Droplet microfluidics is becoming an enabling technology for synthesizing microscale particles and an effective real-time method is essential to monitor the variations in a dynamic droplet generation process. Here, a novel real-time cosine similarity algorithm (RT-CSA) method was developed to investigate the droplet generation process by measuring the droplet generation frequency continuously. The RT-CSA method uses a first-in-first-out (FIFO) similarity vector buffer to store calculated cosine similarities, so that these cosine similarities are reused to update the calculation results once a new frame is captured and stored. For the first time, the RT-CSA method achieved real-time monitoring of dynamic droplet generation processes by updating calculation results over 2,000 times per second, and two pre-microgel droplet generation processes with or without artificial disturbances were monitored closely and continuously. With the RT-CSA method, the disturbances in dynamic droplet generation processes were precisely determined, and following changes were monitored and recorded in real time. This highly effective RT-CSA method could be a powerful tool for further promoting research of droplet microfluidics.

Droplet microfluidics has become a powerful technique and has been applied in a wide range of applications, especially in developing new materials (Günther and Jensen, 2006; Liu and Jiang, 2017; and Wang et al., 2011), such as nanoparticles (Baruah et al., 2018; Li and Lin, 2018), microspheres (Nisisako and Torii, 2008; Xu et al., 2005) and microgels (Headen et al., 2018; Priest et al., 2006; and Rossow et al., 2012). Uniform droplet generation processes will lead to highly uniform microscale particles (Conchouso et al., 2016), since improved homogeneity and reproducibility inside the droplets result in a high uniformity of performing chemical reactions (Phillips et al., 2014). The particle size distribution is often used to characterize the uniformity of a droplet generation process after completion of the droplet generation process (Haeberle et al., 2007; Kim et al., 2015). However, size distribution is an end-point parameter that cannot reveal the dynamic changes during the process in time, for example, disturbances in flow rates or inlet pressures (Wong and Ren, 2016). Therefore, it is essential to closely monitor the changes in dynamic droplet generation processes in a convenient, real-time manner.

A series of methods has been proposed to monitor dynamic droplet generation processes. One method is to use a light scattering technique to monitor the droplet generation process by investigating the relation between incident light and by-passing droplets. Nguyen et al. installed two optical fibers in a microfluidic chip to detect the changes in forward scattering light (Nguyen et al., 2006). Another method is to embed microelectrodes or radio frequency devices in microfluidic devices to monitor the droplet generation process by investigating dielectric property variations of the by-passing droplets. Niu et al. and Elbuken et al. fabricated microelectrodes in a microfluidic chip to measure impedance changes as droplets pass through the channel (Elbuken et al., 2011; Niu et al., 2007). Conchouso et al. used RF devices to monitor dynamic droplet generation processes by measuring subtle changes in resonant frequencies when the processes were disturbed (Conchouso et al., 2016). Although these methods were capable of monitoring dynamic droplet generation processes in real time, the complexity of chip fabrication and system configuration was increased due to the requirement of specialized instruments and microstructures. A third method is microscopic imaging for monitoring the droplet generation process. These methods use a high-speed camera to acquire droplet generation video clips, which is widely used in droplet microfluidic experimental systems (Mazutis et al., 2013). Basu proposed a method based on droplet morphometry and velocimetry (DMV) to monitor droplet generation processes by recognizing droplet interfaces in every frame of the video (Basu, 2013). This method may require a sizeable computational resource, and thus the monitoring may not keep pace with the droplet generation processes.

To achieve quick and convenient monitoring of dynamic droplet generation processes, a cosine similarity algorithm (CSA) was proposed to monitor droplet generation processes at intervals (Zhu et al., 2018). Using the high periodicity of droplet generation processes, the CSA method was able to monitor droplet generation frequencies closely and accurately in both single channel and multiple channels. For dynamic droplet generation processes, the CSA method was able to keep pace with the droplet generation process by calculating a 2.50 s process in 1.67 s. Although the CSA method achieved convenient, accurate and online monitoring of dynamic droplet generation processes, this method updated calculation results at an interval of several seconds. It is still challenging to continuously monitor dynamic droplet generation processes with an image-based method in real time.

