Simulation of jet velocity in the melt-blowing process using the coupled air

Abstract

The polymer jet velocity is one of the most basic and critical factors in the melt-blowing process and has always been difficult to measure online. Much effort has been made on the numerical prediction of the jet velocity. However, little work has involved the complex interaction between the air flow and the polymer. Here, the Level-Set method is used to develop the coupled air–polymer two-phase flow model, and to simulate the polymer jet motion in the melt-blowing process considering the coupled effect of the air and polymer. Meanwhile, high-speed photography is adopted in the experiments to verify the simulation results. The x- and y-components of the jet velocities and the whipping amplitude of the jet motion are discussed. The rapid increase of jet velocity and the decrease of jet diameter show that most attenuation of the polymer jet occurred within a distance close to the die (10 mm). Based on the model, the effects of the processing parameters on the jet velocity are examined numerically.

Keywords

level-Set method coupling simulation melt blowing jet velocity two-phase flow

Melt blowing is a common method used in industry for producing micro fibrous nonwoven materials. These materials are used in a variety of commercial uses, such as filtration, sorbent, and insulation. During melt blowing, a molten polymer jet is injected into a high-velocity and high-temperature air flow field and stretched by the air jets, then solidified and captured upon a collector positioned some distance away from the melt-blowing die (i.e., the component used to inject the polymer jets and air jets in a melt-blowing device). It is obvious that motion of the polymer jet in the air flow field plays a key role in the fiber formation process, and consequently influences the properties of melt-blown materials. To improve the performance of the melt-blowing product, a better understanding of the polymer jet motion is necessary. However, compared with studies on the melt-blowing air flow field, much less has been done on the polymer jet dynamics, including the jet motion path and jet velocity. The following is a brief review of the experimental and theoretical studies on the polymer jet (also called ‘fiber’) motion in the melt-blowing process.

The polymer jet velocity is one of the most basic and critical factors in the melt-blowing process and has always been difficult to measure online. Photography was the first technique performed to acquire jet velocities during melt blowing by Uyttendaele and Shambaugh.¹ In their method, the jet velocity was obtained based on the polymer jet diameter measured by the photographing technique and the assumption of mass continuity. Owing to the backward in photographic technology at that time, the images tend to be blurred when the jet velocity increased, so the primary air velocity they used was low (17–55 m/s).² For jets in a relatively higher air velocity (90 m/s), Wu and Shambaugh³ used Laser Doppler Velocimetry (LDV) to examine jet velocities during melt blowing. Bresee and coworkers^4–6 measured the jet velocities by analyzing triple-exposed images obtained with a high-speed digital camera and high-pulsed laser. They claimed that the machine in their research was working at a commercial condition with the air pressure of 3–4 psi. Unfortunately, owing to the low camera speed (1000 frame/s), the high-speed photographing images they offered did not show the jet whipping during melt blowing. For the first time, Beard et al.⁷ captured the jet whipping (called ‘fiber vibration’ in their work) when 2000 frame/s camera speed was used. However, the images were recorded only at a certain position below the die, and the jet velocity was not studied in their work. Using high-speed photography, the previous work of our group⁸ recorded the jet path with a frame rate of up to 5000 fps, and the online measurement of jet whipping and jet velocity were performed.

Since online measurement of the jet velocity during melt blowing is time and cost consuming, and more importantly, is always limited by the processing and measuring conditions, a conceptually straightforward way of acquiring the jet motion is to employ the numerical method. The one-dimensional,^1,9,10 two-dimensional,¹¹ and three-dimensional^12–14 models of jets in the melt-blowing process have given simulation results of the melt-blown jet motion. However, their predicted jet velocities were under-predicted compared with the experimental data available,^4,5 which could be due to the negligence of the interaction between the polymer and the air in these models. There are also some research works, such as the work of Chung and Kumar¹⁵ and Sinha-Ray et al.,¹⁶ concentrating on the mechanism of jet whipping in the melt-blowing process. As is known, the process of melt blowing involves a complex interplay of the aerodynamics of high-velocity and high-temperature air flow with strong elongational flows of polymer jets. Therefore, the polymer–air interaction, which refers to the coupling of the air flow with the polymer, can have a significant effect on the formation of melt-blown fibers. To the best of our knowledge, few publications have reported the polymer–air coupled model when studying jet motion in the melt-blowing process. The aim of this study is to develop a coupled air–polymer model and to give a better prediction of the polymer jet velocity, which can be useful in designing of the melt-blowing air-polymer field.

