Taylor cone and electrospraying at a free surface of superfluid helium charged from below

Electrically charged metallic micro- and nanoparticles are trapped under a free surface of superfluid He in a vertical static electric field. We observe a static deformation of the charged liquid surface in the form of a Taylor cone and the emission of a charged liquid helium jet (electrospray). Our numeric calculations reproduce the static shape of the cone.

Figure 1

Experimental setup. Left: Top view of the cryostat and optical setup. Right: Vertical cut through the sample cell and electric current measurement circuit.

Figure 2

Schematic of the sample cell with top and bottom electrodes and the charged helium surface.

Figure 3

A static deformation of the free surface of superfluid He (Taylor cone) due to the trapped charge in a static electric field. (a) Negative charge trapped; (b) positive charge trapped. $T=2.1$ K.

Figure 4

Height of the Taylor cone as a function of the plate-to-pin voltage difference. Experimental data: circles connected by dashed line. $U_{\mathrm{pin}}$ is fixed at $-400\mathrm{V}$ and $U_{\mathrm{plate}}$ increased in steps of 100 V; $T=2.1$ K. Calculations (see Sec. 5a): solid curve 1 (red), cone charge $3.2\times {10}^{8}e$; curve 2 (black), cone charge $3.2\times {10}^{7}e$; curve 3 (green), $4\times {10}^{6}e$.

Figure 5

Frames of a fast video recording capturing the process of the charge escape from the Taylor cone. $U_{\mathrm{pin}}=-390$ V, $U_{\mathrm{plate}}\approx +900$ V (ramp from +800 to +1800 V), $T=2.1$ K, single-frame exposure time $\approx 0.19$ ms; time $t=t_0$ corresponds to the beginning of the jet emission. Frame size, $4.6\times 2.5$ mm.

Figure 6

Time dependence of the height of the Taylor cone corresponding to the video recording in Fig. 5. Every data point corresponds to one frame in the video. $U_{\mathrm{pin}}=-390$ V, $U_{\mathrm{plate}}\approx +900$ V (ramp from +800 to +1800 V), $T=2.1$ K, single-frame exposure time $\approx 0.19$ ms. Vertical arrows mark the moments corresponding to the frames shown in Fig. 5. The dashed horizontal line shows the level of the undisturbed liquid.

Figure 7

(a) Voltage ramp applied to the pin electrode $U_{\mathrm{pin}}$ and the ablation laser pulses ($\lambda =532$ nm; pulse energy, 200 $\mu \mathrm{J}$). (b) Electric current due to the charge escape and the height of the observed Taylor cone. $U_{\mathrm{plate}}$, +890 V; $T=2.11$ K.

Figure 8

Electric current pulse associated with the Taylor cone breakdown. (a) No corona discharge, $U_{\mathrm{pin}}=-370$ V, $U_{\mathrm{plate}}=+600$ V; (b) corona discharge starts after the cone breakdown, $U_{\mathrm{pin}}=-400$ V, $U_{\mathrm{plate}}=+600$ V, $T=2.11$ K.

Figure 9

Frames of a fast video recording showing positively charged nano- and microparticles trapped under the surface of a Taylor cone. View from the bottom; each picture covers the area of $7.5\times 7.5$ mm. $U_{\mathrm{pin}}=-800$ V, $U_{\mathrm{plate}}=+1000$ V, $T=2.1$ K. (a) Exposure time, 2 ms; cw laser power, 200 mW; (b–d) exposure time, 10 ms; cw laser power, 55 mW.

Figure 10

Surface profile (curve 1) and charge density (curve 2), obtained from a simulation for an applied voltage difference between tip and bottom plate of 1300 V and a total of $1.75\times {10}^8$ elementary charges ($2.8\times {10}^{-11}$ C) trapped under the surface.