Abstract

Tubular structures of the hydrogel are used in a variety of applications such as delivering nutrient supplies for 3D cell culturing. The wall thickness of the tube determines the delivery rate. In this study, we used the coaxial extrusion process to fabricate tubular structures with varying wall thicknesses using a thermal-crosslinking hydrogel, gellan gum (GG). The objectives of this study are to investigate the thermal extrusion process of GG to form tubular structures, the range of achievable wall thickness, and a possibility to form tubular structures with closed ends to encapsulate fluid or drug inside the tube. The wall thickness is controlled by changing the relative flow velocity of the inner needle (phosphate-buffered saline, PBS) to the outer needle, while keeping the velocity of outer needles (GG) constant. Two pairs of coaxial needles were used which are 18-12 gauge (G) and 20-12G. The controllable wall thickness ranges from 0.618 mm (100% relative velocity) to 0.499 mm (250%) for 18-12G and from 0.77 mm (80%) to 0.69 (200%) for 20-12G. Encapsulation is possible in a smaller range of flow velocities in both needle combinations. A finite element model was developed to estimate the temperature distribution and the wall thickness. The model is found to be accurate. The dynamic viscosity of GG determines the pressure equilibrium and the range of achievable wall thickness. Changing the inner needle size or the flow velocity both affect the heat exchange and thus the temperature-dependent dynamic viscosity.

1 Introduction

Hydrogels, as a class of biomaterials, offer good biocompatibility, varying degradability, and low cytotoxicity [13]. The extrusion of hydrogels is a manufacturing process, which is used in a variety of applications such as bioprinting, tissue engineering, and drug delivery [48]. Different structures, such as scaffolds, porous, and tubular structures, can be fabricated by using this extrusion-based process. For example, scaffolds with a varying surface area to mass ratio for controllable degradation rate [9], porous structures with variable porosity for tailoring mechanical properties [1012], and better cell attachment [13] can be achieved. However, due to the soft nature of hydrogels, the fabrication of precise structures still presents challenges [14].

In addition to the fabrication of scaffolds and porous structures, 3D printing of tubular structures has drawn increased attention. One main application of the 3D printed tubular structure is used to mimick or grow a vascular system for use in tissue engineering [15]. The vascular system is critical for supplying oxygen, growth factors, and nutrients to the cell and removes waste products for large-scale cell growth or organ printing [16]. Without a proper vascular system, the printed cells will not survive, and many researchers have tried to solve this problem [4,6,7,17,18]. Another application for 3D printed tubular structures is in drug delivery. 3D printing is considered to be a transformative technology for creating personalized drug delivery systems [5,19,20]. Hydrogel materials that can be fabricated layer by layer have been used to create a vehicle for drug delivery [21]. Since drug delivery behavior can be characterized by the outer gel layer in gel-formed matrices in drug delivery [22], hydrogel tubular structures printed by coaxial needles can be utilized as a matrix or encapsulate powder compounds or other drugs.

For both applications, tissue engineering and drug delivery, tubular structures serve as the channel for transporting or delivering substances. In order to have a precise control over the transportation or delivery rate, the geometry of the tubular structure, including the hole diameter and the wall thickness, needs to be fabricated with high accuracy. Moreover, tubular structures made by hydrogels are also subject to swelling, and thus, the wall thickness and diffusion behavior can change accordingly [2224]. Therefore, it is critical to develop a fabrication process to have good controllability over the wall thickness.

There are three main approaches to manufacturing tubular structures, including inkjet printing [4], laser-assisted drop on demand printing [17], and extrusion-based methods, which include filament assembly method [18] and using a coaxial needle [16,25]. With inkjet printing, hydrogel inks are jetted and deposited sequentially to form a tubular structure [2,9]. Inkjet printing can achieve high dimensional resolution, depending on the droplet size, but this process requires longer printing time. The filament assembly method extrudes a series of cylindrical lines which stack into a tubular structure without using a support material [18]. In this case, the wall thickness is determined by the filament size. Another extrusion-based approach uses one material to build the outer wall and a sacrificial material to fill the inner core, which is then melted away [26]. The most commonly used method for tube printing is using a coaxial needle [6]. Typically, the hydrogel material is extruded from the outer needle, while the inner needle extrudes a crosslinking solution that helps to solidify the hydrogel material and form the tubular structure. For example, alginate is commonly used due to its ability to be crosslinked with divalent cations, such as Na+, Mg+, and Ca2+. [27]. Thus, the crosslinking solution containing cations is extruded from the inner needle, while the alginate is extruded the outer needle. The calcium cations then diffuse into the alginate solution to form a tube. However, this process does not provide a uniform diffusion level throughout the structure, and it is difficult to predict its in vivo degradation and swelling behavior due to the distribution of calcium cations [28,29].

