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Visible-light-assisted condensation of ultrasonically atomized water vapor on LiNbO3:Fe crystals

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Abstract

Optically massive trapping of the moisture in the air into an adjacent surface is a potential technique in the fields of bacterial adhesion and microfluidic generation, which is quite important to the development of LN-based biological lab-on-chips. Here we demonstrate on a LiNbO3:Fe substrate the visible-light-assisted condensation of the water vapor in a flowing stream created by an ultrasonic atomizer. Through analyzing the dynamic processes of the visible-light-assisted water condensation at different illumination intensities, it is found that the extent of the water condensation, the bending angle of water vapor trails and the interaction range of the condensation effect are highly dependent on the illumination intensity. According to these findings and the simulated trajectories of the water vapor stream at different illumination intensities, we propose that this visible-light-assisted water condensation is an aggregation process of tiny water droplets driven by the dielectrophoretic interaction of inhomogeneous photovoltaic field and also an electrostatic screening course of photovoltaic charges through the charged evaporation of condensed water. The prolonged condensation of water vapor after a high-intensity illumination and that of oil vapor at a super-low evaporation rate are also studied, and the agreement between the simulation and experimental results reinforces the above mechanism. The reported technique, employing the inexpensive, safe-for-cell visible laser beam, is quite convenient for the controllable generation of various biological microdroplets, and thus it is promising for the microfluidic functionality integration of LN-based biological lab-on-chips.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Optically massive trapping of the moisture in the air into an adjacent surface is a potential technique in the fields of bacterial adhesion and microfluidic generation. Recently, the parallel manipulation of micro- and nano-objects utilizing the light-induced electrostatic field on the surface of LiNbO3 (LN) crystals was demonstrated [14]. Since LN crystals already showed great potential in biological photonics [59], this non-contact manipulation way was considered as one promising integrated functionality in LN-based lab-on-chips for biological analysis, clinical diagnostics, and drug discovery [10,11]. The force employed by this parallel manipulation essentially stems from the surface charges generated by illumination (i.e. pyroelectric or photovoltaic effect) [3,4]. By this way, researchers realized dynamic shooting of dielectric liquid [12] and active dispensing of biological liquid [13], as well as a series of accurate operations on nanoparticles [14,15], microcrystals [16], biological cells [17,18], and microdroplets [1923]. In spite of many works reported, this optoelectronic interaction has never been developed for trapping the moisture around the LN substrate, and the corresponding effect on the water vapor, which is associated with the interaction between the photo-excited surface charges and the tiny water droplets near the surface, obviously deserves investigation.

For a long time, light-assisted water condensation on LN substrates has been an important issue relevant to various optofluidic applications as it is connected with the controllable phase transition of aqueous vapor and the spatially confined generation of microdroplets. Generally, this process can be realized by optically altering the wettability of the LN surface. Muir et al. reported for the first time the UV-light-induced wettability change of pure LN surface [24]. Yan et al. carefully studied this wettability transition on the pure LN surface and demonstrated how to reverse it experimentally [25]. Apparently, UV-exposure was necessary for tuning the wettability of the LN surface. However, the usage of expensive UV laser source is disadvantageous to the manufacture of the biological devices employing this technique. Moreover, a majority of living cells in biological microfluidic applications usually cannot stand the UV exposure.

Recently, we showed that the microdroplets can be manipulated on the surface of LiNbO3:Fe (LN:Fe) crystals by the visible laser [2123]. The dopant Fe introduces electron traps (FeLi2+/3+) in the LN lattice and they can induce a strong photovoltaic effect in the visible range. Under the illumination of the visible light, the electrons can be easily photo-excited from Fe2+/3+ traps, forming the current toward the −c surface of the LN substrate (i.e., photovoltaic current). In virtue of the inhomogeneous photovoltaic field, microdroplets were manipulated in multimode with higher efficiency on the crystal surface. Since the electrostatic interaction generated by the visible illumination shows a great effect on the liquid in these cases [21,22], it is highly expected that this interaction can also be utilized to spatially trigger and confine the water condensation, i.e. to realize a visible-light-assisted condensation of water vapor.

In the paper, we create a water vapor stream flowing along the LN:Fe crystal surface by using an ultrasonic atomizer, and the visible-light-assisted condensation of the water vapor on the LN:Fe crystal surface is demonstrated in a real time. Through analyzing the dynamic process of the visible-light-assisted water condensation, we find that it is essentially an aggregation process of tiny water droplets driven by the dielectrophoretic interaction of the inhomogeneous photovoltaic field and furthermore it is an electrostatic screening course of photovoltaic charges through the charged evaporation of condensed water. As the ultrasonic atomizer is capable to produce almost all kinds of vapor, the technique reported here is quite convenient for the controllable generation of various microdroplets.

2. Experiments

The samples were congruent c-cut LN:Fe crystals (0.03 wt% Fe2O3) with thickness of ∼ 1 mm. To modify the sample absorption, we annealed the sample in argon at 1000 °C for one hour. Figure 1(d) shows the UV-VIS absorption spectra of the sample and its absorption at 405 nm is 9.8 cm−1.

 figure: Fig. 1.

Fig. 1. (a) Setup for recording the dynamic process of the visible-light-assisted condensation of water vapor; (b) Scheme of the water vapor stream flowing along the LN:Fe crystal surface and the following visible-light-assisted water condensation; (c) Typical water droplet contact angle on a charged LN:Fe surface; (d) UV-Vis absorption spectra of LN:Fe sample.

