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Extensional properties of macromolecules
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ScienceDirect Extensional properties of macromolecules Francisco Rodrı´guez-Gonza´lez and Luis A Bello-Perez There is increasing interest in the food industry in the development of new or improved commercially available food products. New methods to test the characteristics of raw materials and products are necessary. The viscosity (consistency or texture) of foods is an important rheological variable during processing because it influences the equipment design necessary for food production. Additionally, viscosity determines functionality and consumer acceptance of foods. This review focuses on extensional viscosity characterization as a tool to aim the development of novel and improved food products and processes. Extensional deformation is involved in processes as extrusion, film blowing, and fiber spinning, but it is also important in determining and understanding interactions among food components (e.g., proteins, polysaccharides, and lipids) in food products (e.g., bread, pasta, syrups, snacks, and salad dressings). Address Instituto Polite´cnico Nacional, Centro de Desarrollo de Productos Bio´ticos, Km 8.5, Carretera Yautepec Jojutla, Colonia San Isidro, C.P. 62731, Yautepec, Morelos, Mexico Corresponding author: Bello-Perez, Luis A ([email protected])
Current Opinion in Food Science 2016, 9:98–103 This review comes from a themed issue on Food physics and material science Edited by Osvaldo Campanella For a complete overview see the Issue and the Editorial Available online 9th November 2016 http://dx.doi.org/10.1016/j.cofs.2016.11.003 2214-7993/# 2016 Elsevier Ltd. All rights reserved.
Introduction In recent decades, studies on the physical properties of many food systems have increased because the components and ingredients of food systems are directly related to the quality, nutrition and energy source that they can provide consumers [1–3], particularly lipid-based foods, proteins and carbohydrates. Food quality is defined by texture, color and sensory properties, which promote acceptance and preference by consumers. Food science has devoted several years of research to the study of individual ingredients in food systems, particularly stabilizing agents. Diverse research projects have attempted to elucidate the effects and changes that stabilizing agents in foods produce Current Opinion in Food Science 2016, 9:98–103
through the formation of physical and chemical interactions between macromolecules in the food matrix. Additionally, researchers have focused on the influence of the chemical characteristics of stabilizers on changes in viscous and elastic properties [1,4–17]. Studies on food systems and their ingredients have used several techniques, including differential scanning calorimetry, rheology shear and extensional flow, to determine physical parameters [1,7–17]. This work is a review of research related to rheological studies focused on the extensional flow applied to solid and liquids foods containing polymeric and nonpolymeric food components.
Extensional properties of foods Since the middle of the last century, rheology had many applications in different fields related to the production, handling and quality control of foods [1–3,13,17,18]; rheological studies include determining the deformation and shear rate of food systems produced by external forces [1,3,18]. Determination of the rheological properties of different ingredients and foods is useful because it can elucidate the composition, texture, and structural changes observed during agitation, processing, packaging, storage and consumption [1,3,13,18]. During those processes, foods are subjected to a combination of shear and extensional flow; therefore, it is important to know the structural changes on the food components that are produced by both flows [1,18]. Extensional flow is a deformation that involves elongation of the fluid molecules along the streamlines; according to the resulting deformation, the extensional flow may be classified as uniaxial or biaxial [2,15,17,19]. Uniaxial extensional flow is the most studied and developed from a theoretical and experimental standpoint [20,21–23]. Several studies on extensional flow in dilute, semi-dilute and concentrated polymer solutions have been performed using theoretical, experimental and numerical simulations [2,4,5,10–16,20,21–25]. Trouton proposed a relationship between extensional and shear viscosity for Newtonian fluids that states that: hE = 3h0, where hE is the extensional viscosity in the steady-state and h0 is the shear viscosity in zero-shear; at a low shear rate, Tr = hE/ h0 = 3 [4,15]. Despite the need to know the extensional flow properties of fluids, it was not until the 1970s and 1980s that the work in this field was conducted because of advances in theory development and new equipment technology. That work focused on determining the hE of high viscosity shear fluids (h > 1000 Pa s) as polymer melts [2,4]. Moreover, with the advent of technology and the development of www.sciencedirect.com
