Preparation of biopolymer films by aqueous tape casting processing

Abstract

Biopolymer films have been prepared by continuous aqueous tape casting, using dextran–water solutions. The effect of dextran concentration and solution temperature on the flow behavior was studied by steady and dynamic rheological measurements. Rheological measurements revealed that increasing dextran concentration strongly increased viscosity, while increasing temperature reduced the viscosity marginally, limiting the film processing techniques to tape casting. Elastic effects were also seen in the biopolymer rheology studies, and no changes in the fluid internal microstructure were detected in the rheological measurements. The effect of casting speeds on the biopolymer film thickness was experimentally determined and compared with a pseudoplastic fluid model. Mechanical properties of the biopolymer films presented an isotropic behavior. Adding sorbitol as an external plasticizer produced more elastic films but induced an anisotropic response on the elongation at break.

Keywords

Biopolymer films aqueous tape casting biopolymer rheology non-Newtonian mechanical properties

Introduction

The general concern for using products from renewable resources has increased the development of new materials from vegetable and bacterial origins. Polymers, and monomers which can be converted into polymers by chemical polymerization, can be produced via fermentative processes either with native or engineered strains.¹ The industrial fermentation production of monomers such as lactic and glycolic acids, and biopolymers as bacterial cellulose, pullulan, polyhydroxybutirate, and polyhydroxyalkanoate, is of remarkable importance.^1–3 Among the water soluble biopolymers, starch is perhaps the material that has been most studied in the field of biopolymer processing. Thermoplastic starch is currently prepared by mixing native or modified starch granules, water, a plasticizer such as glycerol, and other additives, in single and twin-screw extruders and high-shear mixers.^4–6 Furthermore, this material can be converted to films and other molded products.^6–8 In this research we studied dextran (DX), which is a polymer produced from sucrose by fermentative processes.⁹ DX is a water-soluble biopolymer totally biodegradable and innocuous with high potential for application in food, pharmaceutical, and chemical industries.^10,11

Tape or solution casting is a processing technique adequate to manufacture films from polymer emulsions and water polymer solutions. Tape casting is a well-established technique for producing single- or multiple-layer ceramic laminates,^12,13 and it has also been used for preparing biopolymer films.^14,15 The process is sketched in Figure 1. Here, the polymer solution is in a container and, the pressure gradient (ΔP) in combination with the carrier belt movement, produces the solution flow through the doctor blade gap (H). Modifying the gap, the doctor blade controls the wet film thickness (δ′) and surface characteristics. The carrier belt moves the film continuously through a drying tunnel where the solvent is removed and a dry film with uniform thickness $(δ')$ is produced. Compared with film extrusion, tape casting requires higher costs due to the necessary solvent evaporation and recovery, but it is an excellent processing alternative for temperature-sensitive polymers. Also, solvent casting produces films that are clear and uniform in thickness, and does not need processing additives for thermal stabilization.

Figure 1.

Tape casting system schematic. The enhanced zone represents the coordinate system and a velocity profile schematic.

In this report, we present the preparation of films by continuous tape casting, of a microbial biopolymer that shows adequate flow conditions with water content as high as 80 weight percent. A detailed rheological study of the biopolymer solution was carried out. Biopolymer films were processed by tape casting, comparing the experimental results with previously reported flow models. The mechanical properties of the films were characterized.

Experimental

Materials

A DX biopolymer obtained by fermentation in the Institute of Biotechnogy of the National University of Colombia with a native and non-genetically modified strain was used in this research. The biopolymer structure corresponds to a modified sucrose whose units are joined by α-(1-6), bonds. The biopolymer is a white powder, soluble in water at room temperature in a wide proportion. Weight average molecular $({\bar{M}}_{w})$ , measured by dynamic light scattering in a zetasizer (nano zs Malvern Instruments), was ${\bar{M}}_{w}$ ∼8900 kDa. Wide-angle X-ray diffraction analysis (WAXD) of DX, did not show any crystalline structures, and, in water solution the polymer did not present any endothermic gelatinization peaks in differential scanning calorimeter (DSC), which indicated that the biopolymer was characterized by an amorphous structure (WAXD and DSC traces are not presented in this report). Polymer solutions were prepared with distilled water, using mechanical stirring with a helix-type blade for 2 hours at 1500 r/min. Mechanical stirring was adequate for preparing solutions up to 20 weight percent solids. For higher concentrations, a two-blade high-shear mixer was used. In order to plasticize the films, sorbitol USP grade (SO) was added to the biopolymer solutions during mixing.

