**1. Introduction**

In 1969, polyvinylidene fluoride (PVDF) was first reported as thermoplastic polymer piezoelectric material (PEM) exhibiting the piezoelectric activity [1]. PVDF based PEMs are classified as stimuli responsive materials and have been employed as standalone or as matrices in composites and layered structures to fabricate stimuli responsive systems for applications such as drug delivery and tissue engineering [2–4]. One of the applications of PVDF based PEMs is intelligent clothing to sense user activities in sports and personalized health care [5–7]. As the precursor for textiles is yarn, which is produced from fibres, various fabrication methods have been employed to produce fibres, such as gas jet spinning, nozzle-free centrifugal spinning, rotary jet spinning, melt blow spinning and

flash-spinning [8,9]. Out of these, electrospinning has been extensively used for the fabrication of fibres; however, it has some limitations. Firstly, it can only be used for polymer systems that are electrically conductive, and secondly, formation of a high fraction of β-phase (which has the highest piezoelectric response) is dependent on very high electric field making the process a safety hazard [10]. As there is electric field involved, it also requires the use of conductive collectors. It also has low yield making it a laborious process and unfit for scale-up demands.

SBS has emerged as an alternative technique to produce sub-micron/nano sized fibres and can relieve the user of the limitations posed by electrospinning. In SBS, a polymer is dissolved into a suitable solvent to reduce its viscosity as thin fibres cannot be produced with very viscous polymer melt [11,12]. The solution is then injected through a nozzle which is surrounded by a concentric outer pipe from which air is purged out. The solution interacts with the air and forms short fibres which fall on a collector. The advantage of SBS is that it can be applied to both electrically conducting and insulating systems and does not require the application of electric field and conductive collectors to initiate fibre processing [13,14]. Moreover, the yield of fibre production is about hundred times higher than that of electrospinning making it suitable for industrialisation [15,16]. The nozzle design is very critical in SBS as it significantly a ffects the airflow field distribution, the air velocity and morphology of the final product [17]. If the internal diameter of nozzle is too large, outsized droplets will be produced resulting in fibres with larger diameters. Similarly, a very small orifice will reduce the throughput, however, it has the potential of producing thin fibres.

The influence of the protrusion length of the polymer solution syringe on fibre dimensions was found to be insignificant [17]. Lou et al. [18] also reported that the e ffect of protrusion length has insignificant e ffect on the fibre morphology. They used four di fferent protrusion lengths: 4, 2, 0 and −2 mm (minus sign shows that the syringe was retracted from the nozzle end by a distance of 2 mm). They reported that the air velocity reaches a maximum in the vicinity of 10–20 mm below the nozzle face. The maximum air velocities were in the range of 170–180 m/s. However, based on practical experiments, they reported that the retracted nozzles resulted in intermittent process with polymer solution blocking the nozzle end. The protruded syringe could produce fibres without such deficiencies.

The attenuation force in solution blow spinning (SBS) is pressurized air and various computational methods have been employed to numerically investigate the influence of air pressure and velocity on the fibre morphology [19–21]. The laminar flow model is considered as the simplest of all available models while the k-ε turbulence model is one of the most commonly used models in computational fluid dynamics (CFD) to simulate mean flow characteristics for turbulent flow conditions with more rapid convergence [18,22]. The k-ε turbulence model is e ffective for solving problems involving reverse flow [12,23]. It is a semi-empirical model based on model transport equations for the turbulence kinetic energy (*k*) and its dissipation rate (ε). Neglecting gravitational e ffects, the transport equations for the *k*-<sup>ε</sup> turbulence model are given below [18,24]:

$$\frac{\partial(\rho k)}{\partial t} + \frac{\partial(\rho k u\_i)}{\partial \mathbf{x}\_i} = \frac{\partial}{\partial \mathbf{x}\_j} \left[ (\mu + \frac{\mu\_l}{\sigma\_k}) \frac{\partial \mathbf{k}}{\partial \mathbf{x}\_j} \right] + 2\mu\_l \left( \frac{\partial u\_i}{\partial \mathbf{x}\_j} + \frac{\partial u\_j}{\partial \mathbf{x}\_i} \right) \frac{\partial u\_i}{\partial \mathbf{x}\_j} - 2\rho \varepsilon M\_t^2 \tag{1}$$

$$\frac{\partial(\rho\varepsilon)}{\partial t} + \frac{\partial(\rho\varepsilon u\_i)}{\partial \mathbf{x}\_i} = \frac{\partial}{\partial \mathbf{x}\_j} \left[ (\mu + \frac{\mu\_l}{\sigma\_\varepsilon}) \frac{\partial \varepsilon}{\partial \mathbf{x}\_j} \right] + 2\mathsf{C}\_{\varepsilon1}\frac{\varepsilon}{k}\mu l \left( \frac{\partial u\_i}{\partial \mathbf{x}\_j} + \frac{\partial u\_j}{\partial \mathbf{x}\_i} \right) \frac{\partial u\_i}{\partial \mathbf{x}\_j} - \mathsf{C}\_{\varepsilon2}\rho\varepsilon \left( \frac{\varepsilon}{k} + 1 \right) \tag{2}$$

where ρ is density kg/m3, *k* is turbulent kinetic energy m<sup>2</sup>/s2, *t* is time s, *ui* and *uj* are velocity fluctuations in the *i*th and *j*th directions, respectively, μ is viscosity kg/(m.s), μ*t* is turbulent viscosity kg/(m.s), σ*k* and σε are turbulent Prandtl numbers for the kinetic energy and the dissipation rate, respectively, ε is dissipation rate of turbulent kinetic energy, *Mt* is turbulent Mach number, *C*ε<sup>1</sup> and *C*ε<sup>2</sup> are parameters for *k-*ε turbulence model. The flow characteristics for solution blow spinning process have ye<sup>t</sup> not been studied in detail. For example, when air is passed through the air inlet and moves towards the nozzle tip, whether the nozzle will ge<sup>t</sup> choked or not and what will be the influence of choking on the fibre morphology have ye<sup>t</sup> not been reported. A nozzle is choked when the maximum mass flow rate has been reached [25]. Any additional increment in pressure will result in an increase in chamber pressure. Internally the pressure might increase to a value in excess of the rated mechanical strength of the nozzle material which will result in catastrophic failure of the device. Externally of the nozzle, an increase beyond choked conditions can lead to shock wave formation in the nozzle wake. If fluid coming out of the nozzle cannot expand isentropically due to choking an irreversible discontinuity arises called shockwave [26,27]. The shockwave is an abrupt disturbance that causes discontinuous and irreversible changes in fluid characteristics such as speed, density, temperature, and pressure. As a result of the gradient in temperature and velocity being caused by the shock, heat is transferred, and energy is dissipated within the gas. These processes are thermodynamically irreversible [28]. As the nozzle design and the attenuation force (pressurized air) are of utmost importance in SBS, both numerical (CFD) and experimental methods were used to investigate the fibre formation. CFD was used to investigate the convergence point for high speed air as it comes out of the nozzle. The polymer solution syringe was positioned such that it did not choke due to the reversal of air flow. The produced fibres did not show any bead formation at higher pressure values indicating that optimized SBS can successfully produce submicron PVDF fibres.
