Influence of Processing Conditions on the Basis Weight Uniformity of

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The Influence of Processing Conditions on the Basis Weight Uniformity of Melt-Blown Fibrous Web: Numerical and Experimental Study Guangwu Sun, Jingru Yang, Sanfa Xin, Ranxue Yu, and Xinhou Wang Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00829 • Publication Date (Web): 28 Jun 2018 Downloaded from http://pubs.acs.org on July 1, 2018

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Industrial & Engineering Chemistry Research

The Influence of Processing Conditions on the Basis Weight Uniformity of Melt-Blown Fibrous Web: Numerical and Experimental Study Guangwu Sun1, Jingru Yang2, Sanfa Xin1, Ranxue Yu3,4, Xinhou Wang3,4,*

1

School of Fashion Engineering, Shanghai University of Engineering Science, Shanghai, PR China 2

College of Textiles, Zhongyuan University of Technology, Zhengzhou, P.R. China

3

College of Textiles, Donghua University, Shanghai, P.R. China

4

Key Laboratory of Textile Science & Technology of Eco-Textile, Ministry of Education, Donghua University, Shanghai, P.R. China

Keywords: melt-blowing, basis weight uniformity, processing conditions, CFD simulation

1

ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Basis weight uniformity of the melt-blown fibrous web is attracting considerable interesting, because it directly affects the application performance of the nonwovens. There are numerous studies which introduce factors of processing conditions on the basis weight uniformity based on their final applications. However, theoretical research is still scarce. This paper described the numerical modeling (bead-viscoelastic element fibrous model) involving fibrous web structure generation and BWU evaluation. Four processing conditions including velocity of air jet and suction, die to collector distance and moving speed of collector on the basis weight uniformity of fibrous web were quantitatively analyzed. Additionally, the computational fluid dynamics simulation was employed to study the air flow (including the suction) in the melt-blowing process. The simulated results were in a good agreement with the experimental data. The numerical model was practical and could better be used to research the problems on fibrous web formation and structures.

1. Introduction In melt blowing process, the molten polymer is firstly extruded by the die. And then it is drawn and gradually solidified by high speed air jet to form the superfine fibers. These fibers are finally deposited on the grid-like collector to form fibrous web. The final melt-blwon (MB) nonwovens are subsequently produced by bonding the fibrous web with two hot rollers. Due to their inherent properties such as large fiber surface area, MB nonwovens are suitable for filtration1, insulation2, and liquid absorption3 applications.

In general, the MB nonwovens with good basis weight uniformity (BWU) have the uniform distribution of characteristic parameters, such as mass, porosity and thickness, etc. These characteristic parameters will directly influence the applied performance of MB products. For example, in filtration process, a MB nonwoven filter generated by non-uniform fibrous web may be failure because it allowed large particles to pass through the thin spots in the fiber sheet. How to fabricate a uniform fibrous web is a complicated engineering problem, because BWU is strongly dependent on the comprehensive effect of various processing conditions in MB. Until now, many researchers studied this issue by the experimental methods. For instance, according to the experimental study of Lee and Wadsworth4, the temperature and speed of air jet influenced the web structure and properties in a similar way. Increase of them both caused a decrease in pore size and air permeability, but an increase in filtration efficiency. It is believed that a decrease in the fiber diameter causes more fibers-entanglements. Bresee et al5-8 performed a series of experiments to study the influence on the MB fibrous web properties including pore, orientation, BWU by image analysis technology. In their study, the air jet was considered as a main factor 2


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which affected the BWU of fibrous web. Another experimental approach based on BWU study was reported by Chhabra9, who confirmed that the increasing die to collector distance (DCD) helped to generate uniform fibrous web with finer fibers. Because the finer fibers reduced the basis weight difference among different parts of the fibrous web. Xu et al10 reported a series of melt blowing experiments by employing polypropylene chips. They found that the thickness, maximum and average pore size of fibrous web were enlarged as the DCD increased. And BWU gradually became worse as polymer mass flow rate increased.