In this paper, we propose a real-time cosine similarity algorithm (RT-CSA) method as a novel real-time image-based monitoring method that can keep pace with the recording of droplet generation processes in real time. As an improvement of the previous CSA method, the real-time version of the CSA method is established by adding a first-in-first-out (FIFO) similarity vector buffer to the previous CSA method. The cosine similarities between newly acquired frames and the reference frame are updated into the buffer regularly. Droplet generation frequencies and their CVs are recalculated after the completion of each buffer updating. Two dynamic pre-microgel droplet generation processes were monitored in real time with the RT-CSA method. Artificial disturbances were precisely determined, and the changes in droplet generation uniformity were closely monitored at 2,000 updates per second, in synchronization with video frame acquisition. This highly effective real-time method could be a powerful tool for further promoting research and development of droplet microfluidics.

PDMS (polydimethylsiloxane) base and its curing reagent (Sylgard 184) were purchased from Dow Corning (Midland, MI). Aquapel was purchased from PPG Industries (Pittsburgh, PA). Novec 7500 was purchased from 3M Inc. (St. Paul, MN). Fluoro-Surfactant was synthesized as previously described (Fischlechner et al., 2014; Holtze et al., 2008). Brilliant blue was purchased from Shanghai Dyestuff Research Institute Co. Ltd. (Shanghai, China). Acrylamide, bis-acrylamide, APS (ammonium persulfate) and TEMED (tetramethylethylenediamine) were purchased from Aladdin Reagent Inc. (Shanghai, China).

The droplet generation chip was designed as a flow-focusing droplet generator with a 70-μm-wide and 70-μm-high nozzle (Zhu et al., 2018). The droplet generation chip was fabricated with soft lithography as described earlier (Xia and Whitesides, 1998; Zhu et al., 2018). Briefly, PDMS base and its curing agent were thoroughly mixed and degassed in a vacuum oven (BZF-30, Shanghai Boxun Industry & Commerce Co. Ltd., China). Then, the mixture was cast onto an SU-8 mold fabricated with conventional photolithography (CapitalBio Corporation, China) and cured at 80 °C for 55 min in an oven (DFZ, Beijing Zhongxingweiye Instrument Co. Ltd., China). Next, the PDMS slab was peeled off the SU-8 mold, punched for inlets and outlets, and bonded to a glass substrate using oxygen plasma treatment (Femto, Diener Electronic, Germany).

A conventional droplet generating and monitoring platform was established as described earlier (Mazutis et al., 2013; Zhu et al., 2018). The droplet generation chip was placed on the stage of an inverted microscope (XDS-1B, Chongqing Optical Instrument Corporation, China). Two syringe pumps (LSP02-1B, Longer Precision Pump Co. Ltd., China) were used to inject the oil phase and the water phase into the droplet generation chip through the inlets. Video clips of the droplet generation processes were captured with a high-speed camera (MotionBlitz EoSens 1, Mikrotron, Germany).

Crosslinker premix was used as the oil phase, 0.5% (w/w) Fluoro-Surfactant and 0.4% (v/v) TEMED dissolved in Novec 7500. Meanwhile, acrylamide premix was used as the water phase, consisting of 6.2% (w/v) acrylamide, 0.18% (w/v) bis-acrylamide, 0.3% (w/v) APS and 7% (w/v) brilliant blue dissolved in double-distilled (DI) water. The droplets were generated with the droplet generation chip by injecting the oil phase at 2.0 mL/h and the water phase at 1.0 mL/h into the designated inlets. For the droplet generation process with artificial disturbance, oil injection was interrupted from 2.00 s to 6.00 s after the beginning of video clip acquisition. The spatial resolution of the video clip was set at 512×62 pixels, and the frame rate of the high-speed camera was set to 2,000 fps, more than ten times of droplet generation frequencies. 40,000 frames were selected and saved in H264 coding format. The video clips acquired with the high-speed camera were converted to AVI files with the VideoWriter module in Matlab (Mathworks Inc., Natick, MA).

The mean frequencies and their CVs of each droplet generation process were automatically calculated and updated with a customized Matlab program based on the RT-CSA method. The computational time was obtained from the tic/toc functions with 10 repetitive computations and analyzed with Matlab Profiler.

