An experimental and computational study is presented on the interfacial dynamics of a colloidal fluid having both high electric conductivity and high magnetic permeability in the presence of simultaneous electric and magnetic stresses on the fluid/air interface. A transient computational model is developed that simultaneously solves the Navier-Stokes equation and Maxwells’ static equations to predict the transient geometry of the fluid subject to electric and magnetic stresses. This model is first applied to predict the onset of spray emission from a capillary needle electrospray source subjected to a magnetic field. The experimentally determined onset of emissions at each magnetic field agreed well with those predicted by the simulation tool. The predictive modeling tool was then applied to analyze the interfacial profile of a sessile droplet subjected to both electric and magnetic fields. The model captured the geometric evolution of the droplet for voltages up to approximately 85% of the critical onset voltage; near the onset, the model slightly overpredicted the droplet deformation. Using the interfacial stress obtained from the modeling tool, a quantitative discussion is made regarding the roles and magnitudes of the electric and magnetic stress components on the lead-up to the emission instability.

1.
L. B.
King
,
E.
Meyer
,
M. A.
Hopkins
,
B. S.
Hawkett
, and
N.
Jain
, “
Self-assembling array of magnetoelectrostatic jets from the surface of a superparamagnetic ionic liquid
,”
Langmuir
30
(
47
),
14143
14150
(
2014
).
2.
L.
Mkrtchyan
,
A.
Zakinyan
, and
Y.
Dikansky
, “
Electrocapillary instability of magnetic fluid peak
,”
Langmuir
29
(
29
),
9098
9103
(
2013
).
3.
G.
Taylor
, paper presented at the
Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences
,
1964
.
4.
J.
Melcher
and
G.
Taylor
, “
Electrohydrodynamics: A review of the role of interfacial shear stresses
,”
Annu. Rev. Fluid Mech.
1
(
1
),
111
146
(
1969
).
5.
J.
Sherwood
, “
The deformation of a fluid drop in an electric field: A slender-body analysis
,”
J. Phys. A: Math. Gen.
24
(
17
),
4047
(
1991
).
6.
J.
Brancher
and
D.
Zouaoui
, “
Equilibrium of a magnetic liquid drop
,”
J. Magn. Magn. Mater.
65
(
2
),
311
314
(
1987
).
7.
H. A.
Stone
,
J. R.
Lister
, and
M. P.
Brenner
, paper presented at the
Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences
,
1999
.
8.
V.
Koromyslov
,
A.
Grigor’ev
, and
M.
Rybakova
, “
Disintegration of a drop in an external electrostatic field
,”
Tech. Phys.
47
(
6
),
682
689
(
2002
).
9.
C. T.
O’Konski
and
H. C.
Thacher
, Jr.
, “
The distortion of aerosol droplets by an electric field
,”
J. Phys. Chem.
57
(
9
),
955
958
(
1953
).
10.
P.
Rowghanian
,
C. D.
Meinhart
, and
O.
Campàs
, “
Dynamics of ferrofluid drop deformations under spatially uniform magnetic fields
,”
J. Fluid Mech.
802
,
245
262
(
2016
).
11.
A. N.
Tyatyushkin
and
M. G.
Velarde
, “
On the interfacial deformation of a magnetic liquid drop under the simultaneous action of electric and magnetic fields
,”
J. Colloid Interface Sci.
235
(
1
),
46
58
(
2001
).
12.
A.
Zakinyan
,
E.
Tkacheva
, and
Y.
Dikansky
, “
Dynamics of a dielectric droplet suspended in a magnetic fluid in electric and magnetic fields
,”
J. Electrost.
70
(
2
),
225
232
(
2012
).
13.
C.
Gollwitzer
,
A.
Spyropoulos
,
A.
Papathanasiou
,
A.
Boudouvis
, and
R.
Richter
, “
The normal field instability under side-wall effects: Comparison of experiments and computations
,”
New J. Phys.
11
(
5
),
053016
(
2009
).
14.
A.
Boudouvis
,
J.
Puchalla
, and
L.
Scriven
, “
Magnetohydrostatic equilibria of ferrofluid drops in external magnetic fields
,”
Chem. Eng. Commun.
67
(
1
),
129
144
(
1988
).
15.
A.
Papathanasiou
and
A.
Boudouvis
, “
Three-dimensional instabilities of ferromagnetic liquid bridges
,”
Comput. Mech.
21
(
4-5
),
403
408
(
1998
).
16.
S. N.
Reznik
,
A. L.
Yarin
,
A.
Theron
, and
E.
Zussman
, “
Transient and steady shapes of droplets attached to a surface in a strong electric field
,”
J. Fluid Mech.
516
,
349
377
(
2004
).
17.
A.
Ramos
and
A.
Castellanos
, “
Equilibrium shapes and bifurcation of captive dielectric drops subjected to electric fields
,”
J. Electrost.
33
(
1
),
61
86
(
1994
).
18.
O.
Lavrova
,
G.
Matthies
,
T.
Mitkova
,
V.
Polevikov
, and
L.
Tobiska
, “
Numerical treatment of free surface problems in ferrohydrodynamics
,”
J. Phys.: Condens. Matter
18
(
38
),
S2657
(
2006
).
19.
P. D.
Prewett
and
G. L. R.
Mair
,
Focused Ion Beams from Liquid Metal Ion Sources
(
Research Studies Press
,
1991
).
20.
R.
Krpoun
and
H. R.
Shea
, “
A method to determine the onset voltage of single and arrays of electrospray emitters
,”
J. Appl. Phys.
104
(
6
),
064511
(
2008
).
21.
R. E.
Rosensweig
,
Ferrohydrodynamics
(
Courier Dover Publications
,
1997
).
22.
Electrohydrodynamics
, International Centre for Mechanical Sciences Courses and Lectures No. 380, edited by
A.
Castellanos
(Springer,
1998
).
You do not currently have access to this content.