, here we simulated numerically the spatial distribution of the electric field E generated by considering a fixed temperature variation ΔT ¼ 15 K for different crystal sizes, to find the best conditions for achieving the high-rate droplet ejection. The fairly small value of ΔT was chosen keeping in mind the potential use of this set-up for accumulating biomolecules, and thus avoiding conditions that may cause their thermal damage. The surface of the meniscus is taken to be spherical with a radius of 0.4 mm in accordance with the side view images experimentally recorded with a digital camera (see the Video 1, Supporting Information). The meniscus must have the same electrical potential as the contact wire that is electrically connected to the backside of the LN crystal (see Figure 1a), keeping in mind that the electrical relaxation time of the aqueous sample is much shorter than the characteristic time of all other involved processes. [27] We focused our attention on two values of the crystal thickness d (0.5 and 1 mm) and on four values of the side length a (2, 6, 10, and 14 mm). For these simulations, we refer to the coordinates shown in Figure 1a, and we studied the distribution of E strength first at X ¼ 0 (center of the crystal) along the Z axis, and second, at Z ¼ 0.01 mm, namely close to the surface of the crystal, along the X axis from 0 (center of the crystal) up to the edge of the crystal. See Experimental Section for details about the simulation procedures. Figure 2a shows the E distribution along the Z axis at X ¼ 0. Here, Z ¼ 1 mm and Z ¼ 1.37 mm correspond, respectively, to the upper surface of the target slide, namely the surface where the droplets are accumulated, and to the apex of the liquid meniscus pending from the orifice (see the scheme in Figure 1a). The field strength increases significantly in the vicinity of the meniscus, as is usually the case near a strongly curved conductive surface. Moreover, it increases with increasing the crystal side length but the field increment is negligible at a ≥ 6 mm. Thicker crystals (d ¼ 1 mm, red lines) always generate fields about twice that of thinner crystals (d ¼ 0.5 mm, black lines). That is in agreement with the fact that electric potential difference between þz and Àz surfaces of a pyroelectric crystal is proportional to the crystal thickness (see Experimental Section). Figure 2b shows the results for the E distributions along the X or Y axis (note that two axes are equivalent due to problem symmetry) for Z ¼ 0.01 mm. First of all, the spiking effect of the electric field is clearly evident in correspondence of the edge of the crystal for all d and a, with E values ranging from about 2.3 kV mm À1 , in case of d ¼ 0.5 mm and a ¼ 14 mm, up to about 7.7 kV mm À1 in case of d ¼ 1 mm and a ¼ 2 mm. This suggests to use the central region over the crystal as source for the electric field, namely at X ¼ Y ¼ 0, to avoid the highly inhomogeneous field. The blue horizontal line corresponds to the typical value of the electrical breakdown threshold in air under normal laboratory conditions (about 3 kV mm À1 ). Thereby, Figure 2b clearly shows that E values overcome an electric breakdown threshold at the edges of the LN plate with a ≤ 6 mm and a ≤ 10 mm for the thin and thick crystals, respectively. Here, intensive generation of ions due to a corona discharge and their accumulation on the surface of the crystal are expected, leading to a decrease in the pyroelectric potential. [28] It is reasonable to assume that the rate of ion generation increases with an increase in the area of the crystal, on which an electrical breakdown occurs. Figure 2b shows that this area enlarges with the plate side length decreasing and thickness increasing. In contrast, the amount of accumulated external charges required for a noticeable drop in the pyroelectric potential should be proportional to the crystal surface area. As a result, the characteristic decay time is expected to increase with increasing surface and decreasing thickness of the crystal plate. We investigated experimentally this decay time as a function of crystal size. The corresponding results will be presented and discussed in the next section. www.advancedsciencenews.com www.aem-journal.com In summary, the simulations along Z axis demonstrate that the highest E is achieved using the thicker crystal (d ¼ 1 mm) and side length a ¼ 6 mm, with a negligible difference for increasing a. These results are consistent with the simulation results along the X axis that identify with the side length a ≥ 6 mm, which can provide a sufficiently long p-jet process. Therefore, the overall simulations carried out in this section demonstrate that we have to focus our attention on crystal samples with side length a ≥ 6 mm.

