Multilayered encapsulation has been of great interest for various pharmaceutical, chemical, and food industries. Fabrication of well-defined capsules with more than one shell layer still poses a significant fabrication challenge. This study aims to investigate the feasibility of using a coaxial nozzle to fabricate double-layered (core–shell–shell) capsules during vibration-assisted dripping. A three-layered coaxial nozzle has been designed, manufactured, and tested for double-layered capsule fabrication when using sodium alginate solutions as the model liquid material for inner and outer shell layers and calcium chloride solution as the core fluid. To facilitate the droplet formation process, a vibrator has been integrated into the fabrication system to provide necessary perturbation for effective breakup of the fluid flow. It is demonstrated that double-layered alginate capsules can be successfully fabricated using the proposed three-layered coaxial nozzle fabrication system. During fabrication, increasing the core flow rate leads to an increase in capsule and core diameters while the inner and outer shell layer thicknesses decrease. Increasing annular flow rate results in an increase in capsule diameter and inner shell layer thickness while the outer shell layer thickness decreases. An increase in the sheath flow rate leads to an increase in capsule diameter and outer shell layer thickness but has no significant effect on the core diameter and inner shell layer thickness.

Introduction

Encapsulation, a process involving the complete envelopment of selected core material with a well-defined porous or impermeable membrane, has been attracted much attention during past decades and widely used in many fields including chemical, pharmaceutical, and food industries, as well as in various applications related to agriculture, biotechnology, and medicine, to name a few [14]. Function wise, encapsulation has been utilized to immobilize, protect, and control the release of entrapped materials such as flavor, pharmaceutical materials, and even living cells [5].

For the fabrication of multilayered capsules, various technologies have been studied, including coaxial nozzle (or compound nozzle)-based dripping and jetting [613], droplet collision [14], and bulk emulsification by utilizing stirring/mixing [15]. During compound or coaxial nozzle-based fabrication, coaxial nozzles are used to produce the core droplet surrounded by a shell. When the flow rates of core and shell solutions increase, the droplet formation mechanism may change from dripping [5,16] to jetting [6,9]. A liquid core jet can be surrounded by an annular jet, which may be further surrounded by a carrier stream [9,17]. For some applications, additional stimuli may be applied to facilitate the droplet formation process such as an electric field [6,1820] or vibration [9,21] as during microsphere fabrication [22]. During droplet collision, two inkjet nozzles are utilized to make droplets from different solutions such as aqueous and polymer solutions. After the collision of two inkjetted droplets, a polymer film is generated at the interface between two solutions due to the solvent exchange mechanism, and a compound droplet is fabricated with the polymer solution as the shell layer [14]. During bulk emulsification, there are two typical emulsification steps: a core material is first stirred in a shell polymer bath, and then double-layered emulsion is achieved by stirring the formed emulsion in another emulsifier bath [23]. The process can be improved by combining the co-nozzle extrusion with emulsification. By using a microcapillary device, the coaxial flow is formed at the exit of a tapered tube, and the outermost fluid is pumped through the outer coaxial region from an opposite direction; as the compound flow passes through the exit orifice, it ruptures into core–shell capsules [7]. While this approach simplifies the two emulsification step-based conventional fabrication process, the outermost fluid is used to emulsify the coaxial flow into core–shell capsules instead of being a layer of the capsules. In addition, it is difficult to fabricate a double-layered coaxial glass microcapillary device as well as to control the formation of a three-layered compound flow in an emulsification flow. Thus, it is not practical to extend this approach to fabricate capsules with a well-defined core–shell–shell structure.

The objective of this study is to investigate the feasibility of using a coaxial nozzle to fabricate double-layered (core–shell–shell) capsules during vibration-assisted dripping. Of the fabrication technologies described above, compound or coaxial nozzle-based dripping/jetting [10] is favored due to its easy implementation in an apparatus similar to a microsphere fabrication device using single nozzle jetting [2426]. As expected, the proposed multilayered capsule fabrication process will produce monodisperse capsules with one core material enclosed by more than one surrounding shell material. Although single-layered (core–shell) capsules were successfully fabricated by the aforementioned fabrication approaches [7,9,27], to date the fabrication of multilayered capsules has not been explored. This study is the first to investigate the feasibility of multilayered capsule fabrication using the coaxial dispensing mechanism and how the geometry of the resulting multilayered capsules can be controlled by adjusting corresponding flow rates. Sodium alginate (NaAlg) has been selected in this study as the model hydrogel material to fabricate double-layered capsules, and calcium chloride has been used as the crosslinking agent to facilitate the formation of alginate capsules. To facilitate the droplet formation process, ultrasonic vibration has been applied to the coaxial nozzle during dripping. The proposed coaxial nozzle-based multilayered capsule fabrication system has been validated during the fabrication of double-layered alginate capsules, providing a versatile approach for effective capsule fabrication. While alginate and calcium chloride solutions are utilized in this study, the proposed approach is also applicable to capsule fabrication from suspensions.

