Microfluidics enables the production and manipulation of multi-phasic mixtures such as gas bubbles, liquid droplets and multiple emulsions with unparalleled precision and control.
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d Leveraging advanced techniques in micro/nano-fabrication, precise microchannels can be manufactured to control droplets and bubbles for a wide range of advanced applications [1]. For example, chemical reactions can be induced in single droplets, providing a unique platform to conduct high-throughput analyses and synthesis with minimal reagents use and reduced waste [2][3][4]. Furthermore, droplet microfluidics facilitates the encapsulation of delicate biological materials such as cells and proteins under mild conditions that preserve their functionality and viability, which is particularly well-suited for the development of low-cost and highly efficient biomedical diagnostics and therapeutics [5][6][7]. The precision and scalability of droplet microfluidics enables fabrication of functional particles such as microbubbles, microcapsules and nanoparticles with precisely designed morphology and functionality, enhancing disease diagnostics as well as controlled release and targeted delivery of various pharmaceutical actives [8][9][10].
Achieving consistent uniformity in the production of droplets and bubbles throughout the operation of microfluidic devices is crucial for harnessing the full benefits of this technology.
The maintenance of uniformity is, however, challenged by several factors, which necessitates continuous user intervention to adjust flow rates and pressures, ensuring that the droplet and bubble production maintains the desired dimensions and properties. Even seemingly negligible changes in operating conditions can cause large fluctuations in performance of device output because of the sensitivity of flow behaviors of fluids at the microscopic scale. Over time, the performance of microfluidic devices may be further compromised by issues such as surface fouling, changes in wetting properties, channel clogging and the solvent-induced swelling of the microfluidic devices [11][12][13]. These factors introduce additional layers of complexity in This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d achieving and maintaining the uniformity of droplet and bubble generation, posing significant challenges to the scalability and reliability of microfluidic applications.
Developing autonomous microfluidic systems capable of self-adapting to changing conditions would enable the precise formation of a wide array of droplets and bubbles with complex composition and morphology without direct operator intervention [14]. The realization of such a capability will enhance the efficiency and effectiveness of droplet and bubble microfluidics and simultaneously lead to new applications that leverage the full potential of this versatile technology.
A few recent studies have demonstrated the ability to control droplet microfluidics, using technologies such as neural networks and reinforcement learning to gather insight on flow regimes in microfluidics over various flow conditions [15,16]. Other techniques involve the use of impedance electronics embedded into the microfluidic device as a sensor for measuring microbubble diameter as a function of the voltage measured or measuring the interference pattern created by focusing a laser on droplets in the outlet channel using piezoelectric transducer [17,18]. Vision Development Module within LabVIEW (National Instruments™) has been used for droplet detection and control using a virtual instrument [19]. In addition, feedback sensors have been developed for precise control of flowrates and pressures in microfluidic devices offchip [20,21]. Despite these advances, many of these approaches use highly sophisticated sensing techniques that involve specialized equipment not traditionally used in microfluidics, do not have the ability to easily measure process variables on-chip, and do not have the ability to control the This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d system when it is disturbed to reach different flow regimes, such as one in which bubbles or droplets are not produced.
In this study, we introduce an autonomous microfluidics system that relies simply on microscopic imaging and is trained with a convolutional neural network (CNN) to return the process to the desired microbubble production flow regime. Our system is able to control the size of microfluidic bubble production using only commercially available pressure controllers, a microscope, and a high-speed camera, all of which are commonly employed in microfluidic setups. We generate gas bubbles in a flow-focusing device by applying pressure to the dispersed gas phase using a high-pressure nitrogen canister. Additionally, we use pressure-driven flow, also from a high-pressure nitrogen canister, to pressurize a liquid reservoir, thereby pushing the liquid into the microfluidic chip. Pressure driven flow of the aqueous phase is chosen over commercially available syringe pumps because of their significantly reduced response times without periodic fluctuations [22]. Gas bubbles are selected over liquid droplets due to their greater size variability for various reasons including the compressibility of the gas phase, large interfacial tension, and significantly different viscosity of the two phases, necessitating enhanced control.