Several studies have attempted to investigate the manufacturing process of tube printing and the tube dimensions both experimentally and theoretically [25,30]. However, most studies used the chemical-crosslinking material, such as alginate, with the coaxial needle method and have focused on specific parameters such as flowrates, concentrations, and diffusion of the crosslinking ions within structures. Gellan gum (GG) is another hydrogel material that has been used in both tissue engineering [3133] and drug delivery [34,35]. Unlike alginate, GG forms the hydrogel under appropriate aqueous conditions and can be thermally crosslinked. The gelation temperature is the most significant factor in this process. By using temperature as the crosslinking method, the use of the crosslinking solution can be avoided so that complications associated with using chemical crosslinking such as nonuniform divalent cations distribution, or concentration throughout the structure can be alleviated. However, the process of the thermally crosslinked hydrogel for manufacturing tubular structures has not been studied extensively yet.

The goals of this research are to investigate the coaxial extrusion process to fabricate tubular structures using GG, a thermal-crosslinking hydrogel, and to study the controllability of wall thickness and encapsulation. A finite element model was first developed to predict the temperature change of GG during the extrusion process. This model provides a guideline for selecting a proper extrusion temperature for the actual experiments. Experiments were then conducted to investigate the controllability of wall thickness and the feasibility of forming encapsulated structures by varying the flowrate ratio of the coaxial needle. The finite element model is expanded to predict the resulting wall thickness and provide a deeper understanding of the process.

2 Method

2.1 Materials.

Gellan gum hydrogels were prepared as follows: low-acyl gellan gum (LAGG) (Gelrite G1910, Sigma-Aldrich, St. Louis, MO) and high-acyl gellan gum (HAGG) (Modernist Pantry, York, ME) were purchased. LAGG and HAGG were mixed by a ratio of 85:15 w/w. The powder mixture was then added to de-ionized water to a 4% w/v ratio. The mixture was heated using a stirring water bath (Major Science, Saratoga, CA) for 2 h at 93 °C. The hydrogel was poured into syringes and kept at a constant temperature of 53 °C in the water bath before using. Phosphate-buffered saline (PBS) tablets (P4417, Sigma-Aldrich) were used to create a PBS solution. The tablets were dissolved in de-ionized water with a ratio of one tablet per 200 ml. The final pH value (pH 7.4 at 25 °C) was checked for the concentration of PBS. PBS dyed with food coloring, in order to allow for better visualization was used in the inner needle. For this experiment, the PBS was intended to simulate the drug which would be encapsulated within the tube.

The dynamic viscosity of the material was studied using a rheometer (ARES-G2, TA Instrument, New Castle, DE). A 50 mm diameter cone plate with 0.0196 rad was used. 1% strain rate and 10.0 rad/s angular frequency were used. Cooling curves, starting from 78 °C and lowering down to 30 °C with 1 °C steps, were used to determine the viscosity of GG.

2.2 Experimental Setup.

Figure 1 shows the overview of the experimental setup which consists of three parts: the extrusion control system, temperature control unit, and coaxial needle. For the extrusion system, two 25 ml syringes were used. Each syringe was placed in a syringe pump (Fusion 101, CHEMYX, Stafford, TX). The GG syringe was wrapped with a copper heating sleeve which is connected to the temperature control unit. A temperature sensor (Model # 56A-1002-C8, Alpha Technics, Oceanside, CA) was attached on the cooper sleeve. A microcontroller (Arduino UNO R3 Mega 2560, Glendora, CA) was utilized to keep the temperature constant during the extrusion process. The temperature was kept at 53 °C which is slightly higher than the solidification transition temperature determined by the rheology test to avoid needle clogging.

