Needleless electrospinning technology is considered as a better avenue to produce nanofibrous materials at large scale, and electric field intensity and its distribution play an important role in controlling nanofiber diameter and quality of the nanofibrous web during electrospinning. In the current study, a novel needleless electrospinning method was proposed based on Von Koch curves of Fractal configuration, simulation and analysis on electric field intensity and distribution in the new electrospinning process were performed with Finite element analysis software, Comsol Multiphysics 4.4, based on linear and nonlinear Von Koch fractal curves (hereafter called fractal models). The result of simulation and analysis indicated that Second level fractal structure is the optimal linear electrospinning spinneret in terms of field intensity and uniformity. Further simulation and analysis showed that the circular type of Fractal spinneret has better field intensity and distribution compared to spiral type of Fractal spinneret in the nonlinear Fractal electrospinning technology. The electrospinning apparatus with the optimal Von Koch fractal spinneret was set up to verify the theoretical analysis results from Comsol simulation, achieving more uniform electric field distribution and lower energy cost, compared to the current needle and needleless electrospinning technologies.

## I. INTRODUCTION

### A. Current issues in large-scale electrospinning

Electrospinning technology which was first patented by Formhals in 1934^{1} has been widely used to produce nanofibers for diverse applications such as filter media,^{2} sensors,^{3,4} polymer batteries and separators,^{5–7} drug release,^{8,9} tissue scaffolds,^{10,11} wound dressing^{12,13} and so on. Currently, the electrospinning technique which enables mass production of nanofibers has been classified as two categories, i.e., multiple needle (or channel/nozzle/capillary) type^{14–18} and needleless type. Multineedle electrospinning, in spite of the advantage of higher productivity than single needle, its disadvantages such as spinning channel clogging and difficulty in cleaning, especially the “End effect”^{19} has severely hindered its industrialization due to its generation of non-uniformity in electric field intensity. Liu^{14,15,20–24} et al has made a lot of efforts to minimize or eradicate the End effect phenomenon in multineedle electrospinning towards massive electrospinning and high productivity of nanofibers, however, the channel clogging remains the barrier towards massive and nonstop electrospinning process.

In recent years, a lot of published works has been devoted to improve the electrospinning productivity, and various needleless geometries, such as roller and wire commercialized by Elmarco with the brand name Nanospider™,^{25} as well as ball, disk, coil, ring^{26–29} have been used to produce nanofibers at large scale. Although a series of needleless geometrical spinnerets without tips have been designed and commercially applied successfully, tipped needleless electro spinnerets are expected to provide with higher electric field intensity and better distribution. In previous work, the authors designed a sawtooth shaped needleless electrospinneret,^{18} with which finer nanofibers were prepared at lab scale at relatively low voltage.

### B. Proposed needleless electrospinneret based on Von Koch Fractal Curves

In the current study, a novel tipped needleless electrospinneret was proposed by the authors based on Fractal Theory. The rudiment of Fractal Theory was established on the basis of Koch snowflake, which is a mathematical curve and one of the earliest fractal curves that has been described, and appeared in a paper titled ‘On a continuous curve without tangents, constructible from elementary geometry’ in 1904, by the Swedish mathematician Helge von Koch,^{30–32} and was developed by B. B. Mandelbrot in 1975,^{33} named based on some phenomena of physical relevance, such as the threshold of percolating, the oceanic coastlines, represented by self-resembling fractal. Fractal structure could be constructed in steps starting from a given shape, and rescaling it continuously down to a microscopic length scale. Von Koch curve is the simplest geometric figure (Fig. 1) of Fractal structure, formed by an iterative procedure, with the dimension given by:

where *N* is the number of subdivision at each step and *s* is the scaling factor.^{32}

The Koch curve is created by initiating with an equilateral triangle, then recursively altering each line segment according to the following steps as shown in Fig. 1: (0) draw a line segment; (1) divide the line segment into three parts with equal length, draw an equilateral triangle which has the middle segment as its base and points upward, with 1/3 length of the line segment in step 0 as its side length, and then erase the base of the regular triangle in the middle of the line in step 0. The geometric structure obtained this way is referred to as the first level Koch curve, as shown in step 1, Fig. 1; (2) the second level Koch curve is achieved by repeating the same steps based on step 1, as shown in step 2, Fig. 1; and (3) the third level Koch curve could be reached by repeating the same steps based on step 2, as shown in step 3, Fig. 1.