The Level-Set method (LSM) is one of the most powerful numerical techniques available for computing and analyzing moving boundaries using a fixed mesh in various situations. The primary advantage of the LSM lies in its accurate computation of two-phase flows with complex topological changes.¹⁷ It has been applied to simulate the single bubble boiling behavior,¹⁸ the coalescence of a water droplet in an oil phase,¹⁹ the free rising droplet,²⁰ etc. In a previous study of our group,²¹ this method was adopted to simulate the jet velocity in the electrospinning process. For the case of melt blowing, the polymer could be considered as viscous fluid. Thus, the pneumatic-driven polymer drawing process during melt blowing could be perceived as gas–liquid two-phase flow. Based on these considerations, in the present work, we adopt the LSM to simulate the polymer jet motion and predict jet velocities in the melt-blowing process. To experimentally verify the model, high-speed photography is employed to investigate the characteristics of the polymer jet motion and obtain polymer jet velocities. This research aims to establish an easily accessible method to study the polymer jet dynamics during melt blowing.

Model constructions

Geometry

The common slot die, which is predominant in melt-blowing production, is taken as a research object. Figures 1(a) and (b) show the cross-sectional view and the end-on view of the die with the single polymer orifice used in this research. The main geometric parameters of the die are the nose-piece width f (1.28 mm), slot angle α (30°), slot width e (0.65 mm), slot length l (6 mm), and the orifice diameter d (0.42 mm). Also shown is the coordinate system. The origin is at the center of the die face, with the x-direction traversing the major slot axis; the y-axis is in the downward direction under the die, and the z-direction (not shown) is perpendicular to the x-y plane.

Figure 1.

Profiles of the two-dimensional model of the melt blowing die: (a) cross-sectional view and (b) end-on view of the die; (c) and (d) show the computational domain and boundary conditions for the air flow field.

Figures 1(c) and (d) show the computational domain adopted in this study. For the slot die, the air flow field is designed such that the air is supplied in the form of two converging rectangular air flows. It is found that the z-component of the air velocity is small enough to be negligible, and therefore the jet path in the region near the die is almost in the x–y plane.^22,23 In view of the above-mentioned facts, the computational domain in this study is set to be two-dimensional with the size of 20 mm in the x-direction and 50 mm in the y-direction. According to the results of previous studies, most of the jet attenuation was found to occur within 2 cm from the die.^24–26 Therefore, the computational domain is large enough to study the jet acceleration and jet attenuation below the die.

Governing equations

In this study, the LSM was applied to simulate the air–polymer (jet) two-phase flow during melt blowing. A variable, ∅, is used to determine the position of the interface between the two fluids. In a transition layer close to the interface, ∅ goes smoothly from 0 to 1. The 0.5 contour of the Level-Set function defines the interface, where equals 0 in air and 1 in polymer. The Level-Set function can thus be considered as the volume fraction of the polymer. The interface moves with the fluid velocity (u) at the interface. The transport of the fluid interface separating the two phases is given by²⁷

\frac{\partial Ø}{\partial t} + \nabla (Ø u) + γ [(\nabla \cdot (Ø (1 - Ø) \frac{\nabla Ø}{| \nabla Ø |})) - ɛ \nabla \cdot \nabla Ø] = 0

(1)

where u denotes the fluid velocity. The thickness of the transition layer is determined by ɛ. For this model,

ɛ = h_{c} / 2

, and h_c is the characteristic mesh size in the region where the jet passes by. The parameter

γ

determines the amount of reinitialization. A suitable value for γ is the maximum velocity magnitude occurring in the model.^26-27

The air flow injected from the die is considered to be turbulent. The Reynolds-averaged Navier–Stokes (RANS) equations that form the basis of the solutions performed here are presented in Equation (2)

\begin{matrix} ρ \frac{\partial u}{\partial t} + ρ (u \cdot \nabla) u \\ = - \nabla p + \nabla \cdot [(μ + μ_{T}) (\nabla u + (\nabla u)^{T})] + F \end{matrix}

