Analysis of the Calcium Alginate Gelation Process Using a Kenics

Analysis of the Calcium Alginate Gelation Process Using a Kenics...
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Analysis of the Calcium Alginate Gelation Process Using a Kenics Static Mixer Takuro Hozumi,† Seiichi Ohta,‡ and Taichi Ito*,†,‡ †

Department of Chemical System Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan Center for Disease Biology and Integrative Medicine, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

‡

ABSTRACT: A static mixer is a useful applicator for in situ cross-linkable hydrogels such as dental materials, hemostats, and tissue engineering scaffolds. The gelation of calcium alginate hydrogel containing carboxymethyl cellulose using a Kenics static mixer was carefully analyzed in terms of flow rate, the number of mixing elements, pressure drop, and homogeneity of the formed hydrogels as expressed by the coefficient of variance (COV). Pressure drop increased monotonically with Damköhler number (Da), defined as the ratio of the residence time in the mixer to the gelation time of hydrogels. Conversely, COVs reached maximum values with increasing Da and finally decreased for any number of elements. In addition, shear moduli of the formed hydrogels differed with COVs. These results suggest that it is helpful, when controlling the homogeneity and mechanical properties of hydrogels, to consider the balance between residence time in the mixer and the gelation time of the precursor polymer.

1. INTRODUCTION In situ cross-linkable hydrogels, which can be formed simply by mixing two reactive solutions, have attracted much attention in the biomedical field.1 Because the precursor solutions are liquids, the gels can fill any desired location, including small cavities and curved surfaces. In addition, large incisions are not required to place the hydrogels into the body because they can be administered by injection. Therefore, in situ cross-linkable hydrogels currently have potential uses in a variety of biomedical applications, such as bioadhesives,2 hemostatic agents,3 drug delivery,4 scaffolds for tissue engineering,5 and antiadhesive materials.6 Fibrin sealant, which is frequently used in surgical operations, is a well-known clinical example of the use of natural in situ cross-linkable hydrogels.7 Although new in situ cross-linkable hydrogels have been extensively studied8,9 using various cross-linking reactions,10 the formation process of hydrogel has not been analyzed sufficiently. For medical applications, many hydrogel properties, such as mechanical strength, degradation kinetics, diffusivity of growth factors or drugs, and cell migration and viability in and/ or on the hydrogel must be controlled. These functions strongly depend on the mixing and reaction processes during gel formation, in addition to chemical structure, because two viscous precursor polymer solutions must be mixed well to enable the collision of reactive functional groups or moieties. Because of the importance of mixing, a static mixing process is useful for in situ gelation. A static mixer is a tubular motionless mixer, inside which mixing elements are inserted.11 When fluids are injected into a static mixer, it promotes the mixing of fluids by generating flows in the radial and tangential directions via these mixing elements. Depending on the geometry of the mixing elements, static mixers are categorized into several types, including the Kenics, SMX, or SMV types. Static mixers have traditionally been used for the simple mixing of gases, liquids, and solids.12,13 In addition, they are now used for the fabrication of polymeric materials.14,15 Polymer © XXXX American Chemical Society

microspheres have been prepared by emulsification of monomers via a static mixer and subsequent cross-linking approaches, such as thermal,16 ionic,17 or photo cross-linking.18 Recently, new in situ cross-linkable hydrogels composed of collagen/polyethylene glycol (PEG)19 and chitosan/polyglutamate20,21 and formed using a static mixer have been reported as scaffolds for tissue engineering. In addition, Kenics type static mixers are widely used for the injection of impression materials in dentistry or new hemostats in surgery.22−25 Despite the usefulness of static mixers, the details of the gelation process inside the mixer have not been discussed to date, probably because of the complexity of these phenomena. To clarify the process of gelling of in situ cross-linkable hydrogels, calcium alginate is an ideal model substance. Alginate (Alg) is a natural ionically cross-linkable polysaccharide comprising repeating units of α-L-guluronate (G) and β-Dmannuronate (M) in not only homopolymer block structures (GG or MM) but also alternating block structures (GM).26 When mixed with calcium ions (Ca2+), homopolymeric G blocks (GG) in Alg are cross-linked with Ca2+ via the so-called “egg box model”, producing an insoluble hydrogel.27,28 Calcium alginate hydrogel is biocompatible and inexpensive, which enables its use in the food industry,29 drug delivery,30 impression materials in dentistry,31 cell encapsulation,32 and tissue engineering.33,34 In the present study, we studied the gelation process of Alg by Ca2+ with a carboxymethyl cellulose (CMC) additive via a Kenics type static mixer. To enable stable operation of the static mixer, CMC containing CaCl2 was blended with Alg solutions to make the viscosity of two solutions nearly identical. The Kenics static mixer causes a pressure drop lower than that of Received: November 12, 2014 Revised: January 23, 2015 Accepted: January 28, 2015