The real-time cosine similarity algorithm (RT-CSA) method is an upgraded version of the previous cosine similarity algorithm (CSA) method (Zhu et al., 2018) by adding a FIFO similarity vector buffer. As shown in Figure 1, the RT-CSA method consists of five steps. In the first step, droplets are generated with a flow-focusing microfluidic chip, and the dynamic droplet generation process is captured with a high-speed camera. The first frame is designated as the reference frame (Figure 1a). In the second step, the RT-CSA method proceeds to a build-up phase. During the build-up phase, the cosine similarities are calculated between each newly captured frame and the reference frame and sequentially added to the end of a similarity vector buffer with a limited buffer size (Figure 1b, 3,000 cosine similarities in this case). In the third step, once the similarity vector buffer is full, the RT-CSA method proceeds to a real-time phase. During the real-time phase, the cosine similarities are calculated as usual between each newly captured frame and the reference frame. However, once a newly calculated cosine similarity is added to the end of the buffer, the first cosine similarity in the buffer is removed in a FIFO manner, updating the similarity vector in the buffer (Figure 1c). In the fourth step, once the similarity vector is updated, its cyclic auto-spectrum is recalculated, revealing the updated droplet generation frequency and its coefficient of variation (CV) as previously described (Figure 1d) (Zhu et al., 2018). Finally, the calculation results are updated into the monitor results along the timeline in the fifth step (Figure 1e).

FIG. 1.

Schematic diagram of the real-time cosine similarity algorithm (RT-CSA) method for continuous monitoring of dynamic droplet generation processes. (a) Droplets are generated with a microfluidic chip, and the dynamic droplet generation process is captured with a high-speed camera. (b) The build-up phase of the RT-CSA method. The first frame is designated as the reference frame. Once a new frame is captured with the high-speed camera, the cosine similarity between the captured frame and the reference frame is calculated and added to the end of a similarity vector buffer with limited buffer size. (c) When the similarity vector buffer is full, the RT-CSA method proceeds to the real-time phase. During the real-time phase, the similarity vector buffer is updated in a first-in-first-out (FIFO) manner once a new frame is captured. When a newly-calculated cosine similarity is added to the end of the buffer, the first cosine similarity in the buffer is deleted, and the similarity vector in the buffer is updated. (d) The auto-spectrum of the updated similarity vector is calculated to reveal droplet generation frequency and its coefficient of variation (CV) as previously described (Zhu et al., 2018). (e) The calculation results are updated into the real-time monitor results along the timeline.

FIG. 1.

Schematic diagram of the real-time cosine similarity algorithm (RT-CSA) method for continuous monitoring of dynamic droplet generation processes. (a) Droplets are generated with a microfluidic chip, and the dynamic droplet generation process is captured with a high-speed camera. (b) The build-up phase of the RT-CSA method. The first frame is designated as the reference frame. Once a new frame is captured with the high-speed camera, the cosine similarity between the captured frame and the reference frame is calculated and added to the end of a similarity vector buffer with limited buffer size. (c) When the similarity vector buffer is full, the RT-CSA method proceeds to the real-time phase. During the real-time phase, the similarity vector buffer is updated in a first-in-first-out (FIFO) manner once a new frame is captured. When a newly-calculated cosine similarity is added to the end of the buffer, the first cosine similarity in the buffer is deleted, and the similarity vector in the buffer is updated. (d) The auto-spectrum of the updated similarity vector is calculated to reveal droplet generation frequency and its coefficient of variation (CV) as previously described (Zhu et al., 2018). (e) The calculation results are updated into the real-time monitor results along the timeline.

Close modal

To achieve the desired real-time monitoring performance, a similarity vector buffer with appropriate buffer size is required. As shown in Figure 2a, the calculated droplet generation frequencies and their CVs were plotted against different capacities of the similarity vector buffer ranging from 5 to 5,000. When low buffer capacities were used, the calculated droplet generation frequency and its CV fluctuated drastically. For example, when a buffer size below 20 was used, the calculated droplet generation frequency fluctuated between 138.6 Hz and 513.1 Hz with a CV up to 40.7%. When a buffer size between 21 and 50 was used, the calculated droplet generation frequency fluctuated between 144.2 Hz and 202.4 Hz with a CV up to 29.8%. When a buffer size between 51 and 100 was used, the calculated droplet generation frequency fluctuated between 152.9 Hz and 168.9 Hz with a CV up to 18.0%. Such high uncertainty in the calculation results was induced by the limited spectral resolution, which was determined by the buffer size (the number of data points used in fast Fourier transform). On the other hand, an extremely high buffer size only resulted in a longer delay in computation without significant improvement in accuracy. As shown in Figure 2b, with the increase in buffer size, the calculated droplet generation frequency and its CV converged quickly to about 155.2 Hz and 0.5% respectively and remained stable when the buffer size was over 3,000. In this way, a suitable buffer size could be set at 3,000.

