*2.5. Characterization*

CFD was carried out in ANSYS Fluent v19 (ANSYS Inc., Canonsburg, PA, USA). For the CFD simulation, a solid enclosure was built around the nozzle with zero shear slip and meshed consisting of 793,731 nodes and 3,355,960 elements. A steady-state, compressible Navier–Stokes equations was used whose component forms for continuity, x-momentum, y-momentum, z-momentum, and energy are given below, respectively, where *p* is pressure, q is heat flux, *u*, *v*, and *w* are velocity components, ET is total energy, Re is Reynolds number, and Pr is Prandtl number.

$$\frac{\partial(\rho u)}{\partial x} + \frac{\partial(\rho v)}{\partial y} + \frac{\partial(\rho w)}{\partial z} = 0 \tag{3}$$

$$\frac{\partial(\rho u^2)}{\partial \mathbf{x}} + \frac{\partial(\rho uv)}{\partial y} + \frac{\partial(\rho uw)}{\partial z} = -\frac{\partial p}{\partial \mathbf{x}} + \frac{1}{\text{Re}} \left[ \frac{\partial \tau\_{xx}}{\partial \mathbf{x}} + \frac{\partial \tau\_{xy}}{\partial y} + \frac{\partial \tau\_{xz}}{\partial z} \right] \tag{4}$$

$$\frac{\partial(\rho uv)}{\partial \mathbf{x}} + \frac{\partial(\rho v^2)}{\partial y} + \frac{\partial(\rho vw)}{\partial z} = -\frac{\partial p}{\partial y} + \frac{1}{\text{Re}} \left[ \frac{\partial \tau\_{xy}}{\partial \mathbf{x}} + \frac{\partial \tau\_{yy}}{\partial y} + \frac{\partial \tau\_{yz}}{\partial z} \right] \tag{5}$$

$$\frac{\partial(\rho uw)}{\partial \mathbf{x}} + \frac{\partial(\rho vw)}{\partial y} + \frac{\partial(\rho w^2)}{\partial z} = -\frac{\partial p}{\partial z} + \frac{1}{R\varepsilon} \left[ \frac{\partial \tau\_{xz}}{\partial \mathbf{x}} + \frac{\partial \tau\_{yz}}{\partial y} + \frac{\partial \tau\_{zz}}{\partial z} \right] \tag{6}$$

$$\begin{split} \frac{\partial (\mu \mathbf{F})}{\partial x} &+ \frac{\partial (\upsilon \mathbf{F} \mathbf{r})}{\partial y} \\ &= -\frac{\partial (\upsilon p)}{\partial x} - \frac{\partial (\upsilon p)}{\partial y} - \frac{\partial (\upsilon p)}{\partial z} - \frac{1}{RePr} \left[ \frac{\partial q\_x}{\partial x} + \frac{\partial q\_y}{\partial y} + \frac{\partial q\_z}{\partial z} \right] \\ &+ \frac{1}{Re} \left[ \frac{\partial}{\partial \mathbf{X}} (\mu \tau\_{xx} + \nu \tau\_{xy} + \nu \tau\_{xz}) + \frac{\partial}{\partial \mathbf{y}} (\mu \tau\_{xy} + \nu \tau\_{yy} + \nu \tau\_{yz}) \\ &+ \frac{\partial}{\partial z} [\mu \tau\_{xz} + \nu \tau\_{yz} + \nu \tau\_{zz}] \right] \end{split} \tag{7}$$