A

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Industrial & Engineering Chemistry Research other types of static mixers;35 therefore, it is suitable for the mixing of various viscous liquid systems, including Alg solution. The effects of process parameters, e.g., flow rate, number of mixing elements, and the concentration of the pregel polymer solution on the pressure drop during the mixing procedure, and the coefficient of variance (COV), expressing the homogeneity of formed hydrogels, were investigated. Finally, the effect of COV on rheological properties was evaluated using a rheometer. Although the gelation process inside the static mixer is complex, we have organized the data, for the first time, simply in terms of the dimensionless Damköhler number (Da), defined as the ratio of the residence time in the mixer to the gelation time of hydrogels.

2.3. Characterization of the Precursor Polymers Alg and CMC. The viscosities of 1 wt % Alg, 3 wt % Alg, 1 wt % CMC, and 2 wt % CMC dissolved in phosphate-buffered saline (PBS) and 1.5 wt % κ-carrageenan dissolved in deionized water were measured by viscometer (TVE-22H; TOKI Sangyo Co. Ltd., Tokyo, Japan). On the basis of this result, we determined the concentration of CMC in all CaCl2 and KCl solutions in order to adjust their viscosities to that of Alg solutions or κcarrageenan solution in the following experiments. We used PBS as a solvent for all Alg and CaCl2 solutions and deionized water for κ-carrageenan and KCl solutions, unless otherwise noted. The batch gelation times (τg) of Alg hydrogel and κcarrageenan hydrogel were measured as previously reported.6 A 100 μL sample of 1 or 3 wt % Alg solution or 1.5 wt % κcarrageenan solution and the same volume of 10−100 mM CaCl2 solution or 1 M KCl solution containing 1 wt % CMC as an additive were dropped on a plastic dish and stirred by a magnetic stirrer at 200 rpm. During the stirring, we observed the gelation behavior of the solution and measured the gelation time, which was defined as the time required for the solution to form a globule. We measured τg four times for each sample and used the average value as a data point. 2.4. Static Mixer Apparatus. We assembled a mixing apparatus for the fabrication of in situ cross-linkable hydrogels, as shown in Figure 2. The Kenics static mixer (product number: 7700811) was purchased from Nordson EFD LLC (East Providence, RI) and consisted of a series of helical mixing elements, whose diameter, length, aspect ratio, and twisted angle were 4.8 mm, 4.0 mm, 0.83, and 180°, respectively. The right-handed and left-handed elements were arranged one after another along the axial direction. The leading edge of each element was oriented at 90° to the trailing edge of the foregoing edge. We used the static mixers with 4, 8, 12, and 16 elements, the lengths of which, L, were 16.5, 32.5, 48.5, and 65 mm, respectively. The double-barreled syringe and twocomponent injection set (Duploject System, 5 mL) was a gift from Baxter International Inc. (Deerfield, IL). The leading edge of the static mixer and the double-barreled syringe were connected with commercial plastic fitting kit (731-8228, Female Luer to Female Luer, or 731-8229, Female Luer Tconnector, Low Pressure Fitting Kit; Bio-Rad Laboratories, Hercules, CA). A picture of the connection between the double-barreled syringe and the static mixer is shown in Figure 2D. The leading edge of the first element was set at the angle of 0° to the line tying the two outlets of the double-barreled syringe. Because this angle was responsible for the mixing results as previously reported,37 we set the angle to 0° for all the experiments. They were set on a syringe pump (ELCM2WF10K-AP; Oriental Motor Co. Ltd., Tokyo, Japan) to control the flow rate. Between the static mixer and the double-barreled syringe, a pressure gage (AP-12s and AP-13, Keyence Co. Ltd., Osaka, Japan) was connected to the flow channel to measure the pressure drop in the static mixer. A gastight syringe was also connected at this point to inject green dye to enable us to visualize flow patterns inside the static mixer. 2.5. In Situ Gelation through the Static Mixer. Using the above-mentioned experimental setup, we mixed the same amount of 1 or 3 wt % Alg solution or 1.5 wt % κ-carrageenan solution with 0, 50, or 100 mM CaCl2 solution or 1 M KCl containing 1 wt % CMC, changing the operating conditions, such as the axial velocity and the number of mixing elements.