(2)

In addition, mass conservation has to be satisfied by solving the continuity equation given by

\frac{\partial ρ}{\partial t} + \nabla \cdot (ρ u) = 0

(3)

The common two-equation turbulence model k–ω is applied as a closure for the RANS equations. The equations for the k–ω model take the form shown below

ρ \frac{\partial k}{\partial t} + ρ (u \cdot \nabla) k = \nabla \cdot ⌊ (μ + μ_{T} σ_{k}^{*}) \nabla k ⌋ + P_{k} - β_{0}^{*} ρ ω k

(4)

\begin{matrix} ρ \frac{\partial ω}{\partial t} + ρ (u \cdot \nabla) ω = \nabla \cdot [(μ + μ_{T} σ_{ω}) \nabla ω] \\ + α \frac{ω}{k} P_{k} - ρ β_{0} ω^{2} \end{matrix}

(5)

The equation parameters are defined as follow: u is the velocity field; t is time; p is pressure; $μ_{T}$ is the turbulence viscosity; F is the volume force; k is the turbulence kinetic energy; ω is the specific dissipation rate; P_k is the production term; $α, σ_{k}^{*}, σ_{ω}, β_{o}, β_{o}^{*}$ are turbulence model parameters, which are set to be 0.52, 0.5, 0.5, 0.072, 0.09, respectively. ρ and μ are the density and viscosity of the two-phase flow, respectively, and are expressed as functions of ϕ, as shown in the following

ρ = ρ_{air} + (ρ_{poly} - ρ_{air}) Ø

(6)

μ = μ_{air} + (μ_{poly} - μ_{air}) Ø

(7)

Here, $ρ_{poly,} ρ_{air,} μ_{poly}, μ_{air}$ denote the constant density and viscosity of the jet and air, respectively. It is worth noting that only in the narrow region close to the interface where $Ø$ varies between 0 and 1 are ρ and μ different from the pure liquids.

Equation (4) represents the kinetic energy equation, while Equation (5) represents the specific dissipation rate equation. The turbulence viscosity and production term are modeled as

μ_{T} = ρ \frac{k}{ω}

(8)

P_{k} = μ_{T} [\nabla u : (\nabla u + (\nabla u)^{T}) - \frac{2}{3} (\nabla u)^{2}] - \frac{2}{3} ρ k \nabla \cdot u

(9)

Mesh generation and boundary conditions

The mesh condition is provided in Figure 2. The computational domain was meshed with structured mesh, which is highly space-efficient compared with unstructured mesh. To improve the computation accuracy of the air–polymer mixing area, we added a mesh control domain in which a finer mesh was specified.

Figure 2.

Mesh for the computation domain.

As shown in Figures 1(c) and (d), the air entering the computation domain was set as the velocity inlet boundary condition at T = 533.15 K. The polymer entering the computational domain was set as the velocity inlet boundary condition at T = 533.15 K, and μ = 8 Paċs. It is worth noting that the viscosity used was obtained from the measured dynamic viscosity of PP (polypropylene) at 260℃. The left boundary, right boundary, and bottom boundary were set as pressure outlets with ambient pressure P = 0 Pa and T = 293.15 K. The polymer exit was defined as the initial interface between the air and polymer. All other boundaries were assigned the default setting of being a wall at a temperature equal to 533.15 K. In this study, the inlet velocities were obtained according to the size of the exit and the volume flow rates for the air and the polymer. Table 1 lists the volume flow rates and the corresponding velocities of the air and the polymer inlets used in this study.

Table 1.

Flow rates of air and polymer in the form of flow velocity and volume flow rate (slm represents standard L/min)

	Flow velocity	Volume flow rate
Air	73.8 m/s	30 slm
	98.4 m/s	40 slm
	123 m/s	50 slm
	246 m/s	100 slm
Polymer	0.121 m/s	1.0 cm³/min
	0.182 m/s	1.5 cm³/min
	0.242 m/s	2.0 cm³/min

Solution procedure

The LSM was adopted to simulate the air–polymer two-phase flow. A commercial software, Comsol multiphysics, was used for this purpose. Comsol multiphysics uses a finite-element discretization to convert the governing equations to a set of ordinary differential equations (ODEs). The two-phase flow equations constitute a highly nonlinear equation system. A nonlinear solution algorithm was applied to solve the problem. The nonlinear solver iterates to reach the final solution. In each iteration, a linearized version of the nonlinear system is solved using a linear solver. Since the position of an interface almost always depends on its history, simulations using the LSM are always time-dependent. Therefore, a time marching method must also be applied.

