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# Open Physics

### formerly Central European Journal of Physics

Editor-in-Chief: Seidel, Sally

Managing Editor: Lesna-Szreter, Paulina

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Volume 15, Issue 1

# Three-dimensional computer models of electrospinning systems

Krzysztof Smółka
• Corresponding author
• Institute of Mechatronics and Information Systems, Lodz University of Technology TUL, Stefanowskiego Str. 18/22, 90-924, Lodz, Poland
• Email
• Other articles by this author:
/ Anna Firych-Nowacka
• Institute of Mechatronics and Information Systems, Lodz University of Technology TUL, Stefanowskiego Str. 18/22, 90-924, Lodz, Poland
• Other articles by this author:
/ Marcin Lefik
• Institute of Mechatronics and Information Systems, Lodz University of Technology TUL, Stefanowskiego Str. 18/22, 90-924, Lodz, Poland
• Other articles by this author:
Published Online: 2017-12-29 | DOI: https://doi.org/10.1515/phys-2017-0091

## Abstract

Electrospinning is a very interesting method that allows the fabrication of continuous fibers with diameters down to a few nanometers. This paper presents an overview of electrospinning systems as well as their comparison using proposed three-dimensional parameterized numerical models. The presented solutions allow an analysis of the electric field distribution.

Keywords: nanofibers; FEM; electric field; infinity domains

## 1 Introduction

Electrospinning is a straightforward and inexpensive process that produces nanofibers from submicron down to nanometre diameter [1]. Important applications include tissue engineering, medical healthcare, chemical and biological sensors, wound dressings, drug delivery, protective shields in specialty fabrics, filter media for submicron particles in the separation industry and enzyme immobilization and also in the fabrication of micro / nano-devices [2, 3, 4, 5, 6].

The fabrication of nanofibers using anelectrospinning method has attracted considerable attention due to its versatile manoeuvrabilityin production and control of fiber structures, porosity, orientations and dimensions [7]. Unlike conventional fiber spinning techniques (for example wet spinning or dry spinning), which are capable of producing polymer fiber switch diameters down to the micrometre range, electrospinning allows for production of polymer fibers with diameters in the nanometer range [8].

A typical electrospinning set-up consists of a grounded, static collector and one or more spinnerets. In order to achieve various fibre assemblies two main methods of production are used. The first is based on control of the flight of the electrospinning jet through the manipulation of the electric field. The second is to use a dynamic collection device [9]. This paper concentrates on the first method.

In an electrospinning method a hemispherical liquid drop at the tip of a capillary is distorted into a Taylor cone and forms a liquid jet in the presence of an external electric field which results in rapid stretching and rapid solidification. The jet extends initially in a straight line for a certain distance, then suffers a catastrophic bending instability, followed by a looping and spiralling path with increasing circumference [6]. An electrostatic field at the surface of the liquid produces sufficient force that, if the electric field is strong enough, a jet of liquid can be ejected from a surface that was essentially flat before the field was applied [10]. The authors of paper [5, 11] reported that the lower the applied voltage, the finer the fibers, but when the applied voltage is too low, the electric force cannot surpass surface tension and the jet cannot be ejected. So the threshold voltage is an important criteria and its value is usually a few or several kV.

## 2 Computer models

Simulations were used to compute the electric field, electric displacement field and potential distributions in dielectrics under an explicitly prescribed electric charge distribution. The formulation was stationary. The physics interface solves Gauss’ Law for the electric field using the scalar electric potential as the dependent variable.

In the simulation, the Maxwell’s stress tensor is used to calculate electromagnetic forces. In the electrostatics, the force is calculated by integrating: $n1T2=12n1E∙D+n1∙EDT$

on the surface of the object that the force acts on, where E is the electric field intensity, D is the electric flux density and n1 is the surface normal.

In the case of electrospinning devices, correct modelling requires the introduction of infinite elements into the most frequently used finite element methods. Infinite elements represent a region stretching out to infinity. Normally, any model simulates a process within a bounded domain represented by the geometry drawn in the FEM system. The models are delimited by artificial boundaries inserted to restrict the extent of the model to a manageable region of interest.