Our control system actively adjusts either the liquid driving pressure or gas pressure to ensure the bubbles being produced match the user-specified setpoint for the bubble diameter while showing effective setpoint tracking, disturbance rejection, and stability over an eight-hour period. Potentially, our approach can be trained to control the shape of particles produced by This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d microfluidics such as rods and discs, and higher-order geometries such as double emulsions and Janus droplets.
We use a well-established flow-focusing generator to produce gas bubbles [23,24]. This geometry splits the continuous phase into two streams which subsequently surround and pinch off the dispersed phase at a cross junction, as shown in Figure 1. The symmetry of the junction allows for more flexibility in the size and frequency of bubble generation. The immiscibility of the two phases forces bubbles to form through either a dripping or jetting mechanism [25]. The dripping regime involves the periodic breakup of a fluid stream into bubbles due to capillary instability. This instability arises from the interplay of surface tension and viscous forces. The dripping frequency is governed by the capillary number (Ca), representing the ratio of viscous to capillary forces. The jetting regime involves the stretching of a fluid stream into an extended jet due to the dominance of inertial forces or viscous forces over capillary forces. Microfluidic droplets and bubbles produced in the jetting regime are larger and less uniform compared to those formed in the dripping regime due to the unfixed interface position during breakup [26].
Controlling the flows of the two fluid phases to maintain microfluidic generation in the dripping regime is critical to maintaining the uniformity of resulting droplets and bubbles [27].
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d bubble generation. Created with BioRender.com.
In this study, we use a flow-focusing geometry to produce nitrogen gas (dispersed phase) bubbles in an aqueous phase of 0.5 wt% sodium dodecyl sulfate (SDS) dissolved in DI water (continuous phase). The dispersed phase is injected into the device as pressurized nitrogen gas controlled by a differential pressure controller and the continuous phase is injected by using a differential pressure controller to adjust the pressure in a pressurized liquid reservoir and thus drive flow into the microfluidic device as depicted in Figure 1.
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d study have undergone hydrophilic-surface treatment to ensure stable formation of gas bubbles using a 2 wt% polyvinyl alcohol (PVA) solution [12].
PID control is one of the most fundamental types of control and is widely used in industrial applications due to its simplicity and effectiveness [28]. It has been widely studied, can address a wide range of process behaviors, and is straightforward to implement, making it a natural choice for control of microfluidics. PID feedback control operates by continuously comparing the desired setpoint to the process output, giving the error, e. The proportional term responds to the current error, the integral term accumulates past errors to eliminate steady-state discrepancies (offset), and the derivative term accounts for the rate of change of the error, as shown in Equation 1.
where 𝐾 𝑐 is the proportional gain, 𝜏 𝐼 is the integral time-constant in minutes, 𝜏 𝐷 is the derivative time constant in minutes, and 𝑐 𝑠 is the controller bias (actuating signal when 𝑒=0) [28]. These terms are combined to compute the controller output (𝑢(𝑡)), aiming to reduce the error and maintain stable and precise control of the process. In this study, two separate control schemes are explored: manipulating the pressure of the dispersed air phase to control microbubble diameter and manipulating the liquid driving pressure of the continuous phase to control microbubble diameter as illustrated in the control scheme of Figure 1.
Altering the PID tuning parameters 𝐾 𝐶 , 𝜏 𝐼 , and 𝜏 𝐷 can significantly influence the response of the controller; increasing the proportional gain enhances responsiveness, but may lead to
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d overshooting, while adjusting the integral and derivative time-constants affects the elimination of steady-state error and reduces the settling time, respectively. This method has been used in many applications, but it relies on measuring the process output in real-time. Numerous process parameters, including pressure and temperature, can be measured directly using commercially available real-time in-line sensors. However, microfluidic processes currently lack reliable, industry-proven inline sensor technologies that can directly measure the important process variables that need to be controlled such as size, shape, and flow regime. Thus, we use an artificial intelligence (AI)-based approach to create an indirect sensor, known as a soft-sensor, when controlling microfluidics.