Measurement of Electric Potential Decay
We changed the temperature of the pyroelectric crystal by 15 K, as in case of the simulations, with the aim at identifying the crystal size that produces the potential as much stable as possible over time, and hence able to produce the higher number of tiny droplets in a single thermal stimulation. The potential was measured as a function of time t for samples LN of two thicknesses d ¼ 0.5 mm and d ¼ 1 mm with a side length, a, of 1.6, 2.6, 3.6, 7.6, 8.6, and 16 mm. The crystal dimensions are shown as in Figure 1a. The measurements were carried out in an ambient atmosphere at 25 C and 24% relative humidity. Figure 3a shows the schematic view of the equipment used for the pyroelectric potential measurements. We used a commercial Linkam system to control the LN crystal temperature with the time dependence shown in Figure 3b. The temperature was increased from the room value of 25 C up to T ¼ 40 C during the time interval from t ¼ 15 s to t ¼ 45 s and from t ¼ 17 s to t ¼ 27 s for the crystals with d ¼ 0.5 mm and d ¼ 1.0 mm, respectively. After that, the temperature was kept constant (see Experimental Section for details). It is important to note that the diameter of the heating element was 22 mm, which made it possible to cover the entire crystal surface for all values of a studied here. The potential was measured through a commercial Kelvin probe at a distance Z ¼ 1.5 mm from the surface of the crystals (see Experimental Section for details). Figure 3c,d shows the results in case of fixed thickness d ¼ 0.5 mm and d ¼ 1 mm, respectively, and for different values of the side length a.
The electric potential was in the range from 1 to 2.5 kV for crystals with a thickness of 0.5 mm, whereas it could exceed 4.5 kV for crystals with a thickness of 1 mm and a > 7.6 mm, resulting in an electrical breakdown between the crystal surfaces. Therefore, in the latter case, we limited ourselves to a crystal side length of 7.6 mm. Note that, the absolute value of the electric potential can be measured with a rather high error, especially for small LN samples, but it is not important because here we are focused on the relative change in potential over time. [29] The curve of the electrical potential exhibits three main regions Figure 3. a) Schematic view of the setup used for measuring the electrical potential generated by the LN crystal under a stepwise temperature variation. b) Shape of the crystal temperature dependence on time. c,d) Temporal behavior of the electrical potential for the crystals with thickness d ¼ 0.5 mm and d ¼ 1 mm, respectively. The crystal side length a takes discrete values from 1.6 to 16 mm. The dashed blue lines separate the "base," "rise," and "decay" regions.
www.advancedsciencenews.com www.aem-journal.com in all cases, that we call here "base," "rise," and "decay," as shown by the labels in Figure 3c,d. The base corresponds to the initial potential, the rise to potential growth during the linear T increase and the decay region starts when the T value is kept constant. It is worth noting that each a value corresponds to a different sample and therefore the base of the potential curve appears slightly different for each value of a, due to the different pre-existing charge accumulation.
For both values of thickness, the decay accelerates significantly with decreasing a, exhibiting three main rates that we call "fast," "medium," and "slow." The fast rate includes the crystals with a ¼ 1.6 mm (black lines) and a ¼ 2.6 mm (red lines), with negligible differences, whereas the medium region regards the crystal with a ¼ 3.6 mm (green lines). Finally, the slowest decay is achieved for crystals with a ≥ 7.6 mm, with negligible differences for increasing length. In particular, the data shown in Figure 3c,d show, respectively, that 55 s (graph d ¼ 0.5 mm) and 40 s (graph d ¼ 1 mm) after reaching the peak value the potential decays by only 5% in case of larger samples (a ≥ 7.6 mm), with almost constant value later, whereas reduces by about 20% in case of the shorter side length (a ¼ 1.6 mm and a ¼ 2.6 mm) with subsequent further decline over time. These measurements show that a crystal with a side length of more than 8 mm provides a fairly stable electrical potential over time.