The artificial truncation of the domain in models with infinity areas can be done in several ways as presented in existing literature related to various areas (e.g. electromagnetics or mechanics). Some of these FEM systems include special boundary conditions to absorb outgoing propagating waves without spurious reflections; so-called low-reflecting boundary conditions. Others allow impedance boundary conditions, which can account for a finite impedance between the model boundary and a reference at infinity. Such boundary conditions are often efficient and useful but lack some generality and sometimes accuracy [12].

In this research, the authors used COMSOL Multiphysics – a multipurpose software platform for simulating physics-based problems. In this software, the way to accomplish the desired effect of boundary conditions is to apply a coordinate scaling to a layer of virtual domains surrounding the physical region of interest, Figure 1a. As can be seen in Figure 1b, the electric field lines properly close through the infinity areas around the model objects. Unfortunately, in many studies, the lack of such an approach causes the electric field lines to not close and therefore enter perpendicular to the boundary surface or close but are flattened with respect to external boundaries, which may only be correct in spherical systems.

Figure 1

a) Infinity domains in model of typical electrospinning. Note that the edge and corner zones must be drawn as distinct domains in the geometry; b) Electric potential in infinity domains.

Some components of the electrospinning system have dimensions which are many times smaller than the dimensions of others (e.g. the diameter of the needle or pipette is much smaller than its length). This causes difficulties during the process of creating a discretization mesh. Examples of the mesh for selected parts of the electrospinning systems are shown in the Figure 2.

Figure 2

The examples of the FEM mesh in selected parts of the electrospinning systems: a) needle; b) multiple spinnerets.

## 3 Results

A classic electrospinning system consists of three components: a high power voltage supply, a capillary tube with a needle or pipette and a metal collector [11]. In practice, various types of systems are used. The main differences are the type of capillary and shape of the collector. Based on a literature overview, the authors have identified the following types of systems:

• Typical electrospinning (one spinneret) [13] – model 1 (Figure 3a),

Figure 3

Model 1: a) geometry; b) electric field vectors distribution; c) electric potential distribution [V].

• Multiple spinnerets (5 × 5) [13] – model 2 (Figure 4a),

Figure 4

Model 2: a) geometry; b) electric field vectors distribution; c) electric potential distribution [V].

• Typical electrospinning with a tube insulator [14] – model 3 (Figure 5a),

Figure 5

Model 3: a) geometry; b) electric field vectors distribution; c) electric potential distribution [V].

• Controlled deposition using a single ring [15] – model 4 (Figure 6a),

Figure 6

Model 4: a) geometry; b) electric field vectors distribution; c) electric potential distribution [V].

• Controlled deposition using ring electrodes [16, 17] – model 5 (Figure 7a),

Figure 7

Model 5: a) geometry; b) electric field vectors distribution; c) electric potential distribution [V].

• Array of counter-electrodes [9] – model 6 (Figure 8a),

Figure 8

Model 6: a) geometry; b) electric field vectors distribution; c) electric potential distribution [V].

• Parallel electrodes [18] – model 7 (Figure 9a),

Figure 9

Model 7: a) geometry; b) electric field vectors distribution; c) electric potential distribution [V].

• Rotating drum [19] – model 8 (Figure 10a),

Figure 10

Model 8: a) geometry; b) electric field vectors distribution; c - d) electric potential distribution [V].

• Rotating wire drum collector [4, 20] – model 9 (11a),

Figure 11

Model 9: a) geometry; b) electric field vectors distribution; c - d) electric potential distribution [V].

• Drum collector with wire wound on it [13] – model 10 (Figure 12a),

Figure 12

Model 10: a) geometry; b) electric field vectors distribution; c - d) electric potential distribution [V].

• Disc collector [21, 22] – model 11 (Figure 13a),

Figure 13

Model 11: a) geometry; b) electric field vectors distribution; c -d) electric potential distribution [V].

• Blade placed in-line [9] – model 12 (Figure 14a),

Figure 14

Model 12: a) geometry; b) electric field vectors distribution; c -d) electric potential distribution [V].

• Ring collector placed in parallel [23] – model 13 (Figure 15a),

Figure 15

Model 13: a) geometry; b) electric field vectors distribution; c - d) electric potential distribution [V].

• Rotating tube collector with knife-edge electrodes below [24] – model 14 (Figure 16a).

Figure 16

Model 14: a) geometry; b) electric field vectors distribution; c - d) electric potential distribution [V].