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The experimental setup for the visible-light-assisted condensation of the water vapor is shown in Fig. 1(a). An ultrasonic atomizer with a nozzle was used to create a water vapor stream. Through atomizing mechanism, the bulky deionized water was broken into tiny droplets suspending in the air and formed the water vapor stream flowing along the LN:Fe crystal surface (Fig. 1(b)). The signal generator connected with the ultrasonic atomizer was used to control the frequency and amplitude of the ultrasonic vibration, and thus the average diameter and flowing speed of the droplets in the water vapor stream can be tuned manually. Figure 2(a) shows a snapshot of the water vapor created by the ultrasonic atomizer, and a mass of tiny droplets can be clearly seen in the air. Figure 2(b) shows the moment when two tiny droplets are landing on a super-hydrophobic substrate, and their diameter can be estimated to be about 5 microns. Experimentally, the flowing speed of the water vapor stream can be estimated roughly through the average trailing smear (Fig. 2(c)) of the tiny droplets in the water vapor stream, i.e. dividing the average trailing smear length by the exposure time of the camera. The 405 nm-laser (CniLaser) was focused by Objective 1 onto the surface of the LN:Fe sample. A beam of green laser (533 nm) was configured to co-propagate with the water vapor stream above the LN:Fe sample surface. The side Mie scattering from the water vapor was captured through Objective 2 by a camera so that the movement of tiny droplets in the water vapor stream can be recorded in details. The dynamic process of the visible-light-assisted condensation of the water vapor was obtained at two positions. One is below the sample (Position 1, bottom view), and the other is in the right of the sample (Position 2, lateral view). For comparison, we also performed the experiment of the visible-light-assisted condensation of water vapor by using 473 nm- laser beam. Moreover, ultrasonically-atomized oil (transformer oil) vapor was also tried as the object of the visible-light-assisted condensation.

 figure: Fig. 2.

Fig. 2. (a) Snapshot of the water vapor created by an ultrasonic atomizer; (b) Picture of two tiny droplets landing on a super-hydrophobic substrate; (c) The trailing smear of the tiny droplets in the water vapor stream. The trailing smear is due to the fast movement of the tiny droplets when the camera shutter is opening. The trails of some droplets are not clear enough because they are not right located in the focal plane of the camera. The arrows in (b) denote the location of the landing droplets. The L in (c) represents the trailing smear length.

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3. Results and discussions

Figure 3 shows the typical dynamic process of the visible-light-assisted water condensation on the –c surface of LN:Fe crystal, and the intensity of 405 nm-laser is about 2.54×106 W/m2 at the focus. We performed twice the visible-light-assisted water condensation at the same region of the substrate surface, and the interval between the two experiments is about 15 s. As one can see, before the 405 nm-illumination there is almost no water condensation on the surface. Upon the 405 nm-illumination, the droplets with size of tens of microns start to appear around the laser spot. With the continuous illumination, the merging of the droplets occur and the droplets grow gradually till the “off” of 405 nm-illumination. As the droplets generated in this way are quite small, they evaporate quickly in the absence of the 405 nm-illumination. However, when the 405 nm-illumination is applied for the second time, the droplets generate again and the growing rate of droplets is close to that in the first round. This result shows that the visible illumination is capable to trigger and confine the condensation of the ultrasonically-atomized water vapor, and that more promisingly, by this way it is possible to generate an individual microdroplet with controllable size as long as the experimental parameters are set in proper ranges.

 figure: Fig. 3.

Fig. 3. The typical dynamic process of the visible-light-assisted water condensation on the –c surface of LN:Fe crystal. The “on” and “off” states of the 405 nm-illumination are denoted by the purple and gray dots, and the laser spot is marked by the purple halo in the center of the view. The flowing speed of the water vapor stream is 50 mm/s.

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It should also be noticed that the start and stop of the water condensation are almost synchronous with the “on” and “off” of the 405 nm-illumination and the delay of water response to the 405 nm-illumination is usually in the level of sub-second. In order to further demonstrate this timely response of the water condensation, we show in Fig. 4 the dynamic process of the water condensation triggered by a scanning laser, i.e. the laser spot scans on the crystal surface. As one can see, the water condensation tightly follows the scanning spot. This result means that the photo-excited electrostatic field generated on the crystal surface grows and decays very quickly in the presence and absence of the 405 nm-illumination. Since the bulk photovoltaic field generated inside the LN:Fe crystal is often considered to be permanent in an insulating environment [26], we believe that the quick decay of photovoltaic field is due to some kind of electrostatic screening of the surface photovoltaic charges [23]. It is well known that even in deionized water there are still lots of free charges making water conductive, which possibly leads to the quick decay of photovoltaic field in the absence of the 405 nm-illumination. However, continuous illumination can provide sufficient photovoltaic charges to overcome the electrostatic screening from the condensed water, and therefore it can keep the water condensation proceeding and drive the water microdroplets merging and growing bigger (Fig. 3).

 figure: Fig. 4.

Fig. 4. The dynamic process of the water condensation triggered by a scanning laser. The yellow triangle represents the unmovable reference on the substrate surface. The “on” and “off” states of the 405 nm-illumination are denoted by the purple and gray dots, and the laser spot is marked by the purple halo in the center of the view. The laser scanning direction is denoted by the green arrow and the average scanning speed is about 70 µm/s.

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Generally, the surface photovoltaic charge density σ can be given by σ =δtJpv=δtGαI [21,23], where δt is the illumination duration, I is the illumination intensity at the focus, G is the Glass constant, and α is the absorption. As the density of the photovoltaic charges accumulated on the surface is not only associated with the illumination duration but also with the illumination intensity, the effect of illumination intensity on the water condensation is expected. Figure 5 shows the dynamic process of the visible-light-assisted water condensation at different illumination intensities. It is obvious that the water condensation becomes faster and more pronounced with the increase of the intensity. In order to quantify the extent of the visible-light-assisted water condensation effect, we binarize some images of Fig. 5, extract the regions covered by the condensed water (i.e. the white regions in the insets of Fig. 6) and calculate the total area percentage P of the water condensation (i.e. the ratio of the total area covered by the condensed water to the whole image area). In Fig. 6, this total area percentage P is plotted as a function of the product of the illumination intensity (I) and duration (δt). Note that the representative binarized images (the insets in Fig. 6) are extracted from one experimental run (Fig. 5) but the data are obtained from different experimental runs. In fact, the experiments are performed three times for each illumination intensity, and the P value is an averaged result over three runs and the data fluctuation is marked by the error bar. It can be found that P is roughly linear with the product of the illumination intensity (I) and duration (δt), and furthermore the fitting line (P = 1.50×10−6(I×δt) + 0.05) almost passes the original point. This result indicates the visible-light-induced water condensation is indeed a process in which the net surface charges are consumed and the electrostatic screening of the photovoltaic charges occurs. Note that here we evaluate the area of the condensed droplets instead of their volume for two reasons. First, it is not easy to know exactly the height of the condensed droplets in a real-time mode. One possible way to measure the height of the condensed water is introducing an in-situ interferometric system into our experimental setup and then counting the real-time interference fringes caused by condensed water thickness. Second, the variation of the droplet height seems to be neglectable as compared with that of the droplet area. As a matter of fact, the droplet contact angle on a charged LN:Fe surface is quite small (< 20 degree) due to the electrical wetting effect (see Fig. 1(c)) and furthermore the electrostatic attracting sometimes makes the droplets being a little bit flattened on the charged LN:Fe surface. Both of the factors make the area covered by the droplets more sensitive to the product Iδt than the droplet height.

 figure: Fig. 5.

