Integrating a micro-mixing mechanism and on-line thermal processing for the large-scale ejection of polymeric liquid threads for producing ultrafine fibers

Integrating a micro-mixing mechanism and on-line thermal processing for the large-scale ejection of polymeric liquid threads for producing ultrafine fibers Jes´ us Olmedo-Pradas, a Alfonso M. Gañ´ an-Calvo ab and Luis B. Modesto- L´ opez * a Micro/nanofibers are structures that nowadays have a wide range of cutting-edge applications including energy generation and storage devices, smart textiles, cell growth, and tissue engineering. These fibrous materials are mostly produced from polymer solutions spun, under laminar flow conditions, into nanofibers by external forces. However, the turbulent interaction of gas–liquid interfaces offers an innovative approach for the high-throughput production of nanofibers. Here, we present Flow Blurring (FB), a solely pneumatic approach for the massive production of liquid threads of polymer solutions, which relies on a micro-mixing mechanism that triggers a turbulent motion capable of fragmenting a viscous flow. The as-ejected threads are subsequently processed thermally, on-line in a single-step, thus producing micro/nanofibers that form mats. The method operates with relatively large liquid flow rates, equivalent of a high production rate, and is thus suitable for industrial production of engineered nanomaterials. In this work, we used solutions of poly(vinyl alcohol) (PVA) to study its ejection and fragmentation dynamics through computational fluid dynamics (CFD) simulations. In addition, the physics underlying the regulation of the liquid flow rate in FB atomizers are proposed. Fibers with typical diameters in the range 400–800 nm were produced by online heating of the liquid threads. Liquid ejection experiments were performed under different operating conditions thus verifying the capability of the method for synthesizing submicrometer-sized fibers with high uniformity and production rates suitable for scaling up. 1. Introduction Micro and nanobers are ubiquitous structures in cutting-edge applications including electrodes for energy generation and storage devices, smart textiles, cell growth, tissue engineering, coatings, and catalysts. 1 Many of those brous materials are produced from polymer solutions, 2–4 which may contain additives such as nanoparticles, nanotubes, or soluble precursors. 3,5–10 The polymer matrix either serves as a template for micro/nanober fabrication or is the material of interest itself. The applications of such polymer bers are determined not only by the structure of the polymer's repeating building block or their physicochemical surface properties but also by their dimensions, such as their length and diameter. Polymer micro- or nanobers are generally obtained from the drying of a liquid lament drawn from a bulk by external forces as it occurs in techniques such as meltblowing, 11 electrospinning, 3,12–18 or straining ow spinning. 19 The industrial demand for polymeric brous materials has prompted intense research to develop efficient and scalable fabrication methods to produce tailored materials. 11 This quest has oen resulted in the merging of two or more techniques to take advantage of their strengths. Thus, for instance, a centrifugal electrospinning method was presented that diverges from the traditional electrospinning in that it utilizes a type of rotating, bell-shaped ejector 20 instead of the typical, single needle-type. Likewise, a centrifugal multispinning technique was proposed, which consisted of a cylindrical reservoir with orices on lateral, main surface from which the solution was ejected towards a rotating mesh. 21 These methods are based on the ejection and subsequent collection of thin liquid threads, where the interplay of surface tension forces, viscous forces, and other external forces, such as electrical, are evident and critical to achieve rather thin and long brous materials. There should be therefore an energy input to overcome unfavorable forces, surface tension in this case, acting on the threads. Therein, it is consequently required the liquid to be electrically conductive to a Department of Aerospace Engineering and Fluid Mechanics, ETSI, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain. E-mail: [email protected]; Tel: +34-954-48-7339 b ENGREEN, Laboratory of Engineering for Energy and Environmental Sustainability, Universidad de Sevilla, 41092, Spain Cite this: RSC Adv.,2023,13,18511 Received 8th May 2023 Accepted 12th June 2023 DOI: 10.1039/d3ra03070a rsc.li/rsc-advances © 2023 The Author(s). Published by the Royal Society of Chemistry RSC Adv.,2023,13,18511–18524 | 18511 RSC Advances PAPER Open Access Article. Published on 20 June 2023. Downloaded on 9/4/2023 4:45:03 PM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online View Journal | View Issue respond to external stimuli effected by the eld from the collector electrode. Furthermore, from an engineering viewpoint the key features a method should full to be implemented in practical applications are: simplicity and yet robustness, versatility to be used with a wide range of materials, consistency in its feeding system, and capability for large-scale production. In that sense, liquid atomization techniques offer a stable source of precursors and are widely used in materials synthesis. 22 Here, we present the coupling of a micro-mixing-based liquid atomization technique, for generating threads of polymer solutions, with an on-line thermal treatment to achieve high-volume production of ultrane polymer bers. The term micro-mixing refers to an intricate intermixing phenomenon occurring at small length scales, typically within the micrometer range, resulting in the mixing of both uid phases. The approach is based on a pneumatic ejection of polymer solutions at high liquid ow rates, 23–25 of the order of tens of milliliters per hour, much higher than those used by standard techniques (1mLh −1 ), 26,27 followed by thermal treatment with a tubular furnace, in a single-step. Our method uses a so-called Flow Blurring (FB) atomizer 23,25,28–30, to fragment a liquid stream with a gas current, thus generating multiple, thin liquid threads that elongate as they move forward 25,31,32 and are dried in-ight producing micro/nanober mats. Because the method functions with relatively low or medium temperatures it allows for the processing of materials which may undergo thermal degradation when exposed to higher temperatures. A fundamental and unique feature of the method presented herein is its capability of mixing at micrometer length scales both uid phases, liquid and gas. Such vigorous micro-mixing is triggered by a radial implosion of the gas into the liquid stream which causes the formation of bubbles within it. 23 As the bubbles recirculate in the liquid interior and move forward with the main current the fragment the liquid bulk thus originating the threads. 23,29,33–35 Thus, this approach is suitable for the processing of viscous, polymer solutions. Although ow blurring atomization has been performed with water and other Newtonian liquids, its use for production of micro/nanobers remains largely unexplored. Furthermore, we used computational uid dynamics (CFD) simulations as guidance to study the evolution of polymeric solution's ejection patterns and fragmentation, followed by bers' production under different ambient conditions. Herein we used poly(vinyl alcohol) (PVA) as the test polymer due to its ease to dissolve in common solvents such as water or water/ ethanol mixture, and because of its immense range of applications. 36 Furthermore, we delve into the physics underlying the critical ejection process, which dictates the inception of liquid threads leading to ultrane bers. 2. Experimental methods 2.1 Materials and preparation of solutions Poly(vinyl alcohol) (PVA, Mowiol 40–88, CAS: 9002-89-5) of average molecular weight of 205 000 g mol −1 was purchased from Sigma-Aldrich and used as received, without further purication. Water (Wasserlab, Type II, Analytical grade) and ethanol (PanReac, 99.5% v/v, CAS: 64-17-5) were used as solvents. The solutions were prepared by adding a previously weighted mass of PVA powder to a water/ethanol mixture (water mass fraction, c w =0.35) to result in a PVA concentration of 6 wt%. Subsequently, the solution was stirred using a hot plate (Corning PC-420D) until it became homogeneous and transparent. Mild heating was applied during the stirring process to facilitate polymer dissolution. To ensure uniform heating during stirring, the solution was submerged in a water bath. Once the stirring process was nished, the solution was allowed to cool to room temperature before using it in atomization experiments. 