FIG. 2.

Determining the size of the similarity vector buffer. (a) The calculated droplet generation frequencies and (b) their CVs were plotted against different capacities of the similarity vector buffer ranging from 5 to 5,000.

FIG. 2.

Determining the size of the similarity vector buffer. (a) The calculated droplet generation frequencies and (b) their CVs were plotted against different capacities of the similarity vector buffer ranging from 5 to 5,000.

Close modal

The RT-CSA method is able to monitor dynamic droplet generation processes in real time. With an acquisition frame rate at 2,000 fps and a buffer size of 3,000, the computational time was 0.27±0.01 ms every update. Since the duration between the capture of two consecutive frames was 0.50 ms, the RT-CSA method was able to achieve real-time monitoring.

A stable pre-microgel droplet generation process was monitored in real time, as shown in Figure 3. In this process, the flow rates of the oil phase and water phase were set at 2.0 mL/h and 1.0 mL/h respectively. During the process, the RT-CSA method updated the calculation results once a new frame was captured. The calculation results of RT-CSA converged during the build-up phase (1.50 s) and remained stable till the end. During the real-time phase, the calculated droplet generation frequency slowly changed between 147.4 Hz and 156.6 Hz with CV less than 1.0%. The monitor results showed that this droplet generation process was stable.

FIG. 3.

Real-time monitoring of a stable droplet generation process. The changes of (a) droplet generation frequency and (b) its CV of a stable droplet generation process were continuously monitored with the RT-CSA method.

FIG. 3.

Real-time monitoring of a stable droplet generation process. The changes of (a) droplet generation frequency and (b) its CV of a stable droplet generation process were continuously monitored with the RT-CSA method.

Close modal

A pre-microgel droplet generation process with artificial disturbance was monitored in real time, as shown in Figure 4. In this process, the flow rates of the oil phase and water phase remained unchanged, except for the artificial disturbance lasting from 2.00 s to 6.00 s, during which the injection of oil phase was intentionally interrupted. During the build-up phase, the calculation results converged as previously observed. During the real-time phase, the changes in droplet generation frequencies and their CVs were closely followed with RT-CSA at 2,000 updates per second. In the period of artificial disturbance, the droplet generation frequency decreased from 150.7 Hz to 79.7 Hz due to the stop of oil injection (Yobas et al., 2006), accompanied by an increase in frequency CV from 0.5% to 12.2% as a sign of disturbance (Zhu et al., 2018). After the artificial disturbance was removed, the droplet generation frequency increased from 79.7 Hz to 147.6 Hz at 13.0 s, with another increase in frequency CV to 6.7% before dropping to 0.9% at 13.0 s. The RT-CSA method showed that it took about 7.0 s after disturbance removal before the frequency CV dropped below 1.0% and the droplet generation process was finally restored.

FIG. 4.

Real-time monitoring of a droplet generation process with artificial disturbance. The changes of (a) droplet generation frequency and (b) its CV of a droplet generation process with artificial disturbance were continuously monitored with the RT-CSA method. The artificial disturbance was introduced by temporarily stopping the injection of oil phase from 2.00 s to 6.00 s.

FIG. 4.

Real-time monitoring of a droplet generation process with artificial disturbance. The changes of (a) droplet generation frequency and (b) its CV of a droplet generation process with artificial disturbance were continuously monitored with the RT-CSA method. The artificial disturbance was introduced by temporarily stopping the injection of oil phase from 2.00 s to 6.00 s.

Close modal

Overall, the RT-CSA method managed to monitor both the stable droplet generation process and the one with artificial disturbance. The update of monitor results kept pace with the capture of each video frame. The disturbance in droplet generation processes was precisely located, and changes during and after the disturbance were continuously monitored and investigated.