Compared to the classical method with one jet (model 1), increasing the number of jets (model 2) is an easy method to increase the fiber productivity. However, multi-jet electrospinning has shown strong repulsion among the jets. For this reason, it is important to ensure that there is sufficient distance between the jets [25].

By applying a secondary external field (models 3-5) of the same polarity as the jet, it is possible to better control or eliminate the bending instability occurring in classical methods. An insulating tube or additional rings improves efficiency of the electrospinning process [14, 26]. In models 8-11 and 14 fiber deposition can be additionally regulated by controlling the motion of the ground target (cylinder, disc or wire drum).

Usually, the rotating elements are the ground targets (models 8-11). In some cases, the rotating element was used to collect the electrospun nanofibers without any counter-electrode below as a control (model 14). When two conducting collectors are placed in parallel (model 7, 10, 13) or in perpendicular (model 12), it is possible to collect highly aligned nanofibers. The simplicity of using these methods has generated various modifications to obtain different nanofiber assemblies [26].

For these systems a parametrized numerical model was prepared using the COMSOL package. These models allow for calculation of electric field distributions for different dimensions of the systems parts, different distances between the capillary and collector and various voltage values. It was assumed that in each case the needle was under 10 kV, the collector was grounded (0 V) and the closest distance between the needle and the collector was 0.20 m. Detailed information on each configuration can be found in the references indicated above.

The structures of the analysed cases (models 1-14) with the distributions of the electric field vectors and electric potential are shown in Figure 3Figure 16.

Distributions of the electric field intensity E (in a plane parallel to the collector, which was halfway between the needle and the collector) for selected models are shown in Figure 17.

Figure 17

Electric field intensity distributions: a) model 1; b) model 2; c) model 5; d) model 14.

## 4 Analyses of results

In electrospinning systems, the jet of fiber carries the charge and is drawn in the direction of the electric field. Simulating and knowing the electric field profile could be helpful for controlling the jet path and also the nanofiber deposition area and final effects. A few of the jet motion controlling models were based on deflecting the charged particles by creating transverse electric fields (models 3, 4, 5). In these models, the spread of the nanofibers on the target collector can be controlled by using circular rings or tubes. These methods reduce the deposition area.For improving the direction control in the transverse plate, the field can be controlled by using a few (most often two) additional elements with the same polarity or by using additional parts to the collector (models 6, 7, 10, 12, 13). The electrospun jet could be essentially constrained to a focus plane midway between the electrodes. Variations in the magnitude of the deflection field, caused by changing the distance of the plates or their electric potential, can direct the nanofibers into different deposition radii.

In most of the analysed cases, the distribution of the vector E and the equipotential lines are similar. However, some differences in distributions can be observed in model 4 and model 5. This is caused by the additional electrodes (additional rings), each with an applied potential of 5 kV. More differences can be noticed in the E module distributions. The maximum value of electric field intensity E is between 7.6·103 V/m to 105 V/m (model 5). The higher value of E for model 5 is also caused by the additional electrodes in the electrospinning system.

The electrical forces acting on the fluid surface in individual cases reached values of the order of 1-10e6 N/m2. There is a strong relationship between the needle radius and the parameters of the fluid itself.

## 5 Conclusions

The presented models were based on a nozzle with positive applied charge and a flat plate collector or a rotating element, which was electrically earthed. Manipulating the electrical field profile by changing the shape of the elements or adding extra electrodes are the practical techniques that could be used for controlling the jet path and nanofiber deposition place in addition to changing the collection shape and materials.

According to the authors, in the literature there is no uniform comparison of the electric field distributions in different electrospinning systems. The models described in this paper make it possible to choose optimal parameters for the production of nanofibers (e.g. power supply voltage and the distance between capillary and collector), the most appropriate capillary and collector systems and the design of new electrospinning systems.

The properties of the polymer solution have the most significant influence on the electrospinning process. The final effects also depend on the viscous drag force from air and gravity. Since those effects further extend analysis of the structural mechanics, computational fluid dynamics (CFD) is required. An in-depth analysis of the possibility of experimental verification of the obtained results is also needed.

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Accepted: 2017-11-13

Published Online: 2017-12-29

Citation Information: Open Physics, Volume 15, Issue 1, Pages 777–789, ISSN (Online) 2391-5471,

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