Sketches illustrating drop shape and flow streamlines in a uniform direct current (DC) electric field with increasing strength: (a) The drop is spherical in the absence of electric field. (b) Weak fields induce pure straining flow and axisymmetric oblate deformation. (c) In strong fields, the flow acquires a rotational component and the drop is tilted with respect to the applied field direction.
(a) Charge distribution for a sphere with R/P < 1, where R and P are the conductivity and permittivity ratios defined by Eq. (8) . (b) Above a critical field strength E > E Q , where E Q is given by Eq. (2) , constant torque is induced by the misaligned dipole, denoted by P next to the arrow. 6–8
Sketch of the problem: an initially spherical drop (dashed line) subjected to a strong uniform electric field deforms into an ellipsoid (solid line) with a major axis at an angle with the applied electric field. P denotes the induced dipole.
Variation of drop tilt angle (a) and deformation (b) with field strength for a drop with viscosity ratios 14 (solid line), 5 (dashed line), and 1 (long-dashed line). The physical properties of the fluids are the same as in Ref. 3 : R = 0.027, P = 0.56, E Q = 2.7 kV/cm and drop radius is a = 1 mm. For E/E Q < 1 drop deformation is given by Eq. (40) . The dotted-dashed line corresponds to the 2D theory. 10
(a) Variation of drop deformation with time upon application of an electric field with increasing strength for a drop with viscosity ratio 14. Parameters correspond to the experiments in Ref. 3 , R = 0.027, P = 0.56, E/E Q = 1.5, i.e., Ca = 1.54 (solid line), E/E Q = 2, i.e., Ca = 2.74 (dashed line), and E/E Q = 3, i.e., Ca = 6.17 (long-dashed line). (b) Variation of drop deformation with time upon application of an electric field with strength E/E Q = 2, i.e., Ca = 2.74 for drops with different viscosity ratios λ = 1 (solid line), λ = 5 (dashed line), and λ = 14 (long-dashed line).
Variation of drop tilt angle (a) and deformation (b) with field strength for drops with viscosity ratio 14. The points are the experimental data from Ref. 3 for drops with radius a = 0.9 mm (circle), a = 1 mm (square), a = 1.8 mm (diamond), and a = 2.5 mm (triangle). The dashed line is the dipole tilt angle given by Eq. (1) . The tilt angle calculated from the theory, Eq. (22) , and the deformation parameter, Eq. (23) , for a drop with radius 0.9 mm are given by a solid line. The dotted-dashed line corresponds to the 2D theory. 10
Tilt angle and deformation for a drop with viscosity ratio 1.4 and diameter 1.4 mm. The rest of the parameters are the same as in Figure 6 .
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