It is well known that the electrical potential decays gradually over time due to three main factors: i) bulk conductive current; ii) ferroelectric electron emission; and iii) accumulation of screening charges from the ambient atmosphere on the crystal surface. [28,30] Here, the screening from electron emission is negligible because the crystal is exposed to the normal atmosphere, while the bulk conductive screening occurs very slowly with a relaxation time around 10 5 -10 7 s. [30] Therefore, we believe that the electric potential decay over tens or hundreds of seconds is mostly related to the charge recombination on the surface of the crystal through the ambient ions produced by the electric breakdown along the edges of the crystal, i.e., where the breakdown threshold is overcome. [30] Crystals with a longer side and, therefore, a larger surface (see the curves for a > 3.6 mm in Figure 3c) exhibits slow decay, as a smaller surface fraction is covered by screening charges during the same time interval compared with crystals with smaller surface. Among crystals with the same side length, thicker crystals exhibit faster decay as they create a higher electric field at the edges, thereby accelerating the formation of ions in the environment (compare green or blue lines in Figure 3c,d). We can conclude that the experimental results are consistent with expectations based on electric field simulations. However, it is important to note that this study allowed us to find an optimal condition in which electrical potential is stable over time.

High-Rate Accumulation of Aqueous Droplets
Considering the simulation of the electric field and the measurement of the electric potential, we configured the p-jet setup schematically shown in Figure 1a using a crystal sample 1 mm thick and 7 mm side length, which was expected to provide an electric field sufficiently high and stable for several tens of seconds. We loaded about 10 μL of distilled water in the orifice and we positioned the lower face of the loading support at about 300 μm from the top surface of the target slide. The Peltier element was 15 Â 15 mm 2 large and was driven by a step-wise current pulse of 0.5 A (with 0.6 V voltage) provided by a programmed power supply HCS-3300, to raise the crystal temperature from 25 C up to about 40 C. Even if in our study, we used 40 C as the maximum temperature that could damage biological samples in case of application as biosensors, this is not important in these experiments. In fact, what is important for the performance of the device is the change in temperature ΔT, which is able to create a sufficiently strong electric field for activating the liquid jetting. Thus, in the case of biological applications, the required ΔT value can be easily reduced by increasing the crystal thickness, as shown earlier.
The Movie 1, Supporting Information, shows a side view of a typical high-rate droplet ejection occurring after a current is applied. The video was recorded at 50 fps frame rate using a conventional optical system comprising an illuminating LED source, a microscope objective and a PC-controlled camera, which has been described in the study by Rega et al. [18] It demonstrates a continuous deposition of the aqueous droplets drawn from the orifice on the surface of the target slide. The droplet ejection starts 7 s after Peltier power on and finishes after about 46 s, when the electric field decreases to an EHD jetting threshold due to screening charges accumulated on the crystal surface. [26] All droplets are deposited within a target slide area with a diameter of about 150 μm.
We analyzed the images of the recorded movie to evaluate quantitatively the rate of accumulation of the droplets on the target slide. The video frames in the first 14 s were cropped to the region of interest with a width of 500 pixels and a height of 100 pixels, Considering that the pixel size of the images was about 0.6 μm, and the first frame was used as a reference to be subtracted from the others to remove the background (see the Movie 2, Supporting Information). We used here a transmission-based illumination of the water jets and, therefore, the dark pixels in the frame corresponded to the region where there was liquid attenuating the light from the LED source. The contour of that dark pixel area outlined a side view of the deposited water drop together with its reflection in the target slide and so it was used for measurements of various geometrical parameters of the drop such as their height above the target slide, diameter of a base, and deposition coordinate. Other parameters such as a contact angle and a drop volume were calculated from the measured ones (see the Supporting Information for details).