The Koch curve has an infinite length because each time the steps above are performed on each line segment of the figure there are four times as many line segments, the length of each being one-third the length of the segments in the previous step. Hence the total length increases by one third and thus the length at step *n* will be (4/3) *n* of the original triangle perimeter; therefore, the fractal dimension is log4/log3≈1.26.^{34} The Koch is continuous everywhere but differentiable nowhere.^{35} Taking *s* as the side length, the original triangle area is $s234$. The side length of each successive small triangle is 1/3 of those in the previous iteration; because the area of the added triangles is proportional to the square of its side length, the area of each triangle added in the *n*th step is (1/9)th of that in the (*n*-1)th step. In each iteration after the first, 4 times as many triangles are added as in the previous iteration; because the first iteration adds 3 triangles, the *n*th iteration will add 3 × 4^{n−1} triangles. Combining these two formulae gives the iteration formula (Equation (2)):

where *A*_{0} is area of the original triangle. Substituting in $A1\u2018=43A0$ and expanding yields:

As *n* goes to infinity, the limit of the sum of the powers of 4/9 is 4/5, and then

Therefore the area of a Koch snowflake is 8/5 of the area of the original triangle, and thus the *A*_{n+1} > *A _{n}* >

*A*

_{n−1}, i.e., the area under the Koch curve of Level 3 is larger than the area under the Koch curve of Level 2, and the area of the Koch curve of Level 2 is larger than the area under the Koch curve of Level 1, when they have the same structure units.

### C. Simulation process and steps using Comsol Multiphysics

The AC/DC module in Comsol Multiphysics software is employed to simulate the electric field intensity during electrospinning process. The electric field intensity simulation via Comsol software is comprised of the following steps, i.e., (1) set the physical field as electrostatic field; (2) establish the geometric model; (3) set the model parameters, including attribution of materials and boundary conditions; (4) differentiating grids; (5) define the physics; (5) solving the physics; (6) post treatment (visualization).

### D. Objective of the current study

In the current study, linear and nonlinear geometric configurations based on three different levels, including von Koch curves of Levels 1, 2 and 3 will be used as needleless electrostatic spinnerets, seeking for a new avenue to improve the electric field intensity and distribution of needleless electrospinning heads and hence modify nanofiber and web quality meanwhile reduce energy consumption and product cost. The finite element analysis software, Comsol Multiphysics is employed to simulate the electric field intensity. UG software was used for spinneret modeling, and Origin or MS Excel software is used for statistical analysis on the simulated data. The optimal linear Fractal structure will be selected firstly, and then the layout of electrospinnerets constructed with nonlinear Fractal structure including circular and spiral types will be further discussed based on the results from Comsol software simulation and analysis.

## II. MODELING

UG 8.0 (Unigraphics NX, Siemens PLM Software) was employed to model the Fractal based electrospinning process. For conveniently modeling the Fractal structure spinnerets and easily understanding the simulation results, all tips on the second level and third level Fractal structure spinnerets (as Figure 3 shown) are divided into three layers as shown in Figure 2 (tips through red line are defined as layer 1, tips through yellow line named layer 2, tips through green line called layer 3), with the first level Fractal structure spinneret only having one layer of tips, and then the electric field intensity and distribution will be simulated with the finite element analysis software after entering all the relevant parameters required into this software. During the process modeling, the air boundaries were set as infinite boundaries, the receiving plate was set as zero potential, and the spinneret was set as a certain voltage upon the simulation requirements. Then, process meshing and solving could be performed and the electric field intensity and distribution were obtained.

### A. Modeling of linear spinneret

As shown in Figure 3, the linear Fractal structure is used as the spinneret to model the Fractal electrospinning process, taking the second level Fractal structure for instance to address the modeling process. A metallic sheet having linearly aligned five-spinning unit of second level Fractal structure is used as the spinneret, high voltage DC power source is used in this Fractal based electrospinning process, which could be positive or negative in polarity.

The detailed information regarding the parameters used in the process of the linear spinneret modeling, such as the dimensions of the Fractal spinneret and the receiving plate, as well as the receiving distance, is shown in Table I and Figure 4 respectively. The relative dielectric constants for stainless steel (the metallic materials for Fractal spinnerets and receiving plate) and the surrounding air used in the modeling process are 1.5 F/m^{36} and 1.00059 F/m^{37} respectively.