Extensional viscosity of foods Rodrı´guez-Gonza´lez and Bello-Perez 99
electronic components, the first measurements of the extensional properties of low viscosity shear fluids (h 0.01–10 Pa s) were performed in the 1990s [2]. Recent research has discussed that the determination of the extensional properties of low viscosity fluids is influenced by effects of inertia, surface tension, and gravity because the magnitude of these effects are of the same order than viscoelastic responses [4,10,12,13,15]. The development of products (new or improved) with specific functionalities is a daily activity of the food industry. The specific functionalities of foods are necessary because consumers require products with sensory characteristics. Foods are formulated with diverse ingredients, such as hydrocolloids (gums), proteins, sugars, lipids, etc., and they influence the functionality (e.g., texture) and acceptability by consumers. One of the most important functionalities of foods is the viscosity. The addition of hydrocolloids to food formulation produces a ‘stringy’ appearance, meaning the product does not cleanly break when the container is tilted upward. Extensional viscosity measurement was proposed as a method to determine this sensory characteristic property [26]. Methods used to test high viscosity liquids include fiber wind-up and entrance pressure drop, whereas the opposed jets method was used to test low viscosity liquids. Liquid foods were the first materials used to determine hE, an important variable that gives information on the structural features of a liquid; also, hE is used in process design calculations, control processes, food process modeling and for determining the overall and sensory quality of liquid foods. It is well recognized that hE is sensitive to the molecular makeup of macromolecules, such as the chain-length distribution (in branching polymers) and arrangement of macromolecules (mainly proteins and polysaccharides) in the food matrix [27,28,29]. The diverse type of flow occurring during food consumption and processing such as swallowing, atomization, flow through porous media, turbulent flow reduction, etc., involves extensional flow. Solid materials are found in wide variety foods; wheat doughs are some of the most complex solids systems because of their elastic behavior due to the protein fraction and imbibed starch
granules in their network. Food systems are categorized as liquid and solid foods (including semi-solids).
Methods to determine extensional properties of foods From an experimental point of view, some of the largest challenges for determining the extensional properties of fluids are equipment designed to generate a homogeneous extensional shear free flow under steady strain rate conditions [2,20,30]. Despite of the measurement challenges, recently novel instruments to characterize extensional properties of a wide range of polymeric materials has been developed. They include measurement of pressure drops through a contraction in the capillaries and channels [31], using capillary rheometers [2,32], and the use of special rheometers for extensional flow, such as filament-stretching extensional rheometer (FiSER) [4] and capillary break-up extensional rheometer (CaBER) [15,16,20,24]. Therefore, studies on the extensional flow of viscoelastic fluids and diluted low viscosity fluids in shear free conditions have been increasing [2,13,15,16,20,21]. However, few researchers have related the study and determination of the extensional properties of biopolymers in solution [1,4,5,8,10,12,13, 15,16,21,24]. Table 1 summarizes the characteristics of the different instruments that have been used to study the extensional properties of biopolymers in solution and their application ranges. The studies indicate several drawbacks to obtaining information on the analyzed systems that should be considered during experiments.