2. EXPERIMENTAL SECTION 2.1. Materials. Alg (IL-2, Mw = 600 kDa) was a kind gift from KIMICA Co. Ltd. (Tokyo, Japan). Carboxymethyl cellulose (CMC, Mw = 700 kDa) was purchased from SigmaAldrich (St. Louis, MO). Calcium chloride (CaCl2), κcarrageenan, potassium chloride (KCl), triethylamine, ethanol, and dimethyl sulfoxide (DMSO) were purchased from Wako Pure Chemical Industries, Ltd. (Osaka, Japan). Fluoresceine-5thiosemicarbazide (FTSC) was purchased from Life Technologies Inc. (Rockville, MD). 1-Ethyl-3-(3-(dimethylamino)propyl)-carbodiimide hydrochloride (WSCD) was purchased from Peptide Institute, Inc. (Osaka, Japan). 1-Hydroxybenzotriazole (HOBt) was purchased from Tokyo Chemical Industry Co., Ltd. (Tokyo, Japan). Green dye (35 μg/mL green food dye; Kyoritsu Shokuhin Co. Ltd., Tokyo, Japan) was used as a tracer of the flow inside the statix mixer. All the chemicals described above were used as received without further purification. 2.2. Synthesis of FTSC-Modified Alg (Alg-FTSC). To visualize the inner structure, we modified Alg with green fluorescent dye, FTSC (Figure 1), following a previously

Figure 1. Synthetic scheme for fluorescently tagged Alg (Alg-FTSC).

reported method.36 In brief, 0.20 g of Alg was dissolved in a mixture of pure water (15 mL) and ethanol (5 mL). Then, pure water (3 mL) containing 16.8 mg of WSCD and DMSO (3 mL) containing 12 mg of HOBt were added to the solution. Then, 70 μL of triethylamine and 1 mL of FTSC solution (15 mg/mL in DMSO) were added and allowed to react overnight at 110 °C in an oil bath. The polymer solution was purified by dialysis using a dialysis membrane with 6 000−8 000 molecular weight cut off and then lyophilized. The modification ratio by FTSC was estimated via fluorescent intensity, as measured by a spectrofluorometer (FP-8200ST; Jasco Co., Tokyo, Japan). B

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homogeneity, we calculated the coefficient of variance of pixels in the confocal microscopic images with the size of 1800 × 1800 μm2. We obtained pixel data from the images using ImageJ software (National Institutes of Health, Bethesda, MD), and then calculated COV by dividing the standard deviation by the average of the obtained pixel values in eq 3. A̅ is the average pixel value, and Aι is the pixel value of each pixel, ι. We used the averaged value as a data point (n = 3). COV =

1 n−1

∑i (A̅ − Ai )2

(3) A̅ 2.7. Viscoelasticity of the Formed Hydrogels. We measured the rheological properties of hydrogels fabricated under different mixing conditions using a rheometer (VAR100; Reologica Instruments AB, Lund, Sweden). The storage modulus (G′) and the loss modulus (G″) of the hydrogels were measured as a function of oscillation frequency from 10 to 0.01 Hz loading the constant strain of 10 Pa. Wilcoxon rank sum test was performed to analyze the statistically significant difference using Kaleida Graph (Synagy Software, Reading, PA).