Experimental details

Experimental conditions

Experiments were conducted using a laboratory-scale melt-blowing device with a single-orifice slot die. The melt-blowing die adopted in the experiments has the configuration shown in Figures 1(a) and (b). The polymer used was 1100-melt-flow-rate PP (SK, Seoul, Korea) with dynamic viscosity of 8 Paċs at 260℃. The experiments were performed under the same velocities and temperatures of the air and the polymer jet as in the simulations. During the experiments, the conditions were air flow rates of 30 and 40 slm (standard L/min), a polymer flow rate of 1.5 cc/min, a polymer temperature of 260℃ (533.15 K), and an air temperature of 260℃.

Characterization

An i-speed 7 high-speed camera (iX Inc., UK) was employed in our experiments to monitor the jet motion in the melt-blowing process. As a state-of-the–art scientific tool, the camera is capable of recording images up to 500,000 fps. The sensor resolution of the camera is 2048 × 1536 with pixel size 13.5 µm, ensuring the accuracy of the details the camera captures. The camera is connected to a laptop via an appropriate Ethernet network and an Ethernet connector. The camera is controlled by the laptop and the image is displayed on a PC screen. In addition, the camera was equipped with a Tokina AT-X M100 PRO D 100 mm f 2.8 zoom lens (Kenko Tokina Co. Ltd, Japan) to record the images. Figure 3 shows the melt-blowing device and the high-speed camera. In the photographing experiments, the die was viewed in the direction in which the slots are parallel to the axis of the lens (i.e., the z-direction). A region about 14 mm down from the die was monitored at 15,000 fps. The corresponding image size was 47.2 mm × 25.4 mm. Image processing and analysis was conducted with the software supplied with the camera and Adobe Photoshop (Adobe Systems Software Ireland Ltd).

Figure 3.

Melt-blowing device and high-speed camera.

The fiber diameter of the melt-blowing mat was observed using a Hitachi TM3000 desktop scanning electron microscope (SEM, Hitachi High Tech, Tokyo, Japan) at an accelerating voltage of 15 kV 1 hour after gold coating.

Results and discussion

Grid test for mesh independency

The scheme of mesh generation has great influence on the computational results. It is well known that grids with high quality can not only improve the accuracy of computation, but also have better convergence. Therefore, in order to find the optimal grid scheme, extensive computational tests were conducted. We contrasted three different grid schemes: 11,256 (Grid 1), 12,342 (Grid 2), and 13,092 (Grid 3) cells. Figure 4 presents the polymer jet velocity distribution computed with the three different grids schemes above. Little difference is shown in the figures by all the three schemes. Hence, in view of computational efficiency, Grid 1 is adopted in the subsequent computations.

Figure 4.

Comparison of polymer velocity profiles for the three different grid schemes.

Flow characteristics of the polymer jet

Figure 5(a) shows the simulation velocity contour of the melt-blowing air–polymer two-phase flow field at the simulation conditions of 40 slm air flow rate, 1.5 cc/min polymer flow rate, and 8 Paċs polymer dynamic viscosity. Figure 5(b) illustrates the velocity field of the jet, and also shown is the jet path up to 50 mm distance from the die. According to the color legend, the jet is accelerated in a very short distance after issuing from the polymer exit, and decreases slowly afterwards. Of special interest is the whipping phenomenon that can be seen in Figure 5(b), which is caused by the air–polymer interaction without additional perturbation.

Figure 5.

Contour of the velocity field with air flow rate of 40 slm, polymer flow rate of 1.5 cc/min, and polymer dynamic viscosity of 8 Paċs: (a) velocity field of the air-jet mixture; (b) velocity field of the jet.