Fig. 5. The dynamic process of the visible-light-assisted water condensation at different illumination intensities. The “on” and “off” states of the 405 nm-illumination are denoted by the purple and gray dots. The flowing speed of the water vapor stream is 14 mm/s.

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 figure: Fig. 6.

Fig. 6. The total area percentage P as a function of the product of the illumination intensity (I) and duration (δt). The insets are the binarized outputs of some images of Fig. 5, and the calculated P of these figures are plotted as solid squares with corresponding colors. All data are fitted by a red line, and the fitting yields P = 1.50×10−6(I×δt) + 0.05.

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Figure 7 shows the typical dynamic process of the visible-light-assisted water condensation in the lateral view. As one can see, at the beginning the water vapor stream flows almost straight above the crystal surface. However, when the 405 nm-illumination is applied, the vapor stream starts to bend towards the laser spot (the place where violet beam is located in Fig. 7). Note that the green laser beam responsible for shining the water vapor stream is set to avoid illuminating the crystal surface as much as possible and the bending of the vapor stream is mainly caused by the 405 nm-illumination rather than the 533 nm-illumination. This dynamic bending process clearly shows the attractive force generated at the laser spot. Figure 8 shows the images for different illumination intensities recorded by a high-speed camera. In this figure, the trails of tiny water droplets in the stream can be recognized and more details about the bending of the water vapor stream can be observed. At the low illumination intensity (Fig. 8(b)), only the bottom layer of the vapor stream is affected by the attractive force at the illumination region and the bending angles of the vapor trails are very low. However, with the increase of the illumination intensity, the interaction range of the attractive force expends both in the vertical and horizontal directions (Figs. 8(c)–8(e)). In particular, at the intensity of 4.59×107 W/m2 the vapor trails almost in the whole view range show quite large bending angles.

 figure: Fig. 7.

Fig. 7. The typical dynamic process of the visible-light-assisted water condensation in the lateral view. The “on” and “off” states of the 405 nm-illumination are denoted by the purple and gray dots, and the laser beam is highlighted by the bluish violet color. In addition, the vapor stream flow is marked by the dash curve. The sequential images are obtained by the conventional camera with a normal speed and the blurry vapor flow is due to the fast movement of many tiny water droplets.

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 figure: Fig. 8.

Fig. 8. The trails of tiny water droplets in the vapor stream at different illumination intensities. The “on” and “off” states of the 405 nm-illumination are denoted by the purple and gray dots, and the laser beam is highlighted by the bluish violet color. The flowing speed of the water vapor stream is 14 mm/s. The images are obtained by using the snap shot mode of a high-speed camera.

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To clarify the detailed mechanism of this visible-light-assisted water condensation, we have to first rule out the possibility of the laser-induced thermal effect. It is known that any laser-induced thermal effect on LN:Fe crystal usually takes some seconds to respond to the laser illumination. However, the laser-induced effect in our case responds almost instantaneously. Thus, the visible-light-assisted water condensation is more likely to be induced mainly by the electrostatic effect rather than the thermal effect. As a matter of fact, we tried the same experiment on another LN:Fe substrate deposited with a conductive ITO layer and no visible-light-assisted water condensation was found in this case. It proves the direct association of the visible-light-assisted water condensation with the electrostatic effect, because the electrostatic effect of photovoltaic charges are totally screened by the conductive layer while the laser-induced heat still exists in this case [23]. Generally, the photovoltaic field generated on the LN:Fe crystal can reach values as high as 107 V/m [27]. This field extends from the crystal surface to the nearby space and is capable to attract the charged or neutral particles existing in its interaction range through either electrophoretic (EP) or dielectrophoretic (DEP) forces, respectively [27,28]. Thus, we have to make a judgement on the force type (EP or DEP) which governs the visible-light-assisted water condensation, i.e. we must know whether the ultrasonically-atomized water droplets are charged. To determine this, we compare the phenomena on the -c and + c surfaces of the LN:Fe crystals. As shown in Fig. 9, charges with opposite signs are often generated on the -c and + c surfaces of the LN:Fe crystals [2729]. If the ultrasonically-atomized water droplets are charged (EP force dominates the water condensation in this case), then two totally different behaviors (attracting and repelling behaviors) may be observed on the + c and –c surfaces of the LN:Fe crystals. However, we indeed found no obvious difference of visible-light-assisted water condensation between them, indicating that the ultrasonically-atomized water vapor is a mass of neutral tiny droplets and DEP force is responsible for their condensation. The DEP interaction of the inhomogeneous photovoltaic field attracts the tiny droplets in the water vapor stream, leads to the bending of the droplet trajectories, and finally results in the aggregation of the water vapor (i.e. water condensation).

 figure: Fig. 9.

Fig. 9. Photovoltaic charge sign and typical visible-light-assisted water condensation on the –c and + c surfaces of LN:Fe crystal. In spite of the different charge signs on the –c and + c surfaces, no obvious difference of visible-light-assisted water condensation is found between them.