Proposed Coaxial Nozzle-Based Fabrication Approach

The schematic of the proposed multilayered capsule fabrication system is illustrated in Fig. 1(a). During fabrication, different liquid materials are dispensed through their corresponding channels of the coaxial nozzle to form a compound liquid flow, which consists of a core flow, an annular flow, and a sheath flow. A high-frequency vibration is introduced to facilitate the breakup of the compound flow and the formation of double-layered alginate capsules herein. After crosslinking in a collection bath, capsules with a core–shell–shell structure are fabricated. As shown in Fig. 1(a), the multilayered capsule fabrication system has three main components: a multilayered coaxial nozzle, a solution delivery and vibration system, and a collection bath. The key part of the multilayered capsule fabrication system is the three-layered coaxial nozzle (inset of Fig. 1(a)), which enables fabrication and influences the geometry of fabricated capsules. The nozzle consists of a core flow channel to form the core, an annular flow channel to form the inner shell layer, and a sheath flow channel to form the outer shell layer of double-layered capsules. As designed, capsules are formed at the outlet of the coaxial nozzle by dispensing various solution flows through corresponding channels, and the capsule formation process varies based on the velocity or flow rate of each solution and their material rheological and physical properties. The solution delivery and vibration system consists of three syringe pumps to deliver solutions to corresponding channels and an ultrasonic vibrator to vibrate the coaxial nozzle at a given frequency and amplitude to facilitate the breakup of fluid flows and form multilayered capsules more effectively. The collection bath herein also contains a crosslinking agent (Ca2+) to stabilize formed capsules.

The proposed multilayered capsule fabrication system and schematic can be seen in Fig. 1(a). Figure 1(b) illustrates the fabrication process of a double-layered capsule with images showing three representative sequential stages during fabrication: capsule initiation, development, and breakup. Such a system can be used to fabricate double-layered capsules by delivering corresponding solutions through the core flow, annular flow, and sheath flow channels simultaneously. While using the core and annular flow channels only (or using the sheath flow channel only to provide a carrier stream for jet pinch-off control), it can also be utilized to fabricate single-layered (core–shell) capsules. Due to easy implementation, the proposed multilayered capsule fabrication system is applicable to fabricate various single- and double-layered capsules from diverse liquid materials in conjunction with suitable crosslinking mechanisms.

Material Selection and Nozzle Design

Material Selection.

In this study, sodium alginate, a natural polysaccharide, was selected as the model material to fabricate the shell layers of double-layered capsules due to its versatile functionality, mild crosslinking conditions, low cost, biocompatibility, low toxicity, and environmentally friendly nature [28], as well as its wide applications for encapsulation [2932]. As designed, alginate solutions were dispensed through the annular and sheath flow channels to form two shell layers each with a different dye. Aqueous calcium chloride (CaCl2) was selected as the core flow as well as collection bath material, acting as the crosslinking agent for alginate [25,26]. Sodium alginate, a natural hydrogel, is comprised of some binary copolymers including M and G units. When it interacts with some cations such as Ca2+ or Al3+, an ionic gelation process happens, resulting in interchain ionic bonds. For this study, the gelation process leads to stable calcium alginate.

Gelation Process Modeling.

The CaCl2 concentration of the core flow affects the gelation rate of the annular alginate flow when traveling in air. If the CaCl2 concentration is too high, the sodium alginate solution will gel immediately once dispensed out of the nozzle, resulting in a gelled filament before forming a droplet. If the CaCl2 concentration is too low, the gelation rate of the inner surface of the inner shell layer will be slow, resulting in undesirable diffusion between the sodium alginate and CaCl2 solutions. As a result, the inner surface of the inner shell layer may not be well-defined. Thus, it is important to select a suitable CaCl2 concentration to fabricate well-defined multilayered alginate capsules.

Since the CaCl2 concentration of the core flow is of interest, Fig. 2(a) only illustrates the interaction between the CaCl2 core flow and the alginate annular flow. When the alginate solution is dispensed into the ambient environment, it starts interacting with the CaCl2 core flow. The region, which separates the newly crosslinked region from the liquid alginate region, is defined as the reaction front during alginate gelation process. The diffusion of calcium cations through a crosslinked structure is predicted using a traveling-wave hypothesis [33], and the reaction front position G(t), the distance from the inner boundary of a single-layered capsule to the edge of the reaction front, can be estimated as follows [34]:

 
1+θ=(1+LdDcdG(t)dt)exp(1DcG(t)dG(t)dt)
(1)
 
θ=c0Nca0
(2)
where t is the time, Ld is the equivalent filter length for the reaction–diffusion model system, Dc is the calcium cation diffusion coefficient, and θ (Eq. (2)) is the ratio between the calcium cation bulk concentration c0 and concentration of available binding sites Nca0, Nc is the stoichiometric calcium cation-binding capacity per alginate residue as Nc=3/4σ [35], σ is the guluronic acid content of alginate (70% [36]), and a0 is the initial bulk concentration of alginate solution in terms of uronic acid residues (0.025 mol/L herein). By assuming that all the diffusion happens along the radial direction, Ld is taken as 0. Based on the measurement of calcium cation diffusion [37], Dc can be determined accordingly. For a semisteady-state concentration gradient of calcium cations in this study, G(t) is estimated as follows [34]: 
G(t)=2Dcθt+Ld2Ld
(3)

The gelation time is approximated as the breakup period in this study, which can be affected by the material properties and flow rate of the core and shell flows. By considering that the longest breakup period is on the order of 1 s (∼3 s) and the typical annular shell thickness of capsule is on the order of 0.1 mm (∼0.5 mm), the reaction front position G(t) of CaCl2 core flow solution with different concentrations can be calculated. If G(t) is taken as one-tenth of the annular shell thickness, that is assumed to be 0.5 mm, the alginate gelation of the inner surface of the inner shell layer may not significantly affect the jet/flow breakup and capsule formation process. When the CaCl2 concentration decreases to 0.5% (w/v), G(t) is around 0.03 mm (where c0: = 0.275 × 10−2 mol/L and Dc 0.71 × 10−9 m2/s), which is lower than 0.05 mm. As such, the CaCl2 concentration of the core flow is selected as 0.5% (w/v) herein.

After an alginate capsule submerges in the CaCl2 collection bath, its crosslinking mechanism is depicted in Fig. 2(b). To maintain its spherical morphology, the outer surface of alginate capsules should be solidified in a timely manner. Thus, a 2.0% (w/v) CaCl2 solution was used as the crosslinking and collection bath [25]. Finally, alginate capsules are completely crosslinked in the bath as shown in Fig. 2(c).

Material Preparation.

Sodium alginate (Sigma-Aldrich, St. Louis, MO) was used to fabricate the layers of multilayered capsules: 1.0% (w/v) alginate solution for the annular flow and 2.0% (w/v) alginate solution for the sheath flow. During preparation, alginate powder was dissolved in deionized water with continuous stirring until completely dissolved. To distinguish different alginate layers of fabricated double-layered capsules, fluorescent blue 7-amino-4-methylcoumarin (Chem-Impex, Wood Dale, IL) was added to the 1.0% (w/v) alginate solution at a concentration of 0.5% (w/v), and fluorescent green polyethylene microspheres (UVPMS-BG-1.00, 45–53 μm, Cospheric LLC, Santa Barbara, CA) were added to the 2.0% (w/v) alginate solution at a concentration of 0.5% (w/v).

Calcium chloride (Sigma-Aldrich, St. Louis, MO) was used to crosslink the alginate solutions during capsule fabrication. CaCl2 solution was prepared by dissolving CaCl2 powder in de-ionized water with continuous stirring until completely dissolved. Specifically, 0.5% (w/v) CaCl2 solution was prepared as the core flow to crosslink the inner surface of alginate capsules while 2.0% (w/v) CaCl2 solution was prepared as the crosslinking bath to crosslink fabricated alginate capsules as aforementioned.

Rheological Property Measurement.

Rheological properties of alginate solutions with two concentrations (1.0% and 2.0% (w/v)) were measured using a rheometer as in a previous study [38]. By fitting the shear stress-rate data into the Carreau–Yasuda model, the zero-shear-rate viscosity was obtained as shown in Table 1. The surface tension was measured using a tensiometer (DSA10-MK2, Krüss GmbH, Hamburg, Germany) based on the pendant drop method, and the results are listed in Table 1.

Three-Layered Coaxial Nozzle Design and Fabrication

Three-Layered Coaxial Nozzle Design.

The proposed three-layered coaxial nozzle is designed with three main stainless steel components: an inner set, a middle set, and an outer set as shown in Fig. 3(a). In addition to the three sets, Fig. 3(a) also illustrates three channels for fluid dispensing: core, annular, and sheath channels. The inner set has two functions: to provide the core channel for the core flow, and to fit with the middle set to form the annular channel as shown in Fig. 3(b). The middle set is in the center of the coaxial nozzle and provides support to hold the inner set to form the annular channel as well as fit with the outer set to form the sheath channel. The outer set enables the formation of the sheath channel of the coaxial nozzle as shown in Fig. 3(c) in addition to being the fixture of the whole nozzle assembly. The coaxial nozzle is also attached to the vibrator via the outer set. Due to the interest in capsule fabrication and the capacity in micromachining of the stainless steel nozzle sets, the orifice size of each set is designed as follows: The through-hole in the inner set has an inner diameter of 0.5 mm, length of 3.0 mm for its outlet section, and outer diameter of 1.5 mm; the outlet of the middle set has an inner diameter of 2.5 mm and outer diameter of 3.5 mm; and the outlet of the outer set has an inner diameter of 4.5 mm as shown in Fig. 3(a).

The core channel is designed as a straight through-hole in the inner set with a diameter of 0.5 mm based on the typical core size of capsules and the machining capability. Figures 3(b) and 3(c) illustrate the structures of both annular and sheath channels. As seen from these two figures, alginate solutions are injected into the channels from their corresponding inlets, which are perpendicular to the axis of the nozzle. Thus, it is of importance to design the nozzle assembly for uniform flow fields in the channels and at the outlet of the nozzle in order to have well-defined capsules. Specifically, for the annular channel (Fig. 3(b)), the shaping length L3, the compression angle (determined by the inner diameter D and axial length L2), and the distance from the inlet to the inclined channel L1 are to be determined; for the sheath channel (Fig. 3(c)), the shaping length L, the compression angle (determined by the inner diameter D2 and distance from the inlet to the shaping section H), and the outer diameter D1 are also to be determined. Considering the machining capability, the ranges of these structure dimensions are selected as shown in Table 2.

The aforementioned structure dimensions are determined by achieving the uniformity of the flow velocity distribution at the nozzle outlet. In this study, the numerical simulation and analysis of velocity distribution is performed using fluent 15.0 (ANSYS, Canonsburg, PA) to determine the optimal design for the three-layered coaxial nozzle. During simulation, the meshes are automatically generated, the volume flow rate in the annular channel is set to 800 μL/min and that in the sheath channel is set to 1600 μL/min, and the inside walls are set as nonslip. Based on the experimental design, the 1.0% and 2.0% (w/v) NaAlg solutions are used as the annular and sheath flows, respectively, for simulations.

The numerical simulation of the effects of these structure dimensions on the flow velocity uniformity is performed using an orthogonal experiment (L9 (34)) based on the factor and level numbers as shown in Table 2. Overall, nine different combinations of these structure dimensions are selected accordingly as the orthogonal experimental design (Appendix). To evaluate the uniformity of the velocity field at the outlet of the nozzle, 12 points along the circumferential direction at the cross-sectional area of the outlet are selected with an interval angle of 30 deg as shown in Fig. 3(d). The velocities at these 12 points are collected and the standard deviation of the velocity (SD=1/Ni=1N(xix¯)2) is calculated as the criteria to assess the uniformity of the velocity at the outlet, where SD is the standard deviation of the velocity, N is the number of the evaluated points (N = 12 herein), xi is the velocity of ith point, and x¯ is the average velocity. For illustration, some typical velocity distributions of the annular and sheath flows at the outlet of the nozzle are shown in Figs. 3(e) and 3(f). Based on the orthogonal experiment results as shown in the Appendix, the best combination of the structure dimensions are: annular channel (D = 7.50 mm, L1 = 3.00 mm, L2 = 12.75 mm, and L3 = 2.25 mm) and sheath channel (L = 1.50 mm, D1 = 15.00 mm, D2 = 12.00 mm, and H = 8.28 mm) to minimize the SD values of the simulation results.

Three-Layered Coaxial Nozzle Manufacturing.

Based on the computational optimization of the three-layered coaxial nozzle design, a stainless steel nozzle was manufactured. The schematic of the three-layered coaxial nozzle structure is illustrated in Fig. 4(a), and the corresponding velocity field distribution in the annular and sheath channels as simulated are shown in Figs. 4(b) and 4(c). When flowing in the channels, the solutions tend to have a uniform velocity distribution, and the velocity increases evenly in the compression section until the solutions are dispensed out of the nozzle.

The fabricated inner (Fig. 4(f)), middle (Fig. 4(g)), and outer (Fig. 4(h)) sets are also shown in Fig. 4, and they are assembled together and fixed by eight bolts as shown in Fig. 4(d). To avoid the leakage along any interfaces, copper gaskets are used between each two connected parts. To ensure the coaxial alignment of these three channels, four bolts are used to adjust the position of the inner set in the middle set, and another four bolts are used to adjust the position of the inner-middle set subassembly in the outer set as shown in Fig. 4(d). After assembly, fine adjustments for optimal coaxial alignment of the channels are performed under a microscope as shown in Fig. 4(e).

Experimental Setup and Design.

The core (CaCl2), annular (NaAlg in blue) and sheath (NaAlg in green) solutions were provided at different flow rates accordingly using three independent syringe pumps (Harvard Apparatus, Holliston, MA). The three-layered coaxial nozzle as a whole was attached to an ultrasonic vibrator (Etrema Product, Ames, IA), which was driven by an amplified waveform from a waveform generator (33522 A, Agilent Technologies, Englewood, CO). Specifically, the waveform was a sinusoidal wave with a frequency of 100 Hz and an amplitude of 10 V.

To investigate the effects of flow rate on the capsule geometry, different flow rates were used to fabricate double-layered capsules. Specifically, the investigated core flow rates were: 100, 200, and 300 μL/min, the annular flow rates were: 600, 800, and 1000 μL/min, and the sheath flow rates were: 1200, 1600, and 2000 μL/min. After the dissection of gelled capsules, they were imaged using a fluorescence microscope (EVOS FL, ThermoFisher Scientific, Waltham, MA) with the green fluorescent and blue fluorescent channels to distinguish two alginate shell layers. The boundary between the outer and inner layers was determined by finding the most significant color difference. All quantitative values of capsule dimensions were reported as mean ± standard deviation with three samples per group. Statistical analysis was performed using the analysis of variance, and p-values of less than 0.05 were considered statistically significant.

Fabrication Results

Representative Double-Layered Capsules.

By adjusting the flow rates of core, annular, and sheath flows, well-defined double-layered capsules are fabricated at a frequency of about 20 capsules/min based on the current setup. Figure 5(a) shows a schematic of double-layered capsules consisting of a core surrounded by inner and outer shell layers. After fabrication, capsules are submerged in the CaCl2 bath for 20 min for complete gelation, and representative gelled capsules are shown in Fig. 5(b).

Furthermore, Fig. 5(b) inset shows a dissected capsule after complete gelation, and the florescent image of its hemisphere is captured by fluorescence microscopy. As seen from the inset, the inner and outer shell layers are clearly distinguishable with a relatively uniform thickness for each layer, proving the effectiveness of the proposed multilayered capsule fabrication system for the fabrication of double-layered capsules with well-defined geometry.

Effects of Core, Annular, and Sheath Flow Rates on Capsule Geometry.

The effects of core, annular, and sheath flow rates on the dimensions of fabricated capsules are studied in terms of overall capsule and core diameters as well as the thickness of each shell layer. In particular, the effects of core flow rate on the geometry of double-layered capsules are examined by fixing the annular and sheath flow rates at 800 μL/min and 1600 μL/min, respectively, while varying the core flow rate in the range of 100–300 μL/min. The geometries of fabricated double-layered capsules are measured, and their dimensions are shown in Figs. 6(a) and 6(b). As seen from Fig. 6(a), both capsule and core diameters increase with increasing core flow rate. Since the annular and sheath flow rates remain the same, the resulting volumes being dispensed do not vary. As such, the increased core diameter causes a slight reduction of both inner and outer shell layer thicknesses as shown in Fig. 6(b).

The effects of annular flow rate on the geometry of double-layered capsules are examined by fixing the core and sheath flow rates at 200 μL/min and 1600 μL/min, respectively, while varying the annular flow rate in the range of 600–1000 μL/min. The geometries of fabricated double-layered capsules are measured, and their dimensions are shown in Figs. 6(c) and 6(d). As seen from Fig. 6(c), with increasing annular flow rate, the capsule diameter also increases. Since the core and sheath flow rates remain the same, the resulting volumes being dispensed change. Thus, the core diameter does not change (Fig. 6(c)). However, as seen from Fig. 6(d), the increasing annular flow rate increases the inner shell layer thickness, resulting in an increase in overall capsule diameter (Fig. 6(c)) and a reduction of outer shell layer thickness.

The effects of sheath flow rate on the geometry of double-layered capsules are examined by fixing core and annular flow rates at 200 μL/min and 800 μL/min, respectively, while increasing the sheath flow rate from 1200 μL/min to 1600 μL/min to 2000 μL/min. The geometries of fabricated double-layered capsules are measured, and their dimensions are shown in Figs. 6(e) and 6(f). As seen from Fig. 6(e), the increase of sheath flow rate causes the increase of fabricated capsule diameter significantly. Since the core and annular flow rates remain the same, the resulting volumes being dispensed are also the same. As such, both the core diameter (Fig. 6(e)) and the inner shell layer thickness (Fig. 6(f)) change slightly while the outer shell layer thickness increases significantly (Fig. 6(f)).

In this study, the selection of the flow rate ranges is mainly based on experimental observations, and the future fabrication process should be numerically modeled and validated as a function of operating conditions for controlled fabrication of capsules with specific dimensions. In addition, the minimum capsule size fabricated in the study is around 1500 μm (millimeter scale) in diameter. For some applications such as controlled drug delivery, microscale capsules are desirable, and a new multilayered coaxial nozzle set with smaller channel dimensions should be designed and manufactured.

Conclusions and Future Work

A three-layered coaxial nozzle fabrication system is designed and manufactured to make double-layered capsules. To facilitate the droplet formation process, a vibrator is integrated into the fabrication system to provide necessary perturbation for effective breakup of the fluid flow into droplets. Using numerical simulations, orthogonal experiments are conducted to optimize the structure of the three-layered coaxial nozzle, and optimal design is fabricated. Using sodium alginate solutions as the model liquid material for inner and outer shell layers and calcium chloride solution as the core fluid, double-layered capsules are fabricated. Some main conclusions are listed:

  1. (1)

    Double-layered alginate capsules can be successfully fabricated using the proposed three-layered coaxial nozzle fabrication system.

  2. (2)

    Operating conditions (core, annular, and sheath flow rates) affect the dimensions of fabricated double-layered capsules. Increasing core flow rate leads to increasing capsule and core diameters while the inner and outer shell layer thicknesses decrease. Increasing annular flow rate results in increased capsule diameter and inner shell layer thickness while the outer shell layer thickness decreases. Increasing sheath flow rate leads to increased capsule diameter and outer shell layer thickness but has no significant effect on the core diameter and inner shell layer thickness.

Future work includes the further investigation of the compound jet breakup process to unveil the capsule formation mechanism. A vibrator with a larger amplitude should be tested to further improve the breakup efficiency during fabrication. In terms of applications, various chemicals may be encapsulated to test the effectiveness of controlled release of such chemicals, which can be enabled by using fabricated multilayered capsules.

Funding Data

  • U.S. National Science Foundation (Grant No. CMMI-1314834).

Appendix: Design and Simulation Results of Orthogonal Experiments

Table 3 illustrates the design and simulation results of orthogonal experiments, where Xi illustrates the variable X at the ith setting, (variable X = A, B, C, and D as defined in Table 2 and i = 1, 2, and 3 which depicts three different values of the corresponding X), SD is the standard deviation of the velocity which is used to assess the velocity uniformity of the annular and sheath flows at the nozzle outlet location, TiX illustrates the sum of the ith setting of variable X in different designs and TiX=SDiX, tiX is the average value of TiX, and RX is the range of the Xth column and RX = Max(t1X, t2X, t3X) − Min(t1X, t2X, t3X). Herein, RX is used to assess the sensitivity of velocity uniformity to different structure dimensions. From the range analysis as shown in this Appendix, the effects of different structure dimensions on the uniformity of the velocity field is evaluated. Specifically, for the annular channel since RA > RB > RC > RD, the inner diameter of the channel influences the velocity uniformity more significantly than the other dimensions; for the sheath channel since RC > RA > RB > RD, the compression angle influences the velocity uniformity more significantly than the other dimensions. When determining the nozzle dimensions, these key dimensions must be guaranteed first before optimizing the other dimensions in order to have an optimized three-layered coaxial nozzle.

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