In previous studies, polymer jet velocity in the y-direction has always been the focus and jet velocity in the x-direction has been rarely covered. To further understand the characteristics of the polymer jet velocity field, the jet velocity profiles in the y-direction (V_y) and the x-direction (V_x) are both acquired and are shown in Figure 6. As can be seen, in the region of 20 mm × 50 mm below the die, $V_{y}$ is much higher than V_x in magnitude and they are varying in different patterns. $Thelongitudinalvelocity$ , V_y, increases to its maximum, which is as high as 23 m/s from the initial velocity (0.182 m/s) within 10 mm distance, and then gently decreases to 17 m/s when reaching 50 mm away from the die. The transverse velocity, V_x, fluctuates between negative and positive values, indicating bending instability, which is called ‘whipping’, of the jet. The whipping motion is also shown in the jet path in Figure 5(b). After moving a short distance (20 mm) from the polymer exit, the jet begins to drift to the –x or +x regions while it is going downward into the collector, indicating that the jet whipping becomes significant in the x–y plane.

Figure 6.

Comparison of V_y and V_x along the y-direction with inserted figure showing amplified $V_{x}$ . The original point is the center of the die.

Because the polymer flow rate is constant, we applied the volume conservation condition to predict the jet radius (r) up to 10 mm of the initial portion of jet path

π r^{2} V = constant

where V is the simulated velocity, based on which the diameter profile for the air flow rate of 40 slm is calculated and is presented in Figure 7. It is found that the jet diameter decreases from 420 to 37.2 µm within 10 mm distance, with the most rapid drop in the first 4 mm. Given that the air velocity used is far below the industrial condition, the predicted value of the diameter is appropriate.

Figure 7.

The jet diameter profile for air flow rate of 40 slm, polymer flow rate of 1.5 cc/min, and polymer dynamic viscosity of 8 Paċs.

Experimental verification

Aided by the high-speed photography, the jet velocities during melt blowing were measured by analyzing continuous images of the jet path. The information used to figure out the jet velocity involved the interval time ( $Δ t$ ) between two successive fames (i.e., the inverse of the frame rate) and the jet moving distance during the time interval. The method to obtain the jet moving distance is shown in Figure 8. The images were imported into the Adobe Photoshop in which an easily recognizable and traceable marker point was chosen and its position in each frame was acquired. If (x₁, y₁) and (x₂, y₂) were the positions of the traced point in adjacent images, the obtained velocity $(\frac{x_{2} - x_{1}}{Δ t}, \frac{y_{2} - y_{1}}{Δ t})$ was considered as the jet velocity at the position $(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})$ .

Figure 8.

Evolution of the marker point position with frame rate of 15,000 fps. The image area is 4.72 cm × 1.57 cm. The experiment was carried out at an air flow rate of 40 slm and a polymer flow rate of 1.5 cc/min.

In this paper, the longitudinal velocity V_y and the transverse velocity V_x versus the distance from the die were measured. The measurements of the jet velocities under two air flow rates, 30 and 40 slm, are shown in Figure 9. For ease of comparison, the corresponding simulation results are also included. It is worth noting that due to the difficulty of taking measurements of the jet motion in the region very close to the die, the experimental data provided here is started from a position 20 mm away from the die. For the experimental condition with the air flow rate of 30 slm, V_y ranges between 7 to 16 m/s, with the average value of 11.7 m/s. In addition, for the air flow rate of 40 slm, V_y ranges between 12 and 25 m/s, with the average value of 18.6 m/s. The data from measurements fluctuate in the same range with the simulation results of V_y in the region 20–50 mm away from the die, which are around 10 and 20 m/s for the cases of 30 and 40 slm, respectively. It should be mentioned that due to the limitation of the measuring region, the variation trend of V_y is not clearly observed in the experiments. As for V_x, the measurements at the air flow rate of 30 slm range between –2.4 and 2.2 m/s, while the simulation values range between –0.42 and 0.84 m/s. In addition, the measurements of V_x at the air flow rate of 40 slm range between –3.2 and 2.4 m/s, while the simulation values range between –1.1 and 1.7 m/s. The comparison of V_x shows a similarity in value between the simulation and experimental results.

Figure 9.

