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The role of ambient gas in the electrospray cone-jet formation

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Abstract

This article reports on a study into ambient gas's role in forming the electrospray cone-jet mode. The study aims to broaden the current knowledge, which is essentially confined to air as the surrounding medium in the electrospray process. This research is founded on a liquid-gas simulation, including fluid and electrostatic governing equations coupled with charge conservation and volume of fluid (VOF) interface tracking approaches. The application of various ambient gases, i.e., air, oxygen, nitrogen, methane, helium, and hydrogen, has a decisive impact on the cone-jet structure concerning geometrical profiles, which are mainly reflected in the dimensions of the whole cone-jet and the cone alone. The results indicated the altering effects of the ambient gas on equipotential configuration and charge density magnitudes. The flow patterns clarified the role of the gas type in streamlining and vortex creation within the fluid phases. Two validation tests were also performed to compare the simulation results with the experimental charged jet formation and the electrical variation of droplet mean diameter. The results displayed a good agreement supporting the aptness of the model developed.

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The data generated or analyzed during this study are included in the manuscript.

Abbreviations

C :

Volume fraction

Ca :

Capillary number

D 32 :

Sauter mean diameter (μm)

d i,e :

Emitter inner diameter (mm)

d i,o :

Emitter outer diameter (mm)

\(\overrightarrow{E}\) :

Electric field vector (Vm−1)

E 0 :

Radial electric field (Vm−1)

\({\overrightarrow{F}}_{\mathrm{ES}}\) :

Electric force vector (Nm−3)

\({\overrightarrow{F}}_{\mathrm{ST}}\) :

Surface tension force vector (Nm−3)

\(\overrightarrow{g}\) :

Gravity acceleration (ms−2)

\(\overline{\overline{I}}\) :

Identity tensor

I:

Electric Current (nA)

\(\overrightarrow{J}\) :

Electric charge flux (Cm−2 s−1)

K :

Electrical conductivity (Sm−1)

l :

Characteristic length (m)

L :

Length, height (m)

\(\overrightarrow{n}\) :

Normal vector

P :

Pressure (Pa)

Q :

Flow rate (mLh−1)

r:

Radial coordinate, radius (mm)

Re :

Reynolds number

R disk :

Disk radius (mm)

t :

Time (s)

\({\overline{\overline{T}}}_{e}\) :

Maxwell stress tensor

t e :

Electric relaxation time (s)

t m :

Magnetic characteristic time (s)

\(\overrightarrow{u}\) :

Velocity vector (ms-1)

z :

Axial coordinate (mm)

α :

Angle (deg)

γ :

Surface tension coefficient (Nm−1)

ε :

Permittivity (CV−1 m−1)

ε 0 :

Vacuum permittivity (CV−1 m−1)

ε r :

Relative permittivity

κ :

Interface curvature (m)

μ :

Viscosity (mPa·s)

μ m :

Magnetic permeability (Hm−1)

ρ :

Density (kgm−3)

ρ e :

Volume electric charge density (Cm−3)

Φ:

Electric potential (V)

χ :

Taylor number

c :

Cone

c – j :

Cone-jet surface

e :

Emitter

ed :

Emitter to disk

g :

Gas

j :

Jet

l :

Liquid

min :

Minimum

on :

Onset

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Funding

The authors did not receive support from any organization for the submitted work.

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Authors and Affiliations

  1. Sprays Research Laboratory, Iranian Space Research Center, Tehran, Iran

    H. Dastourani & M. R. Jahannama

  2. Electrical and Electronics Engineering Department, Malek Ashtar University of Technology, Tehran, Iran

    A. Eslami-Majd

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Contributions

The authors’ contributions to this work are defined as follow: H. Dastourani contributed in conceptualization, investigation, methodology, software, and writing - review & editing. M.R. Jahannama contributed in conceptualization, investigation, methodology, supervision, and writing - review & editing. A. Eslami-Majd contributed in conceptualization, investigation, and methodology. All authors approved the final manuscript.

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Correspondence to M. R. Jahannama.

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Dastourani, H., Jahannama, M.R. & Eslami-Majd, A. The role of ambient gas in the electrospray cone-jet formation. Heat Mass Transfer 59, 2267–2284 (2023). https://doi.org/10.1007/s00231-023-03404-5

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