To be noted, the computational time (0.27±0.01 ms) took about 55% of the time lapse between two consecutive frames (0.50 ms). The rest 45% of the time lapse was regarded as potential computational time, which could be used to improve the performance of the RT-CSA method in different aspects, including accuracy, scope of view, and update rate.

First of all, the computational time of the RT-CSA method was thoroughly analyzed. The computational time can be divided into two parts: the first part is the calculation of cosine similarity between the newly captured frame and the reference frame, defined as “time for cosine similarity”; the second part is the calculation of monitor results, including fast Fourier transform (FFT), cyclic auto-spectrum, droplet generation frequency and its CV, defined as “time for FFT”. As described earlier, “time for cosine similarity” is approximately proportional to the spatial resolution of the frames, while “time for FFT” is correlated with the buffer size of the similarity vector buffer (the number of data points for fast Fourier transform) (Zhu et al., 2018). To precisely determine the computational time for these two parts, a combinatorial computational time (CCT) for a series of data was measured and determined for “time for cosine similarity” and “time for FFT”. Specifically, combinatorial computational time (CCT) of various “time for cosine similarity” and one “time for FFT” was plotted against the number of cosine similarities in the solid green line. The numbers of cosine similarities were 1, 2, 5, 10, 20, 50, 100, 200, 500, 1,000 and 2,000 respectively, and one set of monitor result was calculated with a buffer size of 3,000. As shown in Figure 5, CCT scaled linearly (r2 > 0.9998) with the number of cosine similarities, since “time for cosine similarity” corresponds to a cosine similarity calculation between one frame and the reference frame. From linear fitting of the curve, “time for cosine similarity” can be derived as 0.10 ms per cosine similarity (slope). Meantime, “time for FFT” can be derived as 0.17 ms per set of monitor results (interception).

FIG. 5.

Computational time of various cosine similarities and one set of monitor results. Combinatorial computational time (CCT) of various cosine similarities and one set of calculation results was plotted against the number of cosine similarities in the solid green line. The numbers of cosine similarities were 1, 2, 5, 10, 20, 50, 100, 200, 500, 1,000 and 2,000 respectively, and the set of calculation results was calculated with a buffer size of 3,000. With linear fitting (r2 > 0.9998), “time for cosine similarity” was determined by the slope as 0.10 ms, while “time for FFT” was determined by the interception as 0.17 ms.

FIG. 5.

Computational time of various cosine similarities and one set of monitor results. Combinatorial computational time (CCT) of various cosine similarities and one set of calculation results was plotted against the number of cosine similarities in the solid green line. The numbers of cosine similarities were 1, 2, 5, 10, 20, 50, 100, 200, 500, 1,000 and 2,000 respectively, and the set of calculation results was calculated with a buffer size of 3,000. With linear fitting (r2 > 0.9998), “time for cosine similarity” was determined by the slope as 0.10 ms, while “time for FFT” was determined by the interception as 0.17 ms.

Close modal

Once “time for cosine similarity” and “time for FFT” are determined, the performance of the RT-CSA method can be further improved by tuning three different parameters: buffer size, spatial resolution, and acquisition frame rate.

Increasing buffer size improved the accuracy of monitor results, since the increase in data points used in FFT improved the spectral resolution. As shown in Figure 6a, the increase in buffer size corresponded to an increase in the interception of the CCT (“time for FFT”) from the solid green line to the green dash-dot line. The interception of the CCT could be increased to 0.40 ms. Since the calculation of cyclic auto-spectrum took up over 99% of the second-part computational time (as noted by Matlab Profiler) and scaled with Nlog2N (N was the buffer size) (Borgioli, 1968), the buffer size could be enlarged by 104.0% to 6,121.

FIG. 6.

Three different ways of using the potential computational time to further improve the performance of the RT-CSA method. The potential computational time could be used by tuning three different parameters. (a) Increasing buffer size increased the interception of the CCT from the solid green line to the green dash-dot line. This interception increase resulted in an increase in spectral resolution and better accuracy of monitor results. The CCT was used up when the green dash-dot line crossed the black dash line at number of cosine similarities = 1. (b) Increasing spectral resolution increased the slope of the CCT from the solid green line to the green dash-dot line. This slope increase resulted in a larger monitor scope, facilitating the monitoring of multiple droplet generation processes. The CCT was used up when the green dash-dot line crossed the black dash line at number of cosine similarities = 1. (c) Increasing acquisition frame rate decreased the time lapse between frames from the horizontal black dash line to the horizontal black dash-dot line. This decrease resulted in a higher update rate of monitoring results, increasing the promptness of RT-CSA. The CCT was used up when the black dash-dot line crossed the solid green line at number of cosine similarities = 1.