The above-mentioned experimental researches provide a good understanding on the fibrous web formation and process conditions. However, experimental adjustment not only is time-costing, but also usually generates deviation of BWU. Therefore, evaluating the BWU of MB fibrous web before its final application even before the whole fabrication is necessary. The numerical simulation is the one method that could provide the predicted assessing results instead of practical experiments. Till now, the numerical modeling work concerning the mechanism between BWU of fibrous web and processing conditions is still scarce throughout the reported literature. To the best of our knowledge, a model called quasi-one-dimensional model, presented by Yarin11, was used for predicting the fiber lay-down patterns on the collector. In their improved work12, the detailed three-dimensional structure, fiber-size distribution and basis weight distribution (BWD) were numerically studied. Battocchio13 also presented a numerical model to describe the fiber dynamics and the fiber lay-down on the collector, the uniformity of the fibrous web was studied and verified by image analysis technology. However, the mentioned researches did not try to numerically study the mechanism between BWD and different processing conditions. In order to further quantitatively study the mechanism, in this work, finite element calculation of the MB air flow was firstly performed. Then we analyzed the influence of processing conditions involving velocity of air jet and suction, DCD, and the moving speed of collector on the BWU based on the model (a type of bead-viscoelastic element model) presented before14. The experimental results were in good agreement with the simulation results. Thus, our numerical study and the results will help commercial manufacturer to avoid non-uniform nonwoven products.

2. Theoretical Section The theoretical section is composed of following three parts: (i) The computational fluid dynamics (CFD) simulation of the airflow; (ii) The dynamic equations of fiber and fibrous web formation; (iii) BWU evaluation. 2.1 Airflow Field CFD Simulation ∂ρ a + div (ρ a Va ) = 0 ∂t

(1)

3



ρa

DVa = ρ a Fa + div (τ a ) Dt

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(2)

 h  ∂ (ρ a Ta ) + div (ρ aVa Ta ) = div  gradT a  + ST ∂t  Ca 

(3)

CFD simulation was a common method to solve the air flow fields of melt blowing process15-20. As an important influence factor of fiber generation, the air jet ejected from the die was usually brought into focus. However, the suction under the collector was always in the cold. In this work, the air flow fields we studied were composed of the air jet and the suction. The CFD simulation was performed to solve the Naiver-Stokes equation (1)-(3) which were the mass conservation, momentum conservation, and energy conservation equations by using Fluent module of ANSYS Software. Fa is the body force of air, τ is the stress caused by viscosity of air, Ca is the thermal capacity of air, and ST is the Viscous dissipation term. The computational domain including the suction and the collector (the staggered cylinders) was shown in Fig.1. The collector was double-layer and made of aluminum by knitting, the mesh size was 1.5 mm × 1.5 mm, the diameter of cylinders in mesh was 3 mm, the gap between two layers was 6 mm. The details of the boundary conditions were as follows:

Inlet 1: This was a narrow plane where the compressed air crushed into the computational fluid domain. It was defined as a “velocity inlet” plane which could be set as 200 m/s, 250 m/s, 300 m/s, 350 m/s, 400 m/s, respectively. The temperature of the Inlet 1 was 583 K. Inlet 2: This was a plane where the suction located. It was also defined as another “velocity inlet” plane which was respectively set as -50 m/s, -40 m/s, -30 m/s, -20 m/s, -10 m/s, 0 in our simulation. Because the suction pressure was negative, so the velocity of suction was also negative. And the temperature of the suction was room temperature (300 K). Outlet: This was the outlet plane which connected with the atmospheric condition (1 atm). Symmetry: The computational fluid domain covered only 1/4 of the total air flow field limited by the symmetry planes for simplifying the calculation. Wall: It was a no-slip wall and the temperature was 583 K.

K-epsilon model was used as the viscous model. Similar with the work of Krutka21, the parameters C1-Epsilon and C2-Epsilon were 1.20 and 2.05, respectively. The solution was considered as convergent when the residual was smaller than 0.001. The obtained 4


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velocity distribution was used for calculating the air drag acting on the fiber.

Figure 1. Computational domain of air flow field

2.2 Numerical modeling of the fiber formation The theoretical background of the present work was described in detail in the previous works of this group22-24. The fiber was described as a model of a series of beads connected by Newton dashpot and Hook spring (Maxwell model), as shown in Fig.2. Each segment of the fiber could be stretched or bended. The beads were driven and drawn by air drag and gravity. The air drag was calculated on the basis of the velocity distribution of the air jet which was obtained from the CFD simulation. The viscoelastic force of beads tending to resist deformation could be calculated based on Maxwell constitutive equations. The mass conservation, energy conservation and the governing equations of the bead-viscoelastic element fiber model were as follows: 1 πρ f d i2−1,i li −1,i = m0 4

miC p , f ,i

mi

dT f ,i

dt

= − hπ

d i −1,i + d i ,i +1 li −1,i + li ,i +1 (T f ,i − Ta ,i ) 2 2

d 2ri = Fdi + Fvei + Fbi + mi g dt 2

In Eqs.(4-6), subscript (i − 1, i ) is the fiber element (i − 1, i ) which is composed of bead i and bead i − 1 .

