Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-06-20T00:03:44.615Z Has data issue: false hasContentIssue false

The emission properties, structure and stability of ionic liquid menisci undergoing electrically assisted ion evaporation

Published online by Cambridge University Press:  06 January 2022

Ximo Gallud*
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 02139 Cambridge, MA, USA
Paulo C. Lozano
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, 02139 Cambridge, MA, USA
*
Email address for correspondence: ximogc@mit.edu

Abstract

The properties and structure of electrically stressed ionic liquid menisci experiencing ion evaporation are simulated using an electrohydrodynamic model with field-enhanced thermionic emission in steady state for an axially symmetric geometry. Solutions are explored as a function of the external background field, meniscus dimension, hydraulic impedance and liquid temperature. Statically stable solutions for emitting menisci are found to be constrained to a set of conditions: a minimum hydraulic impedance, a maximum current output and a narrow range of background fields that maximizes at menisci sizes of 0.5–3 ${\rm \mu}{\rm m}$ in radius. Static stability is lost when the electric field adjacent to the electrode that holds the meniscus corresponds to an electric pressure that exceeds twice the surface tension stress of a sphere of the same size as the meniscus. Preliminary investigations suggest this limit to be universal, therefore, independent of most ionic liquid properties, reservoir pressure, hydraulic impedance or temperature and could explain the experimentally observed bifurcation of a steady ion source into two or more emission sites. Ohmic heating near the emission region increases the liquid temperature, which is found to be important to accurately describe stability boundaries. Temperature increase does not affect the current output when the hydraulic impedance is constant. This phenomenon is thought to be due to an improved interface charge relaxation enhanced by the higher electrical conductivity. Dissipated ohmic energy is mostly conducted to the electrode wall. The higher thermal diffusivity of the wall versus the liquid, allows the ion source to run in steady state without heating.

Type
JFM Papers
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Anderson, D.G. 1965 Iterative procedures for nonlinear integral equations. J. ACM 12 (4), 547560.CrossRefGoogle Scholar
Basaran, O.A. & Scriven, L.E. 1989 a Axisymmetric shapes and stability of charged drops in an external electric field. Phys. Fluids A 1 (5), 799809.CrossRefGoogle Scholar
Basaran, O.A. & Scriven, L.E. 1989 b Axisymmetric shapes and stability of isolated charged drops. Phys. Fluids A 1 (5), 795798.CrossRefGoogle Scholar
Basaran, O.A. & Scriven, L.E. 1990 Axisymmetric shapes and stability of pendant and sessile drops in an electric field. J. Colloid Interface Sci. 140 (1), 1030.CrossRefGoogle Scholar
Basaran, O.A. & Wohlhuter, F.K. 1992 Effect of nonlinear polarization on shapes and stability of pendant and sessile drops in an electric (magnetic) field. J. Fluid Mech. 244, 116.CrossRefGoogle Scholar
Bazant, M.Z., Storey, B.D. & Kornyshev, A.A. 2011 Double layer in ionic liquids: overscreening versus crowding. Phys. Rev. Lett. 106 (4), 046102.CrossRefGoogle ScholarPubMed
Beroz, J., Hart, A.J. & Bush, J.W.M. 2019 Stability limit of electrified droplets. Phys. Rev. Lett. 122 (24), 244501.CrossRefGoogle ScholarPubMed
Castro, S. & Fernández De La Mora, J. 2009 Effect of tip curvature on ionic emissions from Taylor cones of ionic liquids from externally wetted tungsten tips. J. Appl. Phys. 105 (3), 034903.CrossRefGoogle Scholar
Castro, S., Larriba, C., Fernandez De La Mora, J., Lozano, P.C. & Sumer, S. 2006 Capillary vs. externally wetted ionic liquid ion sources. AIAA/ASME/SAE/ASEE 42nd Joint Propulsion Conference, 3262–3267.Google Scholar