Model . | Length of Fractal unit/mm . | Base height/mm . | Thickness/mm . | Receiving distance/mm . | Collector dimension/mm3 . | Air space dimension/mm3 . |
---|---|---|---|---|---|---|

First level | 45 | 22 | 2 | 200 | 700×700×2 | 1200×1200×1200 |

Second level | 15 | 22 | 2 | 200 | 700×700×2 | 1200×1200×1200 |

Third level | 5 | 22 | 2 | 200 | 700×700×2 | 1200×1200×1200 |

Model . | Length of Fractal unit/mm . | Base height/mm . | Thickness/mm . | Receiving distance/mm . | Collector dimension/mm3 . | Air space dimension/mm3 . |
---|---|---|---|---|---|---|

First level | 45 | 22 | 2 | 200 | 700×700×2 | 1200×1200×1200 |

Second level | 15 | 22 | 2 | 200 | 700×700×2 | 1200×1200×1200 |

Third level | 5 | 22 | 2 | 200 | 700×700×2 | 1200×1200×1200 |

### B. Modeling of nonlinear Fractal spinneret

The circular and spiral types of second-level Fractal spinnerets having five Fractal structure units were modeled and shown in Figure 4. Considering the convenience in practical electrospinning, the inner radius is designed as 69 mm, external radius 79 mm, and the location numbers of the two nonlinear Fractal spinneret models are also defined and shown in Figure 5(a) and 5(b), respectively.

## III. SIMULATION ON FIELD INTENSITY OF THE FRACTAL SPINNERET MODELS

COMSOL Multiphysics^{38} is a numerical simulation software package that is based on PDE (partial differential equation) to simulate by adopting finite element method in research and engineering. The simulation for electrostatic field formed during electrospinning process follows the Poisson’s Equation (Equation (5)), a partial differential equation (PDE):

where *ξ*_{0} is the relative permittivity of vacuum, *ξ _{r}* is the relative permittivity of the medium,

*ρ*is the space charge density,

*V*is the potential. The PDE (Equation (5)) is the basis for setting each subdomain.

Apart from the numerical values set in subdomain, determining the boundary conditions is another important step to complete and every boundary is constrained by Equation (6):

where *n* is the normal vector of interface, *D* is the dielectric flux density, *ρ _{s}* is the density of surface charge. In the current study, ambient space is confined to a given area in 2D or space in 3D during simulation process, and the electrospinning model is placed in an open space. Therefore, four boundaries linked together as the limited atmosphere are set as the condition of zero charge/symmetry, aiming to reach the purpose of the infinity of surroundings corresponding to the Equation (7):

Boundaries such as between spinneret and atmosphere without any charges (*ρ _{s}* = 0) are constrained by the continuity condition that is expressed as shown in Equation (8):

The other basic principle for simulating the field intensity is the Field Superposition Theory in which the whole electric field intensity at a random position in the electrostatic field is equivalent to the vector sum of field intensity generated by all independent point charge. In physics and systems theory, the superposition principle^{39} also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually. If the system is additive and homogeneous, the superposition principle can be applied. If a homogeneous system *F*(*ax*) = *aF*(*x*), and an additive system satisfies *F*(*x*_{1} + *x*_{2}) = *F*(*x*_{1}) + *F*(*x*_{2}), where *a* is a scalar, then a system that simultaneously has the property of homogeneity and additivity satisfies *F*(*a*_{1}*x*_{1} + *a*_{2}*x*_{2}) = *a*_{1}*F*(*x*_{1}) + *a*_{2}*F*(*x*_{2}), with *a*_{1} and *a*_{2} being the scalars. Therefore, the electrostatic field to be discussed in the current study, which is of the property of homogeneity and additivity at the same time, abides by the operation principle addressed above.

In the current study, Comsol Multiphysics 4.4 software is employed to simulate the field intensity during Fractal electrospinning, and the parameters used for modeling electrospinning process are listed in Table I, where 30kV voltage is applied to the spinneret models, the values of relative dielectric permittivity for surrounding air and the materials of Fractal spinneret are defined as 1.00059 F/m and 1.5 F/m, respectively.