Rheological characterization

Rheological characterization of biopolymer solutions was carried out in a Malvern Bohlin-Instruments CVOR rotational rheometer. For the steady-state measurements, a 40-mm cone and plate setup was used with a 2-degree cone angle. A controlled strain sweep was carried out varying the strain rates $(\overset{\cdot}{γ})$ from $\overset{\cdot}{γ} ~$ 0.01 to 1s⁻¹. Shear stress (τ) and the first normal stress differences (N₁) were recorded as function of $\overset{\cdot}{γ}$ . Testing temperatures between T = 5 and 35℃ were controlled by a Peltier plate. Dynamic experiments were performed in a 20-mm parallel plate arrangement to obtain rheological material functions such as storage modulus (G′), loss modulus (G″) and the tangent of the loss angle (Tan δ). Samples were subjected to a frequency sweep with frequency of oscillatory shear (ω) between 0.01 and 10 rad/s. In order to remain in the linear viscoelastic regime, the shear strain amplitude was kept constant at 2%.

Casting of films

A tape casting laboratory unit was used in the experiments. The solution reservoir had a 1000 ml capacity, and a 200-mm wide doctor blade, equipped with two micrometric screws to control the gap. The reservoir was provided with an electrical heater and a temperature controller. The drying section was 1400 mm long and was equipped with electrical heaters connected to a temperature controller. In order to improve the drying, atmospheric air was circulated over the film opposite to the belt motion at a surface speed of 10 mm/s. Biopolymer solutions were cast on a poly(ethylene terephthalate) film, with controlled speed. The doctor blade gap was fixed at 0.5 and 1 mm. The dried film thickneses were measured 10 times with a micrometer and averaged.

Tensile testing

Tensile stress–strain plots for the dried biopolymer films were measured in the machine and transversal directions, in a Shimadzu 250 kN universal testing machine, with a 100 N load cell, at 5 mm/min cross-head speed. Samples were razor blade-cut in a dog bone shape with a 50-mm length, and 6-mm wide neck. Before tensile testing, specimens were kept at 50% relative humidity and 20℃ for 24 hours. The reported results are the average of five samples.

Results and discussion

Rheological measurements

Figure 2(a) shows the flow properties of biopolymer solutions measured in a 40-mm cone and plate device as function of DX concentration. Biopolymer solutions presented a shear thinning behavior for all concentrations, increasing the shear viscosity for about four orders of magnitude as the concentration increased from 5 to 35%. As the main objective in tape casting was to obtain dry films with regular thickness, relative low viscosities were desirable in order to get good flowability and flat films. However, as biopolymer content increased, it may be more difficult for the solution to flow through the small doctor blade gap due to higher viscosity. As concentration increased, the development of biopolymer solution elasticity was also noticeable, with the increment of the first normal stress difference, N₁. In Figure 2(b) it is seen that for the lowest concentration studied in this research, no normal stresses were developed in simple shear within the range of detection of the rheometer. However, as the concentration increased, the normal stresses are more evident, which is a reflection of the effect of the high-molecular-weight polymeric material in water solution. It is well-known that elasticity in polymeric fluids generates specific characteristics during processing. In particular, fluid swelling (sometimes improperly referred to as die swelling) is a consequence of the release of normal stresses as the fluid leaves the die in film processing. In liquid casting, it may be expected that processing highly concentrated solutions may develop surface evidences of the release of normal stresses, including fluid swelling, which would limit the casting rate. Figure 2(c) shows a plot of N₁ vs. τ. These plots have been used extensively to explain the rheological behavior in molten polymers, polymer blends, and other heterogeneous systems.¹⁶ In Figure 2(c) it is seen that for DX concentrations of 10 and 20%, curves collapse in a single line, indicating that the fluid structure in solution does not change at these concentrations. In the terminal region, the plot corresponding to 35% DX solution deviates from the data for lower concentrations, to lower values of N₁ for the same τ. This result corroborated that for concentrated solutions the flow becomes more difficult.

Figure 2.

Effect of DX concentration on the steady rheological measurements for DX/water solutions with 5% DX (circles), 10% DX (triangles apex down), 20% DX (squares), and 35% DX (diamonds). (a) Shear viscosity (η) vs. shear rate $(\overset{\cdot}{γ})$ , (b) first normal stress difference (N₁) vs. shear rate $(\overset{\cdot}{γ})$ , and (c) first normal stress difference (N₁) vs. shear stress (τ).

