Controlling instabilities of electrified liquid jets via orthogonal perturbations

Whipping is a peculiar nonaxisymmetric instability experienced by electrified liquid jets and utilized in electrospinning to produce fine polymer fibers; however, it manifests itself in a chaotic and uncontrollable fashion. We impose two perturbations in the form of small mechanical oscillations, orthogonal with each other, to alter and curb instabilities of electrified liquid jets. The oscillations cause transverse positioning disturbance to the nozzle and therefore the initial positioning of the jet. The effects of parameters including the excitation frequency, amplitude, and phase difference of the imposed perturbations and the axial electric field are investigated. The steady helicoidal whipping structure with a linearly growing lateral amplitude in air has been demonstrated, offering a feasible solution for electrospinning to fabricate fibers of uniform thickness. Furthermore, the superposition of two sinusoidal orthogonal perturbations enables deposition of complex patterns, such as Lissajous curves.

Figure 1

Schematic of experimental device for controlling instabilities of electrified jets via orthogonal perturbations imposed by two loudspeakers.

Figure 2

Examples of (a) chaotic whipping with no imposed perturbations and (b–e) helicoidal whipping structures of jets emanated from the Taylor cone at constant flow rate $Q=300\mu l/\min$ and axial electric field strength between the two parallel electrodes $E_z=6\mathrm{kV}/\mathrm{m}$ .

Figure 3

[(a)–(g)] Example images of instability transition of electrified jets via changing the excitation frequency of orthogonal perturbations, and (h) the corresponding dispersion curves based on Eq. (2). The inset of (e) is its side view. The axial electric field $E_z=1.15\times {10}^5\mathrm{V}/\mathrm{m}$.

Figure 4

Jet instability mode mapped in the χ-Γ diagram, where the whipping mode is denoted by the green background, whipping assisted bifurcation mode is the region in blue, and the varicose mode is in orange. The data points are the corresponding experimental data partially marked in Fig. 3.

Figure 5

Snapshots of the whipping assisted bifurcation mode at various initial perturbation amplitudes at constant excitation frequency of 1.8 kHz.

Figure 6

Effects of the initial perturbation amplitude $A$ on (a) the distance between the nozzle and the bifurcating point shown in Fig. 5, and (5) the semiopening angle in the whipping assisted bifurcation mode and the whipping mode

Figure 7

Images of the helicoidal whipping structure obtained at various axial electric field strengths without changing other operating parameters.

Figure 8

Effects of the axial electric field strength on the overall current, half-cone angle, and averaged wavelength of the whipping structure.

Figure 9

(a) Patterns of orthogonal perturbation superposition at various phase differences, where the dashed lines $s_1$ and $s_2$ represent the imposed perturbation directions; [(b)–(d)] snapshots obtained from view 1 (insets) and view 2, when $\varphi =\pi /3$, $\pi /6$, 0, respectively.

Figure 10

(a) Snapshots obtained at the inception of whipping assisted bifurcation mode from view 1 at (a) $\varphi =\pi /3$, $f=1.0\mathrm{kHz}$; (b) $\varphi =\pi /6$, $f=0.95\mathrm{kHz}$; (c) $\varphi =0$, $f=0.9\mathrm{kHz}$.

Figure 11

Lissajous trajectories deposited on the lower electrode at various excitation frequency ratios and phase differences. The insets illustrate the corresponding imposed perturbation patterns. The high-speed images on the right show the jet morphology corresponding to figure “V” and figure “8”.