The closure models used were the ideal gas model for density and the Sutherland equation for viscosity. The constants used were for air and mentioned below:

$$
\mu = \mu\_0 \left(\frac{T\_0 + C}{T + C}\right) \left(\frac{T}{T\_0}\right)^{3/2} \tag{8}
$$

where, *T*0 is reference temperature (K), μ0 is reference viscosity (1.716 × 10−<sup>5</sup> kg/m.s) at the reference temperature *T*0 (273 K), *T* is e ffective temperature (110 K), and *C* is Sutherland's constant for given gaseous material. The outlets were all specified as pressure far-field outlets. The inlet to the nozzle was a pressure inlet and remainder were all no-slip wall boundaries. Both laminar and k-ε turbulent simulations were carried out. Although the flow field is inherently turbulent, laminar flow was investigated as a steppingstone and was used to compare the results with turbulent flow simulation. The laminar results are not shown here but can be viewed in the Supplementary Materials (Figures S1–S22). A scanning electron microscope (JSM-6010LV-SEM, JEOL, Tokyo, Japan) was used to investigate the morphology of the produced fibres. Fibre diameter was analysed using Image-J software, average fibre diameter distribution was detected by measuring the distance across fibre boundaries at di fferent imaging scales to ensure consistency.

### **3. Results and Discussion**

Under both laminar and k-ε turbulent flow conditions, a reverse flow was observed in the vicinity of polymer solution syringe outlet as shown in Figure 5. If a polymer solution droplet gets trapped by this reverse flow, there is high possibility that it will not move forward and will choke the syringe/nozzle. This supposition is further supported by the experimental observations reported by Lou et al. [18] who found that the retracted nozzle resulted in an intermittent process with polymer solution blocking the nozzle end. They also reported that the best morphology of fibres was produced when polymer syringe was protruded out by 4 mm.

**Figure 5.** Reverse flow in the vicinity of the polymer solution syringe tip that can choke the syringe.

Velocity, pressure, temperature, turbulent kinetic energy, and density contours at di fferent air pressures are shown in Figures 6 and 7. A magnified set of contours at 4 bar is shown in Figure 8 as the thinnest fibres were produced at that pressure. For clarity of readings large contours have been provided in the Supplementary Materials (Figures S23–S71). Velocity, temperature, and turbulent kinetic energy profiles at six vertical slices (at 0, 1, 4, 6, 16, and 26 mm from the nozzle end) were also calculated and plotted in Figures 9–11, respectively. The values of the parameters and z-velocity were also measured at the horizontal symmetry axis of the geometry and are shown in Figures 12 and 13. They will be referred to as centreline air velocity (*vc*), pressure ( *Pc*), temperature ( *Tc*), turbulent kinetic energy (*TKEc*), and density (ρ*c*) from hereafter.

At 1 bar, *vc* increases quadratically to ~80 m/s at a distance of ~0.7 mm from the air outlet, then slows down due to reverse flow until hits zero, and then shoots up to ~120 m/s at a distance of ~7 mm and then starts to gradually decrease. The exact value of air velocity may change due to polymer solution droplets in the flow field. Due to flow reversal, the *Pc* initially decreases quadratically to <sup>~</sup>−3 kPa at a distance of ~0.5 mm, after which it starts to increase until hits zero at a distance of ~1 mm, saturates at ~3 kPa at a distance of ~1.7 mm, and then gradually flattens out. The minimum *Tc* recorded at ~4 mm was 291 K (18 ◦C) which was 7 K cooler than the ambient temperature which was set at 298 K (25 ◦C). The maximum TKEC was ~1 kJ/kg recorded at ~1.3 mm from the air outlet. Experiments were conducted at 1 bar in order to produce fibres using the setup shown in Figure 3. Despite changing the feed rate between 2 mL/h to 10 mL/h, fibres could not be formed. This was ascribed to that the polymer solution droplets kept falling on the floor just ahead of the nozzle. Therefore, it is believed that air velocity of 120 m/s is not high enough to generate PVDF fibres. Similar trends were observed at 2–10 bars for CFD results; however, fibre morphology was significantly a ffected by air pressure.

**Figure 6.** k-ε turbulence flow contours through SBS nozzle at di fferent air pressures: ( **A**,**B**) velocity (m/s), ( **C**) pressure (Pa), (**a**) 1 bar, (**b**) 2 bar, (**c**) 3 bar, (**d**) 4 bar, (**e**) 5 bar, (**f**) 6 bar, (**g**) 10 bar.