Cloupeau, M. & Prunet-Foch, B. 1989 Electrostatic spraying of liquids in cone-jet mode. J. Electrostat. 22 (2), 135159.CrossRefGoogle Scholar
Coffman, C.S. 2016 Electrically-assisted evaporation of charged fluids: fundamental modeling and studies on ionic liquids. PhD thesis, Massachusetts Institute of Technology.Google Scholar
Coffman, C.S., Martínez-Sánchez, M., Higuera, F.J. & Lozano, P.C. 2016 Structure of the menisci of leaky dielectric liquids during electrically-assisted evaporation of ions. Appl. Phys. Lett. 109 (23), 231602.CrossRefGoogle Scholar
Coffman, C.S., Martínez-Sánchez, M. & Lozano, P.C. 2019 Electrohydrodynamics of an ionic liquid meniscus during evaporation of ions in a regime of high electric field. Phys. Rev. E 99 (6), 063108.CrossRefGoogle Scholar
Coffman, C.S., Perna, L., Li, H. & Lozano, P.C. 2013 On the manufacturing and emission characteristics of a novel borosilicate electrospray source. In 49th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 4035.Google Scholar
Coles, T.M., Fedkiw, T.P. & Lozano, P.C. 2012 Investigating ion fragmentation in electrospray thruster beams. In 48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit 2012, 3793.Google Scholar
Collins, R.T., Jones, J.J., Harris, M.T. & Basaran, O.A. 2008 Electrohydrodynamic tip streaming and emission of charged drops from liquid cones. Nat. Phys. 4, 149154.CrossRefGoogle Scholar
Courtney, D.G., Li, H.Q. & Lozano, P.C. 2012 Emission measurements from planar arrays of porous ionic liquid ion sources. J. Phys. D: Appl. Phys. 45 (48), 485203.CrossRefGoogle Scholar
Courtney, D.G. & Shea, H.R. 2015 Influences of porous reservoir Laplace pressure on emissions from passively fed ionic liquid electrospray sources. Appl. Phys. Lett. 107 (10), 103504.CrossRefGoogle Scholar
Fernández de la Mora, J. 2007 The fluid dynamics of Taylor cones. Annu. Rev. Fluid Mech. 39 (1), 217243.CrossRefGoogle Scholar
Fernández De La Mora, J., Genoni, M., Perez-Lorenzo, L.J. & Cezairli, M. 2020 Measuring the kinetics of neutral pair evaporation from cluster ions of ionic liquid in the drift region of a differential mobility analyzer. J. Phys. Chem. A 124 (12), 24832496.CrossRefGoogle Scholar
Fernández De La Mora, J. & Loscertales, I.G. 1994 The current emitted by highly conducting Taylor cones. J. Fluid Mech. 260 (special issue), 155184.CrossRefGoogle Scholar
Forbes, R.G. 1997 Understanding how the liquid-metal ion source works. Vacuum 48 (1), 8597.CrossRefGoogle Scholar
Forbes, R.G., Ganetsos, T., Mair, G.L.R. & Suvorov, V. 2004 Liquid metal ion sources at Aston in the 1980s and what followed. Proc. R. Microsc. Soc. 39, 218226.Google Scholar
Fragkopoulos, A.A. & Fernández-Nieves, A. 2017 Toroidal-droplet instabilities in the presence of charge. Phys. Rev. E 95 (3), 033122.CrossRefGoogle Scholar
Gallud, X. 2019 A comprehensive numerical procedure for solving the Taylor-Melcher leaky dielectric model with charge evaporation. MSc Thesis, Massachusetts Institute of Technology.Google Scholar
Gamero-Castaño, M. 2002 Electric-field-induced ion evaporation from dielectric liquid. Phys. Rev. Lett. 89 (14), 147602.CrossRefGoogle ScholarPubMed
Gamero-Castaño, M. & Fernández De La Mora, J. 2000 Direct measurement of ion evaporation kinetics from electrified liquid surfaces. J. Chem. Phys. 113 (2), 815832.CrossRefGoogle Scholar
Gamero-Castaño, M. & Hruby, V. 2001 Electrospray as a source of nanoparticles for efficient colloid thrusters. J. Propul. Power 17 (5), 977987.CrossRefGoogle Scholar
Gamero-Castaño, M. & Magnani, M. 2019 Numerical simulation of electrospraying in the cone-jet mode. J. Fluid Mech. 859, 247267.CrossRefGoogle Scholar
Gañán-Calvo, A.M., Dávila, J.M. & Barrero, A. 1997 Current and droplet size in the electrospraying of liquids. Scaling laws. J. Aerosol Sci. 28 (2), 249275.CrossRefGoogle Scholar