The Fractal model established with UG 8.0 software based on the structural/dimensional parameters addressed above is transferred to Comsol software, and the attribution of materials and boundary conditions are also introduced to Comsol software via a stream of commends. The simulation results are obtained after running for a while as short as a few minutes or as long as several hours.

In order to obtain the optimal Koch fractal spinneret which may generate uniformly distributed nanofibers and even spinning jets at low cost, the electric field intensity and distribution of linear spinnerets were simulated and analyzed with Comsol software based on three layers, including Layer 1, Layer 2, and Layer 3. The definitions for different layers are indicated in Fig. 2, where the highest tips on the horizontal red line are defined as Layer 1 tips, composed of three tips from Koch curves of Level 1, Level 2 and Level 3 respectively; the Layer 2 tips stand for the tips located on the horizontal yellow line, including two tips from lever 2 Koch curve, and two tips from Level 3 Koch curve, with each pair of tips symmetrically located around its geometric center on Levels 2 and 3 Koch curves respectively; Layer 3 tips refer to the four tips on the horizontal green line, including two pairs of tips from Levels 2 and 3 Koch curves respectively. There is equal distance between the tips on Layers 1 and 2, and between the tips on Layers 2 and 3, which is convenient for the subsequent simulating, analyzing and comparing the field intensity and distribution of the Koch fractal spinneret.

The tipped Koch curves could be made into needleless electrospinning spinnerets in linear or nonlinear type for large-scale nanofiber production, and the latter could include two kinds of spinnerets, which are circular and spiral types of spinnerets, respectively, as shown in Fig 5(a) and 5(b) respectively. As easily seen from Fig. 5(a) and Fig. 11(c), only the upper half circumferences of the nonlinear Koch curve fractal spinnerets could generate nanofibers when located in the electric field, which, however, will generate different electric field intensity values at different tip locations on the upper half circumferences of the nonlinear spinnerets due to different receiving distances. Therefore, the simulation and analysis will be performed based on different tip positions on the upper side of the nonlinear spinnerets, i.e., the upper side of the circumferences of the two nonlinear spinnerets would be divided into several different sections based on the radius angles to understand the field intensity at different tip locations of the spinnerets.

Following the similar strategy used in linear spinnerets, the nonlinear spinnerets will be divided into five layers for easy simulation and analysis, i.e., totally 11 lines were drawn from all the tips towards the center point of the circles (the side views of both spiral spinneret and circular spinneret would be the same round shape, as shown in Fig. 11(c)). The upper half circles of the two nonlinear spinnerets are divided into 10 parts with unequal areas or radius angles for each part, and the angles being 0°, 13°, 36°, 59°, 72° and 85° respectively. The angles on the right side of the longitudinal axis are imparted positive values and negative values are given to the angles on the left side of the longitudinal axis, which is the line with radius angle of 0°.

## IV. RESULTS AND DISCUSSION

### A. Field intensity and distribution of linear Fractal spinneret model

The electric field intensity of the tips at the three linear Fractal structure spinneret models including the first, second and third levels of Koch curves was simulated and calculated using Comsol Multiphysics 4.4, the resultant electric field profiles were shown in Figure 6, where (a), (b) and (c) stand for the field intensity distribution on the first, second and third levels of Koch curve Fractal structure spinnerets respectively, (d), (e) and (f) represent the zoomed-in field intensity distribution on single Fractal structure units of the first, second and third levels of Koch curve Fractal structure spinnerets respectively. The color bar on the right side of Figure 6 indicates the field intensity against color, with red color indicating high field intensity and dark color representing low field intensity.

#### 1. Overall field intensity distribution

The overall distribution of electric field intensity of electro spinnerets with Fractal structure of Levels 1, 2 and 3 is depicted in Figure 7, in which the spinneret with Level 1 Koch Fractal structure shows highest field intensity 41.98 kV/cm, and the lowest coefficient of variation (CV) 13.89%, which is because that only 5 tips exist on Level 1 Fractal spinneret, and all the five tips are located at the same layer (the first layer), resulting in high field intensity and low CV value. The other spinnerets showed lower field intensity and higher CV values due to they have more tips located at different layers, leading to broader distribution in field intensity and hence lower field intensity but higher CV values.