ρ f is the fiber density. d and l are the diameters and

length of fiber, respectively. m0 is the initial fiber mass and was determined by the polymer flow rate. h is the convective heat transfer coefficient. C p , f is the thermal capacity of fiber. Ta is the temperature of air flow which was obtained from the CFD simulation. T f is the temperature of fiber. Fd is the air drag, Fve is the viscoelastic force, Fb is the surface tension. ri = ixi + jyi + kzi is the spatial position of bead i .

Figure 2. Schematic of a bead−viscoelastic fiber element 5



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All of the equations of the numerical model could be found in the Support Information. Combined with the simulated air flow, BWU would be evaluated by using the following procedure: 1. At the beginning of modeling, the fiber segment was formed by two neighboring beads i and i − 1 . The length of the fiber segment was 1 mm, which was equal to the initial straight part25. Initial physical properties were given to the two beads, including density, mass, diameter, and so on. 2. As the procedure ran, beads in the system were driven by the air drag and gravity, which was calculated based on the Eqs. (A4−A13) in the Support Information and the velocity distribution of the air jet mentioned in section 2.1. The viscoelastic force could be calculated by employing Eqs. (A14-A16). The surface tension could be solved by applying Eqs. (A17-A19). The procedure could export the spatial position of beads at every time step. 3. If the vertical distance between bead i and the orifice was larger than L (L is an independent variable), then a new bead i + 1 appeared at the position of the orifice. The initial physical properties were also given to the new bead. 4. As the procedure continued to run, if the distance between bead i − 1 and the orifice was identical to DCD, i.e., bead i − 1 had landed on the collector, then the computer recorded flying-time ti −1 of bead from the die to the collector and the coordinates of bead i − 1 as (xi∗−1 , yi∗−1 ) . When bead i − 1 landed on the collector, the computer exported the time ti and the coordinates (xi∗ , yi∗ ) . Meanwhile, the coordinate of bead

(

∗ ∗ i − 1 had been updated to xi + (ti − ti −1 )s, yi

)

because of the movement of collector

along the x-direction (MD direction) with speed s . All of the specification of the polymer properties and processing conditions used in the simulation were listed in Tab.1.

Table 1. Specification of the Polymer (polypropylene) Properties and processing conditions

Explanation

Symbol

Value

Total number of beads

N

400

Fiber density22

ρf

598.28 kg/m3

6


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Air density

ρa

1.293 kg/m3

Air dynamic viscosity

µa

0.297×10-4 Pa·s

Initial temperature of fiber

Tf

583 K

Initial diameter

df

949 µm

Air jet temperature at the die

Ta

583 K

Elastic modulus

E

2.8×104 Pa

It should be emphasized that our group presented in the past a custom-written Matlab program which was employed to simulate the formation of fiber and fibrous web in melt blowing22-24. The program traced motion of beads by calculating the forces acting on the beads and velocity of beads. In this study, we further numerically study the influence of the processing conditions on the BWU based on our previous work14.

2.3 BWU evaluation BWU was evaluated by using the parameter called “basis weight coefficient of variation (BWCV)”. Herein, BWCV was used for expressing the basis weight dispersion among different parts of a fibrous web. It is evaluated as following expressions: BWCVCD ,MD =

STDCD ,MD BWCD , MD

Where, P

BWCD =

pw

p =1 w =1

P P

BWMD =

W

∑∑ BW W

∑∑ BW

pw

p =1 w =1

STD CD =

W P



W

∑  ∑ BW p =1

w =1

pw

 − BW CD  

2

7



 P  = ∑  ∑ BWpw − BWMD  w=1  p =1  W

STDMD

BW pw

2

n 1 πρ f ∑ d i2-1,i li-1,i 4 i=2 = BWT

Herein, P × W is the quantity of separated pieces of each fibrous web. BWCV MD ,CD is the BWCV along machine direction (MD) and cross direction (CD) of a fibrous web.

STD is the standard deviation of normalized basis weight of fibrous web. BW pw , the normalized basis weight of each piece, it is the basis weight of single piece to the total fibrous web weight BWT ratio. p and w represent the row and column order of fibrous web piece, respectively. n is the total number of beads in one piece of fibrous web. According to the Eq. (7), BWCV means the ratio of the standard deviation to the mean value of different pieces along MD or CD. Therefore, the abundant basis weight dispersion of different pieces results in a larger BWCV which means a worse BWU. While, a smaller BWCV leads to a better BWU.