3. RESULTS AND DISCUSSION 3.1. Characterization of the Materials. The viscosities of Alg and κ-carrageenan solutions at different concentrations are shown in Figure 3. The viscosity of each solution decreased

Figure 2. (A) Schematic of our experimental apparatus. (B) Kenics static mixers used in this study. The numbers of elements in the mixers are 16, 12, 8, and 4 (from top to bottom). (C) Image of our experimental apparatus. (D) The connection between the doublebarreled syringe and the static mixer.

The pressure drop was monitored, and the flow patterns in the mixer were observed in real time. In this study, to analyze the effect of mixing conditions on pressure drop and hydrogel formation, we calculated Da, a dimensionless number defined as the ratio of the residence time in the static mixer (τr) to τg, expressed as τ Da = r τg (1) In eq 1, τr was obtained as L τr = v

Figure 3. Viscosity of Alg and CMC solutions with different concentrations. Shear rate was changed from 1 to 383 s−1. (2)

almost linearly with shear rate on a double-logarithmic scale, suggesting that they behaved as pseudoplastic fluids. At constant shear rate, the viscosity of Alg solution increased with increasing polymer concentration. When two solutions are mixed through the static mixer with the double-barreled syringe, the balance of viscosity between these solutions is important. If the viscosity of one solution is markedly higher than that of the other, it is difficult to eject identical volumes of solution simultaneously. To adjust the viscosity of metal ion solutions to that of the precursor polymer solution, we added CMC. The viscosities of the CMC solutions used are also plotted in Figure 3. The viscosity of CMC solutions showed similar dependence on shear rate and polymer concentration as Alg solutions. It was found that the viscosity of a 1 wt % CMC

where L and v represent the axial length of the static mixer and the axial velocity controlled by the syringe pump, respectively. τg was obtained using the stirrer experiment described above. 2.6. Confocal Microscopic Observation of the Formed Hydrogels. Homogeneity of the hydrogels fabricated under various mixing conditions was evaluated by visualizing the inner structure of the hydrogels by confocal microscopic observation. We added 0.01 mg/mL of FTSC-modified Alg (Alg-FTSC) to the Alg or κ-carrageenan solution prior to mixing for hydrogel fabrication and observed the formed hydrogels via a confocal laser microscope (LSM510 META NLO; Carl Zeiss AG, Jena, Germany) with a 5× objective lens. An argon laser (488 nm) with a LP filter of 505 nm was used. As an indicator of C

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which shows the solutions were mixed along the elements. In contrast, in the case of 100 mM CaCl2 solution, where gelation occurs during mixing, green clusters were intermittently observed. We believe this green cluster indicated stagnation of flow caused by the formed calcium Alg hydrogel. Specifically, the stagnation caused by interruption of flow by gelation caused the pressure to rise, which then flushed the gel, resulting in the intermittent stagnation patterns shown in Figure 5B. These results suggest that mixing of in situ cross-linking hydrogels is more complex than that of normal fluids and that the flow pattern in the mixer strongly depends on the condition of gelation. 3.3. Pressure Drop in the Process. Figure 6 shows the dependence of pressure drop on the number of elements and axial velocity. The pressure drop is an important factor when handled during surgery. Figure 6A shows the effect of the number of elements in the mixer on pressure drop. The

solution was almost comparable to that of the precursor polymer solutions used in the mixing experiments. Therefore, we subsequently chose a 1 wt % concentration of CMC to add to all metal ion solutions. To evaluate the gelation properties of Alg hydrogel and κcarrageenan hydrogel, we measured the gelation time of each hydrogel (Figure 4). For calcium Alg hydrogel, τg decreased

Figure 4. Gelation time of calcium Alg hydrogels for various Alg and CaCl2 concentrations. The results are expressed as averages ± standard deviation (n = 4).