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As mentioned above, this water condensation may consume the net surface charges through the screening of the photovoltaic charges. Generally speaking, the electrostatic screening happens only when the conductive liquid can gain charges from external sources, for example it is connected with ground, but the water vapor in our case is a mass of neutral tiny droplets insulated by the surrounding air. Thus, there must be other way for the condensed water to gain charges for screening the photovoltaic charges. Since the condensed water evaporates quickly in the absence of the 405 nm-illumination (see Fig. 3), the visible-light-induced water condensation has to be considered as the combination of both condensation and evaporation, i.e. it is essentially a competition process between condensation and evaporation. It has been proved that the water evaporation may carry charges from the water/air interface. In [30], this process is attributed to the accumulation of protons or hydroxide ions at the evaporation front. As the evaporation creates net charges inside the water, and thus it is highly possible that the photovoltaic charges are screened in this way. Figure 10 plots the scheme for the electrostatic screening of the photovoltaic charges through the evaporation of the condensed water. When the neutral tiny droplets flow over the illuminated region, they are polarized and attracted towards the surface due to the electrostatic interaction from the photovoltaic charges (Fig. 10(a)). The water vapor is then condensed on the surface, and the electrostatic interaction leads to the appearance of charges on the water/air interface (Fig. 10(b)). Later, the water evaporation carries charges from the water/air interface, and consumes the net charges on the surface (Fig. 10(c)). Through the continuous water condensation, the net charges on the surface are totally consumed, i.e. the surface photovoltaic charges are completely screened (Fig. 10(d)). Even though the photovoltaic charges can also be screened by the free charges in the air, the water condensation and the following evaporation of the condensed water definitely accelerates this screening process. In fact, it is often found after the shutdown of the 405 nm-illumination that, a little part of condensed water located right at the illumination spot is very hard to evaporate (Fig. 11). This is an evidence of the electrostatic screening of the photovoltaic charges, because the electrostatic screening charges are quite dense at the illuminated spot and their existence slows down the evaporation of the local condensed water. Note that the residual water is not likely caused by the pinning of the random surface irregularities because we never found the similar abnormal pheromone in the evaporation process of the water droplet that we put on the LN:Fe surface by using a common nozzle.

 figure: Fig. 10.

Fig. 10. The scheme for the electrostatic screening of the photovoltaic charges through the evaporation of the condensed water.

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 figure: Fig. 11.

Fig. 11. The water evaporation process after the visible-light-induced condensation. A little part of condensed water located right at the illumination spot (denoted by the yellow circle) is very hard to evaporate. The “on” and “off” states of the 405 nm-illumination are denoted by the purple and gray dots.

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In Fig. 12, we simulate the visible-light-assisted water condensation at different illumination intensities, i.e. the aggregation process of the neutral tiny droplets under different inhomogeneous photovoltaic fields. It is assumed in the simulation that, all the tiny droplets in the water vapor stream flow with a same initial speed (V0=14 mm/s) along the direction parallel to the crystal surface, the photovoltaic charges accumulate on the surface in a rate proportional to the light intensity, and the aggregation of each tiny droplet on the surface consumes a fixed amount (Qwater ∼2.1×10−10 C) of net charges on the surface to realize the electrostatic screening. The effect of air resistance and gravity on the water vapor stream is ignored in this simulation because it is too week as compared with the electrostatic interaction. The distribution of the photovoltaic charges on the -c surface is set as a replica of the intensity profile [31]:

$${\sigma }_- = {\delta \textrm{tG}\alpha \textrm{I}}\left( {{\textrm{x,y}}} \right) = {\delta {\textrm{tG}}\alpha }{\textrm{I}}_{0}{\textrm{Exp}}\left[ {-2\left( {{\textrm x}^{2} + {\textrm y}^{2}} \right)/{\omega }^{2}} \right]$$
where δt is the irradiation time, G (3.3 pA/cm) is the Glass constant at 405 nm, Ι0 is the max intensity, α (9.8 cm−1) is the sample absorption at 405 nm and ω (50 µm) is the radius of the laser spot. The incident laser power P equals to the integration of I(x,y) over the illuminated area. The DEP interaction of the inhomogeneous photovoltaic field governs the movement of the tiny droplets in the water vapor stream, and it can be given as [27]:
$${\textrm{F}_{DEP}} = {\alpha }\nabla {\textrm{E}^2}\quad \textrm{and}\quad \alpha = 2\pi{\textrm{r}^3}{\varepsilon _0}{\varepsilon _m}\frac{{{\varepsilon _p} - {\varepsilon _m}}}{{{\varepsilon _p} - 2{\varepsilon _m}}}$$
where E is the photo-induced space charge field, r (2.5 µm) is the average radius of the tiny water droplets and ɛp (80) and ɛm (1) are the relatively dielectric constants for the water and air. For an explicit charge density σ, the electric potential V and the electric field E are calculated through the electrostatic equations E= -${\nabla}$V and${\nabla}$(ɛ E)= σ. As the droplets are tiny here, they are treated as particles for calculating DEP force.

 figure: Fig. 12.

Fig. 12. The simulated trajectory of the water vapor stream during the visible-light-assisted condensation at different illumination intensities. The tiny droplets in the stream are plotted as solid round particles with their trails and color representing the instantaneous velocities. The instantaneous electrostatic field generated by the photovoltaic charges is also plotted in a color scale. The initial speed of the water vapor stream is set as 14 mm/s.

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The simulation shows that the bending angle of the vapor trails, the interaction range of the attractive DEP force, and the area covered by the aggregated droplets (i.e. the condensed water) increase with the increasing illumination intensity. These results are in an agreement with the experimental observations mentioned above. In the simulation, we also record the number of the tiny water droplets aggregated on the substrate surface at relatively low (2.54×10 6 W/m2) and high (2.27×107 W/m2) illumination intensities. By comparing Figs. 13(a) and 13(b), we find that the average aggregation rate of the tiny water droplets goes up almost linearly with the illumination intensity. It is straightforward because the strong DEP force produced by the high-intensity illumination enhances the aggregation of the tiny water droplets. Besides, the response of the water condensation is much faster at the high intensity than at the low intensity. This result is consistent with the experimental response of the water condensation shown in Fig. 5.

 figure: Fig. 13.

Fig. 13. Temporal evolution of the number of tiny water droplets aggregated on the substrate surface in the simulation of the visible-light-induced water concentration at low (a) and high (b) illumination intensities. (c) Number of the tiny oil droplets during the visible-light-induced concentration of ultrasonically-atomized oil (transformer oil) vapor. The “on” and “off” moment of the illumination are denoted by the purple and green dots.

