**3. The numerical simulation and experiments verification**

In order to further reveal the injection molding mechanism and influencing rules of the processing parameters for EFD jet deposition 3D printing technology, this part will be focused on the investigation of printing performance under different conditions by means of numerical simulation and experimental verification. For the numerical simulation, the properties of substrate (or the printed layers), the printing height, and the variety of printing materials have been studied by the finite element simulation software (COMSOL MULTIPHYSICS), and the simulation results are verified by experiments. The results can be seen as follows.

#### **3.1. The effects of different substrate materials**

In order to display the electrostatic induction between the nozzle and the substrate, the intensity and the distribution of the electric field around nozzles under four different kinds conditions (no substrate, PET substrate, glass substrate, and copper substrate) were studied by finite element simulation. The relative permittivity of PET, glass, and copper substrate is 4, 10, and 1, respectively.

The reason why the substrate can change the electric field distribution is that the charges inside the substrate will redistribute by the effect of the electric field. For conductive substrate, there are lots of free charges inside the conductor, which can move freely inside the conductor. While for the insulating substrate such as PET and glass, only small amount of movable free charges can be found inside the insulating substrate, and most of charges are bounded in micro-displacement. Therefore, the electrostatic induction of the dielectric substrate is weaker than that of conductive substrate. When the conductive substrate stays in the condition of electrostatic balance, a large amount of free charges are gathered on the surface of the conductive substrate, which makes the direction of the electric field from the nozzle change to the conductive substrate. Therefore, a stronger electric field can be obtained between the nozzle

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Compared with the existing EHD jet printing, the EFD jet deposition 3D printing has better applicability for different substrate materials. The EHD jet printing technology usually requires good conductivity of the target substrate, otherwise the insulating substrate with a thickness limitation must be placed on a grounding conductor. The EFD jet deposition 3D printing technology can be used in any material of substrates because the electrostatic induction can be generated in various materials, which is not limited by the conductivity or dielectric properties of the substrate. **Figure 5** shows that the Taylor cone and stable cone jet can be formed at the nozzle by using for different material substrates (conductive stainless steel, semiconductor silicon chip, and insulating glass). The distance between the tip of the nozzle and the substrate is set as 2 mm, and the printing material is low viscosity resin (100 mPa.s). The critical voltage of cone jet for conductive stainless steel, semiconductor silicon chip, and

The experimental results show that the EFD jet deposition 3D printing is suitable for many types of substrates. And the critical voltage needed for the conductive substrate is smaller than that for the insulating substrates, which is consistent with the simulation results. Therefore, the conclusion can be proposed that the EFD jet deposition 3D printing can greatly expand the

**Figure 5.** Different target substrates (a) copper plate; (b) silicon plate; and (c) glass plate.

and conductive substrate to provide a greater driving force for droplet jetting.

insulator glass are 2100, 2500, and 3000 V.

scope and the field of applications.

The simulation results of distribution and intensity of electric field with different substrates were shown in **Figure 4**. The color represents the intensity of electric field, and the arrow indicates the direction of the electric field. As shown in **Figure 4**, under the condition of no substrate, the electric field emitted by the conductive nozzle diverges anywhere, and the intensity of the electric field at the tip of the nozzle is small. While under the conditions with substrates, it can be seen that the electric field from the conductive nozzle is terminated on the surface of the substrate, and the electric field strength between the conductive nozzle and the substrate is significantly enhanced, and the electric field intensity at the tip of the nozzle is more obvious. In these four conditions, the intensities of electric field at the tip of the nozzle are 618.1, 2794.8, 2794.9 and 3227.8 V/mm, respectively. The intensity of electric field on the copper substrate is significantly higher than that of the other three cases.

**Figure 4.** The simulation results of electric field under different substrate conditions: (a) no substrate, (b) PET, (c) glass, and (d) copper.