The contact angle of 74 was obtained by averaging over the all cases of droplet deposition. The volume was slightly different for each droplet and it is well known that the evaporation rate decreases with increasing volume. Hence, for some jet events, we had an overlapping of a droplet on the previous one, when not evaporated completely. Therefore, to quantify each droplet volume as best as possible, we subtracted the volume of the deposited liquid at the frame preceding to the jet event, to remove the contribution from the previous droplet not evaporated completely. The events of droplet deposition are shown in Figure 4, which present the frames extracted from the Movie 1, Supporting Information. Figure 4b,d shows the deposition of the first and second droplets, and Figure 4a,c shows frames preceding these events, respectively. Figure 4e shows all www.advancedsciencenews.com www.aem-journal.com deposition events of individual droplets versus time, represented by peaks with a height equal to the droplet volume V, expressed in picoliters. The figure demonstrates that we identified 92 jets of individual droplet within %14 s, whereas 14 multiple (2-3) droplet ejection events were excluded from the analysis. A time interval between two adjacent jetting events ranges from 0.10 to 0.66 s. Note that, typically EHD droplet jetting is nonperiodic for low liquid flow rates. [26] Droplet volumes range from 5 to 25 pL with an average of 14 pL and a standard deviation of 4.8 pL.
The following analysis aims to estimate how many droplets overlap on the restricted area of a target slide. To this end, we calculated the diameter of the area that each ejected droplet with a known volume V can cover and the X coordinate of its deposition (see the Supporting Information for details).
The diameter of the covered area (here, we call this area a "droplet spot" for brevity) was calculated on the assumption that a deposited droplet has a 74 contact angle with the target slide surface and forms a spherical interface with air. The histogram in Figure 4f shows the frequency distribution for a droplet spot diameter. The mean value of a droplet spot diameter D mean is 42.5 μm.
To calculate the barycenter coordinate of the deposited droplet, we retrieved a series of images (see the Movie 3, Supporting Information) obtained by subtracting the previous frame from each frame of the Movie 2, Supporting Information. Here, the dark pixels, which correspond to the contribution of the previous droplet not evaporated completely, are excluded from the image of the deposited droplet. Then, we found a barycenter coordinate of the deposited droplets using a standard procedure integrating the grey levels of the pixels. The histogram of the frequency distribution of the barycenter coordinate is shown in Figure 4g. The histogram demonstrates that 74 droplets have the barycenter coordinate in a region about 40.6 μm wide, which is less than D mean , and so the droplet spots overlap at least partially within www.advancedsciencenews.com www.aem-journal.com this region. This can provide %70-fold increase in the surface density of the analyte molecules dissolved in the aqueous sample compared with the deposition of a single drop. It is noteworthy that, first, this increase is underestimated as we excluded the jets with multiple droplets, and second, the surface density of molecules can be enhanced simply by increasing the accumulation time of the droplets. In contrast, the flow of droplets can be interrupted, if necessary, by increasing the distance between the loading support and the pyroelectric crystal.
In conclusion, we developed here a new p-jet configuration able to produce a quasistatic pyroelectric field which allows us to achieve high-rate accumulation of tiny aqueous droplets in a single thermal stimulation. The key feature relies on the Peltier-based heater element, able to apply a single rise temperature onto a small piece of LN crystal. We optimized the LN crystal thickness and side length to produce pyroelectric field sufficient for EHD droplet dispensing during time interval of about 40 s. The experimental results demonstrate accumulation of more than 70 tiny aqueous droplets during the first 14 s on the target area with a diameter of less than 40 μm. We believe that this technique could open the route to easy accumulation of biomolecules for high-sensitive detection of highly diluted biomarkers.