Experimental results of velocity against the simulation results with air flow rates of 30 and 40 slm, a jet flow rate of 1.5 cc/min and a viscosity of 8 Paċs: (a) velocity in the y-direction (V_y); (b) velocity in the x-direction (V_x).

Both the simulation and experimental results show that the longitudinal velocity V_y under the 40 slm air flow rate is higher than that under 30 slm air flow rate. A similar phenomenon is observed in the profile of the transverse velocity V_x, although the variation trend for the measured velocity is not that clear due to the broad distribution of the measured values.

Figures 10(a) and (b) show the SEM images for fibers produced at the air flow rates of 30 and 40 slm, and Figure 10(c) shows the comparison of average fiber diameters between the experimental values and simulation values. Obviously, the fiber produced at the air flow rate of 40 slm has a finer diameter than that at the air flow rate of 30 slm for both simulation results and experimental results. The predicted values are larger than the experimental values and they are of the same order of magnitude. This could be explained by the under-prediction of the jet velocity by the simulation, and the negligence of jet whipping in the diameter calculating method. Furthermore, we are unable to obtain the fiber 8 mm away from the die in the experiment. Notably, due to the fact that the air velocity used in the experiment is far below the industrial condition, the fiber diameters shown in the SEM images are larger than the melt-blowing product used in practical applications.

Figure 10.

Scanning electron microscopy images of the fiber produced at the air flow rates of 30 slm (a) and 40 slm (b), and a comparison between the experimental and simulation values (c).

To further verify the model, the amplitudes of jet whipping were measured for comparison with the simulation results. The whipping amplitude is defined as the maximum lateral displacement at position y. Our previous experimental study⁸ developed a ‘path-overlap’ method, which involved the overlap of 20 successive paths, to obtain the whipping amplitude. The overlapped jet paths resulted in a tapered entity, which is similar to the fiber cone that Rajeev and Shambaugh²⁸ captured. This method was used in this study to obtain the measurement and simulation results of the jet whipping amplitude, which are shown in Figure 11. The observed area of the experiment starts from 20 mm and ends at 67 mm away from the die in the y-direction, while that of the simulation covers 50 mm under the die. As expected, the experimental and simulation results both show that the whipping amplitude increases with the increase of distance from the die exit, and the whipping amplitude at the air flow rates of 40 slm is slightly higher than that at the air flow rate of 30 slm.

Figure 11.

Experimental and simulation whipping amplitudes of jet motion with air flow rates of 30 and 40 slm, a polymer flow rate of 1.5 cc/min, and a polymer dynamic viscosity of 8 Paċs.

Comparing the jet whipping amplitude at the distance 20–50 mm away from the die, under the 30 slm air flow rate, the measurements range from 0.16 to 3.61 mm, while the simulation results range from 0.33 to 1.41 mm. For the whipping amplitude under the 40 slm air flow rate, the measured values range from 0.23 to 4.2 mm, while the calculated values range from 0.78 to 3.32 mm. Compared with the previous studies,^11–13 the whipping amplitude of our model has made a further step toward the practical values.

The experimental results have verified that the coupled air–polymer model established in this study could effectively predict the motion of the polymer jet. Therefore, the effects of the processing parameters of special interest on the jet velocity could be explored numerically based on this model.

Effects of processing parameters

We examined the effects of the air flow rate, polymer flow rate, and polymer viscosity on the jet velocity. Figure 12 shows how the air flow rate influences the jet velocity, and the corresponding average velocities of the jet for different air flow rates are presented in Table 2. It can be observed that the average velocity of the jet in both the x- and y-directions increases with the air flow rate significantly. When the air flow rate reaches 100 slm (246 m/s of the air velocity), which is generally used in industry, the corresponding maximum values of V_y and V_x would reach 107 and 19 m/s, respectively. Notably, such a high V_x value indicates drastic jet whipping in the melt-blowing process when the commercial air velocity is applied. Obviously, finer fibers will be prepared under a higher air flow rate.

Figure 12.

Effects of the air flow rate on the jet velocity for a polymer flow rate of 1.5 cc/min and a polymer viscosity of 8 Paċs: (a) jet velocity in the y-direction; (b) jet velocity in the x-direction.

Table 2.