Besides steady rheology, we used oscillatory shear rheology to understand the nature of the viscoelastic behavior of the biopolymer solutions. For this purpose, DX/water solutions were subjected to frequency sweep in parallel plate rheometer, and G′ and G″ were recorded for biopolymer concentrations from 5 to 40%. The characteristic effect of concentration is seen for the biopolymer solutions as G′ and G″ became higher as the biopolymer concentration increased as presented in Figure 3(a) and (b), respectively. It is worth noting, that at small ω, the slope of the logarithmic plots of G′ vs. ω (Figure 3(a)) and G″ vs. ω (Figure 3(b)) approach ∼2 and ∼1, respectively, which is a feature of the linear viscoelastic behavior of flexible homopolymers and polymer solutions.^16,17 Figure 3(c) shows the log G′ vs. log G″ plots for the biopolymer solutions. These plots are very sensitive to changes in the internal microstructure of the polymer system.¹⁶ A closer look at Figure 3(c) indicates that the traces for all compositions collapse in a single line with slope approaching two in the terminal region indicating that at different concentrations the internal fluid microstructure remained unchanged. At this point we can identify that besides molecular entanglement, DX and water may interact via hydrogen bonds, and what we learned from Figure 3(c) is that the same kind of interactions are present for all the concentrations studied.

Figure 3.

Effect of DX concentration on the dynamic shear rheometry for DX/water solutions, with 5% DX (circles), 10% DX (triangles apex down), 20% DX (squares), 35% DX (diamonds), and 40% DX (triangles apex up). (a) Storage modulus (G′) vs. oscillatory shear frequency (ω), (b) loss modulus (G″) vs. frequency (ω), and (c) storage modulus (G′) vs. loss modulus (G″).

The effect of temperature on the rheological properties of biopolymer solutions is presented in Figure 4. In Figure 4(a), we see that DX/water solutions presented pseudoplastic behavior in all the temperatures studied T ∼ 5℃, 15℃, 25℃, and 35℃. Also, the viscosity decreased as the temperature increased, which is the anticipated behavior for most fluids. Viscosity data in the Newtonian region at low shear rates $(\overset{\cdot}{γ} < 0.1 s - 1)$ $η_{0}$ could be adjusted to the following model: $η_{0} = - 9.2 + 3259 / T (K)$ . However, by comparing Figures 4(a) and 2(a), it can be concluded that the effect of concentration on viscosity is much stronger than the effect of temperature. Polymer processing operations take place at temperatures well above the melting point or glass transition temperature (T_g) in order to obtain good flow conditions. From Figure 4(a), it is seen that increasing the solution temperature in order to reduce the viscosity and facilitate the casting process may be detrimental for the operation due to the higher evaporation rate, which increases the polymer concentration and therefore the viscosity (see Figure 2). Thus, the water in the biopolymer/water solutions acts as a plasticizing agent and cannot be removed until the polymer is in the final shape. Therefore, the biopolymer would not be easily processed by film extrusion or any traditional methods to manufacture films in the plastics industry. The temperature effect on the viscoelastic properties of 20% biopolymer solutions is also presented in Figure 4. The plots of G′ vs. ω in Figure 4(b) shows the expected behavior of a reduction in the modulus as T increased and G′ approaching G′ ∼ ω² at low frequencies. Figure 4(c) shows the 20% biopolymer–water solution at different temperatures. It is seen that all the data in the log G′ vs. log G″ plot collapsed into a single line with the slope approaching 2.0 in the terminal regime. According to Han,¹⁶ this temperature-independent behavior is characteristics of polymer systems where the internal fluid structure remains unaltered with temperature, which was also observed in Figure 3(c) at different DX concentrations.

Figure 4.

Rheological behavior of DX/Water solutions with 20% DX at T = 5℃ (circles), 15℃ (triangles), 25℃ (squares) and, 35℃ (diamonds). (a) Shear viscosity (η) vs. shear rate $(\overset{\cdot}{γ})$ , (b) storage modulus (G′) vs. oscillatory shear frequency (ω), and (c) storage modulus (G′) vs. loss modulus (G″).