Experimental Section 3.1 Air flow field measurement The velocity distribution of the air jet was measured by hot-wire anemometer (Model 55P11, Dantec Dynamics Inc., Denmark) in the room temperature. As shown in Fig.3, the sensor was installed on the removable holder, which could move a certain distance along a direction after each measurement (the measurement was performed several times at each measurement point). The experiment was respectively performed in the different air flow fields, and the results were compared with simulated results in the section 4.1.

Figure 3. Experiment: measurement of air flow

3.2 Fibrous web fabrication In MB experiment, the employed polymer was polypropylene (purchased from Huada Co., Ltd., China), the experimental instrument was a melt blowing machine with a single orifice which was also purchased from the above company. For comparing with simulation, the experimental processing conditions were the same with that of the simulated ones. They included: air jet velocity with the range of 200 m/s to 400 m/s, 8


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suction speed with the range of 0 to 50 m/s, moving speed of collector with the range of 4 cm/s to 14 cm/s, die to collector distance (DCD) in the range of 10 cm to 40 cm. As stated in Eq. (7), the collected fibrous web was separated into P × W pieces (In this work, for an example, P = 4 and W = 6). Each piece was weighed following the standard ISO 9073-1. And the BWCV value was calculated according to Eqs.(7-8). The results of experiment and simulation were given in the section 4.3.

4. Results and Discussion 4.1 The experimental and simulated results of air flow field In this work, to numerically study the influence of processing conditions on the BWU, different air jets were adopted and calculated. In the past few decades, the attenuation rule of the air jet velocity had been almost completely studied by experimental and numerical method26-29, but the study about suction was still scarce. We expect to provide the analysis about the simulation of suction in this section. Therefore, the MB air flow velocity in the x-z plane without (inlet 2 velocity = 0 m/s) and with suction (inlet 2 velocity = -50 m/s) were respectively shown in the Fig.4. The calculated velocity curves and experimental results are shown in the Fig.5. The results of all air flows could be found in the Support Information.

Figure 4. (a) Velocity contour in the x-z plane of simulated air flow without suction; (b) Velocity contour in the x-z plane of simulated air flow with suction velocity 50 m/s

Figure 5. the air flow speed with different suction speeds

In Fig.4, it could be seen that two air jets which were accelerated and ejected from dual slots of the die mixed together below the die. After fusion, the air jet gradually spread in the opening environment, meanwhile, the speed of air jet rapidly decayed. When the air jet was close to the collector, it passed through the mesh of the collector with cylinder shape, and its velocity was firstly increased and then reduced to almost zero below the mesh. This was a classical hydro-mechanical phenomenon called “flow around cylinder”. Air flow could spread in the collector by accelerating and passing through the gaps between the cylinders.

The verified experimental process was introduced as follows. Originally, the test domain was chose to be the length of 0 ~ 0.1 m under the die. Because air jet velocity 9



was larger than the range of the hot-wire anemometer when z < 0.04 m. Additionally, due to the obstruction of collector at z = 0.08 m and the difficult to test the air flow velocity inside the collector, so the measuring domain of air jet velocities was only 0.04 m ≤ z ≤ 0.08 m. Thus, the measuring position to the die along the threadline was 0.04 m, 0.05 m, 0.06 m, 0.07 m, 0.08 m. Our experimental results were compared with the simulated ones in Fig.5. According to numerical points and curves, it could be seen that the experimental data and the simulated data are in good agreement in the domain z ≤ 0.06 m. This showed that the simulation results could exhibit the characteristic of the air flow field. So, we can still obtain the characteristic of the air flow field on the basis of the simulated results even without experimental data under collector. According to the whole curves in Fig.5, in the domain z ≤ 0.06 m, the suction had little influence on the air jet. But in the domain 0.08 m ≤ z ≤ 0.1 m, the effect of suction on the air jet value will gradually increase as the distance increases. The suction could obviously promote the air flow velocity and will directly affect the fiber lay-down on the collector. Therefore, the suction under the collector is worth researching deeply.

4.2 Fibrous web structure and basis weight distribution

Figure 6. Predicted and fabricated fibrous web: (a) simulation snapshot and experimental picture; (b) predicted and measured BWD

The overall view of the predicted deposition of MB fibers on a moving collector was shown in Fig.6(a). The predicted fibrous web was collected at 25 cm, where molten polymer vigorously bended and flapped due to the action of the air drag force. The fibers were collected on the moving collector at a constant speed. In Fig.6 and hereinafter, the x coordinate was reckoned in the MD, the y coordinate was reckoned in the CD. Experimental fibrous web picture was also displayed for comparison. The morphology of predicted and experimental fabricated fibrous web also exhibited uniform and non-uniform part. The uniform part consisted of evenly distributed fibers and was located in the middle of the web, while the non-uniform part was composed of fewer fibers and existed in the edge of the web.