with increasing CaCl2 concentration. In addition, a threshold CaCl2 concentration was identified, below which gelation did not occur, even after 1 h of mixing. The threshold CaCl2 concentrations for 1 and 3 wt % Alg solution were 40 and 20 mM, respectively. τg of κ-carrageenan hydrogels prepared by mixing 1.5 wt % κ-carrageenan and 1 M KCl with 1 wt % CMC was 6.0 ± 0.8 s (average ± standard deviation). The τg values obtained were used in the following dimensionless number analysis. 3.2. Visualization of the Flow. We mixed the Alg solution and CaCl2 solution containing CMC additive using a custommade static mixer system. Figure 5 shows the trajectory of the

Figure 5. Trajectory of green dye in the initial 8 of the 16 elements static mixer for Alg solution with (A) 0 mM and (B) 100 mM CaCl2. The concentration of Alg was 3 wt %, and the axial velocity was 1.46 mm/s.

green dye in the static mixer, where 3 wt % Alg solution was ejected with 0 or 100 mM CaCl2 solution at an axial velocity of 1.46 mm/s. The flow patterns in the static mixer differed markedly between the cases with or without gelation. In the case of 0 mM CaCl2 solution, where gelation did not occur, one green line was observed on each side of the first elements. The green line was divided into two lines and got thinner at the third element and finally the overall solution became green,

Figure 6. Effect of (A) the number of elements at axial velocity of 1.46 mm/s and (B) axial velocity in the 16 elements static mixer on the pressure drop. Various concentrations of Alg (1 or 3 wt %) and CaCl2 (0 or 100 mM) solutions were used. The pressure drop was measured every 0.1 s until it reached steady state and then averaged. The results are expressed as averages ± standard deviation (n ≥ 36). Inset in (A) shows a magnification of the results for 3 wt % Alg solution with 0 mM CaCl2. D

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Industrial & Engineering Chemistry Research pressure drop increased linearly with an increasing number of elements, whether or not gelation occurred. It has been reported that when mixing nonreactive fluids, which corresponds to the case of 0 mM CaCl2 in our system, the pressure drop has a linear relationship with the number of elements in a static mixer.38 This relationship was applicable even to the reactive fluids in the present study, i.e., fluids that form gels during mixing. In contrast, the effect of axial velocity on the pressure drop was quite different between the cases where gelation occurred or not for both Alg hydrogel and κcarrageenan hydrogel (Figure 6B). When the concentration of CaCl2 or KCl was 0 mM, the pressure drop increased monotonically with an increase in axial velocity, which agrees well with the results reported for other nonreactive fluids.39 However, in the case of 100 mM CaCl2 or 1 M KCl, where gelation occurs during mixing, the pressure drop changed with axial velocity in a more complex fashion; it first increased and then decreased with increasing velocity, and in the case of 1 wt % Alg and κ-carrageenan, then increased again. We consider that this complex behavior was caused by two opposite roles that axial velocity plays in pressure drop. Increase in axial velocity usually results in a high pressure drop, as shown in the case of 0 mM CaCl2. At low axial velocity, the increase in the axial velocity enhanced mixing of precursor polymer and metal ions, which facilitated the gelation. Thus, the pressure drop increased dramatically. On the other hand, when the axial velocity was further increased, the relatively shorter residence time decreased the degree of gelation because of the insufficient reaction time, which resulted in the gentle decrease in the pressure drop. In addition, the pressure drop increased again in κ-carrageenan and 1 wt % Alg with metal ions at further higher axial velocity because of the extremely short residence time, the curve of which was similar to that of uncross-linked solution. Their pressure drops gradually approached the pressure drop of solutions without metal ions. The competition of these two opposite contributions from axial velocity would determine the complex pressure drop behavior, shown in Figure 6B. To clarify the mechanism underlying the observed dependence of pressure drop in Figure 6, we calculated Da from all the experimental points in Figure 6A,B and plotted them against the pressure drop, normalized by the pressure drop for the 0 mM CaCl2 or KCl case. Results are shown in Figure 7. All hydrogels showed a similar trend with Da: a monotonic increase to a constant value with increasing Da. An increase in Da means that the gelation time becomes shorter relative to the residence time. When Da was less than 10, the hydrogels were more likely to be formed inside the mixer rather than outside, which would result in an increase of the pressure drop. In contrast, with Da larger than 10, the normalized pressure drop slightly decreased because of poor mixing. In short, a clear correlation between the pressure drop and Da was found for the mixing of both Alg hydrogel and κ-carrageenan hydrogels via the static mixers. 3.4. Homogeneity of the Hydrogels. Cross-linking density is closely linked to the mechanical strength of hydrogels, which is critical to achieving the practical application of in situ cross-linkable hydrogels. We investigated the effects of process parameters on the homogeneity of the formed hydrogels. To evaluate homogeneity, we used the COV of the pixels in fluorescent images of hydrogels. We prepared hydrogels of fluorescently tagged Alg, observed them via confocal microscope, and calculated the COV from pixel values in the confocal microscopic images. A higher COV reflects