2.2 Density, surface tension, and viscosity measurements The density of the PVA solution was obtained by weighting a known volume of solution and was found to be 885.3 kg m −3 . The surface tension of the polymeric solution in air was measured with a KSV Instruments' contact angle meter (model CAM100) set up in a pendant drop conguration for static measurements in the range 0–180°. The instrument is equipped with a FireWire video camera module with a resolution of 640 × 480 pixels and with a light-emitting diode, monochromatic, light source. The objective lens provided with the camera is telecentric with a 55 mm focal length. The instrument's so- ware applies a curve tting using the Young–Laplace equation to calculate surface tension, which in this case was found to be 0.0324 N m −1 . The solution viscosity was characterized using a TA Instruments rheometer (Discovery HR-3) with cone–plate conguration with a gap of 52 mm. The cone angle and the plate diameter were 2.009° and 60 mm, respectively. Temperature control is achieved using a Peltier plate equipped in the instrument. The zero-shear viscosity, m 0 , was taken as the viscosity at the lowest shear rate measured (25 Pa s). The viscosity measurements were performed at room temperature and ambient relative humidity (in the range of 50–60%). 2.3 Experimental setup for microber production Fig. 1a depicts the experimental setup consisting of a tubular furnace (Carbolite Gero TF1-1200) equipped with a ceramic tube and a FB nebulizer (Ingeniatrics Tecnolog´ ıas, Seville, Spain). A cylindrical, metallic mesh, formed by galvanized wires (Fig. 1b), was placed in the interior of the ceramic tube to collect the brous material and provide it with structural support. The tubular furnace has a maximum operating temperature of 1200 °C. Nevertheless, in our experiments the operating temperature ranged from 150 °C to 600 °C. Such range corresponds to the nominal furnace temperature (T f ), which is higher than the real temperature (T r ) in the interior of the ceramic tube. Two temperature proles along the lube length are presented in Fig. 1c to highlight such difference and to quantify T r in the tube. As shown in the graph, there is a zone with a length of 20 cm in the central part of the furnace where the temperature is nearly-constant. The temperature gradient from the tube's center to its extremes is caused because of both ends are open (to allow for a free gas ow) and not thermally insulated. 18512 |RSC Adv.,2023,13,18511–18524 © 2023 The Author(s). Published by the Royal Society of Chemistry RSC Advances Paper Open Access Article. Published on 20 June 2023. Downloaded on 9/4/2023 4:45:03 PM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online The ceramic tube had inner and outer diameters of 7.4 cm and 8.4 cm respectively, and a length of 80 cm. The Flow Blurring atomizer consists of two concentric tubes, with the inner one carrying the liquid and the outer one carrying the gas. It is characterized by its nominal orice diameter D= 1200 mm and gap H=250 mm, thus resulting in a F=H/D= 0.21 (Fig. 2a). It has two inlets, one for the 6 wt% PVA solution and the other for the gas (air) ow. The air overpressure (DP g ) was measured with a digital manometer (Digitron 2026P) to deliver a specic gas ow rate (Q g ) measured by a digital ow meter (Red-y compact series, Vögtlin Instruments) as indicated in Fig. 1. The polymer solution was supplied pneumatically by feeding pressurized air into a hermetic, liquid container. The liquid ows through a polyamide tube with outer diameter 4 mm, inner diameter D i =2.5 mm, and length L=0.88 m. The liquid ow rate, Q l , was thus controlled by adjusting the overpressure in the liquid container, DP l , together with the gas overpressure DP g . The FB atomizer's unique geometry causes the gas ow to collapse radially inward towards the liquid stream coming from the liquid feeding tube at the atomizer discharge zone (Fig. 2a). As a result, a stagnation region is formed at the discharge of the liquid feeding tube, where the pressure exceeds that of the outer ambient environment P a equal to a fraction of DP g . Regarding the experimental procedure, the FB atomizer was positioned at the furnace entrance. As a result, the polymer laments, once ejected, passed through the ceramic tube where the applied heat facilitated rapid solvent evaporation. Depending on the liquid ow rate and furnace temperature, the laments could either fully dry in-ight, resulting in ber formation, or undergo partial drying. In the former case, solid bers would impact both the mesh's wall, which runs parallel to the main ow direction, and the end wall, perpendicular to the ow direction. Conversely, if the laments only partially dried, wetted bers may impact both walls of the mesh, completing their drying process aer landing. Once the atomization experiment concluded, the mesh was carefully removed from the furnace to prevent potential thermal degradation of the bers. When detaching the brous material from the mesh collector, it is crucial to differentiate between material deposited on the mesh's lateral wall and that deposited on the crosssection of the outlet zone (refer to Fig. 1b). All experiments were conducted under atmospheric conditions at an average ambient temperature of 25 °C and relative humidity of 45%. 2.4 CFD simulations 2.4.1 Mesh geometry. CFD simulations have been carried out to further understand the physics of the micro-mixing phenomenon occurring in the interior of the ow blurring atomizer. The geometry used for the simulations was selected based on the specications of the manufacturer and on an image of a 3D tomography image of a typical FB atomizer. The resulting mesh is depicted in Fig. 2b and was generated using a structured mesh approach. In these simulations, the atomizer is characterized by an inner diameter D=0.7 mm and the geometrical parameter F=0.14. This is to ensure that the studies capture the essence of the phenomenon considering that the upper bound limit for the micro-mixing to take place is F=0.25. Otherwise, the operation regime may shifrom the micro-mixing in the FB regime towards the so-called Flow Focusing regime. 23 Also, notice that the discharge zone, where the laments develop, was modelled large enough not only to capture the ejections, but also to observe possible interactions among themselves. A 3D structured mesh composed of 2 454 027 tetrahedrons was implemented for simulations. Thin elements were positioned in regions where the micro-mixing and the ejections Fig. 1 (a) Experimental setup, (b) sketch of metallic mesh for fiber collection, and (c) furnace temperature profile. © 2023 The Author(s). Published by the Royal Society of Chemistry RSC Adv.,2023,13,18511–18524 | 18513 Paper RSC Advances Open Access Article. Published on 20 June 2023. Downloaded on 9/4/2023 4:45:03 PM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online occur. Conversely, the size of elements at positions away from those regions of interest is considerably larger to decrease the computational cost without incurring in gross solution errors. The mesh quality was assessed using two the so-called orthogonal quality and skewness. Both of these parameters exceeded 0.9 and were lower than 0.5, respectively, in the regions of high interest, namely the micro-mixing zone and the discharge zone. These values indicate a highly reliable mesh in those critical areas. The simulation was conducted for a sufficient duration to allow the phenomenon to reach a steady state, in which the underlying rules governing the micro-mixing and ejection phenomena appeared to remain consistent over time, considering the inherently chaotic nature of the phenomenon. It is noteworthy to mention that we have extensive experience observing the ejection phenomena with ultra-high-speed cameras. That valuable knowledge is benecial in understanding simulations' results, and in turn, it could be helpful to avoid excessive mesh renements that would otherwise consume computational resources. 2.4.2 Modelling physics. The Navier–Stokes continuity and moment equations were used to study the dynamics of ow blurring atomization of polymer solutions, which are represented by the following expressions: vr vtþV$ðruÞ¼0(1) rvu vtþu$Vu¼VpþV$mVuþVuTþdzzfsðV$nÞn (2) Here, u=(u,v,w) denotes the velocity eld where u,vand ware the velocity components in the x,yand zdirections, respectively; tdenotes time; and pis the pressure eld. The third term on the right-hand side of eqn (2) refers to the interface zone. This term is a delta-type function whose value is non-zero only at the interface between the gas and liquid, that is, when z=z f , thus allowing to represent the effect of the curvature at the interface, normal to the surface of the two uids. Additionally, Fig. 2 (a) Sketch of a 2D cross-sectional view of FB atomizer; D=700 mm and H=100 mm; (b) structured mesh for CFD simulations. Fig. 3 Images of CFD simulations of water atomization. (a) So-called turbulent flow focusing with DP g =200 kPa. Flow blurring with DP g = 350 kPa: (b) bubbly flow in the interior of the liquid; (c) perspective view of the FB regime, (d) cross-sectional view just upstream of the outlet of the liquid feeding tube; (e) lateral view of the FB regime. The color scale represents the volume fraction of both phases, red: a l of water =1, and blue: a g of air =1. 18514 |RSC Adv.,2023,13,18511–18524 © 2023 The Author(s). Published by the Royal Society of Chemistry RSC Advances Paper Open Access Article. Published on 20 June 2023. Downloaded on 9/4/2023 4:45:03 PM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online the gravity effect has been neglected because the Bond number Bo =r l gD 2 /sin our system is below unity, where r l and sare the density of the liquid and its surface tension respectively. The solution of the problem has been tackled using the commercial CFD soware, ANSYS Fluent®. The PISO scheme is used to solve the pressure–velocity coupling. Within the spatial discretization, the Green-Gauss Node Based Model is used and the PRESTO! method has been selected for the resolution of the pressure terms. Additionally, a second-order upwind scheme has been selected for the momentum resolution and the transient problem has been formulated following a Bounded Second Order Implicit Scheme. High order term relaxation has been used to achieve a faster convergence and VOF solution stability controls was activated to avoid oscillations and divergence phenomena during training. Furthermore, a variable time step was selected based on the Courant–Friedrichs– Lewy (CFL) number, which controls the convergence comparing the temporal and spatial feedforward. CFL number was xed at a value of 2, giving a timestep of the order of 10 −8 seconds. The inlet conditions were specied as Pressure Inlet for both the gaseous and liquid phases. The discharge zone was dened as aPressure Outlet at ambient, atmospheric pressure and no suction conditions. Finally, when simulating FB atomization of polymeric solutions, a power-law viscosity model was implemented to consider the shear-rate dependant viscosity. The multiphase system was modelled using the volume-of- uid (VOF) framework, which is a surface-tracking technique applied to a xed Eulerian mesh. It was designed to study the Fig. 4 Sequential frames of CFD simulations of PVA solution atomized in the FB regime. DP l =200 kPa, DP g =300 kPa. The atomizer 2D geometry is depicted in inset 4. The color bar represents aof both phases, red: a l of PVA solution =1, and blue: a g of air =1. Fig. 5 Sequential frames of CFD simulations of PVA solution atomized in the FB regime. DP l =200 kPa, DP g =330 kPa. The atomizer 2D geometry is depicted in inset 4. The color bar represents aof both phases, red: a l of PVA solution =1, and blue: a g of air =1. © 2023 The Author(s). Published by the Royal Society of Chemistry RSC Adv.,2023,13,18511–18524 | 18515 Paper RSC Advances Open Access Article. Published on 20 June 2023. Downloaded on 9/4/2023 4:45:03 PM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online position of the interface between immiscible uids. VOF is a multiscale approach with a wide range of applications including the prediction of jet breakup, the motion of bubbles in a liquid, and the steady or transient tracking of liquid–gas interfaces. In this work, the VOF framework was implemented to study the evolution of the interface between the polymer solution and air as a result of their mixing at the micrometer length scale. The tracking of the interface between the two uid phases was accomplished by the solution of a continuity equation for the volume fraction of the liquid. This equation has the following form, 1 rlv vtðalrlÞþV$ðalrluÞ¼m a/lm l/a;(3) where _ m l/a is the mass transfer rate from the liquid to the gas phase, _ m a/l is the mass transfer rate from the gas to the liquid phase, and a l is the volume fraction of the liquid phase. The volume fraction of the gaseous phase (a g ) was computed with a l +a g =1. The density (r) and the viscosity (m) of the uid mixture are assumed to depend on the volume fraction as: r=a g r g +a l r l , m=a g m g +a l m l , where m g is the viscosity of the gaseous phase. To cope with the turbulent ow and the viscous effects taking part in the formation of inner bubbles and subsequent lament ejections 23,24,32,33 the LES (large eddy simulation) model was selected. In LES, large eddies are resolved directly using the Navier–Stokes equations, while small eddies are resolved applying a Reynolds-Averaged-Navier–Stokes (RANS) model. The main feature of the LES model is the ability to spatially lter small-scale phenomena, which is performed by the following expression: fðxÞ¼ðF fx0Gx;x0dx0 where Fdenotes the uid domain, Gis the lter function that determines the scale of the resolved eddies, f(x ′ ) is the actual value of the ow variable, and f(x) is the ltered ow variable. 35 The subgrid-scale stresses are computed from: sij 1 3skkdij ¼2mtSij where  S ij is the rate-of-strain for the resolved scale and m t is the subgrid-scale turbulent viscosity, which was modelled using the Smagorinsky–Lilly model, mt¼rLs2ffiffiffiffiffiffiffiffiffiffiffiffiffi 2SijSij q where L s is the mixing length for subgrid scales, which is computed with L s =min(k×d,C s ×D) where kis the von K´ arm´ an constant (typically 0.4), dis the distance to the closest wall, C s is the Smagorinsky–Lilly constant and Dis the local grid scale. C s is used to adjust the magnitude of subgrid-scale turbulence, which was determined to be 0.23 for Fig. 6 Transformation mechanisms during ejection of polymer solution threads. (a) elongation, (b) droplet to filament, and (c) ejection. Red indicates a l =1, and blue indicates a g =1. Table 1 Characteristic velocity and liquid vein diameter calculated with scaling laws Case DP g (kPa) r l (kg m −3 )Q l (L h −1 )U*(m s −1 )L*(mm) 1 300 885.3 3.041 18.408 214.225 2 330 885.3 1.615 19.307 152.430 Fig. 7 Characteristic values obtained from simulations for PVA with DP l =200 kPa and DP g =300 kPa (a and b); and DP g =330 kPa (c and d). Images on the left side are velocity contour plots and those on the right side are volume fraction contour plots. 18516 |RSC Adv.,2023,13,18511–18524 © 2023 The Author(s). Published by the Royal Society of Chemistry RSC Advances Paper Open Access Article. Published on 20 June 2023. Downloaded on 9/4/2023 4:45:03 PM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online homogeneous isotropic turbulence within the inertial subrange. However, it was observed that this value resulted in excessive damping of large-scale uctuations in the presence of mean shear and in transitional ows near solid boundaries, and it needs to be reduced in such regions. A value of approximately 0.1 yields optimal results for a broad range of ows, and this value is the default option in ANSYS Fluent®, and thus it was employed in this study too. 35,37 3. Results and discussion 3.1 Computational results 3.1.1 CFD model validation. FB atomization of lowviscosity, Newtonian liquids has been studied extensively both theoretically and experimentally by us and others. 23,29,30,38 From the seminal work of Gañ´ an-Calvo, 23,30,38 several authors have reported direct observations of the formation of bubbles in the interior of the liquid feeding tube, in the surrounding of its tip, which is considered the main feature of this type of liquid atomization. 25,33–35,39,40 Such knowledge of the technique as well as our experience identifying various underlying phenomena 23,29,31,38,41 allow us to use simulations as a solid tool to interrogate more complex systems. Therefore, to validate our computational approach for polymer solutions, rstly, simulations of FB atomization of water were carried out. In these set of simulations, the liquid overpressure (DP l ) was set at 200 kPa while the gas overpressure (DP g ) was varied to study its effect on the atomization dynamics. Here, we present two cases: DP g = 200 kPa and DP g =350 kPa. In the rst case, despite the geometrical constrain F< 0.25, which dictates whether the micro-mixing occurs, the gas overpressure is not sufficiently high so as to implode into the liquid feeding tube. As a result, a gas cavity and inner bubbles are not formed and thus the micro-mixing is not triggered. As depicted in Fig. 3a, in this case, a surface-disturbed liquid jet is ejected, which corresponds to the regime known as Turbulent Flow Focusing (TFF 30 ). Under these conditions, a nearly axial liquid vein (red color) surrounded by a liquid mist composed of droplets is ejected. Also, the conical shape of the ejection is remarkable thus representing the dynamics of TFF reported theoretically by us. 30 By increasing the gas overpressure to 350 kPa, the ow blurring regime is achieved (Fig. 3b–e). Particularly, the perspective view of Fig. 3b depicts inner bubbles (blue color) in the interior of the tube. In this case, the DP g is sufficiently high to implode into the liquid feeding tube and produce the inner gas cavity, thus triggering the micro-mixing mechanism. Furthermore, a cross-sectional view (Fig. 3d) at a position just upstream of the liquid feeding tube's outlet evidences the presence of numerous inner bubbles not only in the vicinity of the walls, but also in positions close to the central axis of the tube. The bubbles introduce a turbulence component into the liquid, which causes the mixing at micrometer length scales that leads to the formation of a polydisperse aerosol. The formation of bubbles in the atomizer interior is the main characteristic of the ow blurring regime as reported by us and others. 23,30,34,35 Rather than a liquid vein surrounded by droplets as in the TFF (Fig. 3a), in this case, the outcome is a ne aerosol. In this situation, the development of a boundary layer appears to be responsible for the formation of a thin air layer between water and the tube wall. 24 Note that the simulation captured the recirculation of the gas ux observed by us and other authors, 42,43 which is indicated by the presence of a bubble (mainly green color) in the center of the liquid feeding tube (Fig. 3e). The qualitative results presented here agree with the physical characteristics of ow blurring atomization process Fig. 8 Velocity fields values obtained from simulations for PVA with DP l =200 kPa and DP g of (a) 300 kPa; (b) 330 kPa. Table 2 Summary of experimental conditions DP g (bar) Q g (L min −1 )DP l (bar) Q l (mL h −1 )T f (°C) T r (°C) Set 1 1.30 20 1.1 68.18 300 195 0.82 15 0.71 50.37 1.80 25 1.43 38.17 2.29 30 1.82 34.96 Set 2 0.82 15 0.71 50.37 150 75 300 195 450 315 600 435 © 2023 The Author(s). Published by the Royal Society of Chemistry RSC Adv.,2023,13,18511–18524 | 18517 Paper RSC Advances Open Access Article. Published on 20 June 2023. Downloaded on 9/4/2023 4:45:03 PM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online that are reported in the literature. 23,24,32 It is important to emphasize that such bubble can be observed in both Fig. 3c and d, as they represent the same timestep from perspective and lateral views, respectively. The phenomenon is similar to that of Fig. 3b, where all internal bubbles are distinctly highlighted in blue. It is noteworthy to mention that in these simulations the bubbles do not consist entirely of air in the majority of cases. This is evident in Fig. 3d, where a lateral bubble exhibits a predominantly blue color (indicating a predominantly air- lled composition), while other greenish regions likely represent smaller bubbles. Owing to limitations in mesh resolution, the precise denition of bubble edges is not achieved, resulting in the simulation depicting these areas as regions with an approximate air-to-liquid volumetric fraction ranging from 40% to 60%. In spite of that, the simulations capture the essence of the phenomenon, and we thus conclude that the model is adequate to proceed with simulations of ow blurring atomization of polymer solutions as well as to obtain valid qualitative and quantitative results. 3.1.2 Simulations of PVA solutions' atomization in the ow blurring regime. For the simulation of ow blurring atomization of a 6 wt% PVA solution in water and ethanol (water mass fraction c w =0.35) a power-law viscosity model was implemented to take into account the shear-rate dependant viscosity that characterizes the non-Newtonian behavior of the polymer solution. The approach is similar to that of water (the mesh is the same): the PVA overpressure, DP l was xed at 200 kPa, while the gas overpressure was varied. Here, we present results for two cases: DP g =300 kPa (Fig. 4) and DP g =330 kPa (Fig. 5). There exist key differences between atomization of PVA and that of water. For instance, rather than a gas cavity, in the PVA cases the air stream envelops the liquid jet and causes the diameter of liquid stream to reduce as it proceeds forward, out of the liquid feeding tube. Furthermore, a thin liquid column is ejected in both PVA cases, which downstream breaks up producing liquid laments. This behavior was indeed observed by Ramos-Escobar et al. 24 and Mar´ ın-Brenes et al., 44 using PVA and poly(ethylene oxide) solutions. Comparison of simulations of both PVA cases evidences the effect of DP g or decreasing Q l . For lower DP g , the ejected liquid column appears to have a larger characteristic diameter and travels further before it breaks up. The sequential frames of Fig. 4 depict a continuous liquid vein that appears to move in a chaotic fashion driven by the turbulence, and lament fragmentation is not observed. Conversely, rising the gas overpressure DP g leads to an ejection of a thinner liquid column, which rapidly breaks up producing lament-like ejections in a chaotic and turbulent fashion, as shown in the frames of Fig. 9 Fiber diameter distribution for varying Q l [mL h −1 ] of (a) 68.18, (b) 50.37, (c) 38.17, and (d) 34.96.  d f is the geometric mean diameter and s g is the geometric standard deviation. 18518 |RSC Adv.,2023,13,18511–18524 © 2023 The Author(s). Published by the Royal Society of Chemistry RSC Advances Paper Open Access Article. Published on 20 June 2023. Downloaded on 9/4/2023 4:45:03 PM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online Fig. 5, particularly from frame 5 onwards. Rising DP g equals to increasing the available energy to induce liquid lament thinning and its subsequent break up. In FB atomization, DP g in combination with DP l regulate the liquid ow rate, which implies that, in general, for a given liquid overpressure a higher gas overpressure results in a lower Q l . These simulations represent well direct observations reported by Modesto-L´ opez et al., 32 Ramos-Escobar et al., 24 and Mar´ ın-Brenes et al. 44 and conrm that for polymer solutions, in the FB regime, a lower liquid ow rate produces several, dispersed laments, while increasing the liquid ow rate produces a continuum structure. As the liquid structures move downstream, they undergo diverse transformations led mainly by inertio-capillary phenomena. 24,44 Such mechanisms, described by Ramos- Escobar and others 24 distinguish between those involving a single uid entity and those related to two or more liquid structures' interactions. Several of those transformations are present in our CFD simulations herein. Fig. 6a depicts the socalled elongation phenomenon where a relatively thick liquid lament is elongated by means of inertia leading to a thinner structure. The transition from droplet to a lament due to inertia-capillary forces is clearly depicted in Fig. 6b similar to that captured by the high-speed recording of Ramos-Escobar et al. 24 Furthermore, Fig. 6c captures the collision of an upcoming lament with a droplet leading to a new ejection, which later develops into a lament with two small spheres at both ends (see Fig. 5 of ref. 31). The liquid ejection's velocity in the vicinity of the liquid discharge region (U*) and the as-ejected liquid vein's diameter (L*) strongly inuence the evolvement of the liquid laments. A scaling analysis was used to propose an equation for U*based on operation parameters: 24 U* DPg rl1=2 (4) Additionally, in the atomizer interior the Reynolds number was assumed to be Re [1 and Bo 1, which makes it reasonable to neglect gravity effects. Furthermore, in the current case, in which either the liquid ow rate or the viscosity are large enough to prevent the formation of the gas cavity, the characteristic diameter of the liquid vein L*is assumed to be 24 L* Ql U*1=2 (5) The values of U*and L*calculated with eqn (5) and (6) based on the simulations' conditions are summarized in Table 1. The equivalent values obtained directly through the simulations are indicated in Fig. 7. It is noteworthy to mention that the values obtained in the simulations are of the same order of magnitude as those obtained with the scaling law proposed in Ramos- Escobar et al. 24 Both results, from the simulations and from the scaling law, t very well and thus describe the ejection phenomena with the micro-mixing mechanism accurately. Looking at the characteristic diameters, the trend represented by the scaling law indicates that increasing the liquid ow rate produces thicker liquid veins. This phenomenon is also shown in the CFD simulations and can be observed directly in the color plots (Fig. 7). Although the frames shown in Fig. 7 were chosen arbitrarily, the orders of magnitude were veried in several frames to add condence to the results. The liquid ejection velocities away from the exit orice are shown in Fig. 8. Notice the high acceleration that the liquid vein experiences in such region, increasing its velocity from nearly 10 m s −1 to 100 m s −1 in a distance no longer than 5 mm. Furthermore, the order of magnitude of the velocities represented here are consistent with those reported in Modesto- L´ opez et al. 32 measured from ultra-high speed videos which were of the order of 80–100 m s −1 . In order to obtain quantitative data of the laments' diameter downstream of the ejection orice, where the liquid jet has already evolved, measurements were performed using the so- ware ImageJ. 45 Approximately 50% of all measurements were in the range of 40–90 mm while the remaining 50% were in the range of 90–180 mm. Therefore, roughly, a characteristic Fig. 10 Diameter distribution for different T r : (a) 75 °C, (b) 195 °C, (c) 315 °C, and (d) 435 °C. d f represents the geometric mean diameter and s g is the geometric standard deviation. (e) Fibers' geometric mean diameter as a function of real furnace temperature, T r (the green dotted line is to guide the eye only). © 2023 The Author(s). Published by the Royal Society of Chemistry RSC Adv.,2023,13,18511–18524 | 18519 Paper RSC Advances Open Access Article. Published on 20 June 2023. Downloaded on 9/4/2023 4:45:03 PM. This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. View Article Online