Fig.6(b) shows the calculated results according to the Eq.(8), comparing the BWD of the simulated and the experimental fibrous web. The predicted BWD was similar to that of the experimental one. After BWD calculation, the BWCV could be obtained according to the Eq.(7). The influence of processing conditions on the BWCV and the analysis would be provided in the next section. 10


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4.3 The influence of processing conditions on the BWU The processing conditions which were investigated in this study involved: air jet velocity, suction speed, the moving speed of collector and DCD. In order to investigate single factor, other conditions kept constant in the simulation and experiment. All of the data could be found in the Support Information.

4.3.1 The influence of air jet velocity

Figure 7. (a) Simulated BWCV values at various nominal jet velocities; (b) Experimental BWCV values at various nominal jet velocities

Air jet velocity was changed from 200 m/s to 400 m/s, the step length was 50 m/s. Other processing conditions kept constant, the suction speed was 30 m/s, the speed of the collector was 4 cm/s, the DCD was 25 cm. The predicted and experimental results were displayed in Fig.7. It could be seen from Fig.7 that BWCV value was decreased rapidly when air jet velocity was increased until 350 m/s. That meant a more uniform web along both CD and MD was generated in this velocity range. This was reasonable since higher air jet velocity led to the generation of finer fiber. And the web consisted of finer fibers usually had a better BWU. In the study of Bresee30-33, finer fibers were usually observed in the higher air jet velocity. The pores between finer fibers were evenly distributed in fibrous web. They also believed that the fine fiber and evenly distributed small pores generated a uniform fibrous web. But in our experiment, uniformity of the fibrous web became worse when the air jet velocity was larger than 350 m/s. The unstable fibers were easily blown away from the fibrous web if the air jet was enough fast. The high speed air jet destroyed the original fibrous web structure and resulted in the generation of uneven fibrous web.

The experimental and predicted data also demonstrated a common rule that BWCVMD was smaller than that of BWCVCD. The non-uniform part of fibrous web along MD was improved because continuous filaments were fallen on the moving collector and covered the thin part in melt blowing. It was both in line with our observation and the study of Chhabra9.

4.3.2 The influence of suction speed

11



Figure 8. (a) Simulated BWCV values affected by the suction speed; (b) Experimental BWCV values affected by the suction speed

In our simulation and experiment, the processing conditions except for suction speed were constant, the air jet was 300 m/s, the moving speed of collector was 4 cm/s, and DCD was 25 cm. The range of suction speed was from 0 to 50 m/s. The experimental and simulated data were shown in Fig.8. The BWCV values declined whereas the suction air raised. The experimental and simulated results displayed that faster suction could improve the BWU of fibrous web. From our observation, the suction could help the collector gathering the “flies” (the uncontrolled short fibers) as much as possible. In addition, some minor differences between the simulation and the experiment were appeared when the suction speed was larger than 30 m/s. Our experiment detected that, compared with the lower suction speed (30 m/s) could not further affect the BWCV. While, in our simulation, the suction with high velocity could still affect the air jet directly. Because in our CFD simulation of the air flow, the fiber was not existent. Thus, the suction could easily affect the whole air flow and then the BWCV in the CFD stimulation. This deviation between modeling and experiment could be improved if a type of fiber-air coupling model is applied. And corresponding work is performing in our group.

4.3.3 The influence of moving speed of collector

Figure 9. (a) Simulated BWCV values at various collector speeds; (b) Experimental BWCV values at various collector speeds

In order to study the influence of collector speed, other processing conditions were constant. The air jet was 300 m/s, the suction speed was 30 m/s, DCD was 25 cm. The moving speed of collector was changed from 4 cm/s to 14 cm/s. The similar tendency appeared on the experimental and simulated curves in Fig.9. Obviously, the BWU along MD of fibrous web became better gradually with the increasing of the collector speed. It could be seen that the basis weight of fibrous web was more evenly distributed across MD in comparison to the case of the lower collector speed. This was also similar to the predictions in Ghosal’s work12. According to our observation, continuous the filaments were fallen on the collector along MD. Once the speed of collector increased, the BWU appeared a particularly obvious improvement.

12


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4.3.4 The influence of DCD

Figure 10. (a) Simulated BWCV values at various DCD; (b) Experimental BWCV values at various DCD

In this section, the air jet was 300 m/s, the suction speed was 30 m/s, speed of collector was 4 cm/s, and the DCD was in range of 10 cm to 40 cm. In Fig.10, BWCV value was declining and obtained smallest when DCD equaled to 35 cm. Due to the turbulence generated by two air jet from the dual-slots, the fiber revealed extensively whipping near the die. In addition, another reason was that the molten polymer had not been fully attenuated to form fiber. Therefore, it was difficult to collect uniform fibrous web when DCD was smaller. However, according to our observation, some of the fibers might be blown away if the DCD was larger than 35 cm, and the BWU also became worse. Another rule of the curves was that, when DCD was increasing, the difference of BWCV value between MD and CD was reducing. Because of the dual-slots, the lateral displacements of fiber were larger along CD than MD, which led to major BWU difference especially near the die.

Conclusion The comprehensive model outlined in the present work and implemented with simulated air flow filed was used to predict the influence of processing conditions on the BWU and compared the results with the available experimental data. The modeling work was capable of predicting reasonable fiber spacial path and final web structure with both uniform and non-uniform part formed on a moving collector, as well as the BWU for different processing conditions. The predicted variation rule of the BWCV was found to be in a fairly good agreement with the experimental data. It was also found that the increase of processing conditions including air jet velocity, speed of collector, suction speed and DCD led to a gradually improvement of BWU. However, these types of improvement were limited. For instance, the DCD should be shorter than 40 cm, the suction speed was lower, preferably under 30 m/s, and the air jet velocity was preferably less than 350 m/s. In addition, the numerical predictions also suggested that the BWU of fibrous web along CD was worse than that of MD. The comprehensive model of this work elevated the theoretical/numerical capabilities for BWU evaluation of melt blown fibrous web. And our study could guide the fabrication of MB nonwovens with desirable BWU.

13



ASSOCIATED CONTENT

Supporting Information Bead-viscoelastic element fiber model, velocity field of MB air flow calculated by FLUENT software, experimental data of air flow, experimental and predicted data of BWCV.

AUTHOR INFORMATION

Corresponding Author E-mail: [email protected]

ORCID Guangwu Sun: 0000-0001-8667-8119 Jingru Yang: 0000-0002-8780-3919 Sanfa Xin: 0000-0001-6154-4958 Ranxue Yu: 0000-0001-8820-4873 Xinhou Wang: 0000-0001-9377-2883

Funding Sources Dr. Sun received funding from National Natural Science Foundation of China, Project 51703124. Dr. Sun also received funding from Early Development Program of Shanghai University of Engineering and Science, Project 2018-31.

NOMENCLATURE p = row number of fibrous web

w = column number of fibrous web P = total row number of fibrous web W = total column number of fibrous web

Va = velocity of air jet Fa = the body force

14


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Ca = the air heat capacity

ST = the vicious dissipation term i = the numerical order of bead

N = the total number of beads xi∗ = the x coordinate of bead i on the collection screen yi∗ = the y coordinate of bead i on the collection screen

s = the speed of collection screen n = the number of beads in one separated part l = the distance between two neighboring beads d = the diameter of the fiber segment Fd = the aerodynamic force Fs = shear drag Fp = pressure drag

C p = shear drag coefficient C f = the pressure drag coefficient v ti = the relative velocity of bead i in the axial direction v ni = the relative velocity of bead i in the normal directions

ft = unit vector that is parallel to the axis of fiber segment fn = the unit vector normal to fiber axis v ri = the relative velocity of bead i 15



ri = the spatial position of bead i ki = the curvature of bending part

r ' = the first order derivative of r r '' = the second order derivative of r Fvei = viscoelastic force of bead i Fbi = surface tension of bead i

GREEK LETTERS

ρ a = density of air ρ f = the density of polymer

µa = the dynamic viscosity of air jet ϕ = the angle between the fiber axis and the z axis

α = the angle between the projection of the fiber segment on the x-y plane σ = the tensile stress acting on the fiber segment η = the coefficient of surface tension ABBREVIATION MB = melt blowing BWD = basis weight distribution BWU = basis weight uniformity BWCV = variation coefficient of basis weight DCD = die to collection distance MD = machine direction CD = cross direction

16


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REFERENCE (1) Krucinska, I.; Surma, B.; Chrzanowski, M.; Skrzetuska, E.; Puchalski, M. Application of Melt-blown Technology in the Manufacturing of a Solvent Vapor-sensitive, Non-woven Fabric Composed of Poly(lactic acid) Loaded with Multi-walled Carbon Nanotubes. Text. Res. J. 2013, 83, 859-870. (2) Modarresifar, F.; Bingham, P.A.; Jubb, G.A. Thermal Conductivity of Refractory Glass Fibres: a Study of Materials, Standards and Test Methods. J. Therm. Anal. Calorim. 2016, 125, 35-44. (3) Wang, Z.; Espin, L.; Bates, F.S. Water Droplet Spreading and Imbibition on Superhydrophilic Poly (butylene terephthalate) Melt-blown Fiber Mats. Chem. Eng. Sci. 2016, 146, 104-114. (4) Lee, Y.; Wadsworth, L.C. Structure and Filtration Properties of Melt Blown Polypropylene Webs. Polym. Eng. Sci. 1990, 30, 1413-1419. (5) Huang, X.C.; Bresee, R.R. Characterizing Nonwovens Web Structure Using Image Analysis Techniques. Part 1: Pore Analysis in Thin Webs. Int. Nonwovens J. 1993, 5, 13-21. (6) Huang, X.C.; Bresee, R.R. Characterizing Nonwovens Web Structure Using Image Analysis Techniques. Part 2: Fiber Orientation Analysis. Int. Nonwovens J. 1993, 5, 14-21. (7) Huang, X.C.; Bresee, R.R. Characterizing Nonwovens Web Structure Using Image Analysis Techniques. Part 3: Web Uniformity Analysis. Int. Nonwovens J. 1993, 5, 28-38. (8) Chao, X.; Bresee, R.R. Characterizing Nonwovens Web Structure Using Image Analysis Techniques. Part 4. Int. Nonwovens J. 1993, 5, 28-38. (9) Chhabra, R.; Shambaugh, R.L. Probabilistic Model Development of Web Structure Formation in the Melt Blowing Process. Int. Nonwovens J. 2004, 13, 24-34. (10) Xu, Q.; Wang, Y. The Effects of Processing Parameter on Melt-blown Filtration Materials. Adv. Mater. Res. 2013, 650, 78-84. (11) Yarin, A.L.; Sinha-Ray, S.; Pourdeyhimi, B. Meltblowing: Multiple Polymer Jets and Fiber-size Distribution and Lay-down Patterns. Polymer. 2011, 52, 2929−2938. (12) Ghosal, A.; Sinha-Ray, S.; Yarin, A.L.; Pourdeyhimi, B. Numerical Prediction of the Effect of Uptake Velocity on Three Dimensional Structure, Porosity and Permeability of Meltblown Nonwoven lay-down. Polymer. 2016, 85, 19-27. (13) Battocchio, F.; Sutcliffe, M.P.F. Modelling Fiber lay-down and Web Uniformity in Nonwoven Fabric. Modell. Simul. Mater. Sci. Eng. 2017, 25, 1-24. (14) Sun, G.W.; Yang, J.Y.; Sun, X.X.; Wang, X.H. Simulation and Modeling of Microfibrous Web Formation in Melt Blowing. Ind. Eng. Chem. Res. 2016, 55, 17



5431-5437. (15) Sun, Y.F.; Wang, X.H. Optimization of Air Flow Field of the Melt Blowing Slot Die via Numerical Simulation and Genetic Algorithm. J. Appl. Polym. Sci. 2010, 115, 1540-1545. (16) Sun, Y.F.; Wang, X.H. Study on Air Flow Field of the Melt Blowing Slot Die via Numerical Simulation and Multi-Objective Genetic Algorithm. J. Appl. Polym. Sci. 2011, 112, 3520. (17) Wang, Y.D.; Wang, X.H. Investigation on a New Annular Melt-blowing Die Using Numerical Simulation. Ind. Eng. Chem. Res. 2013, 52, 4597-4605. (18) Wang, X.; Ke, Q. Empirical Formulas for Distributions of Air Velocity and Temperature along the Spinline of a Dual Slot Die. Polym. Eng. Sci. 2005, 45, 1092. (19) Wang, X.H.; Chen, T.; Huang, X.B. Simulation of the Polymeric Fluid Flow in the Feed Distributor of Melt Blowing Process. J. Appl. Polym. Sci. 2006, 101, 1570-1574. (20) Chen, T.; Huang, X. Numerical Simulation of the Air flow Flow Field in the Melt Blowing Process. J. Donghua Univ. 2002, 19, 1. (21) Krutka, H.M.; Shambaugh, R.L.; Papavassiliou, D.V. Analysis of the Temperature Field from Multiple Jets in the Schwarz Melt Blowing Die Using Computational Fluid Dynamics. Ind. Eng. Chem. Res. 2006, 45, 5098-5109. (22) Sun, Y.F.; Zeng, Y.C.; Wan, X.H. Three-Dimensional Model of Whipping Motion in the Processing of Microfibers. Ind. Eng. Chem. Res. 2011, 50, 1099−1109. (23) Zeng, Y.C.; Sun, Y.F.; Wang, X.H. Numerical Approach to Modeling Fiber Motion During Melt Blowing. J. Appl. Polym. Sci. 2011, 119, 2112−2123. (24) Sun, G.W.; Song, J.; Xu, L.; Wang, X.H. Numerical Modelling of Microfibers Formation and Motion during Melt Blowing. J. Text. Inst. 2018, 109, 300-306. (25) Sinha-Ray, S.; Yarin, A.L.; Pourdeyhimi, B. Meltblowing: I-basic Physical Mechanisms and Threadline Model. J. Appl. Phys. 2010, 108, 034912. (26) Uyttendaele, M.A.J.; Shambaugh, R.L. The Flow Field of Annular Jets at Moderate Reynolds Numbers. Ind. Eng. Chem. Res. 1989, 28, 1735-1740. (27) Harpham, A.S.; Shambaugh, R.L. Velocity and Temperature Fields of Dual Rectangular Jets. Ind. Eng. Chem. Res. 1997, 6, 3937-3943. (28) Wang, Y.D.; Wang, X.H. Numerical Analysis of New Modified Melt-Blowing Dies for Dual Rectangular Jets. Polym. Eng. Sci. 2014, 54, 110-116. (29) Shambaugh, B.R.; Papavassiliou, D.V.; Shambaugh, R.L. Modifying Air Fields to Improve Melt Blowing. Ind. Eng. Chem. Res. 2012, 51, 3472−3482. (30) Bresee, R.R.; Qureshi, U.A. Influence of processing conditions on Melt Blown Web Structure: Part 1–DCD. Int. Nonwovens J. 2004, 13, 49-55. 18


Page 18 of 35

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(31) Bresee, R.R.; Qureshi, U.A.; Pelham, M.C. Influence of processing conditions on Melt Blown Web Structure: Part 2–Primary Airflow Rate. Int. Nonwovens J. 2005, 14, 11-18. (32) Bresee, R.R.; Qureshi, U.A. Influence of processing conditions on Melt Blown Web Structure: Part 3–Water Quench. Int. Nonwovens J. 2005, 14, 27-35. (33) Bresee, R.R.; Qureshi, U.A. Influence of Process Conditions on Melt Blown Web Structure. Part 4–Fiber Diameter. J. Eng. Fibers. Fabr. 2006, 1, 32-46.

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Figure 1. Computational domain of air flow field 254x190mm (120 x 120 DPI)


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Figure 2. Schematic of a bead−viscoelastic fiber element 254x190mm (120 x 120 DPI)



Figure 3. Experiment: measurement of air flow 254x190mm (120 x 120 DPI)


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Figure 4. (a) Velocity contour in the x-z plane of simulated air flow without suction; 254x190mm (120 x 120 DPI)



(b) Velocity contour in the x-z plane of simulated air flow with suction velocity 50 m/s 254x190mm (120 x 120 DPI)


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Figure 5. the air flow speed with different suction speeds 110x82mm (600 x 600 DPI)



Figure 6. Predicted and fabricated fibrous web: (a) simulation snapshot and experimental picture; (b) predicted and measured BWD 254x190mm (120 x 120 DPI)


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Figure 7. (a) Simulated BWCV values at various air jet velocities; 110x82mm (600 x 600 DPI)



(b) Experimental BWCV values at various air jet velocities 110x82mm (600 x 600 DPI)


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Figure 8. (a) Simulated BWCV values affected by the suction speed; 110x82mm (600 x 600 DPI)



(b) Experimental BWCV values affected by the suction speed 110x82mm (600 x 600 DPI)


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Figure 9. (a) Simulated BWCV values at various collector speeds; 110x82mm (600 x 600 DPI)



(b) Experimental BWCV values at various collector speeds 110x82mm (600 x 600 DPI)


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Figure 10. (a) Simulated BWCV values at various DCD; 110x82mm (600 x 600 DPI)



(b) Experimental BWCV values at various DCD 110x82mm (600 x 600 DPI)


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TOC 254x190mm (120 x 120 DPI)


Influence of Processing Conditions on the Basis Weight Uniformity of

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