Ice nucleation in high alternating electric fields: Effect of electric field strength and frequency

Icing is a severe problem for many technical systems such as aircraft or systems for high-voltage power transmission and distribution. Ice nucleation in water droplets is affected by several influencing factors like impurities or the liquid temperature, which have been widely investigated. However, although an electric field affects nucleation, this influence has been far less investigated and is still not completely understood. The present work is focused on the influence of high alternating electric fields on ice nucleation in sessile water droplets, which is examined for a systematic variation of the electric field frequency and strength. All experiments used to determine the influence of a single parameter like the electric field strength or frequency are performed with the same set of droplets to ensure well-defined conditions and a high repeatability of the procedure. For each parameter variation a large number of nucleation events is observed and analyzed. Droplet survival curves and the nucleation site density are used to analyze the experiments and to determine the influence of the electric field on ice nucleation. Especially for high electric field strengths, a significant influence on nucleation is observed. Some droplets freeze earlier, which leads to a higher median nucleation temperature. On the other hand, the lowest temperature required to freeze all droplets is almost constant compared to the reference case without an electric field. It is shown that not all droplets are affected by the electric field in the same way, but the influence of the electric field on ice nucleation is rather of singular nature. In addition, the frequency of the applied electric field has an impact on the nucleation behavior. The present experimental data quantitatively demonstrate the effect of an electric field on ice nucleation and improves our understanding of heterogeneous nucleation of supercooled water subjected to high alternating electric fields.

Figure 1

Schematic of the experimental setup and its components, republished from Ref. [28] with permission conveyed through Copyright Clearance Center, Inc.

Figure 2

Top-view images showing a drop matrix consisting of drops with a mean size of $d=1.04$ mm placed on the sapphire substrate. The drop matrix is shown at different moments during a nucleation experiment, illustrating the gradual decay of the ratio of liquid droplets in the ensemble. (a) Unfrozen droplet ensemble at $\vartheta =-13.99{}^{\circ }\mathrm{C}$, (b) partially frozen ensemble at $\vartheta =-22.23{}^{\circ }\mathrm{C}$, and (c) completely frozen ensemble at $\vartheta =-25.06{}^{\circ }\mathrm{C}$. Example video data of ice nucleation can be found as Supplemental Material [31].

Figure 3

Change of the nucleation temperature due to the electric field $\widehat{E}, \mathrm{\Delta }{\vartheta }_n={\vartheta }_n{{|}_{\widehat{E}>0}-{\vartheta }_n|}_{\widehat{E}=0}$, shown for all droplets in the present experiments. ${\vartheta }_n{|}_{\widehat{E}>0}$ and ${\vartheta }_n{|}_{\widehat{E}=0}$ denote the nucleation temperature of a droplet observed with and without an electric field. The horizontal dotted lines illustrate the temperature band of $\pm 4.55\mathrm{K}$ around $0\mathrm{K}$, which corresponds to the maximum deviation of the droplet nucleation temperature for low electric field strength.

Figure 4

(a) Droplet survival curves for varying electric field strength obtained with the same ensemble of droplets for all experiments. Ratio of current number of liquid droplets $N_{\mathrm{l}}$ to the initial number of liquid droplets $N_0$, depending on the ensemble temperature $\vartheta$. (b) Nucleation site density $n_{\mathrm{si}}$ of corresponding data as a function of temperature $\vartheta$. The experiments begin without an electric field and the electric field strength $\widehat{E}$ is gradually increased after each experimental run for a constant frequency of $f=50\mathrm{Hz}$ and a mean droplet diameter of $d=1.04\mathrm{mm}$.

Figure 5

Characteristic temperatures ${\vartheta }_x$ for the decay of a droplet ensemble depending on the electric field strength $\widehat{E}$. The present data correspond to the experimental series already shown in Fig. 4. The temperature ${\vartheta }_x$ of an ensemble represents the temperature, where $N_{\mathrm{l}}/N_0=x$.

Figure 6

Droplet survival curves for two different sets of droplets serving to examine the influence of previous exposure to electric field strength on ice nucleation. The index of $\widehat{E}$ designates the droplet set. Data with index 1 was obtained by starting with a low electric field strength, which was then continuously raised. The data with index 2 started with the highest electric field strength, which was then stepwise lowered. The frequency of the electric field was held constant at $f=50\mathrm{Hz}$.

Figure 7

Characteristic temperatures ${\vartheta }_x$ for the decay of a droplet ensemble depending on the electric field strength $\widehat{E}$. The ensemble is initially exposed to the highest electric field strength, which is then continuously lowered after a minimum of three repetitions. The data correspond to the experimental series already shown in Fig. 6. The temperature ${\vartheta }_x$ of an ensemble represents the temperature, where $N_{\mathrm{l}}/N_0=x$.

Figure 8

Variation of the nucleation temperature of the individual droplets of a typical droplet ensemble obtained with the electric field turned off. Nucleation temperature of a droplet measured in two further repetitions of the experiment shown as a function of the nucleation temperature obtained in the first experiment.

Figure 9

Variation of the nucleation temperature of the individual droplets of a typical droplet ensemble obtained with the electric field of a constant frequency $f=50\mathrm{Hz}$. Nucleation temperature of a droplet measured in two further repetitions of the experiment shown as a function of the nucleation temperature obtained in the first experiment. The plus signs indicate the first and the circles the second repetitions. The color and size of the individual symbols corresponds to the electric field strength between $\widehat{E}=0\mathrm{kV}$/cm and $\widehat{E}=7.16\mathrm{kV}$/cm.

Figure 10

Change of the mean freezing temperature for varying field strength, $\mathrm{\Delta }{T}_{\widehat{E}}={\overline{T}}_{\widehat{E}}-{\overline{T}}_0$, depending on the temperature difference corresponding to the highest field strengths, $\mathrm{\Delta }{T}_{{\widehat{E}}_{\max }}={\overline{T}}_{{\widehat{E}}_{\max }}-{\overline{T}}_0$. Each symbol corresponds to a specific droplet and the symbol type and color refer to the electric field strength under consideration. The colored regions indicate the trends for the varying electric field strength.

Figure 11

(a) Droplet survival curves for a constant electric field strength $\widehat{E}=2.26\mathrm{kV}$/cm and varying frequency depending on the droplet temperature $\vartheta$, and (b) corresponding nucleation site density $n_{\mathrm{si}}$. The mean diameter of the used droplets is $d=1.09\mathrm{mm}$.

Figure 12

Characteristic temperatures ${\vartheta }_x$ for the decay of a droplet ensemble depending on the frequency $f$ of the electric field exposed with a constant electric field strength of $\widehat{E}=2.26\mathrm{kV}$/cm. The present data correspond to the experimental series already shown in Fig. 11. The temperature ${\vartheta }_x$ of an ensemble represents the temperature, where $N_{\mathrm{l}}/N_0=x$.