ac electric fields drive steady flows in flames

We show that time-oscillating electric fields applied to plasmas present in flames create steady flows of gas. Ions generated within the flame move in the field and migrate a distance $\delta$ before recombining; the net flow of ions away from the flame creates a time-averaged force that drives the steady flows observed experimentally. A quantitative model describes the response of the flame and reveals how $\delta$ decreases as the frequency of the applied field increases. Interestingly, above a critical frequency, ac fields can be used to manipulate flames at a distance without the need for proximal electrodes.

Figure 1

(a) Schematic illustration of the experimental setup; the cubic combustion chamber is drawn to scale. The dotted circle illustrates the field of view for the schlieren images below. (b) Schlieren images of a premixed, NaOH-doped methane flame following the application of an oscillating electric field of magnitude 100 kV${}_{\mathrm{rms}}$/m at 1 kHz.

Figure 2

Static fields. (a) Schlieren images of a premixed methane flame without (top) and with (bottom) NaOH dopant directly after the application of a static electric field of 280 kV/m. (b) Electric current as a function of the applied field strength for a premixed methane flame with and without ion doping. The solid and dashed lines illustrate the space-charge-limited and reaction-limited responses, respectively; the fit used for the space-charge response is $I=(1.1\times {10}^{-16}\mathrm{A}{\mathrm{m}}^2{\mathrm{V}}^{-2})E_0^2$. (c) Characteristic gas velocity $u$ as a function of field strength for the NaOH-doped flame; “positive” and “negative” refer to the sign of the charged species driving the jet. The solid curve is $u=(2.9\times {10}^{-6}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1})E_0$.

Figure 3

Oscillating fields applied to NaOH-doped, premixed methane flames. (a) Characteristic gas velocity $u$ as a function of frequency $\nu$ and field strength $E_0$. The solid lines correspond to $u=(2.9\times {10}^{-6}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1})E_0$ as obtained from Fig. 2c. (b) Average electric dissipation rate $\Phi$ as a function of frequency $\nu$ and field strength $E_0$. The solid lines are theoretical predictions of the charge transport model. The dashed line illustrates the transition from the low-frequency regime to the high-frequency regime as defined by the condition $\delta \sim L$. The parameters used in the model are as follows: electrode spacing, $L=0.1\mathrm{m}$; flame width, $b={10}^{-2}\mathrm{m}$; flame thickness, $a={10}^{-4}\mathrm{m}$; mobility, $K=1.05\times {10}^{-4}{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}$; recombination rate, $k_r=1.90\times {10}^{-13}{\mathrm{ions}}^{-1}{\mathrm{m}}^3{\mathrm{s}}^{-1}$; ionization rate, $k_i=1.09\times {10}^{20}\mathrm{ions}{\mathrm{m}}^{-3}{\mathrm{s}}^{-1}$; and flame area, $A_f=3.90\times {10}^{-3}{\mathrm{m}}^2$ (see Ref. [16] for details).

Figure 4

(a) Schematic illustration of the 1D model showing the ionization region $g\left(x\right)$ and the time-averaged field squared $\langle E^2\rangle$. (b) Electrohydrodynamic response of the flame using glass-insulated electrodes for static ($E_0=75\mathrm{kV}/\mathrm{m}$; left) and oscillatory ($E_0=75{\mathrm{kV}}_{\mathrm{rms}}/\mathrm{m}$, $\nu =800\mathrm{Hz}$; right) fields.