Average velocity of the jet for different air flow rates

Air flow rate (slm)	${\bar{V}}_{y}$ (m/s)	${\bar{V}}_{x}$ (m/s)
50	27.49	2.26
40	20.07	0.72
30	11.12	0.16
100	66.77	7.91

Figure 13 depicts the jet velocities under three different polymer rates, and the corresponding average velocities of the jet for different polymer flow rates are shown in Table 3. It is shown that the average velocities of jet in both the x and y directions decrease with the increase of polymer flow rate, leading to an increasing effect on the jet diameter. Apparently, a smaller polymer mass results in a higher attenuation of the polymer jet when subjected to the same drawing force. Figure 14 depicts the effect of polymer dynamic viscosity on the jet velocity, and Table 4 presents the corresponding average velocities of the jet for different polymer dynamic viscosities. It is found that along with the increase of polymer dynamic viscosity comes a decrease of average velocities of the jet in both the x- and y-directions. That is to say, the jet diameter increases with the increase of the polymer dynamic viscosity. According to these analyses, we suggest using higher air flow rates and lower polymer flow rates, and choosing the polymers with smaller viscosity for producing finer melt-blown fibers.

Figure 13.

Effects of the polymer flow rate on the jet velocity with an air flow rate of 50 slm and a polymer viscosity of 8 Paċs: (a) jet velocity in the y-direction; (b) jet velocity in the x-direction.

Figure 14.

Effects of the polymer viscosity on the jet velocity for an air flow rate of 50 slm and a polymer flow rate of 1.5 cc/min: (a) jet velocity in the y-direction; (b) jet velocity in the x-direction.

Table 3.

Average velocity of the jet for different polymer flow rates

Polymer flow rate (cm³/s)	${\bar{V}}_{y}$ (m/s)	${\bar{V}}_{x}$ (m/s)
1.0	29.20	4.77
1.5	27.49	2.26
2.0	19.42	0.90

Table 4.

Average velocity of the jet for different polymer dynamic viscosities

Dynamic viscosity (Paċs)	${\bar{V}}_{y}$ (m/s)	${\bar{V}}_{x}$ (m/s)
8	27.49	2.26
10	27.13	0.83
12	24.17	0.21

Conclusions

In this work, numerical simulation, which included the coupling of the air flow and polymer, was used to investigate jet motion in the melt-blowing process. The simulation results present the polymer jet velocity field and the jet path in the area 20 mm × 50 mm under the die. The model showed that the jet velocity in the y-direction (longitudinal direction) was much higher than that in the x-direction (transverse direction). The transverse velocity and the jet path indicate the whipping of the jet. Moreover, based on the jet velocity calculated in the model and mass continuity equation, the jet diameter was predicted. In the verification experiments, high-speed photography was employed to investigate the jet velocity and whipping amplitude. Through comparison, the jet velocity and whipping amplitude of the simulation results were demonstrated to be close to the experimental results. Finally, by numerically analyzing the effects of the air flow rate, polymer flow rate, and polymer viscosity on the jet velocity, it was discovered that the increase of the air flow rate would lead to the decrease of the polymer jet velocity on average, while the increase of the polymer flow rate and polymer viscosity would result in the increase of the polymer jet velocity on average. Thus, we suggest using higher air flow rates and lower polymer flow rates, and choosing polymers with smaller viscosity for producing finer melt-blown fibers. Compared with the previous simulation work, the model built here has made an important step in closing the gap between simulation values and experimental values. We believe that the advancement achieved is due to the coupling effect included in the model. The model proposed here is expected to be a promising tool to guide design in the melt-blowing air–polymer field. Since elasticity of the polymer is not considered, the model is suggested to be applied for polymers with lower Deborah numbers that behave in a more fluid-like manner.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation of China (Grant Number 11672073).

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Simulation of jet velocity in the melt-blowing process using the coupled air–polymer model

Abstract

Keywords

Model constructions

Geometry

Governing equations

Mesh generation and boundary conditions

Solution procedure

Experimental details

Experimental conditions

Characterization

Results and discussion

Grid test for mesh independency

Flow characteristics of the polymer jet

Experimental verification

Effects of processing parameters

Conclusions

Footnotes

Declaration of conflicting interests

Funding

References