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Another noticeable result is regarding the prolonged water condensation after the shutdown of the high-intensity illumination (Fig. 13(b)), i.e. even when the high-intensity illumination is off the aggregation of the water vapor does not stop immediately. This simulation result is reasonable because the accumulating rate of the photovoltaic charges under the high-intensity illumination is so high that the slow aggregation of the water vapor cannot fulfil the complete screening of the photovoltaic charges in a short time. As a matter of fact, the charge consuming rate of the condensed water, i.e. the screening rate of the photovoltaic charges depends not only on the aggregation rate of the water vapor but also on the evaporation rate of the water (this process takes away the net charges). If we replace the water in the simulation with the liquid with a super-low evaporation rate, for example, transformer oil (an oil droplet consumes far less net charges than a water droplet in the simulation), a much more pronounced effect due to the heavily incomplete screening of the photovoltaic charges can be obtained (Fig. 13(c)).

We verify the above simulation result both by using the high-intensity 405 nm-illumniaition and by using ultrasonically-atomized oil (transformer oil) vapor stream. The dynamic processes of the visible-light-assisted condensation in both cases are shown in Fig. 14. It can be seen that, after the shutdown of the 405 nm-illumniaition the condensed water continues to evolve for a few seconds and then becomes motionless completely (Fig. 14(a)). This prolonged water condensation can also be found in the lateral view of Fig. 7, where another high intensity of 4.59×107 W/m2 is adopted. As compared to the water case, the prolonged effect on the oil condensation is more pronounced even after a low-intensity illumination (3.19×106 W/m2). As predicted by the simulation, the oil condensation can last for tens of seconds after the shutdown of the 405 nm-illumination (Figs. 13(c) and 14(b)). The agreement between the simulation and experimental results reinforces our mechanism about the visible-light-assisted water condensation.

 figure: Fig. 14.

Fig. 14. (a) The prolonged water condensation after the shutdown of the high-intensity illumination (2.27×107 W/m2). (b) The heavily prolonged oil condensation after the shutdown of the low-intensity illumination (3.19×106 W/m2). The “on” and “off” states of the 405 nm-illumination are denoted by the purple and gray dots.

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It should be emphasized that the experimental difference between water and oil condensation is the best proof for the argument about the charge consuming during the water evaporation. As we demonstrate above, at the low-intensity illumination the stop of the water condensation is almost synchronous with the “off” of the 405 nm-illumination. We believe that in this moment the water evaporation immediately consumes the accumulated photovoltaic charges, otherwise the water condensation will be prolonged for a long time. By contrary, we observe a tens-of-second prolonged oil condensation after the shutdown of the 405 nm-illumination. This result means that accumulated photovoltaic charges are hardly consumed in the case of oil, which is consistent with the super low evaporation of oil in the air.

Another issue we have to discuss is regarding the net charge amount consumed by the ultrasonically-atomized tiny droplet through its evaporation. Since the water evaporation depends on many experimental factors including the local humidity, temperature and area of air/water interface, it is not easy to theoretically predict the net charge amount (Qwater) consumed by one tiny water droplet. Nevertheless, we still can estimate the value of this parameter through the balance between the production and consumption of the photovoltaic charges in the experiments. As discussed above, the stop of the water condensation is almost synchronous with the “off” of the 405 nm-illumination at the low-intensity illumination (I = 2.54×106 W/m2), indicating a fast balance between the production and consumption of the photovoltaic charges. By carefully reviewing the video of the visible-light-assisted water condensation, we are able to count roughly the number (N∼300) of ultrasonically-atomized tiny droplets landing on the illuminated region of the LN surface during the illumination period (δt = 2.33 s). Basing on the Eq. (1), we can calculate the total amount (Qtotal=6.3×10−8 C) of the charges produced by the illumination and get the approximate charge amount (Qwater∼2.1×10−10 C) consumed by one tiny water droplet. In fact, the value of Qwater is utilized in the simulation of this case and the simulated number of the tiny water droplets aggregated on the LN surface turns out to be 180, which marginally matches the value of N obtained from the experimental observation. By contrary, the net charge amount (Qoil) consumed by one tiny oil droplet is set as two order magnitude lower than Qwater in the simulation. This is because the saturated vapor pressure of water is usually at least two order magnitude higher than the transformer oil, i.e. the transformer oil has a much lower evaporation rate than water. The simulation predicts the heavily prolonged oil condensation after the shutdown of the 405 nm-illumination, which is consistent with the experimental observation.

Since the aggregation of the water vapor can fulfil the immediate screening of the photovoltaic charges, the bulk photovoltaic field close to the surface cannot reach saturation in a short time. Note that in the traditional situation the bulk photovoltaic field inside the LN:Fe crystal usually saturates in less than one second at such an illumination intensity. However, near the surface the charge screening from the external sources (i.e. the ultrasonically-atomized water flow) can slow down significantly the establishment of the local bulk photovoltaic field, therefore the short-time approximation for the surface charge density (Eq. (1)) can be still valid in the time scale studied here.

It is well known that UV illumination, especially the illumination below 365 nm, can reduce the cell viability significantly. The 405 nm-laser used here is located in the visible range and its damage to the cell can be ignored theoretically. In this work, we selected 405 nm as the main operating wavelength because it is high-efficiency for producing photovoltaic current as compared to other longer wavelength. As a matter of fact, the operating wavelength can be replaced by anyone in the range from 400 ∼ 700 nm. As an example, we show the water condensation induced by the 473 nm-illumination in Fig. 15. Evidently, the water condensation is triggered and confined successfully by the illumination. As compared to the case of 405 nm-illumination, the 473 nm-illumination takes a little bit longer time to reach a similar extent of water condensation. Despite the inefficiency of the 473 nm-illumination, its longer wavelength should be much safer for cell. If necessary, the wavelength around 700 nm can also be adopted for more carefully handling the biological microdroplets. To create aqueous microdroplets containing living cell in various LN-based biological applications, water microdroplets have to be generated in advance. By utilizing the reported technique, it is possible to accurately generate water microdroplets with controllable size on the LN:Fe surface. This technique can be integrated on a hydrophobic LN platform where the transportation and splitting of water microdroplets [32] were realized recently. Thus, we can develop a complete all-optical system for sequentially creating and transferring aqueous microdroplets.

 figure: Fig. 15.

Fig. 15. The water condensation induced by the 473 nm-illumination. The “on” and “off” states of the 473 nm-illumination are denoted by the blue and gray dots.