The reason why the substrate can change the electric field distribution is that the charges inside the substrate will redistribute by the effect of the electric field. For conductive substrate, there are lots of free charges inside the conductor, which can move freely inside the conductor. While for the insulating substrate such as PET and glass, only small amount of movable free charges can be found inside the insulating substrate, and most of charges are bounded in micro-displacement. Therefore, the electrostatic induction of the dielectric substrate is weaker than that of conductive substrate. When the conductive substrate stays in the condition of electrostatic balance, a large amount of free charges are gathered on the surface of the conductive substrate, which makes the direction of the electric field from the nozzle change to the conductive substrate. Therefore, a stronger electric field can be obtained between the nozzle and conductive substrate to provide a greater driving force for droplet jetting.

**3.1. The effects of different substrate materials**

4, 10, and 1, respectively.

28 3D Printing

and (d) copper.

In order to display the electrostatic induction between the nozzle and the substrate, the intensity and the distribution of the electric field around nozzles under four different kinds conditions (no substrate, PET substrate, glass substrate, and copper substrate) were studied by finite element simulation. The relative permittivity of PET, glass, and copper substrate is

The simulation results of distribution and intensity of electric field with different substrates were shown in **Figure 4**. The color represents the intensity of electric field, and the arrow indicates the direction of the electric field. As shown in **Figure 4**, under the condition of no substrate, the electric field emitted by the conductive nozzle diverges anywhere, and the intensity of the electric field at the tip of the nozzle is small. While under the conditions with substrates, it can be seen that the electric field from the conductive nozzle is terminated on the surface of the substrate, and the electric field strength between the conductive nozzle and the substrate is significantly enhanced, and the electric field intensity at the tip of the nozzle is more obvious. In these four conditions, the intensities of electric field at the tip of the nozzle are 618.1, 2794.8, 2794.9 and 3227.8 V/mm, respectively. The intensity of electric field on the

**Figure 4.** The simulation results of electric field under different substrate conditions: (a) no substrate, (b) PET, (c) glass,

copper substrate is significantly higher than that of the other three cases.

Compared with the existing EHD jet printing, the EFD jet deposition 3D printing has better applicability for different substrate materials. The EHD jet printing technology usually requires good conductivity of the target substrate, otherwise the insulating substrate with a thickness limitation must be placed on a grounding conductor. The EFD jet deposition 3D printing technology can be used in any material of substrates because the electrostatic induction can be generated in various materials, which is not limited by the conductivity or dielectric properties of the substrate. **Figure 5** shows that the Taylor cone and stable cone jet can be formed at the nozzle by using for different material substrates (conductive stainless steel, semiconductor silicon chip, and insulating glass). The distance between the tip of the nozzle and the substrate is set as 2 mm, and the printing material is low viscosity resin (100 mPa.s). The critical voltage of cone jet for conductive stainless steel, semiconductor silicon chip, and insulator glass are 2100, 2500, and 3000 V.

The experimental results show that the EFD jet deposition 3D printing is suitable for many types of substrates. And the critical voltage needed for the conductive substrate is smaller than that for the insulating substrates, which is consistent with the simulation results. Therefore, the conclusion can be proposed that the EFD jet deposition 3D printing can greatly expand the scope and the field of applications.

**Figure 5.** Different target substrates (a) copper plate; (b) silicon plate; and (c) glass plate.

#### **3.2. The effect of different distance between nozzle and substrate**

The distance between the nozzle and substrate is another key parameter for the EFD jet deposition 3D printing, which has an important impact on printing results. The effect of distance ranging from 0.4, 0.3, 0.2, and 0.1 mm on the electric field were simulated by COMSOL software, as shown in **Figure 6**. The intensity of electric field on the droplet surface is 3376.8, 3816.3, 4669.5 and 6910.5 V/mm, respectively. It can be seen that with the decrease of distance, the electric field formed between the conductive nozzle and the substrate is much enhanced, especially at the tip of the nozzle.

During the experiments, the distance between the conductive nozzle and the glass substrate is set as 2 mm, and the printing material is low viscosity resin (viscosity 100 mPa.s), and the voltage is 3000 V. It can be observed that the thickness of glass substrate ranging from 1.2 to 12 mm, the EFD jet deposition 3D printing can achieve stable and reliable printing. The experimental results show that the EFD jet deposition 3D printing can truly achieve the 3D printing by means of electrostatic induction between the nozzle and the target substrate (or

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The available materials for EFD jet deposition 3D printing are extensive and variable, such as organic polymer materials, bio-materials, nanoscale composites, metal, and non-conductive materials. Furthermore, the viscosity range of the printing materials is very broad because of the enough electric stress provided by the strong electric field to drive jetting. The line patterns with high resolution and high quality (line-width roughness) have been well produced

the printed layers) (**Figure 7**).

**3.3. The printing materials**

**Figure 7.** Reliably printing in variable heights and locations of printhead.

**Figure 8.** The features printed with various printing materials.

Due to the distance limitation between the conductive nozzle and the conductive substrate (or conductor under insulating substrate), the maximum distance of the EHD jet printing technology is usually not more than 3 mm, This caused great challenges in the macro/micro scale manufacturing for EHD jet printing. The EFD jet deposition 3D printing technology has broken through the distance limitation of the traditional EHD jet printing, and can truly realize the macro/micro-scale manufacturing. When the high voltage power is applied to the conductive nozzle, the required electric field can be formed between them under the action of electrostatic induction only if moving nozzle closed to the target substrate (or the printed layers). Therefore, this proposed technology can print on any structure surface.

The experiments have been done to investigate the stability of the Taylor cone shape and the cone jet in the printing process influenced by the substrate thickness, as shown in **Figure 7**.

**Figure 6.** The simulation results of electric field at different nozzle heights: (a) 0.4 mm, (b) 0.3 mm, (c) 0.2 mm, and (d) 0.1 mm.

During the experiments, the distance between the conductive nozzle and the glass substrate is set as 2 mm, and the printing material is low viscosity resin (viscosity 100 mPa.s), and the voltage is 3000 V. It can be observed that the thickness of glass substrate ranging from 1.2 to 12 mm, the EFD jet deposition 3D printing can achieve stable and reliable printing. The experimental results show that the EFD jet deposition 3D printing can truly achieve the 3D printing by means of electrostatic induction between the nozzle and the target substrate (or the printed layers) (**Figure 7**).

#### **3.3. The printing materials**

**3.2. The effect of different distance between nozzle and substrate**

substrate is much enhanced, especially at the tip of the nozzle.

The distance between the nozzle and substrate is another key parameter for the EFD jet deposition 3D printing, which has an important impact on printing results. The effect of distance ranging from 0.4, 0.3, 0.2, and 0.1 mm on the electric field were simulated by COMSOL software, as shown in **Figure 6**. The intensity of electric field on the droplet surface is 3376.8, 3816.3, 4669.5 and 6910.5 V/mm, respectively. It can be seen that with the decrease of distance, the electric field formed between the conductive nozzle and the

Due to the distance limitation between the conductive nozzle and the conductive substrate (or conductor under insulating substrate), the maximum distance of the EHD jet printing technology is usually not more than 3 mm, This caused great challenges in the macro/micro scale manufacturing for EHD jet printing. The EFD jet deposition 3D printing technology has broken through the distance limitation of the traditional EHD jet printing, and can truly realize the macro/micro-scale manufacturing. When the high voltage power is applied to the conductive nozzle, the required electric field can be formed between them under the action of electrostatic induction only if moving nozzle closed to the target substrate (or the printed

The experiments have been done to investigate the stability of the Taylor cone shape and the cone jet in the printing process influenced by the substrate thickness, as shown in **Figure 7**.

**Figure 6.** The simulation results of electric field at different nozzle heights: (a) 0.4 mm, (b) 0.3 mm, (c) 0.2 mm, and

(d) 0.1 mm.

30 3D Printing

layers). Therefore, this proposed technology can print on any structure surface.

The available materials for EFD jet deposition 3D printing are extensive and variable, such as organic polymer materials, bio-materials, nanoscale composites, metal, and non-conductive materials. Furthermore, the viscosity range of the printing materials is very broad because of the enough electric stress provided by the strong electric field to drive jetting. The line patterns with high resolution and high quality (line-width roughness) have been well produced

**Figure 7.** Reliably printing in variable heights and locations of printhead.

**Figure 8.** The features printed with various printing materials.

using four different types of materials, including the photosensitive resin, nanosilver conductive paste, polycaprolactone (PCL), and conductive silver adhesive, as shown in **Figure 8**.

pattern has been successfully printed on a glass slide, as shown in **Figure 9(b)**. The average line width in this pattern is about 40 μm, and the line pitch is about 150 μm. Due to the ability of depositing materials directly as desired patterns on the substrate with a simple fabrication process and high efficiency, the proposed printing method can be adapted for applications in thin-film transistors, optical elements, organic light-emitting diodes, photonics crystals, and

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By using the conductive nanosilver paste, the proposed printing method can be applied for fabrication of metal-mesh patterns used in various electronics such as flexible displays, solar cells, touch panels, etc. **Figure 10** shows the optical images of the printed metal-mesh patterns. The line width and spacing of the metal mesh in **Figure 10(a)** are 20 and 250 μm, respectively. And the line width and spacing in **Figure 10(b)** are 10 and 150 μm, respectively. The line resolution of the printed metal-mesh patterns is less than 20 μm, which is almost invisible to the naked eye. It indicates that the proposed technology is promising to fabricate an invisible fine transparent electrode with good electricity and optical properties, which can be widely applied to electronic devices without any cosmetic issues due to the appearance of metal pattern.

The EFD jet deposition 3D printing technology is mainly used for liquid printing materials, it also can be used for printing molten polymer materials by changing the nozzle structure. The material feeding unit is integrated into the printhead to shorten the distance between material feeding unit and the nozzle, because solid state printing material is difficult to be delivered to the nozzle through pipeline. The double heating module is used to heat both nozzle and feeding unit. The purpose of heating feeding unit is to keep the printed material in the melting state with certain fluidity, and that of heating nozzle is to ensure the quality and precision of the printing process. Instead of utilizing polymer solutions as the printing material, the molten EFD jet 3D printing employs molten polymers as the printing materials. Due to the printing material is PCL with a melting point of about 60°C. A heating module with a heating temperature of 80°C is utilized to melt the solid polymer into flowing melts. Moreover, the molten polymer solidifies very quickly that benefits for the layered manufacturing of high aspect ratio structures. **Figure 11**

**Figure 10.** Metal-mesh patterns with (a) line width of 20 μm and spacing of 250 μm; (b) line width of 10 μm and spacing

**4.2. The micro-scale "wall" structure (two-dimensional structure)**

DNA microarrays.

of 150 μm.

The materials in the experiment have different fluidic properties and the viscosity. The viscosity of the photosensitive resin is 800 cP while the viscosity of nanosilver conductive paste is 5000 cP. The heating system was used for molding of PCL because of its solid-state at RT. The nozzle with an inner diameter of 250 μm is adopted to print objects with a line width of 10 μm, where the reduction ratio in dimensions between the nozzle and the printed line reaches 25:1.

The viscosity of the conductive silver adhesives at ambient temperature is 8000 cP, the inner diameter of the nozzle is 250 μm, the line width of the object to be printed is 200 μm, and the print patterns must have good morphology. The results showed that the EFD jet 3D printing is suitable for almost any materials, compared to existing 3D printing technology. It is unexamined for its potential to provide high-resolution (that is, ~10um) patterning of materials with ultra-high viscosity.