Fig. 1
Overview of the experimental setup
Fig. 1
Overview of the experimental setup

Two different sized pairs of coaxial needles were prepared. The size of the outer needle, 12 Gauge (with an outer diameter of 2.77 mm and an inner diameter of 2.16 mm), was the same for both pairs. For the inner needle, two different needles were used. The first needle was 20 Gauge (an outer diameter of 0.91 mm and an inner diameter of 0.6 mm), 20-12G, and the second inner needle was 18 Gauge (with an outer diameter of 1.27 mm and an inner diameter of 0.84 mm), 18-12G. As illustrated in Fig. 2, GG was extruded in between the outer needle and inner needle, while PBS was extruded through the inner needle. The extruded structures were allowed to fall into a Petri dish filled with room-temperature PBS, which was placed underneath the coaxial needle. This was done to ensure that GG solidified quickly once it came out of the coaxial needle.

Fig. 2
(a) Cross-sectional view of the 3D modeled coaxial needle and (b) the modeled geometry and boundary conditions in comsol
Fig. 2
(a) Cross-sectional view of the 3D modeled coaxial needle and (b) the modeled geometry and boundary conditions in comsol
The speed of extrusion for each fluid was controlled by the flowrate of the syringe pump. The flowrates were calculated based on cross-sectional area and flow velocity. Based on average flow velocity, the flowrates were calculated by
Vflow=vflowAneedle
(1)
where Vflow is the volume flowrate (mm3/s), vflow is the average flow velocity (mm/s), and Aneedle is the cross-sectional area of the needle (mm2).
Because GG is a thermal-crosslinking hydrogel, it solidifies as the temperature cools down. In the experimental setup, the GG temperature was kept at 53 °C, and once it entered to the coaxial needle, it is subject to cooling by air convection as well as the PBS flow. The flow velocity determines how much cooling the GG is subject to. In order to determine a proper flow velocity, a finite element model was developed (to be introduced in Sec. 3). Once the baseline flow velocity was determined, the same flow velocity was implemented to both the GG (outer needle) and PBS (inner needle). In this case, the PBS flow velocity is at 100%. Then, the flow velocity of PBS was decreased or increased to alter the GG wall thickness until the tubular structure could not be formed. To determine the diameter of the tube and the wall thickness, an optical microscope (Stereo microscope, Amscope, CA) was utilized. Tube diameter and hole size were measured for each individual tube sample, and an average wall thickness was calculated by the equation listed below:
twall=dtubedhole2
(2)
where twall is the average wall thickness of the tube (mm), dtube is the outer diameter of the tube (mm), and dhole is the diameter of the lumen inside of the tube (mm). Five trials were done for each experimental condition. Each sample was measured three times, and the average value was determined. In addition, the feasibility of forming encapsulated ends of the tubes by shutting down PBS flow was also observed.

3 Finite Element Modeling

The finite element model was developed for two purposes. First, the temperature profile of the GG flow was analyzed to determine a proper extrusion velocity. Second, the model was used to predict the wall thickness of GG at different velocity ratios of GG and PBS.

3.1 Model Configuration and Setup.

Figure 2 shows the sectional view of the coaxial needle and the configuration of the finite element model. The model was simplified to include only the straight portion of the needles. Two assumptions were made: first, when the GG and PBS flows enter the straight portion of the needle, the flow is fully developed; second, the temperature change from the GG syringe to the straight portion of the needle is negligible.

This model was developed using the level set model with the heat transfer model in comsol multiphysics 5.3 (COMSOL, Inc., Burlington, MA). Heat transfer in fluid was applied to both GG and PBS, and air convection in the needle wall was applied to the needle wall. The governing equations used in this model are as follows:

The Navier–Stokes equation for laminar flow:
ρut+ρ(u)u=[pI+μ(u+(u)T)]+F
(3)
where ρ is the density, u is the fluid velocity vector, p is the pressure, t is the time, I is the identity matrix, and F is the body force and the continuity equation:
(u)=0
(4)
Heat transfer is calculated by
ρCPTt+ρCPuT+q=Q
(5)
where Cp is the specific heat, T is the temperature, q is the heat flux, k is the thermal conductivity, and Q is the heat of transfer, and
q=kT
(6)

Table 1 lists the material properties used in this finite element model. For PBS, the temperature-dependent dynamic viscosity, specific heat, density, and thermal conductivity of water adopted from the comsol material library were used. For GG, the dynamic viscosity was measured experimentally, as shown in Fig. 3. The thermal conductivity of GG was determined based on the equation given in a previous study [36]. Specific heat and density of water, also adopted from the comsol material library, were applied for GG. For the needles, properties of stainless steel from the comsol material library were used.