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Since the LN:Fe crystal has an obvious absorption in the visible range, heat released by the optical interaction has to be considered. As the laser beam is incident at the bottom surface of sample in our work, the heating effect on the top surface (where the visible-light-assisted water condensation happens) is less pronounced as compared with the bottom surface. For optically manipulating water microdroplets a hydrophobic layer is often fabricated on the LN substrate, this less heat-conductive layer may further suppress the heating effect on the microdroplet.

The light-assisted water condensation reported there is essentially an aggregation process of tiny water droplets driven by the DEP interaction of the inhomogeneous photovoltaic field, which is quite different from the ultrafast-laser-induced water condensation reported by Kasparian et al. [33,34] and Liu et al. [35,36]. In their case, self-guided filaments generated by ultrashort laser pulses ionize chemical molecules, generate high density of charges allowing efficient photo-oxidative chemistry of the air molecules, and finally trigger the water-cloud condensation in the free, sub-saturated atmosphere. Different from their works, the CW laser is used in our case and its intensity is not sufficient to generate any nonlinear optical effect in the air, for example, multiphoton ionization of air molecules. Although the contributing mechanism in our case also includes the electrostatic effect, the causing charges are generated through the photovoltaic effect of LN:Fe, a weak-light nonlinear effect in crystals rather than the conventional strong-light nonlinear effect in the air.

4. Conclusion

In summary, we demonstrate the visible-light-assisted condensation of water vapor on a LiNbO3:Fe substrate. The dynamic processes of the visible-light-assisted water condensation at different illumination intensities are recorded in both bottom and lateral views. Through analyzing these data, it is found that the total area percentage of the water condensation is roughly proportional to the product of the illumination intensity and duration, and moreover the bending angle of the water vapor trails and the interaction range of this condensation effect highly depend on the illumination intensity. According to these findings, we propose that the visible-light-assisted water condensation is an aggregation process of tiny water droplets driven by the DEP interaction of an inhomogeneous photovoltaic field and also an electrostatic screening course of photovoltaic charges through the charged evaporation of the condensed water. Based on this mechanism, the trajectories of the water vapor stream are simulated at different illumination intensities, and the results are consistent with the experimental observations. In addition, the prolonged condensation of water vapor after a high-intensity illumination and that of oil vapor with a super-low evaporation rate are also studied, and the agreement between the simulation and experimental results further reinforces the above mechanism. The reported technique, employing the inexpensive, safe-for-cell visible laser beam, is quite convenient for the controllable generation of various biological microdroplets, and therefore it is promising for LN-based biological analysis, clinical diagnostics, and drug discovery.

Funding

National Natural Science Foundation of China (11874014); Natural Science Foundation of Tianjin City (F2017202238); Natural Science Foundation of Hebei Province (17JCYBJC16500).

Acknowledgments

We thank Prof. Yongfa Kong for his help on sample preparation. The authors are indebted to the referee for the valuable comments.

References

1. J. Villarroel, H. Burgos, A. Garcia-Cabanes, M. Carrascosa, A. Blazquez-Castro, and F. Agullo-Lopez, “Photovoltaic versus optical tweezers,” Opt. Express 19(24), 24320–24330 (2011). [CrossRef]  

2. C. Arregui, J. B. Ramiro, A. Alcazar, A. Mendez, H. Burgos, A. Garcia-Cabanes, and M. Carrascosa, “Optoelectronic tweezers under arbitrary illumination patterns: theoretical simulations and comparison to experiment,” Opt. Express 22(23), 29099–29110 (2014). [CrossRef]  

3. M. Carrascosa, A. García-Cabañes, M. Jubera, J. B. Ramiro, and F. Agulló-López, “LiNbO3: A photovoltaic substrate for massive parallel manipulation and patterning of nano-objects,” Appl. Phys. Rev. 2(4), 040605 (2015). [CrossRef]  

4. A. García-Cabañes, A. Blázquez-Castro, L. Arizmendi, F. Agulló-López, and M. Carrascosa, “Recent Achievements on Photovoltaic Optoelectronic Tweezers Based on Lithium Niobate,” Crystals 8(2), 65 (2018). [CrossRef]  

5. R. Rega, O. Gennari, L. Mecozzi, S. Grilli, V. Pagliarulo, and P. Ferraro, “Bipolar Patterning of Polymer Membranes by Pyroelectrification,” Adv. Mater. 28(3), 454–459 (2016). [CrossRef]  

6. Y. Kong, F. Bo, W. Wang, D. Zheng, H. Liu, G. Zhang, R. Rupp, and J. Xu, “Recent Progress in Lithium Niobate: Optical Damage, Defect Simulation, and On-Chip Devices,” Adv. Mater.1806452 (2019).

7. P. Minzioni, R. Osellame, C. Sada, S. Zhao, F. G. Omenetto, K. B. Gylfason, T. Haraldsson, Y. B. Zhang, A. Ozcan, and A. Wax, “Roadmap for optofluidics,” J. Opt. 19(9), 093003 (2017). [CrossRef]  

8. A. Blázquez-Castro, A. García-Cabañes, and M. Carrascosa, “Biological applications of ferroelectric materials,” Appl. Phys. Rev. 5(4), 041101 (2018). [CrossRef]  

9. G. Bettella, R. Zamboni, G. Pozza, A. Zaltron, C. Montevecchi, M. Pierno, G. Mistura, C. Sada, L. Gauthier-Manuel, and M. Chauvet, “LiNbO3 integrated system for opto-microfluidic sensing,” Sens. Actuators, B 282, 391–398 (2019). [CrossRef]  

10. T. Yang, P. Paiè, G. Nava, F. Bragheri, R. Martinez Vazquez, P. Minzioni, M. Veglione, M. Di Tano, C. Mondello, R. Osellame, and I. Cristiani, “An integrated optofluidic device for single-cell sorting driven by mechanical properties,” Lab Chip 15(5), 1262–1266 (2015). [CrossRef]  

11. T. Yang, G. Nava, P. Minzioni, M. Veglione, F. Bragheri, F. D. Lelii, R. M. Vazquez, R. Osellame, and I. Cristiani, “Investigation of temperature effect on cell mechanics by optofluidic microchips,” Biomed. Opt. Express 6(8), 2991–2996 (2015). [CrossRef]  