Gañán-Calvo, A.M., López-Herrera, J.M., Rebollo-Muñoz, N. & Montanero, J.M. 2016 The onset of electrospray: the universal scaling laws of the first ejection. Sci. Rep. 6 (1), 32357.CrossRefGoogle ScholarPubMed
Gañán-Calvo, A.M. & Montanero, J.M. 2009 Revision of capillary cone-jet physics: electrospray and flow focusing. Phys. Rev. E 79 (6), 066305.CrossRefGoogle ScholarPubMed
Garoz, D., Bueno, C., Larriba, C., Castro, S., Romero-Sanz, I., De La Mora, J.F., Yoshida, Y. & Saito, G. 2007 Taylor cones of ionic liquids from capillary tubes as sources of pure ions: the role of surface tension and electrical conductivity. J. Appl. Phys. 102 (6), 064913.CrossRefGoogle Scholar
Gebbie, M.A., Dobbs, H.A., Valtiner, M. & Israelachvili, J.N. 2015 Long-range electrostatic screening in ionic liquids. Proc. Natl Acad. Sci. USA 112 (24), 74327437.CrossRefGoogle ScholarPubMed
Gomer, R. 1979 On the mechanism of liquid metal electron and ion sources. Appl. Phys. 19 (4), 365375.CrossRefGoogle Scholar
Herrada, M.A., López-Herrera, J.M., Gañán-Calvo, A.M., Vega, E.J., Montanero, J.M. & Popinet, S. 2012 Numerical simulation of electrospray in the cone-jet mode. Phys. Rev. E 86 (2), 247267.CrossRefGoogle ScholarPubMed
Higuera, F.J. 2003 Flow rate and electric current emitted by a Taylor cone. J. Fluid Mech. 484 (484), 303327.CrossRefGoogle Scholar
Higuera, F.J. 2008 Model of the meniscus of an ionic-liquid ion source. Phys. Rev. E 77 (2), 026308.CrossRefGoogle ScholarPubMed
Hill, F.A., Heubel, E.V., Ponce De Leon, P. & Fernando Velásquez-García, L. 2014 High-throughput ionic liquid ion sources using arrays of microfabricated electrospray emitters with integrated extractor grid and carbon nanotube flow control structures. J. Microelectromech. Syst. 23 (5), 12371248.CrossRefGoogle Scholar
Iribarne, J.V. 1976 On the evaporation of small ions from charged droplets. J. Chem. Phys. 64 (6), 2287.CrossRefGoogle Scholar
Krpoun, R. & Shea, H.R. 2008 A method to determine the onset voltage of single and arrays of electrospray emitters. J. Appl. Phys. 104 (6), 064511.CrossRefGoogle Scholar
Krpoun, R., Smith, K.L., Stark, J.P.W. & Shea, H.R. 2009 Tailoring the hydraulic impedance of out-of-plane micromachined electrospray sources with integrated electrodes. Appl. Phys. Lett. 94 (16), 163502.CrossRefGoogle Scholar
Legge, R.S. & Lozano, P.C. 2011 Electrospray propulsion based on emitters microfabricated in porous metals. J. Propul. Power 27 (2), 485495.CrossRefGoogle Scholar
Levi-Setti, R., Crow, G. & Wang, Y.L. 1985 Progress in high resolution scanning ion microscopy and secondary ion mass spectrometry imaging microanalysis. Scan. Electron. Microsc. 2 (Pt 2), 535552.Google Scholar
Li, Z.C. & Lu, T.T. 2000 Singularities and treatments of elliptic boundary value problems. Math. Comput. Model. 31 (8–9), 97145.CrossRefGoogle Scholar
Lozano, P.C. 2006 Energy properties of an EMI-Im ionic liquid ion source. J. Phys. D: Appl. Phys. 39 (1), 126134.CrossRefGoogle Scholar
Lozano, P.C. & Martínez-Sánchez, M. 2002 Experimental measurements of colloid thruster plumes in the ion-droplet mixed regime. In 38th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 3814.Google Scholar
Lozano, P.C. & Martínez-Sánchez, M. 2005 Ionic liquid ion sources: characterization of externally wetted emitters. J. Colloid Interface Sci. 282 (2), 415421.CrossRefGoogle ScholarPubMed
Mehrabian, H. & Feng, J.J. 2013 Capillary breakup of a liquid torus. J. Fluid Mech. 717, 281292.CrossRefGoogle Scholar
Miller, C.E. & Lozano, P.C. 2020 Measurement of the dissociation rates of ion clusters in ionic liquid ion sources. Appl. Phys. Lett. 116 (25), 254101.CrossRefGoogle Scholar
Mori, Y. & Young, Y.N. 2018 From electrodiffusion theory to the electrohydrodynamics of leaky dielectrics through the weak electrolyte limit. J. Fluid Mech. 855, 67130.CrossRefGoogle Scholar