Physics of extensional properties During a study on the extensional flow of polymer solutions, it is common to establish a dimensionless number for dynamic measurements and material functions, for example the Trouton ratio (Tr = hE/h0). This expression is a function of the Hencky strain (eH = e0t) and Deborah number (De = le0), where l is the longest relaxation of the molecules constituting the polymer solution, which can be obtained from small strain oscillatory flow dynamic tests. Furthermore, methodologies established
Table 1 Summary of extensional rheometer designs and application to biopolymers in solution. Instrument type Entrance flow Opposed jet Geometries with a hyperbolic contraction Filament stretching, constant volume, medium viscosity Capillary breakup rheometry
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Flow
Shear viscosity range (s 1)
Limitations
Uniaxial extension Uniaxial extension Uniaxial extension
>1 0.01–1 0.01–500
Variable strain rate, mixed with shear Variable strain rates and strain histories Variable strain rate, mixed with shear
[31] [19] [2,32]
Uniaxial extension, constant strain rate Uniaxial extension
1–1000
Sample gripping limited to medium and high viscosity Inertial and surface tension dominate at low viscosity, variable strain rates
[4]
0.01–10
References
[4,5,8,10,12, 13,15–17]
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for determination of the extensional properties of fluids involve specimen’s surfaces exposed to such forces as gravity (g) and surface tension of the fluid (g), among others. On the other hand, some of the dimensionless numbers involving forces previously mentioned include: the capillary number, Ca = h0e0R/g, where R is a characteristic length in the experiment (i.e., the radius of the filament in cases where a CaBER instrument is used), and the elasto-capillary number, EC = lg/h0R. Finally, for experiments where the force of gravity shows a strong influence in determining the extensional properties of the fluid, the Bond number is used, B0 = rgR2/g, which establishes a relationship between the force of gravity and forces from the fluid surface tension, and where r is the density of the fluid. In some investigations related to the extensional properties of dilute and semi-dilute fluids, dimensionless numbers have been used for the analysis and interpretation of results [13,17,18]. The following section gives more details about the use of dimensionless numbers for the analysis of results obtained with a CaBER. According to the theory developed for extensional flow of viscoelastic fluids [20,30], the changes in the diameter of the filament as a function of the time (D(t)/D0 versus t) are assessed in the CaBER, and they can be used to determine the relaxation time of the fluids [10,13,14,16,17,20,30]. However, only studies of quantitative predictions for dilute solution and empirical relationships for very dilute solutions in extensional flow have been reported [20,31,33– 35]. Furthermore, in extensional flow experiments with a CaBER, the deformation behavior as a function of time is complex, and a steady state for the study of polymers in solution is not reached. Therefore, an extensional viscosity apparent (hE,app = g/Re) is considered, assuming that the extensional stress in the fluid is equal to the surface pressure (g/R) [17,20,30]. Some studies reported [17,30] that for a better interpretation of extensional flow studies on semi-dilute polymer solutions, the curves obtained with a CaBER can be divided into four different regimes. Regime I shows strong contributions from gravity and is characterized by a thinning behavior. For analysis of the flow regime, the Bond number can be used, and you can define the lower limit of the regime. For values below B0 0.2, the effect of gravity may be neglected. Regime II is below the critical Bond number and is controlled by a balance of capillary pressure (g/R) and viscous stress (hEe) on the filament. In this regime, the radius of the filament is still large, which leads to a low extensional rate, with a Newtonian behavior and Tr = 3. In the Regime II, Clasen [30] noted that the extension rate increased as a function of time, while the hE,app remained constant. In the Regime III, a visco-capillary balance is show; however, the surface pressure and hence the extension rate is high Current Opinion in Food Science 2016, 9:98–103
enough so the solution is showing an extensional thinning, originating disentanglement and orientation of the polymers molecules in the solution. In this regime, the apparent extensional viscosity decreases as the extensional rate increases. The Regime IV shows the onset of an elasto-capillary balance, where the surface pressure is in equilibrium with the elastic force of the disentangled polymer chains. Within this regime, the diameter of the filament has an exponential decay with time and then it is close to breakup (see Figures 2 and 3 of Ref. [10]). Conversely, studies in Regime IV on semi-dilute polymer solutions, which are controlled by thinning elastic behavior, have only been developed from a qualitative point of view [36]. In the case of concentrated solutions, analyses have been conducted from a comparative standpoint on the behavior of the dynamic thinning suffering strand in Regime III and IV as a function of time in order to predict when one concentrated polymeric solution would show a transition from the extensional flow regime to Regime III to Regime IV. In this sense, Anna and McKinley [20] proposed the dimensionless number, EC, which relates the elastic part of the viscous material portion to the thinning and break-up of the filament.
