# Electrospinning Mechanism of Nanofiber Yarn and Its Multiscale Wrapping Yarn

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## Abstract

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## 1. Background

## 2. Introduction

## 3. Materials and Methods

#### 3.1. Main Materials and Equipment

#### 3.2. Experimental Method

#### 3.2.1. Self-Made Electrospinning Nanofiber Yarn Forming Device

#### 3.2.2. Preparation of Electrospinning Solution

#### 3.2.3. Analytical Test Method

## 4. Experimental Data and Analysis

#### 4.1. Electric Field Simulation Analysis of Electrospinning Nanofiber Yarn Forming Device

#### 4.2. SEM Image Analysis

#### 4.2.1. Effect of Changing the Distance from the Ring to the Disk on the Surface Morphology of the Fiber

#### 4.2.2. Effect of Changing the Distance between the Tip of the Needle and the Center of the Disk on the Surface Morphology of the Fiber

#### 4.2.3. Effect of Changing the Disk Rotation Speed on the Fiber Surface Morphology

#### 4.2.4. Electrospun Nanofiber-Wrapped Structural Yarns after Changing ${L}_{zp}$

#### 4.3. Mechanical Performance Analysis

#### 4.3.1. Change the Electrospinning Nanofiber Yarn under ${L}_{zp}$

#### 4.3.2. Electrospun Nanofiber-Wrapped Structural Yarns after Changing ${L}_{zp}$

## 5. The Nanofiber-Wrapped Yarn Formation Mechanism

#### 5.1. Wrapping Mechanism under Specific Assumptions

_{0}(mm), and the length of the oriented nanofibers is ${L}_{q}$ (mm). At the same time, the core yarn may be wound up at a winding speed of v (mm/s). The twist angle is β (°), the disk rotation speed is n (r/min), the core yarn is assumed to be a cylinder with a diameter d (mm), the ring diameter is D

_{1}(mm), the disk diameter is D

_{2}(mm), and the disk aperture is D

_{0}(mm), and the twisting time is t (s).

_{0}> L, the oriented nanofibers are stretched during twisting. It is assumed that the elongation at break of the nanofibers is ε, the value of which depends on the nature of the polymer used in the electrospinning solution and the electrospinning process parameters.

_{q}, then:

_{0}’ has the following formula:

_{q}, then

#### 5.2. Wrapping Mechanism under Non-Specific Conditions

#### 5.2.1. Inner and Outer Diameters of the Ring Are Not Ignored

_{1}, and the distance between the end of the disk and the center of the core yarn is x

_{2}. The twisting of oriented nanofibers is shown in Figure 19.

#### 5.2.2. Randomly Fixed Nanofiber ends

_{i}between the nanofibers at the disk and the center of the core yarn is a random variable, which can be a finite number or infinity and can be listed one by one, and its twist angle is one or several finite or infinite intervals. This random variable ${x}_{i}$ is a typical discrete random variable. The probability corresponding to x

_{i}is p(x

_{i}), and the sum of the products is the mathematical expectation of the discrete random variable x

_{i}, denoted as E(x).

_{0}in Figure 18 under the assumption that oriented nanofibers are formed at a fixed displacement between the ring and disk. The reasoning and formula are the same. Because of the random variables, there is no obvious change in the twist angles. In Figure 5, Figure 7 and Figure 9, the twist angles of nanofibers in the same layer are not constant, large or small, which verifies the randomness of this phenomenon. The average twist angles of nanofibers in each layer also verifies the existence of this mathematical expectation law.

#### 5.2.3. Coreless Yarn

_{0}in Figure 18 is the distance from the fiber endpoint on the disk to the center of the disk.