FIG. 6.

Three different ways of using the potential computational time to further improve the performance of the RT-CSA method. The potential computational time could be used by tuning three different parameters. (a) Increasing buffer size increased the interception of the CCT from the solid green line to the green dash-dot line. This interception increase resulted in an increase in spectral resolution and better accuracy of monitor results. The CCT was used up when the green dash-dot line crossed the black dash line at number of cosine similarities = 1. (b) Increasing spectral resolution increased the slope of the CCT from the solid green line to the green dash-dot line. This slope increase resulted in a larger monitor scope, facilitating the monitoring of multiple droplet generation processes. The CCT was used up when the green dash-dot line crossed the black dash line at number of cosine similarities = 1. (c) Increasing acquisition frame rate decreased the time lapse between frames from the horizontal black dash line to the horizontal black dash-dot line. This decrease resulted in a higher update rate of monitoring results, increasing the promptness of RT-CSA. The CCT was used up when the black dash-dot line crossed the solid green line at number of cosine similarities = 1.

Close modal

With the same high-speed camera, increasing spatial resolution increased the monitor throughput since an enlarged scope of view facilitated more droplet generation processes to be monitored at the same time (Zhu et al., 2018). As shown in Figure 6b, the increase in spatial resolution corresponded to an increase in the slope of the CCT (“time for cosine similarity”) from the solid green line to the green dash-dot line. The slope of the CCT could be increased to 0.33 ms. Since the computational time of cosine similarities scaled proportionally with the spatial resolution of the frames (Zhu et al., 2018), the spatial resolution could be enhanced by 230.0%, which could facilitate the monitoring of three such droplet generation processes at the same time.

Increasing acquisition frame rate increased the update rate of the RT-CSA method since the RT-CSA method updated the calculation results once a new frame was captured. As shown in Figure 6c, the increase in acquisition frame rate corresponded to a decrease in the time lapse between frames from the horizontal black dash line to the horizontal black dash-dot line. The time lapse between frames could be decreased to 0.29 ms. Therefore, the acquisition frame rate could be increased by 72.4% to 3,448 fps, increasing the update rate by the same proportion.

The potential computational time was fully exploited when the adapted green line crossed the adapted black line at number of cosine similarities of one. By combining the adjustment of these three parameters, the potential computational time could be distributed on demand in a combination of three different aspects, including increases in accuracy, scope of view, and update rate.

In conclusion, a novel real-time cosine similarity algorithm (RT-CSA) was proposed for the first time to continuously monitor dynamic droplet generation processes. As an improvement of the previous CSA method, a similarity vector buffer was added to store a limited amount of cosine similarities. Once the buffer was full, the RT-CSA method was able to update calculation results in a FIFO way once a new frame was captured by the high-speed camera at 2,000 fps. Both a stable droplet generation process and one with artificial disturbance could be monitored with the RT-CSA method in real time. The disturbance in droplet generation processes was precisely located, and changes during and after the disturbance were continuously monitored and studied. From algorithm perspective, the size of the similarity vector buffer is a crucial parameter that will affect both the accuracy and the efficiency of the algorithm in a trade-off manner. On one hand, a larger buffer can store more cosine similarities, which results in a more accurate calculation of droplet generation frequencies. On the other hand, the increase in the number of data points, induced by a larger buffer, will result in an increased computational time for FFT and a prolonged build-up phase. With the optimization of the buffer size, the computational time of RT-CSA was further studied for potential performance improvement. When the computational time per update was shorter than the duration between two consecutive frames, the potential computational time could be distributed on demand in three different ways to further increase RT-CSA performance in accuracy, scope of view, and update rate. These results demonstrate that RT-CSA is an effective method to monitor dynamic droplet generation processes in real time. The RT-CSA method could be a powerful tool to further promote research and development of the droplet microfluidics.

This work was financially supported by the National Natural Science Foundation of China (Grant no. 81572083 and 81772288) and the Fund from TargetingOne Corporation (Grant no. 20162000009).

The authors declare no conflicts of interest.

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