12. P. Ferraro, S. Coppola, S. Grilli, M. Paturzo, and V. Vespini, “Dispensing nano–pico droplets and liquid patterning by pyroelectro dynamic shooting,” Nat. Nanotechnol. 5(6), 429–435 (2010). [CrossRef]  

13. S. Grilli, L. Miccio, O. Gennari, S. Coppola, V. Vespini, L. Battista, P. Orlando, and P. Ferraro, “Active accumulation of very diluted biomolecules by nano-dispensing for easy detection below the femtomolar range,” Nat. Commun. 5(1), 5314 (2014). [CrossRef]  

14. X. Zhang, J. Wang, B. Tang, X. Tan, R. A. Rupp, L. Pan, Y. Kong, Q. Sun, and J. Xu, “Optical trapping and manipulation of metallic micro/nanoparticles via photorefractive crystals,” Opt. Express 17(12), 9981–9988 (2009). [CrossRef]  

15. J. F. Muñoz-Martínez, M. Jubera, J. Matarrubia, A. García-Cabañes, F. Agulló-López, and M. Carrascosa, “Diffractive optical devices produced by light-assisted trapping of nanoparticles,” Opt. Lett. 41(2), 432–435 (2016). [CrossRef]  

16. I. Elvira, J. F. Muñoz-Martínez, Á Barroso, C. Denz, J. B. Ramiro, A. García-Cabañes, F. Agulló-López, and M. Carrascosa, “Massive ordering and alignment of cylindrical micro-objects by photovoltaic optoelectronic tweezers,” Opt. Lett. 43(1), 30–33 (2018). [CrossRef]  

17. M. Jubera, I. Elvira, A. García-Cabañes, J. L. Bella, and M. Carrascosa, “Trapping and patterning of biological objects using photovoltaic tweezers,” Appl. Phys. Lett. 108(2), 023703 (2016). [CrossRef]  

18. L. Miccio, V. Marchesano, M. Mugnano, S. Grilli, and P. Ferraro, “Light induced DEP for immobilizing and orienting Escherichia coli bacteria,” Opt. Laser Eng. 76, 34–39 (2016). [CrossRef]  

19. M. Esseling, A. Zaltron, W. Horn, and C. Denz, “Optofluidic droplet router,” Laser Photonics Rev. 9(1), 98–104 (2015). [CrossRef]  

20. M. Gazzetto, G. Nava, A. Zaltron, I. Cristiani, C. Sada, and P. Minzioni, “Numerical and Experimental Study of ptoelectronic Trapping on Iron-Doped Lithium iobate Substrate,” Crystals 6(10), 123 (2016). [CrossRef]  

21. L. Chen, S. Li, B. Fan, W. Yan, D. Wang, L. Shi, H. Chen, D. Ban, and S. Sun, “Dielectrophoretic behaviours of microdroplet sandwiched between LN substrates,” Sci. Rep. 6(1), 29166 (2016). [CrossRef]  

22. L. Chen, B. Fan, W. Yan, S. Li, L. Shi, and H. Chen, “Light-assisted splitting of dielectric microdroplets in a LN-based sandwich structure,” Opt. Lett. 41(19), 4558–4561 (2016). [CrossRef]  

23. B. Fan, F. Li, L. Chen, L. Shi, W. Yan, Y. Zhang, S. Li, X. Wang, X. Wang, and H. Chen, “Photovoltaic Manipulation of Water Microdroplets on a Hydrophobic LiNbO3,” Phys. Rev. Appl. 7(6), 064010 (2017). [CrossRef]  

24. A. C. Muir, S. Mailis, and R. W. Eason, “Ultraviolet laser-induced submicron spatially resolved superhydrophilicity on single crystal lithium niobate surfaces,” J. Appl. Phys. 101(10), 104916 (2007). [CrossRef]  

25. W. Yan, D. Zhao, L. Zhang, R. Jia, N. Gao, D. Zhang, W. Luo, Y. Li, and D. Liu, “Optically induced reversible wettability transition on single crystal lithium niobate surfaces,” Appl. Phys. Lett. 111(9), 091603 (2017). [CrossRef]  

26. A. M. Glass, D. von der Linde, and T. J. Negran, “High-voltage bulk photovoltaic effect and the photorefractive process in LiNbO3,” Appl. Phys. Lett. 25(4), 233–235 (1974). [CrossRef]  

27. J. F. Muñoz-Martínez, J. B. Ramiro, A. Alcázar, A. García-Cabañes, and M. Carrascosa, “Electrophoretic versus dielectrophoretic nanoparticle patterning using optoelectronic tweezers,” Phys. Rev. Appl. 7(6), 064027 (2017). [CrossRef]  

28. M. Esseling, A. Zaltron, C. Sada, and C. Denz, “Charge sensor and particle trap based on z-cut lithium niobate,” Appl. Phys. Lett. 103(6), 061115 (2013). [CrossRef]  

29. A. Puerto, J. F. Muñoz-Martín, A. Méndez, L. Arizmendi, A. García-Cabañes, F. Agulló-López, and M. Carrascosa, “Synergy between pyroelectric and photovoltaic effects for optoelectronic nanoparticle manipulation,” Opt. Express 27(2), 804–815 (2019). [CrossRef]  

30. A. V. Shavlov, V. A. Dzhumandzhi, and A. A. Yakovenko, “Charge of water droplets during evaporation and condensation,” J. Aerosol Sci. 123, 17–26 (2018). [CrossRef]  

31. J. F. Muñoz-Martínez, I. Elvira, M. Jubera, A. García-Cabañes, J. B. Ramiro, C. Arregui, and M. Carrascosa, “Efficient photo-induced dielectrophoretic particle trapping on Fe:LiNbO3 for arbitrary two dimensional patterning,” Opt. Mater. Express 5(5), 1137–1146 (2015). [CrossRef]  

32. X. Zhang, K. Gao, Z. Gao, Z. Zan, L. Shi, F. Li, C. Liang, M. Ren, E. R. Mugisha, H. Chen, and W. Yan, “Photovoltaic splitting of water microdroplets on a y-cut LiNbO3:Fe crystal coated with oil-infused hydrophobic insulating layers” unpublished result.