When sensor variables are difficult to measure, soft-sensors can be used to estimate them. There are three types of soft-sensor models: knowledge-based models that rely on first principles, black-box models that are data-driven, and hybrid models that combine the two [29]. In this study, a black-box model consisting of a two-step process is used to estimate the flow regime and diameter of the process output, gas bubbles. The first step in our process is using a convolutional neural network (CNN) for image classification. CNNs have played a crucial role in the development and advancement of computer vision and artificial intelligence (AI) [30]. In this study, a linear architecture CNN is used to classify the microfluidic output into one of three regimes: liquid-dominated flow, air-dominated flow, and microbubble flow, as shown in Figure 2. The second step in our process is using a Hough image recognition algorithm for detection of the microbubbles. This algorithm is designed for feature extraction and gives outputs of their location and diameter. regime without bubble generation, (b) bubble generation in the dripping regime, and (c) airdominated jetting regime.
Our novel soft-sensor operates as follows: first, a CNN trained for image classification determines the current flow regime of the process from a snapshot of the device taken by a highspeed microscope camera. When the process is in a bubble producing dripping regime, an image recognition algorithm measures the diameter of the bubbles being produced. The combination of the CNN and image recognition is the soft-sensor output on which the controller acts to match the bubble diameter to the user-specified setpoint. When the process is not in a bubble producing flow regime, a direct controller action is taken to return the process to the production of gas bubbles. Our two-step approach is superior to other microfluidic control techniques because of its ability to return to the bubble-producing dripping regime when a disturbance causes it to move into a flow regime in which bubbles are not being produced. Our controller acts in real-
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d time and can obtain measurements and adjust setpoints with an average sampling frequency of 108 milliseconds.
Photomasks for microfluidic geometries were purchased from Artnet Pro, Inc. Silicon wafers were cleaned with IPA and DI water before oxygen plasma cleaning (Anatech) for enhanced bonding. SU-8 2025 photoresist was spin coated onto the silicon wafer before soft-baking at 65°C for 3 minutes, then at 95°C for 6 minutes. The wafer was exposed to 160 mJ/cm 2 at 365 nm intensity (ABM). After exposure, the wafer was post-baked for 2 minutes at 65°C and then for 6 minutes at 95°C. Lastly, the silicon wafer was gently agitated for 8 minutes in SU-8 developer.
PDMS (SYLGARD 184) was mixed in a 10:1 weight ratio of elastomer to curing agent. The mixture was degassed in a vacuum chamber for 1 hour to remove all bubbles before curing for 1 hour in an 80°F oven. The resulting elastomer mold was cut from the master and oxygen plasma bonded to a glass slide. 2 wt% PVA was surface coated onto the PDMS for a hydrophilic coating [12].
The aqueous phase in all experiments was 0.5 wt% SDS dissolved in DI water. The aqueous phase was administered using a differential pressure controller (Alicat) to pressurize a liquid reservoir to drive flow into the device. Compressed nitrogen (Airgas) was used for the dispersed phase and was controlled using a differential pressure controller (Alicat). Images used for the control scheme were taken on a Nikon eclipse TE200 inverted microscope with 3 different highspeed cameras, a Photron Mini AX-200, a Phantom Vision Research v7.3, and a Phantom Vision Research v611 proving the adaptability of this approach across multiple microfluidic setups.
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Image recognition was completed using Matlab image recognition functions. Since the bubbles in this work are circular, the function imfindcircles was used. This built-in function uses a Hough transform to isolate features and extract their location and size. Hough transforms are techniques used in computer vision and image analysis for feature extraction [31]. This is used to measure
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d the size, position, and uniformity of every bubble present in an image as part of the soft-sensor output.
Tuning the PID control parameters is required to achieve reliable controller responses. In this study, we tune a single-input, single-output (SISO) controller to control the output diameter of ) , 𝜏 𝐼 = 2.0 𝜏 𝑑 𝑎𝑛𝑑 𝜏 𝐷 = 0.5 𝜏 𝑑 [32]. Small changes in tuning parameters are then made to achieve the desired slightly overdamped response from our controller.
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d variable to a step change in the manipulated variable used for Ziegler-Nichols open-loop tuning [31].
For a step pressure increase from 18.7 to 20.3 kPa, an increase in diameter is shown in Figure 5.
Plotting the tangent line to the curve, the delay time is 1.1 second and the response time is 1 second. These yield K C = 0.125 kPa/μm, 𝜏 𝐼 = 2.2 seconds, and 𝜏 𝐷 = 0.55 seconds.
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d kPa (b) using Ziegler-Nichols tuning. Instead of the gas pressure, the flowrate of the continuous phase is manipulated by varying the liquid driving pressure. For a driving pressure step change from 31.7 kPa to 29.6 kPa, the delay time is 1.2 seconds, and the response time is 2.3 seconds, yielding K C = -0.21 kPa/μm, 𝜏 𝐼 = 2.4
seconds, and 𝜏 𝐷 = 0.6 seconds, as shown in Figure 6.
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d in liquid pressure from 31.7 kPa to 29.6 kPa (b) using Ziegler-Nichols tuning.
Setpoint tracking by PID control holds significant importance in optimizing process performance, ensuring close adherence to desired operating conditions and allowing for switches to new operating setpoints. For many microfluidic processes, effective changes in bubble/droplet diameters are required for different applications. For example, the gas bubble diameter is crucial in determining its resonance frequency, particularly in applications where bubbles serve as a contrast agent in ultrasound sonography [33]. In the context of microfluidic reactors, the droplet diameter plays a crucial role in influencing the reaction rates and kinetics of associated chemical processes [34].
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With our controller, we can dynamically manipulate either the continuous phase (aqueous flowrate via liquid driving pressure), or the dispersed phase (air pressure) to reach a desired setpoint, output bubble diameter. aqueous flowrate for increases in diameter setpoint.
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d aqueous flowrate for decreases in diameter setpoint.
We also perform tests with constant pressure while manipulating the aqueous flowrate via liquid driving pressure to achieve the new setpoint as shown in Figures 9 and 10. The controller can achieve changes in setpoint for increases in diameter as shown in Figure 9 and for decreases in diameter as shown in Figure 10. Again, these responses are overdamped, not allowing any overshoot, and it is seen that response times are considerably faster using pressure driven flow for the aqueous phase than widely used commercially available syringe pumps seen in Figures S3 and S4.
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d at constant air pressure for increases in diameter setpoint. while at constant air pressure for decreases in diameter setpoint.
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Disturbance rejection is needed to overcome all potential disruptions during process operation. This is especially important in intricate microfluidic processes in which minute variations can have large impacts on the process outputs due to inherently-small length scales. Such disturbances in microbubble production occur due to changes in air pressure, aqueous phase flowrate, fouling, clogging, changes in wetting properties, and external factors that cannot be anticipated [11,12,14]. For example, a random physical vibration such as one produced by motion of a person near the microfluidic set-up can significantly impact the uniformity of the resulting bubbles.
Our control system is superior to many microfluidic controllers because its CNN architecture allows it to recover from sharp disturbances that would otherwise move to non-bubble generating flow regimes, as shown in Figures 11 and 12. In Figure 12a, there are no bubbles being produced at a pressure of 29.3 kPa, so the controller linearly increases the pressure until bubbles are generated and the controller obtains an error for PID diameter control. The onset of bubble production occurs 21.5 seconds later at a breakthrough pressure of 41.9 kPa shown in Figure 12b. Now that bubbles are being produced and the controller can measure an error, PID control takes over and reduces the pressure to 35.7 kPa to reach the intended setpoint shown in Figure 12c. Basic PID control cannot achieve this transition to bubble creation because without bubbles, there is no way to obtain the current error. A recovery of flow regime video is shown in Video S5. Although neural networks for microfluidics control have been reported, their controllers are trained in the bubble generating regime only and do not account for the complex nature of bubble
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d breakup at elevated pressures or flowrates often needed to achieve breakthrough and induce breakup [16]. flow by reaching the breakthrough pressure of 41.9 kPa and tapering down to 35.7 kPa to achieve a setpoint of 70 μm corresponding to images in Figure 12. Diameter values of zero indicate no bubbles production. This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d (a) (b) (c) Figure 12. Time series response to sharp disturbance knocking flow out of a bubble producing flow regime. (a) System that has been disturbed and is in a liquid dominated flow regime -no longer producing bubbles. (b) Moment breakthrough pressure is reached by CNN allowing bubbles to be produced. (c) Controller continued to reduce the pressure from the breakthrough pressure to reach the setpoint diameter of 70 μm. To track the CNN's activation frequency in disturbance recovery, a one-hour test is conducted at a constant setpoint, beginning with a dispersed phase pressure of 0 kPa. The CNN increases the pressure to initiate bubble production, after which PID control maintains the setpoint. The CNN activates if disturbances push the system into liquid-or air-dominated flow regimes. Over the This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d
hour, PID control maintained the setpoint 99.2% of the time, but the CNN's disturbance recovery is crucial for sustained bubble production, as shown in Figure S6. This experiment demonstrates the controller's ability to start from a zero pressure condition using the CNN to drive the pressure up into the bubble production regime.
In addition to large disturbances, our controller overcomes disturbances small enough to create error only in the bubble diameter. As mentioned, two separate control schemes can be employed:
altering dispersed phase pressure to regain the setpoint after a disturbance in flowrate as shown in Figure 13 and manipulating flowrate by changing liquid driving pressure to maintain setpoint after a disturbance in pressure as shown in Figure 14. The former shows a slightly overdamped response as the pressure slowly decreases without overshoot to regain the diameter setpoint after the flowrate disturbance. The pressure response is able to regain the setpoint in under 20 seconds. The latter is also a slightly overdamped response to return the diameter to the setpoint following a sharp increase in dispersed phase pressure that causes the diameter to increase quickly above the setpoint. The controller increases the liquid driving pressure and thus the aqueous flowrate returns the bubbles to the setpoint in only 20 seconds.
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d overcome a flowrate disturbance caused by a change in liquid driving pressure (c). pressure (c) to overcome an air pressure disturbance (b).
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Another important aspect of disturbance rejection is the ability to remain stable for long periods of time. A typical operating shift in manufacturing industries in the US and many countries is eight hours [35] during which many changes in operating conditions can occur. Figure 15 shows performance of a gas bubble generation process left unattended without control measures (i.e., the flowrate and the pressure are kept constant). Over extended durations, frequent disruptions in flow conditions lead to significant variations in the output bubble size. Remarkably, only 2.16% of the produced bubbles fall within 5% of the initial bubble diameter. The exact cause of these disruptions is unknown, necessitating the implementation of a control system to counteract them, as they cannot be systematically eliminated from the process. pressure (b) at constant aqueous flowrate.
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This drastic variability is avoided with control action, as shown in Figure 16. Despite disturbances, the controller adjusts the pressure to maintain the setpoint. Throughout the eighthour period, our controller achieved 99.2% accuracy, with bubbles deviating by no more than 5% from the setpoint. Notably, the pressure required to satisfy the setpoint must be increased gradually by over 50%; while we do not fully understand the physical origin of such an adjustment in the pressure, this result nevertheless highlights the importance of feedback control to enable stable and robust microfluidic manufacturing. pressure (b) at constant aqueous flowrate.
Microfluidic devices offer precise control for producing droplets and bubbles crucial for various industries. Transitioning from laboratory to industrial-scale operations poses challenges presented by disturbances, fouling, and changes in device performance. These necessitate
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d continuous monitoring and adjustments to manipulated variables that maintain user-specified setpoints. The integrating feedback controllers herein enhance product uniformity and reduce the labor-intensive tasks associated with process maintenance, addressing a critical need in scaling-up microfluidic processes for industrial applications. Our experimental results show that PID control is a resilient feedback control mechanism, relying on a soft-sensor to obtain error measurements using artificial intelligence in the face of unreliable physical measurements. Our CNN-driven, soft-sensor identifies flow regimes enabling the controller to regain bubbleproducing flow regimes when shifted by disturbances to undesired regimes. In addition to selfrecovery, our controller reduces errors while maintaining setpoints, countering disturbances, and stabilizing operation over long times. Our controller permits over 99% of bubbles produced This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d
This preprint research paper has not been peer reviewed. Electronic copy available at: https://ssrn.com/abstract=4920634 P r e p r i n t n o t p e e r r e v i e w e d