Fig. 3
Dynamic viscosity of GG
Fig. 3
Dynamic viscosity of GG
Table 1

Material properties

PBSGGStainless steel
Dynamic viscosity (Pa·s)0.0017–0.0015Temperature-dependent as shown in Fig. 3 n/a
Specific heat (J/(kg K))4180–42004180–4200500–515
Density (kg/m3)9999997775
Thermal conductivity (W/(m K))0.6–0.660.574 [36]13.9–14.5
PBSGGStainless steel
Dynamic viscosity (Pa·s)0.0017–0.0015Temperature-dependent as shown in Fig. 3 n/a
Specific heat (J/(kg K))4180–42004180–4200500–515
Density (kg/m3)9999997775
Thermal conductivity (W/(m K))0.6–0.660.574 [36]13.9–14.5

The following boundary conditions were prescribed:

  1. Incoming flow is fully developed
    u(r,z)z=0
    (7)
    where r is the radius of the needle and z is the direction of flow.
  2. Temperature of the PBS inlet is fixed at room temperature (measured at 27 °C), temperature of the GG inlet is fixed at 53 °C.

  3. Axial symmetry is applied.

  4. Air convection is applied at the outer edge of the needle with
    q=h(TairT)
    (8)
    where Tair is the temperature of air and h is the heat transfer coefficient (25 W/m2 K).

The mesh was generated by the automatic meshing generator in comsol. The mesh sensitivity test was performed with 3651, 7618, 11,375, and 37,784 elements. When the mesh is finer than 7618 elements, no significant changes on wall thickness is observed. Therefore, the final mesh consists of 7618 domain elements and 887 boundary elements. The comsol Multifrontal Massively Parallel sparse direct Solver (mumps) was used in this study. All data were analyzed after the model reached steady-state.

3.2 Determination of Baseline Flow Velocity.

In order to determine the baseline flow velocity, three velocities (1 mm/s, 5 mm/s, and 10 mm/s) were simulated by the finite element model. The same velocity was used for PBS and GG. A proper flow velocity is important because GG solidification depends on the cooling effect due to air convection and the PBS flow. When the flow velocity is too fast, it does not allow GG to cool down and solidify, and thus, is not able to form a stable tubular structure. On the other hand, when the flow velocity is too slow, GG can solidify inside the needle and cause clogging. From the result of the rheology test, as shown in Fig. 3, it can be seen that GG solidification occurs in the temperature range between 42 and 49 °C. It is assumed that the ideal extrusion condition is to have the temperature of GG cool to this range in between the end of the inner needle and the end of the outer needle. The temperature profile of GG was analyzed for the three flow velocities.

3.3 Numerical Study of Controllability Over Wall Thickness.

In Sec. 3.2, the same flow velocity was prescribed for both GG and PBS. In this study, varying flow velocities of PBS were prescribed, while a constant flow velocity of GG was used, and the resulting wall thickness from each condition was analyzed. To calculate the wall thickness, the boundary profile of the 0.7 volume fraction ratio of GG (70% of GG and 30% PBS) was extracted from the end of the inner needle to the end of the outer needle. The average wall thickness in this region was calculated. The effect of extrudate swell was assumed to be similar across all cases since the flow velocity of the outer needle remains constant. Therefore, when calculating the wall thickness, the outer diameter of the tube was assumed to be the same as the inner diameter of the outer needle. In addition, the effects of varying flow velocities on the temperature profile, pressure distribution, and viscosity of GG were also studied.

4 Result and Discussion

4.1 Baseline Flow Velocity

4.1.1 Finite Element Modeling.

Figure 4 shows the temperature distribution inside the coaxial needle (18-12G) with flow velocities of 1 mm/s, 5 mm/s, and 10 mm/s. Figure 4(a) shows the temperature profile along the Z-axis at the inner wall of the outer needle. The 1 mm/s flow velocity shows a steady temperature decrease along the Z-axis. For 5 mm/s and 10 mm/s, most temperature change occurs at the first 10 mm region. Figures 4(b) and 4(c) show the temperature profile across the radial direction at the end of the inner needle and outer needle, respectively. In both locations, the 1 mm/s flow velocity results in a much lower temperature than those resulted by 5 mm/s and 10 mm/s. In all cases, the temperature is relatively uniform across the radial direction. As described in Sec. 3.3, the desired temperature range is 42–49 °C between the ends of the inner and outer needle. Both cases of 5 mm/s and 10 mm/s flow velocities satisfy this criterion. Thus, we concluded that 5–10 mm/s is a proper range of flow velocity to be used. Therefore, we used 5 mm/s and 10 mm/s as the baseline flow velocity for all experiments. The 1 mm/s flow velocity is too slow to use because it allows more time for air convection, causing the hydrogel to cool too quickly.

Fig. 4
Temperature profiles with different flow velocities: (a) along the Z-direction at the inner wall of the outer needle, (b) across the radial direction at the end of the inner needle, and (c) across the radial direction at the end of the outer needle
Fig. 4
Temperature profiles with different flow velocities: (a) along the Z-direction at the inner wall of the outer needle, (b) across the radial direction at the end of the inner needle, and (c) across the radial direction at the end of the outer needle

4.1.2 Experimental Validation.

Figure 5 shows the results of GG extrusion at different temperature settings. In Fig. 5(a), when the temperature or flow velocity is too high, the GG does not solidify in time, subsequently allowing the GG and PBS to mix inside the coaxial needle. Figure 5(b) shows the result of extrusion at a proper temperature or flow velocity. In this case, a continuous tubular structure can be formed. On the other hand, when the initial temperature is too low, GG starts to solidify, while it is inside of the syringe. Figure 5(c) shows an undesirable tubular shape when the temperature is too low. The tube begins to break into smaller pieces and fails to encapsulate any PBS. When this occurs, it is still possible to print, but an overall low-quality tube is produced. As a result, the printed tube is very fragile and does not provide any structural integrity. If the temperature becomes even lower, clogging occurs and the syringe pump stalls. Similarly, if the extrusion flow velocity is too low, allowing longer cooling time, a proper tube cannot be printed due to the solidification of GG inside of the needle.

Fig. 5
Extrusion results at different temperatures: (a) when temperature is too high, GG and PBS mix together, (b) at a proper temperature, the continuous tube is formed, and (c) when the temperature is too low, slight clogging occurs and the broken structure is formed
Fig. 5
Extrusion results at different temperatures: (a) when temperature is too high, GG and PBS mix together, (b) at a proper temperature, the continuous tube is formed, and (c) when the temperature is too low, slight clogging occurs and the broken structure is formed

4.2 Encapsulation.

Figure 6(a) shows a segment of the encapsulated tubular structure in which the dyed PBS fluid is contained. For applications of drug delivery, the tube must be closed on both ends in order to contain the drug inside of the tube. By shutting down PBS flow, it is possible to form closed ends that encapsulate the fluid inside. However, this close-end feature tends to fail more often at a higher flow velocity, such as 10 mm/s. As shown in Fig. 6(b), encapsulation cannot be achieved and an open end is observed. Tube printing was possible at certain conditions even though encapsulation could not be achieved. Moreover, at a high flow velocity, uneven wall thickness or distribution of encapsulated fluid can be observed, as shown in Fig. 6(c). Therefore, it was concluded that 5 mm/s is the optimal flow velocity for further experiments.

Fig. 6
Encapsulation of the tubular structure: (a) successful encapsulation, (b) open end tube, and (c) closed-end tube and uneven distribution in the tube
Fig. 6
Encapsulation of the tubular structure: (a) successful encapsulation, (b) open end tube, and (c) closed-end tube and uneven distribution in the tube

4.3 Control of Wall Thickness.

Figure 7(a) shows the experimental result of wall thickness in the case of 20-12G with varying flow velocities of PBS relative to that of GG. The range of controllable wall thickness is from 0.770 ± 0.0165 mm (80% relative velocity of PBS) to 0.69 ± 0.0510 mm (200% relative velocity of PBS). From 80% to 180% relative velocity, tubes with closed ends were formed. However, at 200% relative velocity, forming a tube with a closed end was not feasible. Figure 8(a) shows an example of the properly printed tube with a uniform wall thickness. When the flow velocity of PBS was below 80%, the lumen space of the tube is no longer uniform, as shown in Fig. 8(b). This ununiform distribution of PBS is similar to what can be observed in Fig. 6(c). The 200% relative velocity of PBS was the highest velocity in which a tube could be formed. The significant difference between flow velocities of PBS and GG can cause structural failure to the process.

Fig. 7
Wall thicknesses formed with different relative velocities of PBS: (a) 20-12G and (b) 18-12G; solid line: experiment, dashed line: simulation, •: closed end, ○: open end, ▴: failed
Fig. 7
Wall thicknesses formed with different relative velocities of PBS: (a) 20-12G and (b) 18-12G; solid line: experiment, dashed line: simulation, •: closed end, ○: open end, ▴: failed
Fig. 8
Cross sections of the tubular structures: (a) a properly extruded tube and (b) when the PBS flow velocity is too low
Fig. 8
Cross sections of the tubular structures: (a) a properly extruded tube and (b) when the PBS flow velocity is too low

Figure 7(b) shows how the wall thickness changes with varying flow velocities of PBS for the combination of the 18-12G needle. The achievable wall thickness ranged from 0.618 ± 0.0160 mm (100% relative velocity of PBS) to 0.499 ± 0.0185 mm (250% relative velocity of PBS). Tubes with closed ends can only be formed with PBS velocities from 100% to 160%. In comparison to the case of 20-12G, 18-12G uses a larger inner needle, and thus, encapsulating PBS inside the tube was more difficult. On the other hand, continuous tubes can be formed when the relative velocity of PBS is up to 250% which is higher than that of the 20-12G combination. When the flow velocity is above this range, the process becomes unstable and the lumen is no longer located at the center of the tube.

A previous study by Li et al. studied the effect of flowrate on the inner diameter of hollow alginate fibers fabricated by the coaxial extrusion [30]. In their study, the crosslinking agent was extruded from the inner needle (21G), while the alginate hydrogel was extruded from the outer needle (16G). The range of wall thickness from Li et al.’s study is estimated to be about 0.35–0.5 mm, which is comparable to our results, given that the sizes of needles are different. Both studies show a similar trend; when the flowrate or flow velocity of the inner needle increases, the wall thickness decreases.

Figures 9(a) and 9(b) show the boundary lines of PBS and GG at different relative flow velocities for 20-12G and 18-12G, respectively, calculated by the finite element model. The average wall thicknesses taken from Figs. 9(a) and 9(b) are also plotted in Figs. 7(a) and 7(b), respectively, indicated by the dashed black line. In general, the simulation results show a similar trend as the experimental results, although the finite element model has a slight margin of error of about 5–15% regarding the wall thickness. This demonstrates that the finite element model can be an accurate tool to predict the resulting wall thickness at different flow conditions. However, the current model does not consider the effect of the flowing PBS on the solidification process along the GG, except the effect of heat exchange. The mixing of PBS and GG may also influence the rheological property of GG. This requires a more extensive study of the GG properties. Some results in Figs. 9(a) and 9(b) show wavy boundary profiles, especially at high flow velocity in the case of 20-12G. The average values of wall thickness along the axial direction were taken to alleviate this effect. Such a wavy boundary profile has been observed in a computational study by Naeimirad et al. [37]. However, experimentally, such a wavy boundary was not observed.

Fig. 9
Boundary lines of PBS and GG at different relative flow velocities for 20-12G and 18-20G. The hatched box represents the wall of the inner needle.
Fig. 9
Boundary lines of PBS and GG at different relative flow velocities for 20-12G and 18-20G. The hatched box represents the wall of the inner needle.

Figure 10(a) shows pressure profiles of two different relative velocities, 100% and 200%, for 20-12G. The outer needle (GG) has a much higher pressure than the inner needle (PBS), due to a higher viscosity of GG than that of PBS. The highest pressure occurs at the inlet part of the outer needle. When the relative velocity of the inner needle (PBS) increases from 100% to 200%, the pressure of the outer needle increases by 14%, from 558 kPa to 638 kPa, while the pressure of the inner needle increases by 39%, from 59 kPa to 82 kPa. In the case of 18-20G, as shown in Fig. 10(b), when the relative velocity of the inner needle increases from 100% to 200%, the pressure of the outer needle increases by 46%, from 1476 kPa to 2162 kPa, while the pressure of the outer needle increases by 53%, from 90 kPa to 138 kPa.