Figure 7. Correlation between normalized pressure drop and Da. Data in Figure 6 were used.

increased variability of the samples, i.e., inhomogeneity of the hydrogels in our case. It should be noted that the modification ratio by FTSC to Alg was small enough (0.014%) to neglect its effect on the gelation process. Figure 8 shows typical confocal

Figure 8. Confocal microscopic images of calcium Alg hydrogel. A static mixer with 16 elements was used for mixing. The calculated Da and COV values are indicated in each image.

microscopic images of fluorescently tagged Alg, for inhomogeneous (Figure 8A,C) and homogeneous (Figure 8B) distributions. The COV calculated from Figure 8A (0.312) and Figure 8C (0.47) was lower than that from Figure 8B (0.82), which agrees with the qualitative observations. Figure 9 shows the effect of process parameters and sample composition on COV values of resultant mixtures. Materials that form hydrogels where the concentration of CaCl2 was 100 mM were less homogeneous than those that did not form hydrogels, where the concentration of CaCl2 was 0 mM, because hydrogel formation disturbed the mixing flow generation, as shown in Figure 5. In addition, it was also shown that increasing the axial velocity improved the homogeneity of materials, except for the case of 3 wt % Alg and 100 mM CaCl2. In that case, increasing the axial velocity E

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formed in the elements disturbed mixing by them as described above. Using the data in Figure 9 and some additional data, we plotted COV values as a function of Da (Figure 10). As a result,

Figure 10. Correlation between COV and Da. Data in Figure 9 and some additional experiments were used. Symbols α and β represent the experimental points used in subsequent rheological measurements (Figure 11).

the COV showed the same tendency against Da: first increasing and then decreasing for Alg hydrogels. We can interpret this COV behavior as follows. In the case of low Da, i.e., a long gelation time compared with residence time, gelation occurs mainly after the extrusion; thus, mixed samples are assumed to behave as a sol inside the mixer. In this situation, the precursor polymers are mixed homogeneously before gelation, so the resultant gels would be relatively uniform with a low COV. With increasing Da, the degree of gelation inside the mixer gradually increases, which results in an increase in sample viscosity. In this case, homogeneous mixing of precursor polymers becomes difficult, which leads to nonuniform gel formation with a high COV. When Da is further increased, as mentioned for the pressure drop in section 3.3, some Alg did not form hydrogel inside the static mixer because of insufficient mixing with Ca2+. Consequently, the solution viscosity was decreased by the increased amount of uncross-linked Alg, which resulted in the improved homogeneity. The clear correlation between COV and Da shown in Figure 10 suggests that Da is a useful index for controlling the homogeneity of in situ cross-linkable hydrogels produced in a static mixer, by considering the relative relationship between the residence time and the gelation time. Note that the κcarrageenan hydrogels showed a tendency of COV against Da different from that of Alg hydrogel, the mechanism of which will be investigated in further research. In addition, we analyzed the raw images with fractal dimension using ImageJ; however, all the images took almost the same value, 1.9 (data not shown). As far as we tried, COV is currently the best index of mixing in the present study. Although the COV showed the same tendency against Da, not every curve generated with different element numbers showed a maximum COV at different Da. This means that the Da defined in this research is not a perfect index for expressing