It could be found by further observation on Figure 7 that the spinneret having Fractal structure of Level 2 exhibits significantly higher field intensity 35.06 kV/cm and slightly higher CV value of 15.94% than the spinneret with Fractal structure of Level 3. As the Fractal spinnerets with Levels 2 and 3 Fractal structure have similar values of CV, and Level 2 Fractal structure shows relatively higher field intensity, which facilitates producing finer nanofibers at large scale with lower energy consumption, therefore, the spinneret with Level 2 Fractal structure is chosen as the optimal Fractal spinneret for future practical electrospinning process.

Although Level 1 Fractal spinneret shows the highest field intensity and the lowest CV, fewer spinning jets would be expected during the practical electrospinning because fewer tips exist on the Level 1 Fractal spinneret, which is not beneficial for nanofiber production at large scale. If including the missing tip locations into Level 1 Fractal spinneret at the corresponding tip positions on Levels 2 and 3 Fractal spinnerets, Level 1 Fractal structure is not the optimal spinneret any more, as a result, the Level 2 Fractal structure will become the best spinneret instead, which returns lowest averaged field intensity(9.99kV/cm) and highest CV values(185%) to Level 1 Fractal structure spinneret, turning out to be a fair way to compare the field intensity distribution among the three levels of Fractal spinnerets.

As there are many more tips existing on the spinnerets having Levels 2 and 3 Fractal structure spinnerets, the simulation and analysis on field intensity are performed based on different layers on the Fractal structure spinnerets. The definition about the layers on the Fractal structure spinnerets has been shown in Figure 2.

#### 2. Analysis on field intensity distribution of tips in Layer 1

As shown in Fig. 8, the second level structured Fractal spinneret displays highest field intensity (42.09kV/cm) and the lowest CV (8.46%) at tips of Layer 1 among all the three spinnerets. Based on the layer definition indicated in Figures 5 and 6, and the area calculation method shown in Equation (4), the Level 1 Fractal spinneret should have the least area under its Level 1 Koch curve, and hence it should have the highest density of charge on its surface area, therefore it should have the highest field intensity. Also, there are no smaller tips beside the both sides of the 5 main tips on the Level 1 Fractal spinneret to balance the Columbic force from the neighboring main tips, leading to strongest ‘End effect’ at the two edges of Level 1 Fractal spinneret. However, there are smaller tips located on both sides of the 5 main tips on Levels 2 and 3 Fractal spinnerets, which can balance the Columbic repellence force and hence enhance the field intensity of the main tips (i.e., the first layer of tips) on their spinnerets, therefore, Level 1 Fractal spinneret does not exhibit the highest field intensity but exhibits the highest CV value, and the field intensity distribution of which follows the quadratic equation, *y* = 0.0383*x*^{2}-1.8953*x*+59.236 (R^{2} = 0.9904).

The tips in Layer 1 of the Level 2 Fractal spinneret show the highest field intensity and lowest coefficient of deviation due to a pair of tips located on both sides of the 5 main tips which balance the Columbic force and enhance the electric field force and field intensity, resulting in smallest End effect and CV value of the field intensity of the tips in Layer 1, Level 2 Fractal spinneret, and the field intensity of which follows the quadratic equation, *y* = 0.022*x*^{2}-1.0895*x*+52.009 (R^{2} = 0.8776). In the case of the Level 3 Fractal spinneret, more tips are located on both sides of its 5 main tips, leading to higher Columbic force among the tips and hence the most severe End effect generated at the two edges of the spinneret, this spinneret shows the highest CV value but the lowest field intensity of field intensity of the tips in Layer 1, Level 2 Fractal structure, due to its largest surface area and hence smallest areal charge density among the three levels of spinnerets, with its field intensity distribution following the quadratic equation, *y* = 0.0213*x*^{2}-1.052*x*+45.253 (R^{2} = 0.9831). Therefore, the spinneret with Level 2 Fractal structure is again selected as the optimal spinneret based on the analysis on field intensity of Layer 1.

#### 3. Analysis on field intensity distribution of Layer 2

Since the second layer does not exist on the spinneret with Level 1 Fractal structure, the current analysis will be conducted between the spinnerets with Level 2 and 3 Fractal structure. The comparison of field intensity of the two spinnerets is shown in Figure 9, where the spinneret with Level 2 Fractal structure displays significant high field intensity and almost the same CV value than the spinneret with Level 3 Fractal structure, which is mainly because that there is less surface area and hence higher charge density under the former Fractal curve than the later. Thus, the spinneret with Level 2 Fractal structure is again considered as the optimal spinneret based on the analysis on field intensity of Layer 2.

#### 4. Analysis on field intensity distribution of Layer 3

Since the third layer does not exist on the spinneret with Level 1 Fractal structure, the current analysis will be limited between the spinnerets with Level 2 and 3 Fractal structure. The comparison of field intensity of the two spinnerets is shown in Figure 10, where the spinneret with Level 2 Fractal structure displays much higher field intensity and significantly lower CV value than the spinneret with Level 3 Fractal structure, which is mainly because that there is less surface area and hence higher charge density under the former Fractal curve than the later, and less number of tips in Level 2 spinneret than Level 3 spinneret results in weaker Columbic repellence among the third layer of tips and hence narrower distribution of its field intensity. Thus, the spinneret with Level 2 Fractal structure is again considered as the optimal spinneret based on the analysis on field intensity of Layer 3.

After comprehensive analysis on the overall and layer based field intensity and its distribution of the linear Fractal spinnerets, the optimal structure is selected as the spinneret with Level 2 Fractal structure. However, linear type spinneret will generate non-continuous solution feeding issue during the real electrospinning process which should be taken for consideration during the large-scale electrospinning process. Thus, nonlinear needleless electrospinnerets based on Fractal Theory are proposed to solve the feeding problem, and two typical types of nonlinear Fractal spinnerets are further analyzed in terms of field intensity, its distribution and the energy efficiency, using Comsol software.

### B. Field intensity and distribution of nonlinear Fractal spinneret model

#### 1. Results from Spiral Model

Fig. 11(a) and 11(b) illustrate the electric field distribution on spiral Fractal structure spinnerets. The high intensity electric field is mainly distributed on the semicircle closed to the collector, and the tips nearest to the collector have the highest electric field intensity, i.e., nearer tips to the collector have the higher electric field intensity. The similar strategy is employed in analyzing the field intensity along the circular Fractal spinneret, and between the different spinnerets. For easy analysis on the simulation results from Comsol Multiphysics, the tips on each of the five circular Fractal spinnerets are classified into different layers based on the angles formed between the lines through the tips and the center of the circular Fractal spinnerets, and the longitudinal axis, where the 0° line is located at, as shown in Fig. 11(c).

The spiral Fractal array structure involved in the discussion include totally five spiral spinnerets marked as Numbers 1, 2, 3, 4 and 5 respectively from the left to the right, and the five spiral spinnerets are located at symmetric positions with No.3 spiral spinneret as the center, as shown in Fig. 12, and thus No.1 and No. 5 spinnerets share the same averaged field intensity and distribution, No. 2 and No. 4 spinnerets have the same averaged field intensity and CV values, respectively. Due to the existence of End effect, No.3 spinneret has the lowest field intensity of 19.12 kV/cm, No.2 and No.4 have the medium field intensity of 32.07 kV/cm, and No.1 and No.5 spinnerets have the highest field intensity of 30.90 kV/cm.

#### 2. Results from Circular Model

Fig. 13(a) and 13(b) illustrate the electric field distribution on circular Fractal structure spinnerets. The high intensity electric field is mainly distributed on the semicircle closed to the collector, and the tips nearest to the collector have the highest electric field intensity, i.e., nearer tips to the collector have the higher electric field intensity. The similar strategy is employed to analyze the field intensity along the circular Fractal spinneret, and between the different spinnerets. For easy analysis on the simulation results from Comsol Multiphysics, the tips on each of the five circular Fractal spinnerets are classified into different layers based on the angles formed between the lines through the tips and the center of the circular Fractal spinnerets, and the longitudinal axis, where the 0° line is located at, as shown in Fig. 11(c).

The circular Fractal array structure involved in the analysis include totally five circular spinnerets with the order numbers of 1, 2, 3, 4 and 5 respectively from the left to the right, and the five circular spinnerets are located at symmetric positions with No.3 spiral spinneret as the center, as shown in Fig. 14, and thus No.1 and No. 5 spinnerets share the same averaged field intensity and distribution, No. 2 and No. 4 spinnerets have the same averaged field intensity and CV values, respectively. Due to the existence of End effect, No.3 spinneret has the lowest field intensity of 21.36kV/cm, No.2 and No.4 have the medium field intensity of 22.57kV/cm, and No.1 and No.5 spinnerets have the highest field intensity of 29.97kV/cm.

