**1.2 Mechanism behind electrospinning (ESPNG) of cc/G nanofibers (NFs)**

The process of electrospinning (ESPNG) utilizes an electric field applied to the emitter and a ground terminal to pull back a thread of polymeric solution out of the opening of the emitter. In the process of ESPNG, the Maxwell electrical pressure was set as per ratio, *<sup>V</sup>*<sup>2</sup> *<sup>d</sup>*<sup>2</sup> ; where permittivity was <sup>0</sup> *ε*0 , a high potential power supply was <sup>0</sup> *V*<sup>0</sup> and the electrode spinning gap was shown with <sup>0</sup> *d*0 *:* The critical high potential power supply (*Vc*) was ffiffiffiffiffi *γd*<sup>2</sup> *εR* q , and it must exceeded before any jet could spread out from the needle tip. For, *<sup>γ</sup>* <sup>¼</sup> <sup>10</sup>�<sup>2</sup> *kg=s* 2, *<sup>d</sup>* <sup>¼</sup> <sup>10</sup>�<sup>2</sup> *<sup>m</sup>*, *<sup>ε</sup>* <sup>¼</sup> <sup>10</sup>�<sup>10</sup>*C*<sup>2</sup> *=*ð Þ *Jm andR* <sup>¼</sup> <sup>10</sup>�<sup>4</sup>*m*, a high potential power supply around 10 KV was necessary to form a jet of any type. The polymeric solution of the Laplace condition (utilized in the modeling) in the feeble polarization limit depicts the electrostatics in the fluid stage in an axisymmetric indirect support framework (*r*, *θ*, *ϕ*) with the vertices of the Taylor cone at the source which can be shown using general Eq. (1).

$$\begin{aligned} \, \, \_\text{pr}(r, \theta) &= A\_n r^n P\_n(\cos \theta); \, \_\text{for} \, \theta\_0 \ge \theta \ge 0, \\\, \_\text{pr}(r, \theta) &= B\_n r^n P\_n(\pi - \theta); \, \_\text{for} \, \pi \ge \theta \ge \theta\_0 \end{aligned} \tag{1}$$

Eq. (1), *<sup>V</sup>* <sup>¼</sup> <sup>4</sup> <sup>3</sup> *πr*3, was the drop in the volume of fluid, here the spinning gap *r* which was from the cone vertex of angle 2*θ*<sup>0</sup> to the emitter tip and the state of the drop was said to be utilizing a Taylor cone, accordingly was described as *r* ¼ *R z*ð Þ*:* Later on the *z*- axis was corresponding to the applied electric field with *z*∈ ½ � �*l*, *l* , where *l* was the length if the semi-long pivot of the drop and limit condition *θ*<sup>0</sup> ≥*θ* ≥ 0 represents the boundary condition of the fluid. *Pn* [*x*] was the Legendre's function, where *An* and *Bn* were constants. They suggested a model for ESPNG polymeric nanofibers which relies upon a sink-like flow towards the vertex of the Taylor cone. The course of action of the flow in axisymmetric polar headings ð Þ *r*, *ε*, 0 was given utilizing conditions (2) and (3).

$$v\_r = \frac{vF(\varepsilon)}{r} \tag{2}$$

$$F(\varepsilon) = b \left\{ \mathbf{3} \tanh^2 \left[ \left( \sqrt{\frac{-b}{2}} \right) (a - \varepsilon) + \mathbf{1.146} \right] - 2 \right\} \tag{3}$$

In the above Eqs. (2) and (3), velocity of the radial feed, *vr*, the kinematic solution's resistance to the flow of feed, *v*, the wedge/Taylor cone half angle, *a*, the parameter, *b* which serves to decides the inertial concentration of stream on the Taylor cone vertex/Taylor cone. With that the mass and charge conservations led to expressions for *v* and *σ* in terms of *R* and *E*, also the force and E-field conditions were assessed utilizing second-degree differential equations. Inclination of the stream surface (*R*) was supposed as the highest from the origin of the nozzle and

hence the initial result of *z* was equal to zero. Furthermore, PMs were discussed using the set of Eqs. (4) [67, 68].

$$\begin{aligned} \mathcal{R}(\mathbf{0}) &= \mathbf{1} \\ E(\mathbf{0}) &= E\_0 \\ \pi\_{prr} &= 2r\_n \frac{R\_0'}{R\_0^3} \\ \pi\_{pzz} &= -2T\_{prr} \end{aligned} \tag{4}$$

Here Eq. (4), the radius of the jet initially was 0 *R*0 0 and the formula used for calculating the jet velocity, *<sup>υ</sup>*<sup>0</sup> <sup>¼</sup> *<sup>Q</sup> πR*<sup>2</sup> 0*K*, where the rate of discharge of the polymeric solution, *Q*, and the conductivity of the liquid solution, *K:* Moreover, the electric field (*E*0) was calculated using the formula, *<sup>E</sup>*<sup>0</sup> <sup>¼</sup> *<sup>I</sup> πR*<sup>2</sup> <sup>0</sup>*<sup>K</sup>* and the surface charge density (*σ*0) was calculated using the formula, *εE*0, where the dielectric constant of ambient air was <sup>0</sup> *ε*<sup>0</sup> and the constant was <sup>0</sup> *E*0 <sup>0</sup> which was to be used during simulation of the ESPNG. The viscous stress (*τ*0) was calculated using the formula, *<sup>τ</sup>*<sup>0</sup> <sup>¼</sup> *<sup>η</sup>*0*ν*<sup>0</sup> *<sup>R</sup>*<sup>0</sup> . A Newtonian liquid law of force for the liquid was summed up and for that the shear pressure (*τ*) was given as *<sup>τ</sup>* <sup>¼</sup> *<sup>K</sup> <sup>∂</sup><sup>v</sup> ∂y* � �*<sup>m</sup>* as shown using Eq. (5) [67]. The electric field will overcome the surface tension of the polymer liquid and thereafter through Taylor's cone NFs will be pulled out and ES over the moving cylinder collector.

$$\frac{d(\sigma R)}{dz} \simeq -\left(2R\frac{dR}{dz}\right) / Pe \tag{5}$$

Furthermore, the response of <sup>0</sup> *E*<sup>0</sup> is a function of axial position (*z*) and it can be shown in Eq. (6) [1, 69, 70].

$$\frac{d(E)}{dz} = \ln \chi \left(\frac{d^2 R^2}{dz^2}\right) / Pe \tag{6}$$

**Figure 4.**

**101**

*The (a) ESPNG set up was used to synthesize (b), and (c) the UT - and BF - Cc/G NFs (Reprinted with*

*permission from Ref. [70]. Copyright 2020 IOP Publishing).*

*An Insight into Biofunctional Curcumin/Gelatin Nanofibers*

*DOI: http://dx.doi.org/10.5772/intechopen.97113*

The model discussed above so far was found fit for foreseeing the conduct of the PMs of the ESPNG [67].