Figure 9. COV variations of calcium Alg hydrogels fabricated with different sample compositions (Alg and calcium ion concentrations) and different mixing conditions (number of elements and axial velocity in the static mixer). The Alg concentrations were (A) 1 wt % and (B) 3 wt %. The results are expressed as averages ± standard deviation (n = 3).

did not affect the homogeneity of materials. We believe that this was because the gelation time of 3 wt % Alg and 100 mM CaCl2 solutions was so fast that they formed gels immediately after their entry to the mixer however fast they were ejected. Moreover, it appears that although the number of elements affected the homogeneity of materials, their effect was relatively low compared with that of other parameters. We speculate that the mixing efficiency per unit element decreased as the flow passed through the static mixer from the inlet to the outlet. As shown in Figure 5A, where the concentration of CaCl2 was 0 mM, a green line was observed as the first element was divided and got thinner through the elements, and the overall solution became green after the fourth element. Also, when the concentration of CaCl2 was 100 mM as shown in Figure 5B, the gelation looked to be achieved at the fourth or fifth element. Previous research also reported that nonreactive viscous fluids were well mixed at the fourth or fifth element near the inlet of a static mixer, but mixing efficiency per unit element decreased at the subsequent elements by using striation width measurement.40,41 In addition, when the concentration of CaCl2 was 100 mM (Figure 5B), the gelation looked to be achieved at the fourth or fifth element. Hydrogel F

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Industrial & Engineering Chemistry Research the mixing condition. A significant consideration is mass transfer in the radial direction because residence time is calculated only in an axial direction. In previous research into the gelation of fibrin in straight channels,41 the Graetz number (Gz) was defined by the ratio of the characteristic time of diffusion in the radial direction to that of convection in the axial direction. We believe that it is necessary to consider mass transfer in the radial direction of static mixers in future research. 3.5. Storage Modulus of the Hydrogels. Finally, to address the relationship between homogeneity and the mechanical strength of hydrogels, we measured the rheological properties of hydrogels formed from the same sample composition, 3 wt % Alg and 100 mM CaCl2, but with different COV values, 1.1 and 0.58, corresponding to symbols α and β in Figure 10. The measurement was performed with maximum shear strain of 5 × 10−4. As a result, it was proven that the storage modulus (G′) of the hydrogel with a low COV value (uniform distribution) was higher than that with the higher COV value (nonuniform distribution) (Figure 11), which agrees with the results in previous reports.34 These differences in G′ were shown to be statistically significant through repeated testing (n = 4), although there were some frequency ranges in which the difference was not so significant (Figure 11B). In the case of Alg hydrogels, calcium ions eventually diffused into the alginate regions from CMC regions after mixing and cross-linked in the alginate region. Thus, the differences in G′ were not very significant. Calcium Alg hydrogels are used widely in various applications. However, it is also known to have the disadvantage that it is difficult to control the rate and homogeneity of the cross-linking reaction, resulting in an inhomogeneous gel structure and thus poor mechanical properties.42 To overcome this problem, work to date has focused mainly on the molecular design of precursor polymers.42−47 In this study, we showed that the gelation behavior can also be controlled by changing the mixing conditions for the precursor polymers using a static mixer, even though the chemical structures of the precursor polymers themselves were constant. Examination of the effects of process parameters, such as the number of mixing elements and the flow velocity, revealed that the pressure drop and the homogeneity of hydrogels, which was directly related to mechanical strength, were correlated with Da, suggesting that we can control these factors by taking the balance between the residence time and the gelation time into account. 3.6. Significance and Limitations of the Present Analysis Using Da. In the present study, the gelation process of Alg hydrogels with Ca2+ via static mixers was carefully investigated. There exist several types of in situ cross-linkable hydrogels. Ionic cross-linking occurs by mixing with metal ions, the mechanism of which is different from other cross-linking methods such as covalent cross-linking or enzymatic crosslinking. Covalent cross-linking reaction1,6 may occur only on the boundary between two precursor polymer solutions, while enzymatic cross-linking reaction7 occurs only inside the crosslinked polymer region by the diffusion of enzymes. The gelation process in the static mixer should be investigated for other in situ cross-linkable hydrogels in further studies. To analyze the pressure drop and COV, we calculated Da which was defined as the ratio of the residence time to the gelation time. We found that gelation was not achieved at low axial velocity because of poor mixing even though the residence time was longer than the gelation time. The definition of Da