Fig. 10
Comparison of pressure and dynamic viscosity distribution for 100% and 200% relative PBS flow velocity: (a) pressure profile for 20-12G, (b) pressure profile for 18-12G, (c) dynamic viscosity profile for 20-12G, and (d) dynamic viscosity profile for 18-12G
Fig. 10
Comparison of pressure and dynamic viscosity distribution for 100% and 200% relative PBS flow velocity: (a) pressure profile for 20-12G, (b) pressure profile for 18-12G, (c) dynamic viscosity profile for 20-12G, and (d) dynamic viscosity profile for 18-12G

Figures 10(c) and 10(d) demonstrate the dynamic viscosity of 100% and 200% relative PBS flow velocity for 20-12G and 18-12G, respectively. The dynamic viscosity in the case of 18-12G (Fig. 10(d)) is much higher than that in the case of 20-12G (Fig. 10(c)). In this finite element model, the dynamic viscosity was prescribed as a function of temperature, based on the result shown in Fig. 3. Therefore, the distribution of dynamic viscosity reflects the distribution of temperature. The reason that the dynamic viscosity of 18-12G is much higher because there is more heat exchange between the two fluids, i.e., cooling by PBS, due to the larger-sized inner needle for the PBS flow. When two fluids, PBS and GG, have the same velocity (i.e., 100% relative velocity), the volume flowrate of PBS is 9% and 23% of the volume flowrate of GG for 20-12G and 18-12G, respectively. This difference in PBS flowrates leads to the difference in the cooling effect and thus, in the dynamic viscosity. Similarly, when the flow velocity of PBS increases from 100% to 200%, an increase in the dynamic viscosity can also be observed. In both cases, the increase in viscosity contributes to the increase in pressure, as shown previously in Figs. 10(a) and 10(b).

Regarding the wall thickness, which is determined by the boundary of the two fluids, a pressure equilibrium is reached at the boundary. Therefore, the dynamic viscosity of GG, which affects the pressure and is a function of temperature, is an important factor for the controllability of wall thickness. Varying the flow velocity of PBS not only will affect the temperature but also the dynamic viscosity of GG. The difference in viscosity between the outer needle flow (GG) and the inner needle flow (PBS) is also expected to be a determining factor for the range of controllable wall thickness. In this study, the difference in viscosity for PBS and GG is more than five orders of magnitude and the range of controllable wall thickness is only about 10%. It is expected that if a fluid with a viscosity similar to that of GG is used for the inner needle, a wider range of controllable wall thicknesses can be achieved. There are a few related computational studies on core-annular flows [3840], and the effects of surface tension, viscosity, and flowrate on the boundary between the core and annular flows were studied. In these studies, the annular flow usually has a lower viscosity than the core flow, which is opposite to the case in our study. It has been demonstrated that to achieve a more stable core-annular flow, it is required to have two fluids with very different viscosities. The interaction between two fluids with similar viscosities will need to be further investigated.

In applications of drug delivery, the wall thickness controls the release rate of the drug [22]. Thus, personalized drug delivery can be achieved by altering the wall thickness as well as the volume of the encapsulated medium. Also, in tissue engineering, most tubular structures are aimed to mimic the vascular system, such as supplying nutrition to the cells [16]. This diffusion rate of nutrition can also be controlled by the wall thickness. Therefore, it is beneficial to have a precise control on wall thickness for both applications. One limitation of this research is that we only used air convection during the experiment. Since temperature control for the extrusion process is critical to successfully fabricating high-quality tubes, a tighter controlled environment can be helpful to improve the quality of the fabricated tubes. For example, the needle temperature can be actively controlled or passively insulated to reduce possible temperature variant.

Some limitations to note in this study: First, the effect of extrudate swell was not considered in the finite element model. The extrudate swell can cause an increase in wall thickness of the tubular structure. Second, the extrusion process was only modeled with constant input flowrates, and the dynamic of the encapsulation process was not studied. Further investigation of the encapsulation process in response to a varying flowrate can help to obtain a deeper understanding about the process. Third, only one combination of the inner and outer needle fluid was studied. This does not allow for the investigation of interactions between fluids with different ratios of viscosities.

5 Conclusions

In this research, a fabrication process to create tubular structures of GG with controlled wall thickness using coaxial needles was analyzed. This study demonstrates the feasibility of controlling the wall thickness of the tubular structure by varying the flow velocity of the inner needle. It was found that around 10% reduction of wall thickness can be achieved by increasing the flow velocity of PBS. It was concluded that it is possible to control the wall thickness within a small range for the close-ended tubes and over a larger range with open-ended tubes. The finite element model can predict the wall thickness for different flow velocities with good precision. The model also reveals that the dynamic viscosity of the outer needle fluid is a determining factor for the controllable range of wall thickness.

Acknowledgment

The study was supported in part by the NSF CMMI (Grant No. 1642565) and U.S. Department of Defense – Congressionally Directed Medical Research Programs (Grant No. W81XWH-18-1-0137).

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