Tape casting

From the rheological study we learned that adequate flow conditions for DX are obtained when the polymer is in aqueous solution. Based on the flow properties, biopolymer films were prepared by tape casting at T ∼ 20℃ using a 20% biopolymer–water solution, and after shaping the material all the water used in the processing should be removed. In solution casting, water is removed in a drying tunnel by the combined action of electrical heaters under the carrier film and countercurrent air flow. Projecting to a commercial scale film production, it would be convenient to implement a system where water could be removed as fast as possible. However, a fast drying rate produced many surface defects and film wrapping (results not shown). It was anticipated that film thickness also influenced the drying process. In fact, when a H ∼ 0.5 mm doctor blade gap was used, the film leaves the tunnel with no significant water, while as the gap was increased to H ∼ 1 mm, the water content increased to 60%. Therefore, to maintain the process continuity, it would be necessary to design a tape caster with a drying zone longer that the conventional instruments and also to implement more efficient drying mechanisms.

Hydrodynamic analysis of the flow in tape casting may be considered as a complex problem, considering irregularity of the doctor blade geometry and the development of viscoelastic effects on the film surface. Analytical solutions are only possible for Newtonian and pseudoplastic fluids which can be found in the current literature.^18–22 For the coordinate system presented in Figure 1, the equation of motion can be written as

\frac{\partial P}{\partial z} = - \frac{d τ_{yz}}{dy}

(1)

where

$τ_{yz}$	=	the shear stress
x and y	=	coordinates as in Figure 1

Considering a fluid whose rheological behavior approaches the power law model (equation (2))

τ_{yz} = - m | \frac{{dv}_{z}}{dy} | n - 1 \frac{{dv}_{z}}{dy}

(2)

where

m and n	=	constants (n < 1)
$({dv}_{z} / dy)$	=	the velocity gradient,

following the derivation presented by Tadmor and Gogos,¹⁸ equation (1) can be written in dimensionless form as follows

\frac{d}{d ξ} (| \frac{{du}_{z}}{d ξ} | n - 1 \frac{{du}_{z}}{d ξ}) = 6 G

(3)

where

ξ = y / H

u_{z} = v_{z} / V_{0},

and G is the dimensionless pressure defined as

G = \frac{H n + 1}{6 {mV}_{0}^{n}} (\frac{Δ P}{L})

(4)

Equation (3) can be solved,¹⁸ and the dimensionless thickness of the dry film

δ'

(δ' = h' / H)

is written as

δ' = \frac{α β (6 G) 1 / n}{(1 + 1 / n) (2 + 1 / n)} \frac{ρ_{s}}{ρ_{b}} [| 1 - λ | 1 + 1 / n (2 + 1 / n) - | 1 - λ | 2 + 1 / n + | λ | 2 + 1 / n]

(5)

where

ΔP	=	is the pressure drop calculated as the hydrodynamic head in the reservoir (H_ΔP),
ρ_s and ρ_b	=	the wet and dry film densities ( $ρ_{s} / ρ_{b} ~ 1$ ),
α	=	a correction factor for the film extension width measured at the doctor blade exit
β	=	a factor related to the experimental difference between the dry and wet film weight,
λ	=	the value of ξ where $({dv}_{z} / dy) = 0$

(other symbols as in Figure 1).

Power law parameters m and n were obtained by regression from the data presented in Figure 2(a). The value of λ is found by solving the following non-linear equation:

| λ | 1 + 1 / n - | 1 - λ | 1 + 1 / n + \frac{1 + 1 / n}{(6 G) 1 / n} = 0

(6)

Figure 5 presents the experimental results obtained in tape casting, with the predictions obtained from equations (1) through (4). It is seen in Figure 5 that the analysis for pseudoplastic fluid captures the qualitative aspects of the flow conditions in tape casting. Quantitative agreement, however, is only seen at carrier speeds over 4 mm/s (6G < 4), over-predicting the thickness of the wet films for low casting velocities. It is evident that in the derivation of equations (1) to (6), many assumptions were included, that may originate the differences between the predicted and the experimental values. On the other hand, the error bars of the experimental values in Figure 5 reflect the intrinsic errors generated on the thickness measurements increasing as the carrier speed is reduced.

Figure 5.

Comparison between theoretical predictions predicted with equation (5) (continuous line), and experimental data (squares) of the dimensionless thickness, δ′, for tape casting as function of the dimensionless parameter 6G.