#### 5.3. Analysis of the Uniqueness of the Electrospinning Nanofiber Wrapping Process

#### 5.3.1. Dispersion of Oriented Nanofiber Collection Process

#### 5.3.2. Discontinuity of Fiber Length Direction during Mechanical Twisting

#### 5.3.3. Non-Uniformity of the Twist Angles during Mechanical Twisting and Wrapping Process

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematic diagram of the forming device for electrospinning nanofiber yarn. (

**a**) electrospinning nanofiber yarn forming device. (

**b**) electrospinning nanofiber-wrapped yarn forming device. 1—High voltage DC power, 2—Syringe, 3—Micro-injection pump, 4—Infusion tube, 5—Needle tube, 6—Motor, 7—Receiving disk, 8—Ring, 9—Nanofiber, 10—Ground electrode, 11—Winding system, 12—Core yarn, 13—Unwinding system.

**Figure 5.**SEM image of nanofiber yarns at different distances between the ring and disk. (

**a**) SEM image of nanofiber yarns at ${L}_{hp}$= 3 cm. (

**b**) SEM image of nanofiber yarns at ${L}_{hp}$ = 5 cm. (

**c**) SEM image of nanofiber yarns at ${L}_{hp}$ = 7 cm.

**Figure 6.**The relationship between the ring-to-disk distance and the nanofiber yarn twist angle and nanofiber diameter.

**Figure 7.**SEM images of nanofiber yarns at different distances between the needle tip and the disk center. (

**a**) SEM image of nanofiber yarns at ${L}_{zp}$ = 7 cm. (

**b**) SEM image of nanofiber yarns at ${L}_{zp}$ = 9 cm. (

**c**) SEM image of nanofiber yarns at ${L}_{zp}$ = 11 cm.

**Figure 8.**The relationship between the distance from the needle tip to disk center and the nanofiber yarn twist angle and nanofiber diameter.

**Figure 9.**SEM images of nanofiber yarns at different distances between the needle tip and disk center. (

**a**) SEM image of nanofiber yarns at n = 40 r/min. (

**b**) SEM image of nanofiber yarns at n = 80 r/min. (

**c**) SEM image of nanofiber yarns at n = 120 r/min.

**Figure 10.**The relationship between disk rotation speed and nanofiber yarn twist angle and nanofiber diameter.

**Figure 11.**SEM images of electrospun nanofiber-wrapped yarns. (

**a**) SEM image of electrospun nanofiber-wrapped yarns at ${L}_{zp}$ = 7 cm. (

**b**) SEM image of electrospun nanofiber-wrapped yarns at ${L}_{zp}$ = 9 cm. (

**c**) SEM image of electrospun nanofiber-wrapped yarns at ${L}_{zp}$ = 11 cm.

**Figure 12.**Mechanical properties of nanofiber yarns at different distances between the ring and the disk.

**Figure 13.**Mechanical properties of nanofiber yarns at different distances between the needle tip and disk center.

**Figure 15.**Mechanical properties of nanofiber-wrapped yarns at different distances from the tip of the needle to the disk center.

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**MDPI and ACS Style**

Yan, T.; Shi, Y.; Zhuang, H.; Lin, Y.; Lu, D.; Cao, S.; Zhu, L. Electrospinning Mechanism of Nanofiber Yarn and Its Multiscale Wrapping Yarn. *Polymers* **2021**, *13*, 3189.
https://doi.org/10.3390/polym13183189

**AMA Style**

Yan T, Shi Y, Zhuang H, Lin Y, Lu D, Cao S, Zhu L. Electrospinning Mechanism of Nanofiber Yarn and Its Multiscale Wrapping Yarn. *Polymers*. 2021; 13(18):3189.
https://doi.org/10.3390/polym13183189

**Chicago/Turabian Style**

Yan, Taohai, Yajing Shi, Huimin Zhuang, Yu Lin, Dongdong Lu, Shengbin Cao, and Lvtao Zhu. 2021. "Electrospinning Mechanism of Nanofiber Yarn and Its Multiscale Wrapping Yarn" *Polymers* 13, no. 18: 3189.
https://doi.org/10.3390/polym13183189