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Non-Dimensional Groups for Electrospray Modes of Highly Conductive and Viscous Nanoparticle Suspensions Eduardo Castillo-Orozco1, Aravinda Kar2 & Ranganathan Kumar3*

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Non-Dimensional Groups for Electrospray Modes of Highly Conductive and Viscous Nanoparticle Suspensions Eduardo Castillo-Orozco1, Aravinda Kar2 & Ranganathan Kumar3* www.nature.com/scientificreports OPEN Non-dimensional groups for electrospray modes of highly conductive and viscous nanoparticle suspensions Eduardo Castillo-Orozco1, Aravinda Kar2 & Ranganathan Kumar3* Multiple modes of atomization in electrosprays are afected by viscosity, surface tension and electrical conductivity of the semiconductor nanosuspensions. While the efect of gravity is dominant in the dripping mode, the electric feld degenerates the electrospray mechanism into a microdripping mode that can potentially allow the deposition of semiconductor nanodots on a substrate. Drop size and frequency of droplet formation are obtained as functions of non-dimensional parameters, which agree well with experimental data. The analysis shows that it is possible to produce the desired size and frequency of ejection of monodisperse droplets by manipulating the electrode voltage for any nanosuspension. Patterning of semiconductor structures has a crucial application for fabricating electronic and photonic devices1,2. Nanoparticles ofer the additional beneft of low melting temperature and better mechanical and optical prop- erties compared to the bulk material. Electrosprays present a convenient method to carry these nanoparticles within droplets for deposition of semiconductor materials, e.g., copper-indium-diselenide for solar cells3 and zinc oxide for thin-flm transistors4. Te physics of electrosprays has been discussed in two critical reviews5,6. Te electric forces in microfuidic systems can cause various phenomena including transient, periodic, quasi-steady and steady fows. Te electro- spray mostly used operates in a steady cone-jet spray mode where micro- and nano-droplets are detached from the tip of a capillary tube due to electric force7–10, but in general, it can operate in numerous modes depending on the fow rate and electric potential11–13. Tese modes have been used in inkjet printing with sub-micrometer resolution and minimal clogging14,15. Semiconductor nanoparticles can be suspended in water and electrosprayed on substrates for additive man- ufacturing of electronics. Tis was demonstrated in our recent study16 where low viscosity suspensions were investigated. In electrosprays, the droplets detach from the tip of a capillary tube due to the balance of the elec- trodynamic and hydrodynamic forces acting on the fuid. An electrostatic feld between the capillary tube and an extraction electrode in the vicinity of the tube alters the mode of detaching the droplets, resulting in difer- ent spray characteristics such as dripping, microdripping, spindle, multispindle, and cone-jet spray mode11,17–19. Tus, the electro-capillary interaction provides an additional mechanism to generate diferent modes for the fuid dynamic response of the droplets. Te Taylor Cone jet is formed when high voltage is applied to the capillary tube and the liquid is polarized. Te electric feld around the liquid fowing downward from the capillary tube deforms the liquid meniscus into a Taylor cone from which the micron-sized droplets are emitted. Te electrical conductivity and the liquid fow rate can afect the dropsize9,20. Te microdripping mode, which is a stable method to generate uniform droplets carrying semiconductor nanoparticles for deposition on substrates, follows the initial dripping mode that occurs at lower electric poten- tial. Te production of fne monodisperse droplets from a precursor suspension is of interest. Tese suspensions can have high viscosity and high density due to high particle concentration21,22. Hijano et al.23 found that in an 1Escuela Superior Politecnica del Litoral, ESPOL, Facultad en Ingenieria Mecanica y Ciencias de la Produccion, Campus Gustavo Galindo, Km. 30.5 Via Perimetral, Guayaquil, P.O. Box 09-01-5863, Ecuador. 2CREOL, The College of Optics and Photonics, University of Central Florida, 4000 Central Florida Blvd, Orlando, Florida, 32816, USA. 3Department of Mechanical and Aerospace Engineering, University of Central Florida, 4000 Central Florida Blvd, Orlando, Florida, 32816, USA. *email: [email protected] SCIENTIFIC REPORTS | (2020) 10:4405 | https://doi.org/10.1038/s41598-020-61323-5 1 www.nature.com/scientificreports/ www.nature.com/scientificreports (c) (e) Semiconductor ρ μ σ γ r0 r0 (μS/ nanosuspension (g/ml) (mPa.s) cm) (mN/m) (mm) (mm) Ca Bo Cae Si, 2 wt% in DI water 1.010 1.48 991.6 46.7 1.20 1.18 0.035 0.202 0–2.91 Si, 5 wt% in DI water 1.033 1.82 1391.6 48.2 1.21 1.19 0.031 0.204 0–2.90 Si, 10 wt% in DI water 1.060 2.72 1411.2 47.1 1.19 1.13 0.083 0.209 0–3.21 SiC, 2 wt% in DI water 1.051 1.56 484.0 47.7 1.19 1.19 0.048 0.203 0–2.61 SiC, 5 wt% in DI water 1.127 4.79 545.0 48.5 1.20 1.19 0.139 0.220 0–2.57 SiC, 10 wt% in DI water 1.193 12.05 582.0 59.9 1.19 1.23 0.279 0.151 0–2.69 ZnO, 10 wt% in DI water 1.103 1.46 741.0 55.1 1.25 1.29 0.041 0.190 0–3.08 ZnO, 30 wt% in DI water 1.438 2.09 1400.0 52.4 1.07 1.08 0.055 0.204 0–2.88 ZnO, 50 wt% in DI water 1.930 18.50 1782.0 54.3 1.05 1.07 0.405 0.254 0–2.92 Table 1. Physical properties and relevant parameters of semiconductor nanosuspensions in DI water. (c)Drop radius in the absence of electric feld, calculated using Eq. (6). (e)Drop radius in the absence of electric feld from experiments. electrospray of low viscosity fuid, the process depends on two non-dimensional parameters: normalized fow rate and electric Bond number which is a measure of the square of the voltage. Te current paper deals with the inception of a viscous droplet in the dripping regime as well as the microdripping regime. Hence, the relevant non-dimensional parameters that will be discussed include electric capillary number (similar to electric Bond number used in23), viscous capillary number and Bond number. In our early work16, low viscosity suspension of capillary number (Ca) of 0.1 or less were used. Terefore, the viscous efect is not signifcant to include Ca as a parameter, and drop size and frequency could be plotted as a simple function of electric capillary number (Cae), Bond number (ratio of gravity to surface tension force) was not explicitly considered. In this paper, a more detailed theoretical analysis will be reported. Tis paper focuses on high viscosity suspensions of 0.03 < Ca < 0.4 with high electrical conductivity. For these suspensions, the viscous efects become important and afect the conical meniscus. Here, in addition to the interfacial, gravity and electric forces, viscous force will play a decisive role in the non-dimensional analysis. Experimental results for droplet diameter and drop frequency will be presented in terms of a unique combination of relevant non-dimensional parameters such as electric Capillary number, viscous Capillary number, and Bond number that are derived from a simple force balance. Correlation will be developed for non-dimensional radius and frequency of emission of 0.5 droplets in terms of the non-dimensional group Cae/[Bo(1 + Ca)] . Results Te experiments were performed for a number of suspensions with a wide range of physical properties, voltages from 0 to 5000 V (Table 1). Te presence of semiconductor nanoparticles inside the droplets, particularly the electrical conductivity of the nanomaterials, will infuence the transition of the microdroplet modes. Experiments were carried out at low fow rates corresponding to Stokes fow to investigate the modes of nanosuspensions in laminar electrospray of droplets. Electrospray in the dripping mode has negligible inertial and viscous efects24,25, while in the microdrip- ping mode the viscosity afects the conical meniscus at the tip of the capillary tube from which the droplets are detached. Both modes are inherently quasi-static for a constant fow rate of the suspension into the capillary tube. In addition, a fuid of higher viscosity has the advantage of decreasing the jet diameter26. Te droplet grows to a steady-state size and detaches from the tube, and this process repeats in a periodic manner to ensure the dis- charge of droplets at a certain frequency. Te droplet radius observed in this study is between 1.3 mm–0.65 mm in the dripping mode and 74 μm–150 μm in the microdripping mode. Te droplet formation rates are measured between 0.2–1.5 droplets per second in the dripping mode and 100–650 droplets per second in the microdripping mode, respectively. In the dripping mode, the droplets are formed from a hemispherical or ellipsoidal meniscus, while the electric feld-induced stretching of the fuid develops a conical meniscus called the Taylor cone. A neck develops between the meniscus and a pendant liquid flament at the end, which becomes thinner with time and eventually collapses releasing a droplet. Tis droplet ejection process is periodic and monodisperse. Figure 1 compares the growth of the conical meniscus due to the presence of electric force in the microdripping mode both in low viscous and high viscous suspension. Here, the conical meniscus and hence the ejected droplet are relatively small, as is the gravity force. For the high viscosity fuid, the electric force stretches the liquid to form the meniscus and the liquid flament, while the viscous friction prevents the elongation of the liquid flament, and the surface tension force frst resists the formation of this pendant flament, but once the droplet is detached, the restoring force of the cap- illary efects turns the spindle-shaped liquid flament into a spherical droplet. Te relative infuence between the viscous and interfacial force is seen when the capillary number increases in the microdripping mode.
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