Mechanical properties

Tensile tests were performed on the tape cast films in the flow or machine direction (FD or MD) and in the transverse direction (TD). As the polymer was cast from an isotropic solution and drying took place under no flow conditions, no differences in the mechanical behavior between FD and TD were anticipated. Figure 6 compares the tensile strength (TS) and the elongation at break (DX) for DX films processed from a 20/80 DX/water solution and dried at two conditions: (1) ambient conditions for 48 hours without air flow, and (2) in the tape casting machine tunnel at T ∼ 60℃ and countercurrent air flow. In fact, as it can be seen in Figure 6, for the DX films, no appreciable differences in the mechanical properties were detected for the biopolymer films between MD and TD considering the high data inconsistency, it may be concluded that under the casting and drying conditions, no molecular orientation was induced. It is interesting to note in Figure 6, that films dried at ambient conditions for 48 hours showed higher tensile strength than the films dried in the tunnel at 60℃ and with countercurrent air flow. Elongation at break on the other hand is higher for the films dried in the tunnel. In the drying tunnel, water leaves the sample faster, with the possibility to form microscopic surface defects which may act as stress points affecting the film mechanical response. This result highlights the importance of the drying process in tape casting and it is anticipated that structuring of DX films may be possible with this technique.

Figure 6.

Tensile strength (TS) and elongation at break (EB), in the flow direction (FD) and in the transverse direction (TD), for dextran (DX) and dextran/sorbitol (DX/SO) films processed by tape casting.

Figure 6 also presents the tensile test results for the DX/SO dry films containing 10% SO. SO is a water-soluble solid polyalcohol, which is an efficient plasticizer for biopolymer films. These films were tape cast from a DX/SO/water 18/2/80 and dried at ambient conditions for 48 hours. In DSC measurements carried out in a DSC 2910 TA Instruments at a heating rate of 10℃/min and nitrogen atmosphere (traces not presented), it was found that the T_g for the pure biopolymer at room conditions (∼12% water in the films) was T_g ∼ 48℃, while for films containing 10 and 20% SO at the same conditions, the T_g values were ∼42℃ and 31℃, respectively. Therefore, the low maximum strength and the larger maximum deformation compared with the pure DX films are not surprising. What is really an unexpected result is the difference in the mechanical behavior between the FD and TD in the elongation at break. This result is a clear indication of molecular orientation, not detected for the unplasticized films. In tape casting, the highest shear is applied to the biopolymer solution during the flow through the doctor blade gap, and therefore, it is reasonable to assume that molecular orientation took place at that moment. In the pure biopolymer films, this molecular orientation is relaxed rapidly and the film mechanical properties are isotropic. This relaxation process is somehow retarded with the presence of sorbitol and a much higher elongation at break was observed in the flow direction.

Conclusion

Aqueous tape casting is an adequate processing technique, for producing continuous films of high water-soluble biopolymers. DX produced by fermentative process is an amorphous water-soluble polymer, which does not plasticize with increasing temperature. DX-water solutions evidenced pseudoplastic behavior in the flow curves, which may be represented by a power–law model. Increasing temperature reduced the solution viscosity. However, as the temperature increased, an important water fraction was evaporated increasing the biopolymer concentration. Elastic effects were also observed with the development of normal stresses in simple shear and in the dynamic rheological measurements. Log G′ vs. log G″ plots did not reflect any change in the fluid internal microstructure neither with concentration nor with temperature. The rheological study demonstrated that DX should be processed in aqueous solution, with relatively high water concentration that has to be removed after shaping the polymer.

A model of tape casting for pseudoplastic fluids was used to compare the experimental values of film thickness with the casting speed. Agreement between experiments and model only occurred at high casting speeds. However, the models used for rheology as well as tape casting do not capture all the phenomenology of the fluid and the process. According to the tensile testing, DX forms rigid films with isotropic behavior. Mechanical properties also show that the rate of drying affects the film performance, probably because the presence of micro-defects in the films subjected to fast drying in the tunnel. SO is an efficient plasticizer for DX films, reducing the T_g and increasing the elongation at break. SO also affected the casting process inducing high anisotropy on the mechanical properties.

Footnotes

Acknowledgments

Preliminary testing on tape casting was carried out in the laboratory of Dr. Jairo Escobar at The University of los Andes, Bogotá – Colombia.

Funding

Authors acknowledge the financial support of COLCIENCIAS through the grant number CT 383_2011. DF Vogelsang would like to thank the financial support of COLCIENCIAS through the Programa Jóvenes Investigadores e Innovadores “Virginia Gutiérrez de Pineda”.

Conflict of Interest

None declared.

Biographies

David F Vogelsang obtained his diploma in Chemical Engineering from Universidad de America in Bogota, Colombia, in 2008. For two years, he worked for the Colombian agricultural research center (CORPOICA) with a research grant to study the use of residues of sugar cane processing. In 2013 he defended his MSc thesis in Chemical Engineering at the National University of Colombia. He is currently a graduate student in Chemical Engineering in Michigan State University. His recent research is focused in the study of the properties of polystyrene/nanoclay composites.

Jairo E Perilla obtained his Chemical Engineering and MSc degrees form National University of Colombia, and his PhD – Polymer Engineering from The University of Akron. Perilla is an associate professor of the Department of Chemical and Environmental Engineering at National University of Colombia since 1995. His research interests include polymer processing and rheology, biopolymers for pharmaceutical applications and polymer–silica hybrids.

Gustavo Buitrago is an Associate Professor of the Institute of Biotechnology of the National University of Colombia. Buitrago received his BS in Chemical Engineering and an MSc in Environmental Engineering from the same university. At present, he is responsible for research and administrative duties at the Institute of Biotechnology.

Néstor A Algecira is an Assistant Professor of the Department of Chemical and Environmental Engineering of the National University of Colombia, where he is the Director of the Chemical Engineering Laboratories. Algecira advises several graduate students in the area of Food Engineering. He received his BS and MSc degrees in Chemical Engineering from National University of Colombia.

References

Lee

Kim

Choi

. Microbial production of building block chemicals and polymers. Curr Opin Biotechnol 2011; 22: 758–767.

Tharanathan

. Biodegradable films and composite coatings: Past, present and future. Trends Food Sci Tech 2003; 14: 71–78.

Yua

Deana

Lib

. Polymer blends and composites from renewable resources. Prog Polym Sci 2006; 31: 576–602.

Liu

Zou

. Extrusion processing and characterization of edible starch films with different amylose contents. J Food Eng 2011; 106: 95–101.

Raquez

Nabar

Srinivasan

. Maleated thermoplastic starch by reactive extrusion. Carbohydr Polym 2008; 74: 159–169.

Liu

Xie

. Thermal processing of starch-based polymers. Prog Polym Sci 2009; 34: 1348–1368.

Herrera Brandelero

Eiras Grossmann

Yamashita

. Effect of the method of production of the blends on mechanical and structural properties of biodegradable starch films produced by blown extrusion. Carbohydr Polym 2011; 86: 1344–1350.

López

Zaritzky

Grossmann

MVE

. Acetylated and native corn starch blend films produced by blown extrusion. J Food Eng 2013; 116: 286–297.

Ahmed

Siddiqui

Arman

. Characterization of high molecular weight dextran produced by Weissella cibaria CMGDEX3. Carbohydr Polym 2012; 90: 441–446.

10.

Wang

Nie

Yang

. Dextran and gelatin based photocrosslinkable tissue adhesive. Carbohydr Polym 2012; 90: 1428–1436.

11.

Cote

Willet

. Thermomechanical depolymerization of dextran. Carbohydr Polym 1999; 39: 119–126.

12.

Mistler

Twiname

. Tape casting – theory and practice, Westerville, OH: The American Ceramic Society, 2000.

13.

Hotza

Greil

. Review: Aqueous tape casting of ceramic powders. Mater Sci Eng 1992; A202: 206–217.

14.

Oliveira de Moraes

Scheibe

Sereno

. Scale-up of the production of cassava starch based films using tape-casting. J Food Eng 2013; 119: 800–808.

15.

Steele

TWJ

Huang

Kumar

. Novel gradient casting method provides high-throughput assessment of blended polyester poly(lactic-co-glycolic acid) thin films for parameter optimization. Acta Biomater 2012; 8: 2263–2270.

16.

Han

. Rheology and processing of polymeric materials. V. 1: Polymer rheology, Ney York: OXFORD University Press, 2007.

17.

Macosko CW. Rheology: Principles, measurements, and applications. New York: Wiley-VCH, 1994.

18.

Tadmor

Gogos

. Principles of polymer processing, Hoboken NJ: Wiley, 2006, pp. 117–122.

19.

Joshi

Lam

Boey

FYC

. Power law fluids and Bingham plastics flow models for ceramic tape casting. J Mater Process Tech 2002; 120: 215–225.

20.

Zhang

Wang

. Bingham plastic fluid flow model for ceramic tape casting. Mat Sci Eng 2002; A337: 274–280.

21.

Tok

AIY

Boey

FYC

Lam

. Non-Newtonian fluid flow model for ceramic tape casting. Mat Sci Eng 2000; A280: 282–288.

22.

Sofou

Mitsoulis

. Roll-over-web coating of pseudoplastic and viscoplastic sheets using the lubrication approximation. J Plast Film Sheeting 2005; 21: 307–333.