**Figure 7.** k-ε turbulence flow contours through SBS nozzle at different air pressures: (**A**) temperature (K), (**B**) turbulent kinetic energy (J/kg = m<sup>2</sup>/s2), and (**C**) density (kg/m3), (**a**) 1 bar, (**b**) 2 bar, (**c**) 3 bar, (**d**) 4 bar, (**e**) 5 bar, (**f**) 6 bar, (**g**) 10 bar.

Fibres were successfully produced at 2 bar whose SEM image is shown in Figure 14a and diameter distribution in Figure 14b. Fibres with wide distribution of diameters (between 100–900 nm) were observed and it is important to mention that some beads were also observed on these fibres. At 3 bar, relatively thinner fibres (than at 2 bar) as shown in Figure 14c were produced. The fibres were almost defect free with fibre diameters in the range of 140–700 nm (Figure 14d). At 4 bar, Much thin and bead-free fibres were produced as shown in Figure 14e. Most of the fibres were in 100–350 nm range (Figure 14f) and these were the thinnest fibres produced in the current work. The fibres produced at 5 bar were relatively thick as shown in Figure 14g. There were some intertwined fibre ropes observed at 5 bar and diameter of each rope was measured to ge<sup>t</sup> mean fibre diameter of ~1.5 μm (Figure 14h). At 5 bar, there is drop in temperature due to Joule-Thomson effect up to ~251 K (−22 ◦C). This cryogenic environment can produce residual stresses in the fibres that might have caused them turn and twist around each other while either during flight or after hitting the drum collector and resulted in interlocked fibre ropes. The turbulent kinetic energy (Figure 13c,d) continues to rise

with increasing air pressure and velocity and this increased turbulence might be another factor in destabilizing the fibres in flight.

**Figure 8.** k-ε turbulence flow contours through SBS nozzle at air pressure of 4 bar: (**a**) velocity (m/s), (**b**) turbulent kinetic energy (J/kg = m<sup>2</sup>/s2), (**c**) temperature (K), and (**d**) pressure (Pa).

The z-velocity graphs (Figure 12c,d) hit negative values that confirm reverse flow. It is important to mention that the reverse flow is at the tip of syringe, which suggests that the polymer solution needs to be injected forcibly to pass the barrier created by the reverse flow (Figure 12e,f). There is fluctuation in the temperature as well (Figure 13a,b) due to reverse flow. As air leaves the air outlet, the temperature follows a sinusoidal curve dropping at a distance of ~1 mm from the air outlet, which goes up due to reverse flow, then drops again until it hits the lowest value (~193 K (−80 ◦C) at 10 bar) and finally gradually goes up to the room temperature. A similar trend was observed for turbulent kinetic energy (Figure 13c,d) along the positive ordinate.

The density plots (Figure 13e,f) show that the air is less dense at the nozzle opening. Air imposes frictional drag on the moving objects which is approximately proportional to the square of the velocity of the moving object. A decrease in density and viscosity would mean less frictional drag being exerted on the polymer solution droplet through the air flow field which would be able to move faster and will ge<sup>t</sup> thinner under the influence of attenuating force, i.e., high-speed air. The density graphs hit the peak values at ~4 mm from the nozzle end. This increment in density is propitious as it would exert compressive stresses on the fibres thereby resulting in compact fibres.

**Figure 9.** Velocity profiles at six vertical slices (at distance of 0, 1, 4, 6, 16, and 26 mm from the air outlet) for k-ε turbulence flow plots through SBS nozzle at different air pressures: (**a**) 1 bar, (**b**) 2 bar, (**c**) 3 bar, (**d**) 4 bar, (**e**) 5 bar, (**f**) 6 bar, (**g**) 10 bar, and (**h**) maximum velocity values at different air pressures.

**Figure 10.** Temperature profiles at six vertical slices (at distance of 0, 1, 4, 6, 16, and 26 mm from the air outlet) for k-ε turbulence flow plots through SBS nozzle at different air pressures: (**a**) 1 bar, (**b**) 2 bar, (**c**) 3 bar, (**d**) 4 bar, (**e**) 5 bar, (**f**) 6 bar, (**g**) 10 bar, and (**h**) minimum temperature values at different air pressures.

**Figure 11.** Turbulent kinetic energy profiles at six vertical slices (at distance of 0, 1, 4, 6, 16, and 26 mm from the air outlet) for k-ε turbulence flow plots through SBS nozzle at different air pressures: (**a**) 1 bar, (**b**) 2 bar, (**c**) 3 bar, (**d**) 4 bar, (**e**) 5 bar, (**f**) 6 bar, (**g**) 10 bar, and (**h**) maximum turbulent kinetic energy values at different air pressures.

**Figure 12.** k-ε turbulence flow plots through SBS nozzle at different air pressures: (**<sup>a</sup>**,**b**) velocity (m/s), (**<sup>c</sup>**,**d**) z-velocity (m/s), and (**<sup>e</sup>**,**f**) pressure (Pa).

A significant drop in temperature was observed as air comes out of the nozzle. It can possibly be related to the Joule–Thomson effect inducing temperature drops when high speed fluid quickly escapes through a narrow hole [29]. Static temperature drops during the isentropic expansion process and this drop in temperature is even more evident under supersonic flow where temperature can drop down to 213 K (−60 ◦C) without any cryogenic cooling or use of solid adsorption techniques [28]. It has been reported that PVDF solution temperature influences spinnability of PVDF fibres [15]. The drop in temperature can alter viscosity of the polymer solution as viscosity and temperature are inversely related to each other. When temperature of polymer solution is high, its viscosity will be low, and therefore low attenuation force will suffice to ge<sup>t</sup> thin fibres and vice versa. Attenuation force in SBS is high speed air which means that thin fibres can be achieved at relatively low air pressure and velocity. A higher air pressure results in a higher air velocity and turbulent fluctuations. The higher air velocity will result in thinner fibres but turbulent fluctuations may break the fibres [18]. It has been reported that there is a direct relationship between viscosity of polymer solution and mean fibre diameter. Haddadi et al. [30] incorporated hydrophobic and hydrophilic nanosilica into PVDF and reported that mean fibre diameter increased in both cases. They suggested that the viscosity of polymer solution increased by the incorporation of nanofillers which in turn led to an increase in mean fibre diameter. Yun et al. [31] fabricated Pb(Zr0.53Ti0.47)O3 reinforced PVDF nanofibres and reported that both density and viscosity of the polymer solution increased after the incorporation of PZT. The mean fibre diameter increased until 10 wt % and then gradually decreased when volume fraction was further increased up to 30 wt % [31].

**Figure 13.** k-ε turbulence flow plots through SBS nozzle at different air pressures: (**<sup>a</sup>**,**b**) temperature (K), (**<sup>c</sup>**,**d**), turbulent kinetic energy (J/kg = m<sup>2</sup>/s2), and (**<sup>e</sup>**,**f**) density [kg/m3].

**Figure 14.** (**<sup>a</sup>**,**c**,**e**,**g**) SEM results at 2,3,4, and 5 bar air pressures, and (**b**,**d**,**f**,**h**) their respective fibre size distribution.

The *vc* increases at 6 bar and 10 bar to ~400 and ~450 m/s, respectively. Experiments at 10 bar could not be performed due to the limitation of the setup. However, CFD results provide a useful information that the nozzle did not choke up until 10 bar. The effect of shock structures on the fibre formation has not been determined, however it is likely that the rapidly changing conditions before and after the shock will have a detrimental effect on the fibre morphology [32]. To avoid choking, nozzle diameter, feed rate and air pressure must be carefully optimized [32,33].