#### 3. Comparison of circular and spiral Fractal spinnerets

As shown in Figure 15, the circular and spiral Fractal spinneret arrays have the similar field intensity distribution within the angles between -85° through 85°, with the former having higher field intensity than the later. Additionally, the circular Fractal spinneret shows lower and more regular CV distribution in the angles ranging from -85° to 85°. Therefore, circular Von Kouch Fractal structure is considered as the better type of mass electrospinning as this type of nonlinear Fractal spinneret is capable of providing higher electric field intensity at narrower distribution range, which indicates finer and more uniform nanofiber product could be massively produced at lower energy consumption.

## V. EXPERIMENT OF ELECTROSPINNING ON KOCH FRACTAL SPINNERET

In order to verify the feasibility of the modeling Comsol analysis, the needleless electrospinning apparatus composed of the optimal Level 2 Koch fractal spinneret was set up (as shown in Figure 16). The electrospinning solution containing 8% wt/wt thermoplastic polyurethanes (TPU) was prepared on the magnetic stirrer for 5h at the temperature of 60°C. The nanofiber web was obtained after the electrospinning experiment (shown in Figure 17(a)) at 20 kV voltage, 20 cm fiber receiving distance and 30rpm rotating rate of spinneret, and the scanning electron microscope (SEM, Hitach S-4800, Japan) and Image Pro 6.0 (Media Cybernetics Company) were used to measure the surface micromorphology of the TPU nanofiber web and fiber diameter respectively.

It could be easily seen from Figures 17(b) and 17(c) that the surfaces of the nanofibers are regular and smooth, most fibers having diameter of 657nm with the CV value of 16.2% (without using the traverse mechanism), which have the similar dimension and distribution to the fibers generated from the needle spinnerets, but similar productivity (∼1kg/h) to the currently used needleless electrospinning technology such as the Nanospider™ (100-120kV)from Elmarco, the spiral coil spinneret (50-65kV) from Deakin University, etc., at lower applied voltage, due to the high field intensity generated from the tips on the fractal spinneret.

## VI. CONCLUSIONS

In the current study, a new type of needleless electrospinning technology was proposed towards mass production of nanofibers and their materials products, based on the linear von Koch curves of Fractal Theory. The feasibility of three levels of Koch curve Fractal structure as a new type of needleless electrospinnerets was investigated and discussed based on the simulation results via the finite element analysis software, Comsol Multiphysics. The results indicate that the spinneret having the second level Fractal structure is capable of providing the optimal electric field intensity and its distribution based on the overall analysis and layer based analysis using Comsol Multiphysics. Furthermore, two types of nonlinear Fractal spinneret arrays were constructed using spiral model and circular model, and their field intensity and distribution profiles were investigated comparatively and systematically. The results show that the circular Fractal structure is the optimal nonlinear Fractal spinneret. The setup with the optimal fractal spinneret was prepared to testify its feasibility. The result indicated that the new setup could be used in mass electrospinning process to produce finer and more uniform nanofiber product at much lower voltage and hence lower cost.

## OUTLOOK

Although the second level Koch curve based Fractal structure was selected as the optimal needleless electrospinneret based on the simulation results via Comsol Multiphysics, and the circular Fractal spinneret array has the potential of producing nanofibers at large scale, the End effect, which leads to higher electric field intensity at the two edges and lower electric field intensity in the middle of the Fractal spinneret array, remains an issue during the electrospinning process with the Fractal structure as spinnerets. In the future work, End effect problem is about to be solved by means of several methods including the adjustment of (1) spacing between the circular Fractal spinnerets, (2) the diameter of the circular Fractal spinnerets at two edges, and (3) the applied voltages at the circular Fractal spinnerets at two edges, and so on. In addition, the effect of the electrospinning parameters such as revolving rate of the spinneret, voltage and collector distance will be study in order to further improve the quality of the nanofiber web.

## ACKNOWLEDGEMENT

This work was supported by National Science Foundation of China, with the project approval No. of 51373121.

## REFERENCES

**35**, 21 (