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Abstract

The high-quality standards of bodily absorbent hygiene products require that the adhesive bond between layers be as uniform and consistent as possible. The final adhesive pattern of the product is determined by the dynamics of the adhesive fibre, which in turn depends on the nozzle geometry and on its operating conditions. In order to gain a better understanding of the dynamics of adhesive fibres and the deposited application pattern, an experimental study was conducted on two multi-hole melt blowing (MB) nozzles designed for producing hot-melt adhesives. To this end, the fibre dynamics were captured through the use of high-speed imaging (HSI). The main parameters that govern the fibre dynamics, including its frequency of oscillation, were quantified through use of image analysis. The effect of the operating conditions on the fibre’s frequency of oscillation at the nozzle exit region was studied and the results indicate that increasing air-polymer flux ratios $(m')$ and decreasing dimensionless temperature ratios $(T')$ both increase the fibre whipping frequency. Additionally, information on the fibre dynamics on the two planes of oscillation is obtained by studying the deposited application pattern of hot-melt applications. Other related matters are also treated throughout the article, such as fibre contact in adhesive patterns, which represent one of the major defects that the melt blowing technology of hot-melt adhesives is trying to mitigate. Experimental measurements are presented throughout the article to support the validity of the conclusions.

Keywords

Melt blowing whipping frequency application pattern fibre contact pattern quality

Introduction

In the melt blowing (MB) process, a polymer stream is molten and extruded through a set of nozzles and it is immediately blown and attenuated by a set of convergent high-velocity hot-air jets. The MB process represents about 10% of the nonwoven industry [1] and is particularly effective because it allows the production of nonwoven webs with a high surface area per unit volume, while usually not requiring any further finishing operations [2]. A thorough description of the melt blowing technology is given in reference [1].

One application of the MB process is the production of hot-melt adhesives, which are used in various industrial processes for bonding different kinds of products, such as products that include nonwoven fabrics. After being blown, the polymer fibres are deposited on a moving collector screen, establishing the application pattern, before a product layer is added over them. The MB system comprises an MB head that supports a set of nozzles, where these may have different designs depending principally on the desired application characteristics. Hence, the aim of this article is to determine how the geometrical and the operational factors of each design affect the fibre dynamics and the deposited application pattern, by studying two MB nozzle designs by means of an experimental approach. Depending on the production requirements, the fibres can be extruded either continuously or discontinuously, where in the present work only the continuous extrusion of polymer by non–contact nozzle designs will be studied.

Regarding past work done on the dynamics of melt blowing fibres, R. Shambaugh and coworkers [3,4] studied the vibration in a swirl nozzle and concluded that the fibre frequency is essentially constant along the threadline and increases for decreasing values of air velocity. They also measured the cone thickness and the fibre threadline vibrations on a single orifice slot nozzle and found that the fibre cone cross section is different from a circumference, but rather more of an ellipse. Regarding the fibre frequency, they concluded that it is distinct in the directions parallel and perpendicular to the air slots, and it increases with decreasing polymer temperatures and air velocities. S. Xie and Y. Zeng [5] studied the fibre whipping motion on a single-orifice slot nozzle and found that the fibre frequency decreases with increasing distances from the nozzle exit. More recently, the same authors studied the fibre spiral motion in a swirl die design, concluding that its frequency and amplitude both increase with increasing air pressures. H. Beard et al. [6] reached similar conclusions when studying the frequency of oscillation in the slot and the swirl nozzle. S. Xie, Y. Zheng and Y. Zeng [7] studied fibre attenuation in a slot and a swirl nozzle through the analysis of high speed images and the development of a mathematical model. They concluded that the fibre whipping pattern presents substantial differences in both nozzle designs, while the one exhibited by the slot nozzle is two dimensional, the one of the swirl nozzles is three dimensional and is described as a helicoid. More recently, S. Xie et al. [8] showed that fibre instability might be caused by the fluctuation of the lateral air velocity.

Moreover, the dynamics of the fibre determines the laydown pattern [9]. The present work also intends to address this issue by studying the deposited adhesive pattern produced by the two nozzle designs. Regarding past work done on this subject, A. Yarin et al. [10] studied the diameter distribution of the melt blowing web by modelling the deposition of multiple polymer jets on a screen moving perpendicular to the principal jet direction using a three-dimensional model of the polymer fibre. More recently, G. Sun and coworkers [11] predicted the forming of fibrous webs by developing a theoretical model of the fibre, which is represented by viscoelastic beads, and by describing the airfield through use of software simulation. A. Ghosal et al. [12] studied the effect of the governing parameters of the process in the permeability, porosity and three-dimensional structure of melt blowing nonwoven laydown. The main findings in fibre motion and laydown pattern in the MB process can be found in [13].

From the literature review, it can be observed that there is no universal agreement regarding some issues related to the dynamics of the MB fibre, for example in the relationship between the fibre frequency and the air flow rate. The lack of agreement among some of the above results can be partly explained by the difficulty in studying the dynamics of melt blowing fibres, which oscillate due to the introduction of bending instabilities caused by the airflow field, and which are physically much more difficult to describe than the ones observed in electrospinning [14]. In the present work, high-speed imaging was conducted at higher frame rates than the ones used in previous works, which gave access to information not only about the dominant, but also about the fastest frequencies of the adhesive fibres. This information was used to build an empirical model which allowed studying the laydown pattern and the defects that may appear in it.

Experimental

Description of the nozzle geometry

Since it ensures a consistent bonding between adjacent layers and because the application pattern produced by contiguous nozzles does not overlap, the multi-hole (or laminated) nozzle geometry is popular among MB nozzle designs when it comes to the disposal of hot-melt adhesives in hygiene products. This type of nozzle provides enough control over the application pattern generated, which makes them especially valuable because they ensure the softness of the bonded nonwoven layers. These types of non-contact nozzles present some advantages when compared with contact nozzles, for example, they present better clog resistance and permit bonding on uneven surfaces. They are also better for bonding temperature sensitive materials.

In the present study, two multi-hole melt blowing nozzle designs used to apply hot-melt adhesive to hygiene products intended to absorb bodily fluids were studied. Both designs are industrial prototypes, which were designed based on two existing commercial designs. Laminated melt blowing nozzles consist of an assembly of several metallic plates, where the air orifices and the adhesive capillaries lie. The set of plates is screwed to the body of the nozzle. From this point on, the nozzle designs will be named as A Design and B Design, respectively. Both nozzle designs were studied on a modular MB head with interchangeable modular units placed side by side. The melt blowing head used for the experiments supported five modules, where each of these holds a nozzle with a given number of polymer exits, surrounded each by a certain number of air exits. Whereas the nosepiece of the A design is of the outset-sharp type, the one of the B design is of the flush-blunt type. The A nozzle design has 5 adhesive capillaries, each of them surrounded by 2 air exits, while the B nozzle design has 12 adhesive capillaries, each of them surrounded by 4 air exits. The A and B nozzle designs have a width of 25 mm. The air and the polymer exit areas will be described in terms of their hydraulic diameters, where the hydraulic diameter of one air exit $(L_{R})$ in the A design is 520 µm, the one in the B nozzle design is 250 µm. The hydraulic diameter of one adhesive capillary $(L_{R f})$ in the A nozzle design is 520 µm, while the one in the B nozzle design is 380 µm. The distance between two consecutive adhesive capillaries $(p)$ in the A design is $9.6 L_{R}$ , while the one in the B design is $8.0 L_{R}$ . The length of the adhesive capillary $(L)$ in the A design is $8.6 L_{R}$ and the one in the B nozzle design is $13.5 L_{R}$ .

In the multi-hole nozzle designs, the air exits are often non-parallel to the adhesive exits, hence an angle form between them. The tilt angles between the air exits and the adhesive capillary on the $X Z$ and $Y Z$ planes are different in both designs. The tilt angle on the $X Z$ plane ( $α$ ) is 0 in the A design and is between 30 and 50 degrees in the B nozzle design, while the tilt angle on the $Y Z$ plane ( $β$ ) is non-zero in both designs, being about 2.5 times larger in the A nozzle design than in the B nozzle design. The geometrical difference between both designs is mainly given by the different size and number of the air and polymer exits, as well as in the air tilt angles. The different aerodynamical design of the A and B nozzles means they produce different airflows and therefore, the fibres produced by the two designs present different oscillation dynamics. Further information on the geometry of the nozzle designs can be found in reference number [15].

Figure 1 presents a sketch of the geometry of the two nozzle designs used in the present work together with their coordinate systems, of which the origins are located at the centre of the polymer exit. From Figure 1 it can be observed that in the A design the fibre is blown exclusively in the $Y$ direction, while in the B design it is blown in the $X$ and $Y$ directions.

Figure 1.

Dimensions and parameters defining the nozzle designs: (a) A design and (b) B design. Photos of the nozzles dispensing adhesive: (c) A design and (d) B design.

Polymer characterisation

Hot melt adhesives are mainly composed of a high molecular copolymer, resin and wax [16]. This type of adhesive is commonly solid at ambient temperature, becomes tacky as it is molten and forms a strong adhesive bond as it cools. The adhesive used in the present study is a typical commercial construction polymer (whose commercial name is PM357V) used in the manufacturing of hygiene products, such as diapers and sanitary napkins. The adhesive is manufactured by the company Savaré. More precisely, this is a styrene butadiene styrene (SBS) based adhesive, whose formula includes other components such as hydrocarbon resins, oil minerals and less than 3% in other additives. Based on thermoplastic rubber, its viscosity is 1.6 and 7.3 Pa·s at 170 °C and 130 °C, respectively, presenting a similar thermal behaviour to other hot-melt adhesives used for sanitary applications [17]. Its softening point is about 76 °C (ASTM E 28, water), its flash point is over 200 °C and its maximum running temperature is 170 °C, which establishes the maximum value for the polymer operation temperature in the experiments.

Figure 2 shows the shear viscosity curve of the adhesive, which is given by the Cross Model, from which $µ_{o}$ is the zero-shear viscosity, $λ$ is the relaxation time and $α$ an exponent that accounts for the adhesive’s non-linearity with shear rate. The viscosity measurements have been performed using a parallel plate rheometer, for three different distances between plates (gap width), namely 300, 500 and 700 µm.

Figure 2.

Adhesive’s viscosity as the function of the shear rate at $150$ ^oC.

Experimental facility used for high-speed imaging

Given the velocity of the fibre dynamics present in the melt blowing of hot-melt adhesives, high-speed imaging must be used to capture the fibre oscillation frequency at the nozzle exit region. The experimental facility was comprised of a high-speed camera (Photron FASTCAM Mini AX200) and a cold light source (Tungsten Light Head COOLH dedocool). In order to obtain a sharp contrast between the fibre and the background the images were recorded under backlight conditions. A micrometer allowed the positioning of the camera in the $X$ direction, while a tripod allowed its positioning along the $Z$ direction. In order to focus the adhesive fibre at a single polymer exit (the central one), a long-distance microscope (LDM) (INFINITY, K2/S) was used as the camera’s lens. Considering the working distance (WD) of 305 mm between the camera and the fibre, the LDM established a maximum field of view (FOV) of about 8.7x8.7 mm². By using a level, the camera was positioned horizontally, while its vertical position was adjusted by using the tripod until the top of the camera’s FOV matched with the nozzle exit, within an uncertainty ranging from 60 to 100 µm. The minimum required number of fps required for capturing the fibres’ dynamics turned out to be 14,400 and 19,200 fps on the A and B designs, respectively. The resulting FOV for each case comprised 384 × 1024 and 256 × 1024 pix², which is translated into 3.3 × 8.7 and 2.2 × 8.7 mm², respectively. A totality of 950 frames where recorded on each experiment, which is equivalent to approximately 65 and 50 ms of recording time on the A and B designs, respectively. The shutter speed was set to 1 μm, which turned out to be enough exposure time to obtain both bright and sharp images, with no blur. Recordings were always taken on the second unit placed in the central position of the MB head. More details regarding the experimental facility used for the HSI can be found in reference number [15].

Operating conditions

A two-level, full factorial design of experiments for three operating factors was adopted as the experimental scheme. To this end, the following operating parameters were selected: the air flow rate $(Q_{a})$ , the adhesive mass flow rate $(\dot{m_{f}})$ and the adhesive temperature $(T_{f})$ . All these conditions were taken from real industrial hot-melt adhesive applications for hygiene products. The air temperature $(T_{a})$ was considered to be a constant factor and it was kept at (200 ± 3) °C in all the experiments. Table 1 presents the values that were set on the three factors mentioned above in all the experiments, where the values of $Q_{a}$ and $\dot{m_{f}}$ correspond both to each polymer outlet. As is regularly done in continuous hot-melt applications, the polymer mass flow rate and the airflow were both kept constant during the experiments.

Table 1.

Operating conditions established for the HSI.

A Design				B Design
#Exp.	$Q_{a}$ [NL/min]	$\dot{m_{f}}$ [g/min]	$T_{f}$ [°C]	#Exp.	$Q_{a}$ [NL/min]	$\dot{m_{f}}$ [g/min]	$T_{f}$ [°C]
A1	2.6	1.5	140	B1	1.8	0.6	140
A2	5.4	1.5	140	B2	3.7	0.6	140
A3	2.6	3.0	140	B3	1.8	1.3	140
A4	2.6	1.5	170	B4	1.8	0.6	170
A5	5.4	3.0	140	B5	3.7	1.3	140
A6	5.4	1.5	170	B6	3.7	0.6	170
A7	2.6	3.0	170	B7	1.8	1.3	170
A8	5.4	3.0	170	B8	3.7	1.3	170

In the following, some dimensionless parameters will be defined in order to express the operating conditions of Table 1 in a more compact way. First, a number that considers how much air is destined to a single polymer fibre will be defined as:

m^{'} = \frac{{\dot{m}}_{a}}{{\dot{m}}_{f}} = \frac{ρ_{o} Q_{a}}{\frac{ρ_{f} v_{c c} n_{rpm}}{N_{f}}}

(1)

See the notation section for more information on the quantities. This number will be designated as the air-polymer flux ratio and has already been used in the past by other authors to study how the operating parameters affect the MB process [18,19]. Second, a number that indicates the relative temperature of the air to that of the fibre will be defined as:

T^{'} = \frac{T_{a} - T_{amb}}{T_{f} - T_{amb}}

(2)

This number will be designated as the dimensionless temperature ratio. This dimensionless parameter is similar to the air-polymer temperature ratio defined by R. Shambaugh [18], but it also takes into account the ambient temperature, which was measured by means of a thermometer in all the experiments. Table 2 shows the experimental conditions of Table 1 in non-dimensional form. When performing the measurements, one repetition was conducted for each operating condition of Table 2.

Table 2.

Operating conditions established for the HSI in dimensionless terms.

A Design			B Design
#Exp.	$m'$	$T'$	#Exp.	$m'$	$T'$
A1	2.60	1.52	B1	4.25	1.52
A2	5.41	1.52	B2	9.01	1.52
A3	1.30	1.52	B3	2.12	1.52
A4	2.60	1.21	B4	4.25	1.21
A5	2.70	1.52	B5	4.51	1.52
A6	5.41	1.21	B6	9.01	1.21
A7	1.30	1.21	B7	2.12	1.21
A8	2.70	1.21	B8	4.51	1.21

Measurement procedure of fibre position and whipping frequency

A tailored Matlab program has been developed for analysing the images from the HSI system and determining the $y$ -coordinate of the fibre centreline $(Y)$ as a function of time $(t)$ and distance to the nozzle exit $(Z)$ , at the nozzle exit region (Figure 1). The position of the fibre was determined at 16 evenly spaced points on $Z$ , which spanned the entire Vertical Field of View (VFOV), and throughout the entire recording time.

Once $Y$ is measured on each frame and throughout the entire recording time, the program continues to split the data into time segments spanning four times the fibre’s period of oscillation $(t_{o})$ . Details regarding the estimation of $t_{o}$ will be given in the Fibre dynamics section. Then, with the aim of obtaining information on the fibre dynamics, a regression is performed on each time segment, where the dependent variable is $y = Y / L_{R f}$ and the independent variables are $z = Z / L_{R f}$ and $t$ . Finally, the program retains the best fit obtained. The fit equation corresponds to the general equation of a mechanical travelling wave with power asymptotes and is expressed in nondimensional form, given by equation (3):

y (Z, t) = z^{a} \sum_{i = 1}^{N} s_{Y, i} \sin (k_{Y, i} Z - 2 π f_{Y, i} t + ϕ_{Y, i})

(3)

Where the fibre’s spreading rate $(s_{Y})$ , wave number ${(k}_{Y} = 2 π / λ_{Y})$ , phase angle ${(ϕ}_{Y})$ , fibre wedge exponent $(a)$ and, the item that is most significant for the present work, the frequency of oscillation $(f_{Y}),$ represent the fitting parameters that are adjusted in the regression. The results that are obtained for $f_{Y}$ from the regression will be used in the Results section to quantify the fibre frequency of oscillation, which remains constant throughout the $Z$ coordinate. Sub index $Y$ indicates that the parameter is calculated on the $Y Z$ plane, while sub index $X$ will be used to indicate calculations performed on the $X Z$ plane. Summation index $i$ represents the vibration modes. Equation (3) considers only a finite number of modes of vibration $(N)$ from the infinite number that would constitute the total solution to the travelling wave equation. Fit equations containing from $N = 1$ to $N = 12$ modes have been considered in the fitting process of each experiment and the mode which presented the highest goodness in the fit $(N^{*})$ , given by parameter $R^{2}$ , was selected as the one that best described the fibre dynamics of the experiment. The asymptotes $(y = \pm z^{a})$ restrict the lateral motion of the fibre as a result of the compound action of the aerodynamic, viscoelastic and gravitational forces acting on it. S. Xie and Y. Zeng [20] used a similar approach to study the fibre path described in a swirl melt blowing nozzle, but they imposed linear asymptotes in a single-mode equation with no time dependency, that is, $Y (Z) = (c_{1} Z + c_{2}) \sin (Z)$ .

In order to avoid introducing undesirable effects due to temporal aliasing, the maximum frequency fitted in the models has been limited to be lower than the Nyquist frequency, which is defined as half the sampling rate of the signal, which turns out to be 7,200 and 9,600 Hz in the A and B designs, respectively. The spatial aliasing effects were also considered by setting the maximum wavelength to a fraction of the cameras VFOV. No measurements were performed in those cases in which any type of fibre breakup occurred. Additionally, as the camera’s Horizontal Field of View (HFOV) accounts for a maximum lateral displacement of 1.6 and 1.1 mm in the A and B designs, respectively, occasionally part of the fibre left the cameras FOV, and the position of the points outside the FOV was considered to be half the cameras HFOV. Figure 3 contains two images that illustrate the measuring procedure followed to calculate the fibre’s position in experiments A3 and B1, respectively. The fibre centreline is represented by a yellow line and the vertical tilted dashed lines indicate the fibre wedge, inside which the fibre oscillates, and which are calculated as the maximum displacement of the fibre in the $y$ -coordinate. The uncertainty on the measurement of the fibre’s position is estimated to be proximate to 53 and 37 µm in the A and B designs, respectively. Details concerning this calculation are presented in the Supplemental Material.

Figure 3.

Measurement procedure followed for determining the fibre position $(Y)$ at the nozzle exit region: (a) experiment A3 and (b) experiment B1.

Results

Fibre dynamics

V. Entov and A. Yarin [21] developed the bending instability theory of liquid jets, which determines the critical air velocity to be $U^{*} = {[σ_{f} / (ρ_{a} L_{R f})]}^{1 / 2}$ , which produces the onset of fibre vibrations (see the notation section for information on the figures). In order to test the theory, consider $ρ_{a} = 0.56 kg / m^{3}$ , which corresponds to $T_{a} = 200$ °C, let the adhesive hydraulic diameter $(L_{R f})$ be 520 and 380 µm in the A and B designs, respectively (see the Description of the nozzle geometry section) and consider the adhesive’s surface tension $(σ_{f})$ to be equal to 0.04 J/m². This value of surface tension has been considered previously by other authors for melt blowing fibres [18]. By substituting these values in the equation presented previously, the critical velocities result in 11.4 and 13.3 m/s for the A and B designs, respectively. As both the A and B nozzles reach higher air velocities for the operating conditions studied in the present work [22], the fibre is expected to oscillate in all the experiments. This fact was confirmed by tracing the fibre’s position $(Y)$ during 65 and 50 ms in the A and B designs, respectively, from the die exit up to 9 dimensionless distances $(Z^{'} = Z / L_{R})$ from it, which represents a value on $Z$ above which the fibre stays properly focused and remains inside the FOV. Figure 4 presents three representative plots of $Y$ at $Z' = 9$ as a function of time, for experiments A3, A5 and B1. These plots represent different fibre dynamic behaviours, commonly known as regions of operation [15,18]. In agreement with the bending instability theory, fibre oscillations are observed in all the experiments. The periodic jumps in the fibre amplitude in experiment A5 (see Figure 4(b)) are caused by the formation of shots, which are usually described as “clumps of polymer that appear as a result of the operating conditions” [2]. This observation suggests that, in addition to compromising the uniformity of the fibre and causing heat distortion, shots reduce the edge control and the coverage uniformity of the application pattern.

Figure 4.

Fibre position $(Y)$ as a function of time at $Z' = 9$ , for experiments: (a) A3, (b) A5 (shot), (c) B1.

The process of searching for the fibre’s frequency of oscillation $(f_{Y})$ involved in the non-linear fit of equation (3) requires selecting an initial value for the frequency. For this purpose, the fibre’s frequency of oscillation was calculated as half the number of sign changes in $Y$ divided by the recording time at nine and four points of coordinate $Z$ in the A and B designs, respectively, ranging from $Z^{'} = 1$ to $Z' = 9$ . The deviation was calculated from the frequencies that were measured in each design, resulting in $\pm 29$ , $\pm 87$ and $\pm 105$ Hz for experiments A3, A5 and B1, respectively. Given that the frequency deviation that was calculated in the region from $Z^{'} = 1$ to $Z^{'} = 9$ turned out to be small, the initial frequency was then calculated at the point in which the fibre amplitude is the largest, which is $Z^{'} = 9$ . The frequency at $Z^{'} = 9$ will be termed as the reference frequency $(f_{o} = 1 / t_{o})$ and is quantified in those experiments listed in Table 1 for which the measurements of the fibre position $(Y)$ were not altered, neither by the fibre breakup nor by the presence of fibre loops. Frequency $f_{o}$ resulted in 223, 562 and 1050 Hz for experiments A3, A5 and B1, respectively.

Based on the literature review conducted on the modelling of the path described by blown fibres, it can be concluded that there is no universal model for describing the dynamics of the MB fibre. On the one hand, some authors observed that, although the dynamics described by the fibre in a slot nozzle can be considered to be planar, the one described in a swirl nozzle responds to a helicoidal curve [7]. On the other hand, other authors observed that, when produced with a slot nozzle, the fibre describes a three dimensional oscillatory motion and both its whipping frequency and amplitude present a different value in the $X$ and $Y$ directions of oscillation [4].

In view of this, and as commented in the Measurement procedure of fibre position and whipping frequency section, the fibre dynamics will be described by means of the equation of a mechanical travelling wave (equation (3)), which excludes from the analysis all the experiments that present any sort of fibre breakup (B2, B4, B5, B6 and B8) and the formation of disturbing fibre loops (B7). Thus, only two experiments will be studied on the B nozzle design. The initial values which were set in the search for the frequency $(f_{Y})$ in the regression process are multiples of the mean reference frequency $(f_{o})$ , of the form $m f_{o}$ , $m$ being a different constant for each mode of vibration. For convenience, a frequency that is representative of the entire fibre dynamics will be termed as the effective frequency $(f_{eff})$ and will be defined as the sum of the $N$ -mode frequencies $(f_{Y, i})$ , each weighted by the corresponding spreading rate $(s_{i})$ . The effective frequency can be interpreted as the frequency that best represents the large-amplitude dynamics of the fibre and contains information about the $N$ modes considered in equation (3), as expressed in equation number (4):

f_{eff} = \frac{\sum_{i = 1}^{N} | s_{Y, i} f_{Y, i} |}{\sum_{i = 1}^{N} | s_{Y, i} |}

(4)

Using the values of $f_{Y}$ and $s_{Y}$ that are provided by the regression on $y (z, t)$ (see the Measurement procedure of fibre position and whipping frequency section), the effective frequencies were calculated by using equation (4) and the results obtained are presented with super index * in Table 3. The optimal number of modes ( $N^{*}$ ), the adjusted fibre wedge exponent ( $a^{*}$ ), the reference period of oscillation $(t_{o})$ , which is calculated as $1 / f_{o}$ , and the fit goodness, which is given by $R^{2}$ , are also shown in Table 3. As expected, a large number of experiments present the best fit for $N = 12$ modes, because it is the number of modes that comprises the largest number of fitting parameters. The fibre wavelength $(λ)$ , the phase angle $(ϕ)$ and the spreading rate $(s)$ are not analysed in the present work. The mean percentual difference obtained in $a^{*}$ and $f_{eff}^{*}$ when compared with the values obtained in the repetitions is of 14% and 17%, respectively. The Supplemental Material contains two videos that show the real and modelled (see equation (3)) dynamics exhibited by the fibre in experiments A3 and B1. In the videos it can be observed that the model captures the main trends of the fibre dynamics rather than the instabilities that appear in the fibre oscillation. They also show that if the fibre diameter is large enough, as is the case in experiment A3, the simulated fibre presents a negligible oscillation in the first millimeter from the nozzle exit, which is in accordance with the dynamics predicted by the theory developed by A. Yarin and coworkers [10]. This theory divides the fibre behaviour in an initial straight part, where the fibre is thick and stiff enough to avoid any bending caused by the aerodynamic force of the surrounding air jets, followed by a bending part, in which the fibre diameter is significantly smaller than the one in the straight part, the bending stiffness is significantly reduced and bending perturbations grow. However, as the fibre diameter decreases, fibre oscillations along the first millimetre from the nozzle exit become non-negligible, as is the case in experiment B1, and the fibre dynamical behaviour deviates from the results predicted by the theory.

Table 3.

Parameters obtained for the $N$ -mode travelling wave model: (a) A Design and (b) B Design.

(a) A Design						(b) B Design
#Exp.	N*	a*	$f_{eff}^{*}$ [Hz]	$t_{o}$ [ms]	$R^{2}$	#Exp.	N*	a*	$f_{eff}^{*}$ [Hz]	$t_{o}$ [ms]	$R^{2}$
A1	8	1.87	184	4.06	0.98	B1	12	0.56	1138	1.72	0.7
A2	12	1.42	570	1.76	0.88	B3	12	1.01	555	1.28	0.87
A3	8	1.84	241	4.64	0.89
A4	12	1.27	481	4.06	0.75
A5	12	1.11	634	1.91	0.79
A6	12	1.81	1030	1.25	0.81
A7	8	1.15	392	2.32	0.74
A8	12	1.29	938	1.25	0.84

Figure 5 presents a boxplot containing the obtained $N$ -mode frequencies, which have been divided by experiment. The effective frequencies $(f_{eff}^{*})$ are represented in Figure 5 by black dots. The boxplot informs that the whipping frequency depends on the operating conditions which the experiment is performed under, which will be discussed in the Fibre dynamics section. From Figure 5 it can also be observed that the effective frequencies are lower than the corresponding median frequencies (represented by a solid horizontal line) in all the experiments. Hence, it is possible to conclude that the lowest frequencies dominate the fibre dynamics on both nozzle designs.

Figure 5.

Frequencies of oscillation $(f) and effective frequencies (f_{eff})$ divided by experiment.

The effective frequencies obtained in the present study are consistent with the frequencies that have been measured by other authors on other nozzle designs. For example, S. Xie et al. [5] observed frequencies of about 400 Hz, when studying the fibre whipping motion on a dual slot nozzle at an air pressure of 0.1 MPa, an air temperature equal to 260 °C and a polymer flow rate of 2.6 g/min using a polypropylene with Melt Flow Index (MFI) equal to 900. More recently, the same authors observed frequencies of about 700 Hz [23], when conducting high-speed imaging at 4 mm from the nozzle exit, operating at an air pressure of 1 atm. Concerning the effect of the nozzle design on the fibre frequency of oscillation, H. Beard et al. [6] studied the frequency spectra of the fibre oscillation through the use of the Fast Fourier Transform on a slot and on a swirl nozzle designs and concluded that the dominant frequency of the slot nozzle is about $1 / 3$ that of the swirl nozzle. Whereas in their study two different nozzle designs have been considered, in the present work two configurations of the same geometrical design (multi-hole) have been studied, which partly explains that the frequencies of oscillation that were observed in the A and B designs are proximate.

Figure 6(a) presents the effective frequency $(f_{eff}^{*})$ as a function of the operating parameters $m'$ and $T'$ , where $f_{eff}^{*}$ is expressed in Hertz. Those frequencies that are represented by a dash in Figure 6(a), denote that no measurements were conducted in those experiments. From the figure it can be inferred that, in general, $f_{eff}^{*}$ increases with decreasing values of $T'$ and increasing values of $m'$ . Figure 6(b) shows how $f_{eff}^{*}$ varies with the dimensional operating parameters $Q_{a}, {\dot{m}}_{f}$ and $T_{f}$ for the A nozzle design. From the figure, it becomes clear that the air flow rate is the factor that dominates the fibre frequency of oscillation, while the polymer flow rate has little effect on it. The results obtained on the repetitions confirm this tendency. Figure 6(a) shows that there is a sudden rise in $f_{eff}$ , despite the small change in $m'$ , when going from experiments A1 to A5 (the same occurs going from A4 to A8). This jump in $f_{eff}$ is explained by the fact that experiments A1 and A4 were conducted at a low $Q_{a}$ , while experiments A5 and A8 were conducted at a high $Q_{a}$ (see Figure 6(b)).

Figure 6.

Effective frequency $(f_{eff}^{*})$ in Hertz as a function of the operating conditions: (a) in dimensionless terms (A and B design), (b) in dimensional terms (A design).

Model of the application pattern

Equation (3) describes the motion of the adhesive fibre on the $Y Z$ plane at the nozzle exit region. If the fibre is assumed to describe a sinusoidal motion on the $X Z$ plane, similar to the one described on the $Y Z$ plane but with a different frequency and spreading rate, an equation for $X$ is obtained as a function of $Z$ and $t$ . Furthermore, if coordinate $Z$ in the equations of $Y (Z, t)$ and $X (Z, t)$ is evaluated at the die-to-collector distance $(DCD)$ , which for most hot-melt applications for hygiene products spans from 10 to 30 mm, the resulting pair of equations provides the pattern described by the fibre as it deposits on the collector screen, as a function of $t$ . In the present section, the deposited adhesive pattern will be studied at $Z = 10$ mm, thus the pattern will be obtained as an extrapolation from equation (3).

With the aim of obtaining a mathematical model to predict the deposition of the adhesive pattern, the motion of the adhesive fibre will be described as a sinusoidal three-dimensional path, as it travels from the nozzle exit to the collector screen. Moreover, it will be assumed that the dynamics of the fibre presents a different amplitude and frequency in the $X$ and $Y$ directions of oscillation, whereas the spreading rate will be noted as $s_{X}$ and $s_{Y}$ , respectively, the frequencies will be noted as $f_{X}$ and $f_{Y}$ , respectively. By considering a simplified single-mode model $(N = 1)$ and taking $Z = DCD$ in equation (3), the $X (t)$ and $Y (t)$ coordinates of the fibres’ position can be expressed as given in equation number (5):

Y (t) = A_{Y} \sin (2 π f_{Y} t + δ)

X (t) = A_{X} \sin (2 π f_{X} t)

(5)

For simplicity in the notation, the amplitudes in the $X$ and $Y$ directions have been defined as $A_{Y} = c {DCD}^{a} s_{Y}$ and $A_{X} = c {DCD}^{a} s_{X}$ , respectively, where $c = L_{R f}^{1 - a}$ is a constant that contains information about the nozzle design. Angle $δ$ represents the phase angle of the oscillatory motion, which includes the terms $ϕ_{Y}$ and $k_{Y} DCD$ (see equation (3)). Equation (5) represents a modified form of the Lissajous parametric curves [24], which were investigated in the mid $XIX$ century. Apart from other engineering applications in which they turned out to be applicable, in the present work it will be shown that these curves are also useful in describing the adhesive pattern produced by hot-melt adhesives. For convenience, the spreading rate and frequency of the fibre in the $X$ direction will be expressed as a function of the ones in the $Y$ direction as $s_{X} = s_{Y} / r_{s}$ and $f_{X} = f_{Y} / r_{ω}$ , respectively. Furthermore, if the collector screen is assumed to move at constant velocity $(u_{b})$ in the $X$ direction, then the absolute fibre’s position in the $X$ direction can be expressed as the conveyors displacement plus the oscillatory motion of the fibre, that is, $X (t) = u_{b} t + A_{X} \sin (2 π f_{X} t)$ .

Images of real hot-melt patterns were recorded on the collector screen in experiments A3 and B1 and were used to obtain the parameters required by equation (5) to allow modelling the adhesive pattern (see Figure 7). The images were recorded with $u_{b} = 100$ m/min and at $DCD = 10$ mm. The pattern’s sub-image that appears inside a dashed box in Figure 7 for experiments A3 and B1 correspond to one period of oscillation of the fibre ( $t_{Y}$ ), starting at $X = 0$ and $Y = A_{Y}$ , which corresponds to $δ = π / 2$ for the modelled pattern in equation (5). These two experiments have been chosen for this purpose because, among the studied operating conditions, they turn out to be the ones that generate the most regular and periodic patterns for each design, respectively.

Figure 7.

Real (top) and modelled (bottom) application patterns at $DCD = 10 mm$ , experiments A3 and B1.

Equation (5) requests two input parameters that contain information on the fibre dynamics on the $Y$ direction, namely $f_{Y}$ and $A_{Y}$ , which are obtained from the real pattern images of Figure 7. Whereas $f_{Y}$ turns out to be 384 and 1366 Hz in experiments A3 and B1, respectively, which represents $1.59$ and $1.20$ times $f_{eff}^{*}$ in each case (see the Fibre dynamics section), $A_{Y}$ turned out to be 1.5 and 0.3 mm in experiments A3 and B1, respectively. From these results it can be inferred that the effective frequency tends to be lower than the real frequency exhibited by the adhesive fibre.

Equation (5) also gives two model parameters that provide information on the dynamics in the $X$ direction, which are $r_{s}$ and $r_{ω}$ . The two model parameters have been varied to generate numerous adhesive patterns by means of equation (5). The best-fit pattern was considered to be the one that minimised the pattern discrepancy $(E)$ , which is defined as the average Euclidean distance between the coordinates of the points obtained from the experimental pattern and the ones generated by the modelled pattern with equation (5). The modelled pattern was obtained for different values of $r_{s}$ and $r_{ω}$ and throughout one period of oscillation $(t_{Y} = 1 / f_{Y})$ . The optimal parameters that are obtained by following this procedure are going to be represented with super index *. The experimental patterns of experiments A3 and B1 comprise 189 and 123 points, respectively, which were obtained using an open access software (Web Plot Digitalizer).

The range and the step size which were set for the search of $r_{s}^{*}$ and $r_{ω}^{*}$ are presented in Table 4, resulting in a pattern discrepancy of $E = 0.31$ and $E = 0.16$ mm in experiments A3 an B1, respectively. The set of values adopted for the variation of parameter $r_{ω}$ are $\{\frac{1}{4}, \frac{1}{3}, \frac{1}{2}, \frac{1}{1}\}$ because, in order to obtain a closed Lissajous curve with a period equal to $t_{Y}$ , parameter $r_{ω}$ should be a rational number of the form $1 / n$ , where $n$ is a natural number that represents the number of cycles the fibre completes in the $X$ direction in $t_{Y}$ seconds (see Supplementary Material).

Table 4.

Variation and results obtained for model parameters $r_{s}$ , $r_{ω}$ in experiments A3 and B1.

				$Optimum$
	$Min$	$Step$	$Max$	$A 3$	$B 1$
$r_{s}^{*} = s_{Y} / s_{X}$	${1.10}^{- 2}$	${1.10}^{- 2}$	$4$	$3.0$	$1.1$
$r_{ω}^{*} = f_{Y} / f_{X}$	$1 / 4$	$variable$	$1$	$1 / 2$	$1$

The search ranges presented in Table 4 have been refined based on the results obtained from a first precursory search. Figure 7 shows the real adhesive patterns (top) and the modelled ones (bottom) for experiments A3 and B1. The difference between the corresponding points in both patterns is depicted by black solid lines.

The values obtained on parameters $r_{s}^{*}$ and $r_{ω}^{*}$ provide the best resemblance between the modelled and the real adhesive patterns. Given that in the A design the fibre is blown exclusively in the $Y$ direction, while in the B design it is blown in the $X$ and $Y$ directions with a similar strength, it is expected that the fibre presents very similar dynamics in the $Y$ and $X$ directions in the case of the B design. The results confirm this hypothesis, because $r_{s}^{*}$ and $r_{ω}^{*}$ obtained in experiment B1 are much closer to one than the ones obtained in experiment A3.

Fibre contact

The simplicity of equation (5) facilitates investigating the main defects that can show up in the adhesive pattern, such as fibre contact, which occurs due to the whipping motion of the fibre in the direction of the moving collector screen $(X)$ and manifests through the self-intersection of the fibre strand, thus forming a closed loop. In order to investigate how the operational parameters increase fibre contact, various adhesive patterns were obtained by use of equation (5). To this end, parameters $r_{s}^{*}$ and $r_{ω}^{*}$ that were obtained from experiments A3 and B1 in the Model of the application pattern section were used, and different velocities were imposed on the collector screen $(u_{b})$ , among which $u_{b} = 100$ m/min is included (see Figure 8). From Figure 8 it can be noticed that as $u_{b}$ diminishes fibre contact increases.

Figure 8.

Deposited adhesive pattern at $DCD = 10 mm$ , for different velocities on the collector screen and for experiments A3 and B1.

Fibre contact is avoided if the absolute velocity of the fibre in the $X$ direction is positive, or at least zero, for all $t$ . The limit case is obtained by differentiating the $X$ -coordinate equation in equation (5) with respect to $t$ and equating the result to $u_{b}$ , obtaining a condition on the latter given by equation (6):

u_{b, \min} = 2 π A_{X} f_{X}

(6)

While equation (6) represents a general condition for avoiding fibre contact, regardless of the nozzle design that produces the pattern, it turns out to be a necessary condition to avoid fibre contact in the B design, but it represents just a sufficient condition for the A design. The parity of $n$ is likely to determine whether equation (6) is a necessary condition for avoiding fibre contact or not. In order to clarify this point, $u_{b, \min}$ was calculated for experiment A3 from equation (6) and resulted in 142 m/min. However, Figure 8 shows that fibre contact starts to occur in experiment A3 when $u_{b}$ =30 m/min. This observation confirms that equation (6) suffices for avoiding fibre contact in the A design, but it is not a necessary condition to fulfil. The Supplemental Material contains a development that shows that the minimum velocity on the collector screen required for avoiding fibre contact in the A design is 21% of the value obtained with equation (6). If equation (6) is applied to experiment B1, the minimum velocity on the collector screen results in 138 m/min and if $u_{b}$ is lower than this value, fibre contact occurs for this experiment, as shown in Figure 8.

Discussion

Fibre dynamics

Regarding the fibre’s wedge exponent, Table 3 shows that, in general, $a^{*} \geq 1$ in the A Design, while $a^{*} \leq 1$ in the B Design. This observation suggests that, as $a^{*}$ is slightly different from one in all the experiments, the fibre rarely describes a cone as it falls onto the collector screen, but instead the spreading rate of the fibre in the A design grows with increasing values of $Z$ , while the one in the B design diminishes. In view of this, it is possible to infer that the compound action of the aerodynamic, viscoelastic and gravitational forces is different in both designs. This observation holds for the operating conditions studied in the present work, which for the B design comprise only two experimental points (B1 and B3).

In agreement with these observations, E. Moore et al. [9] observed $a \approx 1$ when studying the fibre produced by a slot nozzle design. Furthermore, S. Xie, Y. Zeng and G. Jiang [25] simulated the fibre whipping motion in a slot melt blowing nozzle by using a two-dimensional Lagrangian numerical model, and observed that the fibre’s lateral displacement $(Y)$ increased with increasing distance to the nozzle exit $(Z)$ . The authors fitted the fibre wedge with a function of the form: $Y = A Z^{1}$ , in which $a$ was considered to be equal to $1$ , and the goodness of the fit resulted in $R^{2} = 0.73$ . The amplitude and frequency of oscillation of the driving force were $1$ mm and $160$ Hz respectively, and the initial fibre diameter was $500$ µm, which are proximate values to the ones of the present study.

Regarding the fibre’s whipping frequency, in Figure 6(a) it can be observed that increasing values of $m'$ and decreasing values of $T'$ both lead to an increase in $f_{eff}$ . From Figure 6(b) it can be inferred that the increase on $f_{eff}$ with $m'$ and $T'$ is caused by an increase in $Q_{a}$ and $T_{f}$ , respectively. The effect of $Q_{a}$ on $f_{eff}$ is in accordance with physical intuition, which suggests that a higher air flow rate provides the fibre with greater momentum, thus increasing its kinetic energy of oscillation and ultimately its frequency of oscillation. The results obtained tally well with the ones presented by H. Beard et al. [6] who found that the frequency of oscillation decreased with decreasing air-polymer flux ratios when studying the slot and the swirl nozzle designs. Other authors stated that an increase in the air velocity would produce an increase in the fibre whipping frequency [3,4], which is also in line with the results obtained in the present study. The increase in $f_{eff}$ with $T_{f}$ could possibly be explained by the decrease in the adhesive’s shear viscosity, which causes a drop in the fibre’s bending stiffness.

4.2 Fibre contact

From equation (6), the following two observations on fibre contact can be pointed out:

Increasing values of $DCD$ and $a$ both increase the chances of fibre contact occurring.

Increasing values of $f_{X}$ also increases the chances of fibre contact occurring.

From the first observation, it can be inferred that fibre contact can be minimised by setting the shortest $DCD$ that the application allows. Taking into account the second observation, and also considering the discussion raised on the effect of $m'$ and $T'$ on $f_{eff}$ (see the Fibre dynamics section), it can be concluded that fibre contact can be minimised by operating at the lowest values on $m'$ and the largest values on $T'$ that the application permits. Alternatively, fibre contact can be controlled by setting a sufficiently large velocity on the collector screen ${(u}_{b})$ , which, in addition to avoiding fibre contact, would also speed up the production rate. Any of the above measures that is taken for reducing fibre contact should be incremented in those designs for which $a > 1$ .

Finally, notice that equation (6) has been obtained from equation (5), which holds for the nozzle exit region. However, as $DCD$ increases, the turbulence intensity of the airfield also increases, and the motion of the fibre is increasingly distorted. If $DCD$ is large enough, fibre contact becomes unavoidable, as shown in Figure 9 for experiment A3.

Figure 9.

Application pattern for two die-to-collector distances, experiment: A3 (a) DCD = 10 mm and (b) DCD = 30 mm.

The two observations given above are valuable from an economical point of view because the reduction of fibre contact would translate into a reduction in the adhesive over spraying, and ultimately in its waste. The production of adhesive strands with no fibre contact present additional desirable features, such as good pattern definition, breathability, permeability, softness and pattern stability. The production of adhesive patterns at operating conditions that are proximate to the fibre contact condition increase the coverage density of the pattern and simultaneously avoid over spraying. Additionally, if $f_{X}$ and $A_{X}$ can be estimated for a given nozzle design on a certain application, equation (6) helps to determine the window of operation of the application and the line speed capabilities of the nozzle design to avoid fibre contact. Nevertheless, in addition to fibre contact, other defects that may arise in the adhesive pattern should also be considered when setting the operating conditions for a certain application. These include machine contamination, adhesive cut-off, and nozzle clogging. Also, dispensing systems should meet specific requirements, not only relative to the quality of the adhesive pattern, but relative to costs as well.

Concluding remarks

In this article, the fibre dynamics of two melt blowing nozzle designs for producing hot-melt adhesives have been studied by means of HSI. Information about the parameters that govern the fibre dynamics, which include the frequency of oscillation, were obtained through image analysis for the two nozzle designs. The effective frequency $(f_{eff})$ is a parameter that contains information on all the modes of oscillation of the fibre and was selected to study the effect of the operating conditions on the fibre dynamics. Two operating parameters, namely the air-polymer flux ratio $(m')$ and the dimensionless temperature ratio $(T')$ , were defined with this purpose in mind. The results suggest that increasing values on $m'$ and decreasing values on $T'$ both increase $f_{eff}$ . The results indicate that laminated plate nozzle designs working under industrial operating conditions produce fibres with maximum frequencies of oscillation of about 4,000 Hz, but those that dominate the dynamics are below 1,200 Hz.

The fibre dynamics in the direction parallel to the movement of the collector screen was inferred by fitting the parametric Lissajous equations to real images of hot-melt patterns. The results obtained suggest that the path followed by the fibre produced by multi-hole nozzles is three-dimensional and, in the case of the A design, its dynamics present significant differences in the $X$ and $Y$ directions of oscillation. The location of the nozzle’s air exits with respect to the polymer exit, as well as how many there are, could partly explain this difference. In addition, fibre contact was studied by further use of the Lissajous equations. The results indicate that, in order to avoid fibre contact, $T'$ should be increased and $m'$ should be decreased. Alternatively, the collector’s velocity $(u_{b})$ should be increased or the die-to-collector distance $(DCD)$ should be shortened.

Supplemental Material

sj-pdf-1-jit-10.1177_1528083720978401 - Supplemental material for Experimental study on the hot-melt adhesive pattern produced by melt blowing nozzle designs

Supplemental material, sj-pdf-1-jit-10.1177_1528083720978401 for Experimental study on the hot-melt adhesive pattern produced by melt blowing nozzle designs by Ignacio Formoso, Alejandro Rivas, Gerardo Beltrame, Gorka S Larraona, Juan Carlos Ramos, Raúl Antón and Alaine Salterain in Journal of Industrial Textiles

Supplemental Material

sj-pdf-2-jit-10.1177_1528083720978401 - Supplemental material for Experimental study on the hot-melt adhesive pattern produced by melt blowing nozzle designs

Supplemental material, sj-pdf-2-jit-10.1177_1528083720978401 for Experimental study on the hot-melt adhesive pattern produced by melt blowing nozzle designs by Ignacio Formoso, Alejandro Rivas, Gerardo Beltrame, Gorka S Larraona, Juan Carlos Ramos, Raúl Antón and Alaine Salterain in Journal of Industrial Textiles

Footnotes

Acknowledgements

The authors are grateful for the support of VALCO MELTON for lending the MB equipment, and the Cátedra Fundación Antonio Aranzábal-Universidad de Navarra is also gratefully acknowledged. The authors also want to acknowledge Juan Villarón for the immense help he provided in the laboratory.

Declaration of conflicting interests

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

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by VALCO MELTON; and Ministerio de Ciencia e Innovación, Gobierno de España, RETOS-COLABORACION 2019 (RTC2019-007057-7).

ORCID iD

Ignacio Formoso

Supplemental Material

Supplemental material for this article is available online.

Appendix

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Supplementary Material

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