Pantano, C., Gañán-Calvo, A.M. & Barrero, A. 1994 Zeroth-order, electrohydrostatic solution for electrospraying in cone-jet mode. J. Aerosol Sci. 25 (6), 10651077.CrossRefGoogle Scholar
Perel, J., Mahoney, J.F., Moore, R.D. & Yahiku, A.Y. 1969 Research and development of a charged-particle bipolar thruster. AIAA J. 7 (3), 507511.CrossRefGoogle Scholar
Pérez-Martínez, C. 2016 Engineering ionic liquid ion sources for ion beam applications. PhD thesis, Massachusetts Institute of Technology.Google Scholar
Pérez-Martínez, C., Guilet, S., Gierak, J. & Lozano, P.C. 2011 Ionic liquid ion sources as a unique and versatile option in FIB applications. Microelectron. Engng 88, 20882091.CrossRefGoogle Scholar
Pérez-Martínez, C. & Lozano, P.C. 2015 Ion field-evaporation from ionic liquids infusing carbon xerogel microtips. Appl. Phys. Lett. 107 (4), 043501.CrossRefGoogle Scholar
Pillai, R., Berry, J.D., Harvie, D.J.E. & Davidson, M.R. 2016 Electrokinetics of isolated electrified drops. Soft Matt. 12 (14), 33103325.CrossRefGoogle ScholarPubMed
Plechkova, N.V. & Seddon, K.R. 2008 Applications of ionic liquids in the chemical industry. Chem. Soc. Rev. 37 (1), 123150.CrossRefGoogle ScholarPubMed
Rayleigh, Lord 1892 XVI. On the instability of a cylinder of viscous liquid under capillary force. Lond. Edinb. Dublin Philos. Mag. J. Sci. 34 (207), 145154.CrossRefGoogle Scholar
Romero-Sanz, I., Aguirre De Carcer, I. & Fernández De La Mora, J. 2005 Ionic propulsion based on heated Taylor cones of ionic liquids. J. Propul. Power 21 (2), 239242.CrossRefGoogle Scholar
Romero-Sanz, I., Bocanegra, R., Fernández De La Mora, J. & Gamero-Castaño, M. 2003 Source of heavy molecular ions based on Taylor cones of ionic liquids operating in the pure ion evaporation regime. J. Appl. Phys. 94 (5), 35993605.CrossRefGoogle Scholar
Saville, D.A. 1997 Electrohydrodynamics: the Taylor-Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29 (1), 2764.CrossRefGoogle Scholar
Schnitzer, O. & Yariv, E. 2015 The Taylor-Melcher leaky dielectric model as a macroscale electrokinetic description. J. Fluid Mech. 773, 133.CrossRefGoogle Scholar
Smith, A.M., Lee, A.A. & Perkin, S. 2016 The electrostatic screening length in concentrated electrolytes increases with concentration. J. Phys. Chem. Lett. 7 (12), 21572163.CrossRefGoogle ScholarPubMed
Sugiyama, M. & Sigesato, G. 2004 A review of focused ion beam technology and its applications in transmission electron microscopy. J. Electron. Microsc. 53 (5), 527536.CrossRefGoogle ScholarPubMed
Swanson, L.W. 1983 Liquid metal ion sources: mechanism and applications. Nucl. Instrum. Meth. Phys. Res. 218 (1–3), 347353.CrossRefGoogle Scholar
Takeuchi, M., Hamaguchi, T., Ryuto, H. & Takaoka, G.H. 2013 Development of ionic liquid ion source with porous emitter for surface modification. Nucl. Instrum. Meth. Phys. Res. B 315, 345349.CrossRefGoogle Scholar
Taylor, G.I. 1964 Disintegration of water drops in an electric field. Proc. R. Soc. Lond. A 280 (1382), 383397.Google Scholar
Terhune, K.J., King, L.B., He, K. & Cumings, J. 2016 Radiation-induced solidification of ionic liquid under extreme electric field. Nanotechnology 27 (37), 375701.CrossRefGoogle ScholarPubMed
Verfürth, R. 1986 Finite element approximation of incompressible Navier–Stokes equations with slip boundary condition I. Numer. Math. 59 (1), 615636.CrossRefGoogle Scholar
Zeleny, J. 1935 The role of surface instability in electrical discharges from drops of alcohol and water in air at atmospheric pressure. J. Franklin Inst. 219 (6), 659675.CrossRefGoogle Scholar
Zhang, S., Sun, N., He, X., Lu, X. & Zhang, X. 2006 Physical properties of ionic liquids: database and evaluation. J. Phys. Chem. Ref. Data 35 (4), 14751517.CrossRefGoogle Scholar
Zorzos, A.N. & Lozano, P.C. 2008 The use of ionic liquid ion sources in focused ion beam applications. J. Vac. Sci. Technol. B 26 (6), 20972102.CrossRefGoogle Scholar