Figure 11. (A) Storage modulus G′ and loss modulus G″ of Alg hydrogels with different COV values (1.1 and 0.58) and Alg solution (values are from ref 48). Hydrogels were formed with the same sample composition (3 wt % Alg and 100 mM CaCl2) but different mixing conditions. The hydrogel with the high COV value (1.1) was fabricated at an axial velocity of 7.3 mm/s using a 16-element mixer, while that with the low COV value (0.58) was formed at 1.46 mm/s using the same mixer. Corresponding experimental points are indicated as α and β in Figure 10. (B) Comparison of storage modulus between the inhomogeneous hydrogel (COV = 1.1, α in Figure 10) and homogeneous hydrogel (COV = 0.58, β in Figure 10). The results are expressed as mean ± standard deviation (n = 4). Wilcoxon rank sum test was used to determine statistically significant differences between data. Statistical significance is indicated as follows: * P < 0.05; n.s., not significant.

should be improved by removing the effect of the axial velocity on mixing together. In addition, another gelation time measurement should be investigated in further research. Although there are some limitations in the present research, this report has significant aspects because few systematic and careful analyses for gelation process via static mixers have been performed. Static mixers are frequently used in medical applications, as well as in chemical plants. Generally speaking, gelling via a static mixer is not desirable in continuous chemical processes, which do not allow frequent washing of the mixer. Therefore, the gelling process has not been studied well so far. However, static mixers in medical applications are compact and disposable, in contrast to those used in chemical plants; thus, G

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Industrial & Engineering Chemistry Research

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they are often used for gelling. The gelling process is difficult to analyze because the reactions induced by mixing affect the viscosity of the fluid at the same time. In the present study, we successfully analyzed the pressure drop and COV in in situ cross-linkable Alg hydrogel preparation in the Kenics static mixer using Da. The present study is a first step in this field and provides a potential approach for analyzing other gelling processes that use a static mixer.

4. CONCLUSION In situ cross-linkable calcium Alg hydrogels were gelled using a Kenics static mixer. The pressure drop during mixing and the homogeneity of resultant hydrogels were found to be highly dependent on process parameters, such as the number of mixing elements and flow velocity. We examined the pressure drop and COV (hydrogel homogeneity index) as a function of Da, suggesting that we can control both of these factors by considering the balance between residence time in the mixer and the gelation time of the precursor polymer. We confirmed that the mixing process is as important as the chemical synthesis of new precursor polymers. In addition, rheological measurements showed that the observed difference in homogeneity was correlated with the mechanical properties of the hydrogels, indicating that the mechanical strength of in situ cross-linkable hydrogels can be controlled via the static mixer by tuning the homogeneity of hydrogels. Our results provide new insights into the fabrication and control of in situ cross-linkable hydrogels for biomedical applications.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel.: +81-3-5841-1698. Fax: +81-3-5841-1697. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank KIMICA Co. for supplying alginate and Baxter International Inc. for supplying a double-barreled syringe. We also thank YMA Scientific Co. for the setup of mixing apparatus. We also acknowledge the Center for NanoBio Integration, the University of Tokyo, for confocal laser microscopy; Prof. Yukio Yamaguchi, the University of Tokyo, for the rheological measurements; and Prof. Toshihisa Ueda, Keio University, for expert advice on static mixing.

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REFERENCES

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DOI: 10.1021/ie5044693 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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DOI: 10.1021/ie5044693 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX