Efficient Bayesian Function Optimization of Evolving Material Manufacturing Processes.

The scale-up of laboratory procedures to industrial production is the main challenge standing between ideation and the successful introduction of novel materials into commercial products. Retaining quality while ensuring high per-batch production yields is the main challenge. Batch processing and other dynamic strategies that preserve product quality can be applied, but they typically involve a variety of experimental parameters and functions that are difficult to optimize because of interdependencies that are often antagonistic. Adaptive Bayesian optimization is demonstrated here as a valuable support tool in increasing both the per-batch yield and quality of short polymer fibers, produced by wet spinning and shear dispersion methods. Through this approach, it is shown that short fiber dispersions with high yield and a specified, targeted fiber length distribution can be obtained with minimal cost of optimization, starting from sub-optimal processing conditions and minimal prior knowledge. The Bayesian function optimization demonstrated here for batch processing could be applied to other dynamic scale-up methods as well as to cases presenting higher dimensional challenges such as shape and structure optimization. This work shows the great potential of synergies between industrial processing, material engineering, and machine learning perspectives.

Introduction

The superior material properties accessed through recent advances in nanotechnology result in an increasing range of commercial products and devices with performances strongly dependent on features in the sub-micron scale. A drive to strictly control morphology and features is, though, often challenged by the need to produce at scale and at market-sustainable costs and rates. The great advantages of the expanded scale of product manufacture go hand in hand with complex production challenges related to the scaling up of laboratory-scale methodologies and boundary condition-sensitive manufacturing.[1−5] Typically, laboratory-scale manufacturing puts a higher priority on retaining “stable and pure” manufacturing conditions, than it does on maximizing materials production per production batch: the latter is not a major driver at the laboratory scale, while the former enables greater scientific understanding of processes. The industrial paradigm is instead typically biased toward the opposite situation, with higher importance given to high per-batch yield and low production costs (time and materials). Scaling-up of laboratory technologies therefore often requires a major shift in processing conditions, with a trade-off between purity and yield.[3]

Innovation of industrial processes is also often hindered by the inherent inertia in industrial processes, as changes to an established process incur significant costs and investments, resulting in the lack of exploration of complex experimental spaces at scale. These main factors are recognized impediments to the translation of novel techniques to large-scale conditions and to the innovation of current industrial manufacturing of high-value materials. Overcoming these limitations will therefore greatly improve the adaptability and efficiency of various industrial batch processes.

This work aims to demonstrate that the scaling up of techniques from the lab-scale to commercial-scale production can be most efficiently driven with the use of adequate machine learning algorithms.

The industrial production of short polymer fibers (SPF) by wet spinning is an ideal system for deploying artificial intelligence because of the complexity of its experimental space and the cost benefit of increasing per-batch production yield. SPF are fibers of micron-size (or below-micron) diameter and finite length.[6,7] Produced by a liquid-in-liquid coagulation process, they are stored and used as colloidal dispersions in a variety of fields. They have received strong interest for applications in filter production, cell growth, 3D printing, and especially innovative textile treatments.

Already commercialized at the 1000 L scale, the production of SPF involves inducing the coagulation of a polymer-containing liquid filament under shear. For this purpose, a polymer solution is introduced into a laminar flow device (Figure ). A liquid filament is formed, which is then stretched and broken while coagulating under shear. The main forces acting in this process are the relative forces of fluid drag, fluid inertia, osmosis, and interfacial tension. The elongation and solidification rates of the filament can be controlled through the selection of polymer, solvent, and coagulant, while the design of the fluidic channel and the flow rates determine the shear forces that stretch the polymer jet before, during, and after gelation. Within a narrow window, the combination of parameters can be balanced such that filaments are formed and broken prior to complete solidification, resulting in the formation of SPF. In a single-pass run, these physical and chemical process conditions can be tuned to obtain fibers with controlled length, diameter, and overall quality.[8] However, because of the large ratio of the coagulant to polymer solution in the shear system, these optimized conditions yield a low concentration suspension of fibers, which is not economical for industrial uptake because of the large consumption of the coagulant. In this type of system, batch processing is commonly used in industry, driven to maximize effective yield per processed batch, using methods such as recirculation and progressive enrichment of a coagulant.[9]

Figure 1

Laminar flow SPF production system. The polymer solution jets out of the nozzle into the coagulant and is subjected to shear forces that stretch it during and after solidification. The design (h, d, and α) and flow (vC, vP) parameters determine the conditions of the solidification and can be tuned to produce fibers with target length and diameter. Bold underlined settings were used for the optimization of fiber production by recirculation.

This work tackles this scale-up problem by utilizing an SPF-manufacturing setup, where the produced fiber dispersion is recirculated as the coagulant for the formation of new fibers (Materials and Methods). Recirculation is effective from a commercial SPF manufacturing perspective because the same volume of the coagulant will be progressively enriched with fibers as it is repeatedly circulated through a device. However, utilizing this approach in the SPF manufacturing paradigm presents two main challenges: (i) the purity of the coagulant varies during the recirculation cycle as more polymer solution is injected, affecting fiber formation and stability, and (ii) circulation through a pumping system can damage the fibers dispersed in the coagulant. The combined effect of coagulant contamination and repeated exposure to shear is particularly difficult to predict, making this technique difficult to scale without the aid of advanced optimization methods. The effects of recirculation on fiber formation and degradation are initially investigated here separately. The outcomes of these preliminary tests are then used to determine a suitable experimental space, which can then be optimized using artificial intelligence approaches to maximize yield while targeting a specific length distribution.

The optimization of such complex experimental spaces is typically driven by the urge to find absolute maxima while spending a minimum amount of time and resources in the process. Bayesian optimization methodologies have been developed for the design of experiments that consider both the expected outcome of the experiments and also the information they provide about the experimental space.[10−14] An adequate balance in this duality between the exploration of the unknown space and exploitation of the best known results ensures the highest value per experiment and therefore low experimental cost.[12,14,15] This strategy has also been adapted for experiments where some variables are hard to change. In this approach, a group of suggestions where such variables are kept constant for time convenience is known as the optimization batch.[16] Moreover, adaptive optimization can be performed using information obtained from the outcomes to update the limits or conditions of the experimental search space along the process.[11] Advances in the evaluation of outcomes have also been published that combine objective measurements and subjective evaluations to provide efficient and reliable feedback for the optimization.

Recently, a new technique has been developed, with the goal to find functions, instead of variable values, that provide optimal results in a dynamic process, providing dynamic control of the function’s shape and variability.[17] These methodologies are utilized here for the optimization of high yield SPF production by recirculation, a suitable real-world challenge with strong commercial and research potential.

Results and Discussion

Characterization of the Recirculation Process

In the SPF system, a fluid filament is injected in an outer flowing coagulant, forming fibers that are collected as a dispersion. If the fiber dispersion is collected directly in the coagulant volume and this is recirculated through a device to increase its solid content, two main effects are to be considered: breakage due to high mechanical shear and contamination of the coagulant that affects the formation of new fibers. These effects will be investigated and the system optimized for targeted fiber length and maximum yield using machine learning.

Recirculation experiments with fixed settings were performed to characterize the fiber production system. These settings were selected to produce fibers of different morphologies based on previous single-pass experiments with identical settings.[8]

In the first minutes of recirculation, all tested conditions produced fibers similar to those from prior single-pass experiments. This is to be expected because the coagulant is still relatively pure. However, the quality of the fibers drastically dropped at a time inversely proportional to the polymer flow rate, suggesting that water content, which increases as a function of the injected polymer solution, has a major effect on fiber formation, likely by affecting solvent/coagulant diffusion kinetics, and therefore affecting the solidification kinetics. This notion is consistent with the osmotic nature of the coagulation process, with solvent exhaustion driving the solidification of the polymer solution jet. As water from the polymer solution is dissolved in the coagulant, the osmotic pressure driving this flow is reduced and so is solvent exhaustion. Initially, this slows down the solidification of the polymer-rich jet, resulting in irregular-shaped fibers and debris. As the coagulant reaches saturation (∼8% V/Vtotal), solidification appears inhibited because of the inability of the coagulant to absorb more water and further injection of polymer solution appears to result in the re-dissolution of previously formed fibers. The evolution of fiber morphology in such cases can be observed in the images from three continuous-injection recirculation samples shown in Figure a. These experiments revealed effective boundaries for recirculation with static production parameters, indicating that a hard limit of the maximum volume ratio of aqueous polymer solution to coagulant exists, for the solvent and coagulant used. To test the effects of water content on fiber formation, a series of separate experiments was performed using the coagulant tainted with different percentages of de-ionized water in a single-pass setup. The results shown in Figure b show consistent fiber production up to 10% V/Vtotal water content and no fibers produced beyond that ratio. Figure shows sample quality evolution in several recirculation experiments (as color lines) along with the controlled water content series (as red dots). Quality in this plot is based on the quick-scoring user guide (Appendix 1). A reduction in fiber quality can be observed in all experiments, related to increasing the water content of the coagulant. This appears as the main boundary condition to be set for successful recirculation and will be taken into account during the optimization of fiber production.

Figure 2

Effect of coagulant contamination on fiber morphology. (a) Evolution of fiber morphology as a function of recirculation time at three different settings and equal recirculation volume VR = 400 mL. The first two settings produced shorter fibers compared to the third, and it was observed that the quality dropped for all samples as recirculation time increased. (b) Fiber samples produced separately in a single-pass (no recirculation) using the coagulant tainted with different amounts of de-ionized water. Water contamination in the coagulant reduces the solvent exhaustion from the polymer jet, slows down solidification, and is the main limitation for fiber yield in the recirculation system.

Figure 3

Consistent reduction of fiber quality as water content in the coagulant increases. Eight samples produced by recirculation are shown (color lines), including three recirculation samples also shown in Figure (marked with *). A series of samples produced adding different proportions of water to the coagulant is also shown as red dots (also in Figure ). It can be seen that the quality of the fibers consistently drops for water contents above 10% V/Vtotal. Saturation of the coagulant avoids further water (solvent) exhaustion from the polymer solution thus stopping fiber formation. Fiber quality score values shown in this plot are evaluated by an expert user based on the scoring guide (see Appendix 1).

The second effect that can be observed in recirculation samples is the reduction of fiber length as recirculation time increases (see Figure a).

The series of experiments performed with different starting water contents (Figure b) in a single-pass setup shows no significant effect of initial water content on fiber length. This suggests that tensile and bending stresses caused by the drag forces during recirculation are a more likely cause of fiber breakage than water content alone. This is a good example of new complexities that can arise in the scale-up of methodologies, and which are difficult to predict or control. It can be deduced that avoiding recirculation in production would be ideal from a product consistency perspective. While this is possible at the laboratory-scale, by using a pristine coagulant, it would be too costly for industrial-scale production.

The degradation of fibers by mechanical stress was studied using two samples, with short and long fibers, produced by single-pass and then recirculated under different conditions. The length of the produced fibers was observed to be determined by the choice of production parameters, as described by a previous study.[8] A set volume (200 mL) of each of these two fiber samples was passed only once through the recirculation setup with a high coagulant speed (vC = 92 cm/s) and without adding any further polymer solution. The device geometry selected for this experiment is chosen to produce the highest acceleration of the coagulant and therefore the highest fluid drag forces in the constriction (h = 9 mm, d = 0 mm, α = 25°). The fiber length distribution in the sample with short fibers showed a non-statistically significant change in the average length (+1.9%) after the cycle, which is comparable to the uncertainty of the measuring methods. However, the long fiber sample showed a reduction of 43% in the average fiber length (Figure ) and a clear shift in the distribution. These results suggest that the breakage of the fibers is also a function of their initial length and can be explained by the proportionality of drag forces to fiber length and the likelihood to exceed the maximum tension withstood by the fibers, which is, instead, a function of fiber thickness. Longer fibers are therefore more prone to breakage than shorter ones for comparable diameters. The magnitude of this non-linear aspect of fiber breakage makes the prediction of the final fiber length distributions very difficult and is of utmost importance for the resulting fiber length distribution of the product.

Figure 4

Effects of recirculation on the length of short and long fibers. Two samples of fiber dispersion were circulated through the SPF system containing short and long fibers, respectively.

The effect of coagulant speed alone on fiber breakage was also studied using a single-pass setup. For this purpose, 200 mL of the dispersion containing long fibers was subjected to one cycle through the setup at a lower coagulant speed (vC = 43 cm/s) resulting in a much smaller reduction in length (−4.6% average, Figure ) compared to what was obtained at a higher speed (92 cm/s). This confirms that the coagulant speed also affects the fiber breakage rates, as expected, likely due to its direct impact on drag forces in the recirculation loop. It is important to notice that coagulant speed affects the dimensions of the produced fibers and simultaneously the rate at which they are broken. Moreover these two effects might have completely different causes. The former is a result of drag forces in laminar flow especially designed for the purpose. The latter is an unplanned effect of this upscaling methodology and needs to be further examined.

Figure 5

Effects of coagulant speed on the length of circulated fibers. Two samples of dispersion with long fibers were circulated only once through the SPF system at low (vC = 43 m/s) and high (vC = 92 cm/s) coagulant speeds, respectively. The resulting samples show a very small reduction of length (4.6%) for the low shear compared to the almost ten times higher for the high shear. This effect is expected because shear forces causing breakage are determined by flow speeds. Fibers in the SPF system can pass through the system tens of times during a regular recirculation process.

The mechanism of fiber breakage was studied by circulating 200 mL of the dispersion with long fibers through the setup without the device at a high coagulant speed (vC = 92 cm/s). This was done to clarify whether fiber breakage is caused by known shear fields in the laminar flow device or in the rest of the equipment, that is, the tubing and the lobe pump. The resulting fiber length distribution does not deviate from that obtained with the device as part of the loop (Figure ). This suggests that most of the post-formation fiber breakage happens in the tubing and lobe pump as opposed to the laminar flow device. It is relevant to consider that laminar flow devices were designed to control the magnitude of shear forces, and that the length of the fibers, as produced through coagulation, is a direct consequence of these forces. Such forces are sufficient to induce breakage of the filaments of polymer-rich phase while in a “plasticized” or “semi-plasticized” state. It is not expected, therefore, that seconds after being produced, a more solidified, stronger, filament would break further by passing through a similar field of shear. On the other hand, the tubing and pump are expected to cause turbulent flow and high shear forces, the magnitude of which is likely greater than those in the device. In summary, the characterization of the recirculation system demonstrated two main effects on fiber morphology: (1) coagulant saturation induced worsening of fiber quality and (2) continuous breakage of fibers is strongly dependent on coagulant speed and particularly affects longer fibers. The first effect resulted in an imposed hard limit at 10% V/Vtotal polymer solution. The potential of the recirculation system to produce fiber dispersions with high yields can be more efficiently exploited with this information.

Figure 6

Comparison of fiber breakage mechanisms. The presence or absence of the laminar flow device in the recirculation setup seems to have no significant effect on the distribution of fiber length. This suggests that turbulent flow and inhomogeneous shear forces in the tubing and lobe pump are the main causes of fiber breakage during recirculation.

Optimization

The main requirements for the scaling up of fiber production include achieving the maximum fiber yield and a controlled fiber length distribution. The recirculation setup was designed to achieve the highest yield and the characterization shows that this can be achieved by setting a final polymer solution content at 10% V/Vtotal. However, controlling the size of the fibers in a dynamic (evolving) recirculation system is not a trivial task, especially considering the complex evolution of the fiber length, as shown by the experiments described above.

Fiber length will reduce as a function of the time spent in the recirculation system, resulting in broader fiber length distributions with increasing time. It has been shown that parameters such as coagulant speed affect the final length distribution simultaneously in several ways including the size of formed fibers and rates of breakage. Higher homogeneity of fiber lengths can, therefore, be expected if the length of fibers being formed were continuously matched to that of the fibers already within the system, with their continuous breakage being considered. Such a strategy requires continuous adjustment of production parameters within recirculation time.

Coagulant speed can be tuned dynamically during production in the SPF system even at larger scale production facilities. It is also the most relevant parameter for controlling the formation of fibers in this system because it is directly related to shear forces that determine fiber formation and breakage. Coagulant speed has been therefore chosen as the main dynamic variable to consider and optimize as a function of recirculation time. The full range of the coagulant speed was made available for optimization (10 ≤ vC ≤ 110 cm/s). A monotonic in-batch increase of coagulant speed was chosen to secure the production of fibers with decreasing length, as is required to obtain the homogeneous distribution of length. Even when simple functions of time are used for this purpose, a multitude of profiles can be designed with monotonic increase.

However, tailored length distributions necessary for the upscaled production of SPF dispersions require an efficient method to discriminate the corresponding coagulant speed profiles.

The batch volume (VR) for the optimization experiments was fixed at 400 mL in order to reduce solvent usage while maintaining sample reproducibility. The speed at which the polymer is injected (vP) determines the water content in the coagulant at any given time of recirculation. Because of the limit of 10% V/Vtotal water content, this results in a total recirculation time (t) inversely roportional to polymer speed (vP). Therefore, a high polymer solution speed was selected (vP = 10.5 cm/s) that minimizes the recirculation time (t = 9 min). Design parameters in the SPF system can be changed only after a laborious procedure (involving reassembling the setup) and have even lower variability in the industrial size machinery. Therefore, these parameters were fixed for the optimization experiments as follows: h = 9 mm, d = 0 mm, and α = 25°.

The optimization of SPF production by recirculation is therefore equivalent to finding the coagulant speed profiles that result in a desired fiber length distribution while keeping other settings fixed. Vellanki’s approach[17] was used to design and optimize coagulant speed profiles aiming to achieve high yield fiber dispersions with a target length of 30 to 80 μm. The Bernstein polynomials used in this approach are a series of smooth functions with both domain and range from 0 to 1 that add up to produce a variable curve (cfr. Figure ). Similarly to other polynomials, their order determines the amount of functions added together and thus the variability of the resulting curve. For a polynomial of order n, the amount of functions used corresponds to n + 1. Five functions (4th order) were used initially for the design of the coagulant speed profiles. The coefficients of each function (Bernstein coefficients) can be tuned to determine the shape of the curve. A monotonic increase of the curve can simply be established by a monotonic increase of such coefficients.

Figure 7

Design of the coagulant speed profiles based on Bernstein polynomials as described by Vellanki et al. The curve produced by the polynomial function basis depends on a number of so-called Bernstein coefficients (seven in this example). This shape is then scaled to fit the experimental limits of coagulant speed (vC) as a function of recirculation time (t) to produce a unique coagulant speed profile. The setting of the coagulant pump and therefore the coagulant speed was adjusted every minute according to this function.

By scaling the range (0–1) of these functions to the range of the coagulant speed and the domain to the 9 minutes of recirculation, coagulant speed settings at every minute of the recirculation process are determined.

Bayesian optimization is then used to find the Bernstein coefficients and therefore the coagulant flow profile that produces the best fiber samples. Thompson sampling is used to generate six coagulant speed profile recommendations per optimization batch.

This strategy selects the first recommendation as the one with the highest expected outcome and then speculates such an expected outcome in order to produce a second recommendation. In doing so for the six samples of each optimization batch, the algorithm ensures the necessary balance between exploration and exploitation.

Bayesian optimization methods, as the one used in this investigation, require the value or quality of the experimental outcomes to be reflected by a numerical value known as the objective function. However, capturing every property by a single number is not a trivial task. Some aspects of the product can be directly measured by automated methodologies and therefore can be standardized. On the other hand, some quality requirements might be difficult or impractical to implement in an efficient optimization process. Our target is the highest number of fibers possible (compared with debris) and with measured lengths falling within a desired range. For this purpose, the objective function is related to fiber quality and is evaluated considering two factorswhere L% is the proportion of fibers within the targeted length range (30–80 μm) and P% is the perceived proportion of the polymer content that is forming fibers as opposed to debris and spheres (Figure ). The former is calculated considering all fiber measurements per sample and the latter is evaluated by an expert user with base on the polymer yield factor guide (cfr. Appendix 2). In this manner, the quality of the samples is directly related to the proportion of the polymer solution that ends up as fibers of a desired length.

Figure 8

Elements of the fiber quality factor (F%—eq ). This factor is designed to capture overall sample quality based on the proportion of polymer that is formed in fibers (P%) and proportion of fibers within the target length range (L%): (a) proportion of polymer that is formed in fibers (P%) is estimated by an expert user based on a scoring guide (Appendix 2) with five possible outcomes (0.0, 0.4, 0.7, 0.9, and 1.0); (b) proportion of fibers within the target length range (L%) is calculated considering the measured fibers in the sample that fall within the region of interest (ROI: 30 to 80 μm). The fiber length distribution of sample B1–S1 is shown as an example.

The settings for the first group of experiments were selected randomly in order to provide an unbiased initial dataset. The defining procedure for an adaptive optimization is to analyze the new recommendations of the optimizer in light of the previous results, in order to update any relevant findings in the optimization limits and methodology.

The first sample of the second optimization batch (B2–S1) showed high amounts of debris and few fibers, much longer than the target range (Figure ). The coagulant speed profile for this sample ran at the lowest coagulant flow for 8 min and increased slightly for the last minute, suggesting that no fibers could be produced at the lowest coagulant speed. This was confirmed in a single-pass experiment run at a coagulant speed vC = 10 m/s which resulted in no fibers, and therefore the lower limit of the optimization range for coagulant speed was doubled starting from optimization batch number 3 onward. This was done by adjusting the equivalence of the lowest limit of the function basis (0) to the new lower limit of the coagulant speed (vC = 20 m/s).

Figure 9

(a) Coagulant speed profiles, (b) fiber length distributions, and (c) microscopy images of significant optimization samples. Six samples are shown including three that achieved best-so-far (B1–S3, B2–S5 and B5–S5), two close calls (B3–S3 and B6–S5), and the worst sample (R2–S1, red), which provided information about the functional limits of the coagulant speed used to update the optimization limits. Good samples have more fibers in the targeted length range. It can be observed that profiles starting at low coagulant speed and finishing toward the middle levels deliver good results. Fiber length distributions shown in part (b) are calculated with a fixed bandwidth of 5 μm to ease comparison.

It was also noticed that the coagulant profiles recommended by the optimizer for the six samples of the third batch had similar shapes. The order of the Bernstein polynomials was therefore increased to 6 (7 coefficients) for the following batches, in order to increase the variability of the coagulant speed profiles. This was done following the procedures described by Vellanki et al. that maintain equivalence of the previous and new profile recommendations.[17]

Seven optimization batches were carried out (Figure ), with two adaptations applied before the third batch as explained above. Each optimization batch presented coagulant speed profiles similar to previous high-score samples and others that investigated innovative shapes, demonstrating a good balance between exploration and exploitation. After seven batches, a variety of profiles were investigated that spanned throughout the experimental space. High scoring samples had similar coagulant speed profiles starting at low coagulant speed settings, with a slow increase and finishing in the middle range (see Figure ).

Figure 10

Evolution of sample quality along the 7 batches of the optimization process. Each optimization batch consists of 6 samples. Total fiber score (F%) is shown on the top in yellow, followed by the two combining factors: polymer yield (P%) in red and length distribution (L%) in green. Samples that resulted best-so-far are marked with a blue triangle.

The optimization process was stopped after the seventh batch of experiments due to the similarity of high-scoring profiles and the spread out sampling of the experimental space, signals of an accomplished optimization. Further trials are unlikely to improve outcomes or provide new information and could result in a lower gain per experiment.

Undesired polymer clusters can be observed in the first batches that make up a considerable amount of the polymer and reduce sample quality (see Figure c). These clusters can be formed by sticking the previously formed fibers with newly injected polymer solution. They can also be formed because of the agglomeration of small particles caused by convection currents during the drying process in the surface of the microscope slide. However, the cause of cluster formation in these samples is not deemed relevant to this work. More importantly, it can be observed that those clusters were eliminated through the optimization process, leading to high quality samples with cleaner fibers. This achievement of the optimization is highly convenient for industrial applications and would be much more difficult to reach using traditional methodologies for the design of experiments.

The knowledge obtained from the optimization is not limited to the best scoring profiles. It can be observed in Figure that most of the fibers produced even in the high scoring samples fall below the region of interest.

Considering that single-pass experiments have been shown to consistently produce fibers in this range,[8] such low performance illustrates the magnitude of the up-scaling challenges.

Conclusions

The characterization and optimization of a recirculation system for the production of high yield fiber dispersions with targeted length distribution has been successfully carried out.

It has been shown that fiber formation has a consistent plateau upon recirculation until it suddenly drops as the water content in the coagulant reaches ∼10% V/Vtotal. Analysis of fiber measurements shows that long fibers are more prone to be broken by turbulence in the pump and tubing. These findings suggest that higher homogeneity in samples can be achieved using a variable coagulant flow within a time limit. Adaptive Bayesian optimization was used to find the coagulant speed profiles that produced high quality fiber samples with the targeted length.

The fine-tuning of dynamic processes using adaptive Bayesian optimization has been demonstrated here on batch-enriching production of SPFs. This strategy has strong potential for the optimization of the evolving manufacturing processes, such as those in batch reactions, fermentation, and other batch production systems which are inherently difficult to optimize because of their evolving state. Approaches of this nature, combining industrial processing, materials science, and machine learning perspectives, offer strong opportunities for accelerating discovery, research translation, and process improvement.

Materials and Methods

The SPF samples were produced with the strategy presented by Sutti et al.[6] and implemented in the production system described in a previous article.[8] This SPF system (Figure ) consists of a nozzle that injects the polymer solution into a channel of variable width (h = 3, 6 or 9 mm) where the coagulant flows. The channel width remains constant for a variable distance (d = 0, 15, or 30 mm) after the injection nozzle allows fiber gelation and is then constricted to 1 mm at a variable angle (α = 10 or 25°) causing an increase in shear forces that affects fiber morphology. Shear forces are also dependent on the initial velocity of the polymer (vP) and especially on the coagulant speed (vC). In contrast to the original SPF system where only the pristine coagulant is used, the setup presented here delivers the fiber suspension back into the coagulant container (Figure ) to be used for further fiber production. This setup involves two new experimental parameters: the coagulant volume used for recirculation (VR) and the running time of the experiments (t).

Figure 11

Recirculation setup for the SPF system. The coagulant is circulated by a lobe pump into the laminar flow device where the polymer solution is injected forming the fibers. The resulting fiber dispersion is returned to the coagulant container and reused as the coagulant, increasing the fiber yield. This updated setup results in two new experimental variables: initial coagulant volume (VR) and the recirculation time (t).

A 16.5% w/v polymer solution was prepared by adding poly(ethylene-co-acrylic acid) (Dow Primacor 5990I) into ammonia solution and stirring overnight at 110 °C. 1-Butanol (>99%, Chem Supply) stored at ∼4 °C was circulated as the coagulant using a lobe pump (UNIBLOC LABTOP 200). The channel was flushed with 400 mL of the coagulant before starting the polymer and coagulant flows at adequate speeds. The polymer solution was injected in the device using 50 mL plastic syringes (Becton Dickinson) and a Legato 270 syringe pump. The fiber dispersion/coagulant vessel was stirred at low speed for recirculation experiments. The water content percentage in the samples was calculated by dividing the injected volume of the polymer solution by the total volume of the coagulant plus solution.

Fiber dispersions were collected from the recirculation beaker using a 10 mL syringe and diluted with ethanol 1:100 V/Vtotal.

The diluted dispersion was then spread on a microscope slide and left to dry in air. Optical microscopy images were taken using an Olympus BX51 microscope with a DP71 camera. An adequate magnification was selected, at which the fibers could be clearly seen and measured depending on their size. Brightness, contrast, and background were adjusted on the images and the length and diameter of the fibers was measured using the Fiber Separation app on Image Pro Premiere 9.2 software. This measuring method automatically detects fiber-like objects in a calibrated image and measures both length and width based on search parameters that can be tuned for optimal results. This method avoids clusters and irregular-shaped objects, resulting in the efficient characterization of the fibers. An average of 340 and a minimum of 53 individual fibers were measured per sample.

The quality of the fiber samples used for the plot in Figure was estimated using a quick-scoring guide (cfr. Appendix 1). This guide is an aid developed by the SPF research group to help users to visually evaluate fiber samples as a function of fiber homogeneity and in the absence of debris. Fiber length distributions are plotted for visualization purposes with a standard normal kernel using the Silverman’s rule of thumb bandwidth: h = 1.06σn(−1/5) where σ is the standard deviation and n is the amount of measurements per sample.

It is to be noted that fiber diameter distributions are typically more uniform than those of length. This is a result of the dependence of fiber breakage (during and after formation) on fiber thickness and ensures that generally, if the length of the fibers is adequate, the width will also fall into a convenient range. For this reason, the width of the fibers has not been separately considered on this work.