33. P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queisser, and R. Salame, “Laser-induced water condensation in air,” Nat. Photonics 4(7), 451–456 (2010). [CrossRef]  

34. S. Henin, Y. Petit, P. Rohwetter, K. Stelmaszczyk, Z. Q. Hao, W. M. Nakaema, A. Vogel, T. Pohl, F. Schneider, and J. Kasparian, “Field measurements suggest the mechanism of laser-assisted water condensation,” Nat. Commun. 2(1), 456 (2011). [CrossRef]  

35. H. Y. Sun, Y. H. Liu, J. J. Ju, Y. Tian, Y. F. Bai, Y. X. Liu, S. Z. Du, C. Wang, T. J. Wang, and J. S. Liu, “Picosecond laser-induced water condensation in a cloud chamber,” Opt. Express 24(18), 20494–20506 (2016). [CrossRef]  

36. Y. H. Liu, H. Y. Sun, J. S. Liu, H. Liang, J. J. Ju, T. J. Wang, Y. Tian, C. Wang, Y. Liu, and S. L. Chin, “Laser-filamentation-induced water condensation and snow formation in a cloud chamber filled with different ambient gases,” Opt. Express 24(7), 7364–7373 (2016). [CrossRef]  

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Figures (15)

Fig. 1.
Fig. 1. (a) Setup for recording the dynamic process of the visible-light-assisted condensation of water vapor; (b) Scheme of the water vapor stream flowing along the LN:Fe crystal surface and the following visible-light-assisted water condensation; (c) Typical water droplet contact angle on a charged LN:Fe surface; (d) UV-Vis absorption spectra of LN:Fe sample.
Fig. 2.
Fig. 2. (a) Snapshot of the water vapor created by an ultrasonic atomizer; (b) Picture of two tiny droplets landing on a super-hydrophobic substrate; (c) The trailing smear of the tiny droplets in the water vapor stream. The trailing smear is due to the fast movement of the tiny droplets when the camera shutter is opening. The trails of some droplets are not clear enough because they are not right located in the focal plane of the camera. The arrows in (b) denote the location of the landing droplets. The L in (c) represents the trailing smear length.
Fig. 3.
Fig. 3. The typical dynamic process of the visible-light-assisted water condensation on the –c surface of LN:Fe crystal. The “on” and “off” states of the 405 nm-illumination are denoted by the purple and gray dots, and the laser spot is marked by the purple halo in the center of the view. The flowing speed of the water vapor stream is 50 mm/s.
Fig. 4.
Fig. 4. The dynamic process of the water condensation triggered by a scanning laser. The yellow triangle represents the unmovable reference on the substrate surface. The “on” and “off” states of the 405 nm-illumination are denoted by the purple and gray dots, and the laser spot is marked by the purple halo in the center of the view. The laser scanning direction is denoted by the green arrow and the average scanning speed is about 70 µm/s.
Fig. 5.
Fig. 5. The dynamic process of the visible-light-assisted water condensation at different illumination intensities. The “on” and “off” states of the 405 nm-illumination are denoted by the purple and gray dots. The flowing speed of the water vapor stream is 14 mm/s.
Fig. 6.
Fig. 6. The total area percentage P as a function of the product of the illumination intensity (I) and duration (δt). The insets are the binarized outputs of some images of Fig. 5, and the calculated P of these figures are plotted as solid squares with corresponding colors. All data are fitted by a red line, and the fitting yields P = 1.50×10−6(I×δt) + 0.05.
Fig. 7.
Fig. 7. The typical dynamic process of the visible-light-assisted water condensation in the lateral view. The “on” and “off” states of the 405 nm-illumination are denoted by the purple and gray dots, and the laser beam is highlighted by the bluish violet color. In addition, the vapor stream flow is marked by the dash curve. The sequential images are obtained by the conventional camera with a normal speed and the blurry vapor flow is due to the fast movement of many tiny water droplets.
Fig. 8.
Fig. 8. The trails of tiny water droplets in the vapor stream at different illumination intensities. The “on” and “off” states of the 405 nm-illumination are denoted by the purple and gray dots, and the laser beam is highlighted by the bluish violet color. The flowing speed of the water vapor stream is 14 mm/s. The images are obtained by using the snap shot mode of a high-speed camera.
Fig. 9.
Fig. 9. Photovoltaic charge sign and typical visible-light-assisted water condensation on the –c and + c surfaces of LN:Fe crystal. In spite of the different charge signs on the –c and + c surfaces, no obvious difference of visible-light-assisted water condensation is found between them.
Fig. 10.
Fig. 10. The scheme for the electrostatic screening of the photovoltaic charges through the evaporation of the condensed water.
Fig. 11.
Fig. 11. The water evaporation process after the visible-light-induced condensation. A little part of condensed water located right at the illumination spot (denoted by the yellow circle) is very hard to evaporate. The “on” and “off” states of the 405 nm-illumination are denoted by the purple and gray dots.
Fig. 12.
Fig. 12. The simulated trajectory of the water vapor stream during the visible-light-assisted condensation at different illumination intensities. The tiny droplets in the stream are plotted as solid round particles with their trails and color representing the instantaneous velocities. The instantaneous electrostatic field generated by the photovoltaic charges is also plotted in a color scale. The initial speed of the water vapor stream is set as 14 mm/s.
Fig. 13.
Fig. 13. Temporal evolution of the number of tiny water droplets aggregated on the substrate surface in the simulation of the visible-light-induced water concentration at low (a) and high (b) illumination intensities. (c) Number of the tiny oil droplets during the visible-light-induced concentration of ultrasonically-atomized oil (transformer oil) vapor. The “on” and “off” moment of the illumination are denoted by the purple and green dots.
Fig. 14.
Fig. 14. (a) The prolonged water condensation after the shutdown of the high-intensity illumination (2.27×107 W/m2). (b) The heavily prolonged oil condensation after the shutdown of the low-intensity illumination (3.19×106 W/m2). The “on” and “off” states of the 405 nm-illumination are denoted by the purple and gray dots.
Fig. 15.
Fig. 15. The water condensation induced by the 473 nm-illumination. The “on” and “off” states of the 473 nm-illumination are denoted by the blue and gray dots.

Equations (2)

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σ = δ tG α I ( x,y ) = δ tG α I 0 Exp [ 2 ( x 2 + y 2 ) / ω 2 ]
F D E P = α E 2 and α = 2 π r 3 ε 0 ε m ε p ε m ε p 2 ε m
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