Experimental Section
LN Crystals: Both sides polished and z-cut wafers of monodomain LN with 0.5 mm thickness and 3 in.-diameter were bought from Crystal Technology Inc. The wafers were cut into square samples with a side length of 1.6, 2.6, 3.6, 5.0, 7.6, 8.6, and 16 mm by a standard precision diamond saw. To obtain LN samples with a thickness of 1 mm, two cleaned LN plates with a thickness of 0.5 mm with the same lateral dimensions and polarization direction were stacked up and glued together with standard thermal paste. The spontaneous polarization P s of the LN crystal changes according to ΔP s ¼ pΔT where p is the pyroelectric coefficient and ΔT is the temperature variation (p ¼ À8.3 Â 10 À5 C m À2 K À1 at T ¼ 298 K). At thermal equilibrium, the spontaneous polarization of the crystal is completely screened by the external charges accumulated on the crystal surfaces and no electric field is present. [28] When the crystal is stimulated through a temperature variation, an uncompensated surface charge density σ ¼ ΔP s and electric potential difference ΔU ¼ σd ε 0 ε appears on the crystal surfaces (here d is crystal thickness and ε 0 and ε are dielectric constants of vacuum and of the crystal, respectively). This potential difference can reach 10 4 V for mm-sized crystal thickness and ΔT of about 10 K.
Heating Element: The crystal plate was mounted with silicone thermal grease from RS components on top of a heater. We used two kinds of heater which were able to heat LN plate homogeneously over its largest surface. The first one was HFSX350 heating-freezing stage from Linkam Scientific Instruments. It had a disk-shaped heating/cooling element with a diameter of 22 mm and was able to provide heating rate up to 90 C min À1 and to keep preselected temperature of the element with precision of 0.1 C. The second one was based on the commercial Peltier element from Laird with lateral dimensions of 15 Â 15 mm 2 driven by a programmable power supply HCS-3300. Temperatures of the heaters and LN crystals were measured by FLIR 7 Infrared Thermal Imaging Camera.
The Contact Wire and Metal Sheet: Equalization of potentials of the liquid meniscus and the underside of the LN crystal significantly increased the electric field strength near the meniscus. Moreover, it helped to compensate the excess of charge accumulating in the liquid sample during the emission of the charged droplets. To this end, we introduced a contact wire electrically connecting the meniscus and a thin metal sheet on the underside of the LN crystal. The contact wire and metal sheet were made of the same 0.05 mm copper foil that covers the surface of the Peltier element and was cut 1 mm wide and 30 mm long to form the wire (in fact, any conductive material can be used for this purpose).
Electric Field Simulation: Finite element method was used for simulation of electric field generated around LN crystal and particularly in the gap between the crystal and the fluid meniscus. LN crystal was represented as a square dielectric plate with the dielectric constant ε ¼ 28.5. The plate was enclosed within a bounding box with dimensions of 160 Â 160 Â 100 mm 3 and with zero potential on its boundaries. Note that to choose the dimensions of that box, there was a trade-off between a stray capacitance introduced by the box and the memory and time usage during the simulation. To decrease the memory and time consumption, the model volume was reduced by a quarter using the symmetry boundaries at ZX and ZY planes which were perpendicular to the LN plate and pass through its geometrical center (see Figure 1a). Electric displacement D was set at the LN crystal surfaces which were perpendicular to the Z axis to describe polarization of the crystal caused by thermal stimulation which was assumed homogeneous. The electric displacement value was defined by the formula D ¼ σ where σ ¼ pΔT is a surface charge density generated on the opposite crystal surface by a temperature variation ΔT. The value p ¼ À8.3 Â 10 À5 C m À2 K À1 was assumed for the LN pyroelectric coefficient.
Measurement of a Surface Electric Potential of Thermostimulated LN Crystal Plates: Surface electric potential of LN crystal stimulated by Linkam heater was measured by two kinds of electrostatic voltmeters: Monroe Isoprobe Model 244 A and TREK Model 341 A for potential up to 3 kV and up to 20 kV, respectively. LN crystal was placed upon the heater, as shown in Figure 3a. The "ground" electrode of the voltmeter was connected to the heater disk and the probe electrode was placed at the distance of about 1.5 mm over the geometrical center of the upper surface of the LN plate.
Optical Recording of Droplets Accumulation: A side view of fluid dispensing was recorded by optical setup consisted of a collimated blue LED M470L3-C1, 10Â objective Mitutoyo BD Plan Apo, and camera CS2100M-USB with frame rate of 50 fps purchased from Thorlabs, Inc. After being processed by ImageJ program, the image data were analyzed using MATLAB.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.