Extensional properties of liquid and solid foods: overview Liquid foods
Haward et al. [10] achieved shear rheological characterization and extensional flow of dilute and semi-dilute solutions of cellulose dissolved in an ionic liquid at concentrations used to produce fibers by electrospinning (fiber spinning and spraying). Extensional flow measurements determine the extensional relaxation time that is related to the elongation of the cellulose molecules through the effect of extensional stress. Haward et al. showed that more concentrated solutions exceeded the limit of entanglements among molecules, causing a significant increase in the extensional relaxation times of these solutions. de Dier et al. [24] investigated the effect of the stiffness of Schizophyllan polysaccharide molecules in solution (water and DMSO) on their extensional properties. They studied the behavior of biopolymers with concentrations in the semi-dilute regime (0.77–5.2 g/L) on the extensional properties. Those authors used a CaBER for extensional flow experiments and observed a thinning fluid filament diameter as a function of time for all solutions analyzed, using DMSO as the solvent. The graphs of the reduction in diameter as a function of time were divided into three flow regimes. The first was related to a Newtonian flow regime, in which the properties of the solvent show a strong influence. The subsequent regime showed exponential decay, and the final regime was linear before www.sciencedirect.com
Extensional viscosity of foods Rodrı´guez-Gonza´lez and Bello-Perez 101
the break-up of the filament. They observed that the extensional relaxation time (lE) showed power-law behavior as a function of the concentration of the biopolymer (lE C0.9). Furthermore, aqueous solutions of Schizophyllan showed a more pronounced Newtonian regime and relaxation times as a function of concentration, showing a higher power index (lE C1.52) compared to DMSO solutions; this result was attributed to a possible increase in chain stiffness based on the solvent used. The determination of extensional relaxation times for Schizophyllan solutions in both solvents establishes the response of the macromolecules, single random coil or triple helical structure, as a function of polysaccharide concentration. On the other hand, Rodrı´guez-Rivero et al. [13] studied the effect of the concentration of alginate solutions free of salts to establish that this biopolymer has a transition from a polyelectrolyte to a neutral polymer. These authors investigated this effect with rheological characterizations, which consisted of shear flow and extensional flow experiments. These results showed that relaxation times were dependent on the concentration of the alginate solutions. The authors found that at large Hencky strain, the concentrated solutions showed a decreased in the apparent extensional viscosity; this pattern is shown when the chains of polymer are fully extended and the diameter of filament decays linearly with the time. Torres et al. [14] studied the extensional flow behavior of guar gum in aqueous solutions over a wide range of concentrations (1–10 g/dL). The authors observed a transition dilute regime and viscous behavior at levels lower than 10 g/dL, but at higher concentrations, the data showed typical behavior for solutions with entanglements and a viscoelastic material (gel-like) structure. Through extensional flow analysis, they also found that solutions with concentrations less than 10 g/dL showed an increase in the apparent extensional viscosity (hE,app) as a function of the Hencky strain (eH), which reached a constant asymptotic value. Similar behavior for high strain values (Hencky > 3) was exhibited by guar gum solutions with concentrations greater than 10 g/dL. However, they showed a maximum value of hE at a value of eH 1.2, which increased with concentration. This maximum was attributed to the presence of entanglements in that concentration range. Moreover, Szopinski et al. [16] studied the rheological properties of shear and extensional flow in polysaccharide guar gum derivatives (carboxymethylhydroxypropyl and hydroxypropyl) in the concentration regimes of semi-dilute and concentrated by dissolving the derivatives in distilled water and adding 0.1 M NaNO3 + 200 ppm NaN3. Szopinski et al. conducted an analysis of the relaxation times obtained from different experiments to establish a characteristic relaxation behavior of fluids under these parameters. These authors found that the extensional relaxation time (lE) of the different solutions was shorter than the shear relaxation www.sciencedirect.com
time that was obtained from shear flow (ls) experiments. They showed that the ratio of the relaxation times shows a power-law dependence parameter with the concentration of polysaccharide solution, that is, lE/ls (C[h]) 2. This result was attributed to two different behavior processes of the polymer chains. The first is a slow process that is related to the shear preventing entanglements of molecules, and the second process, which is carried out in the last extensional flow step, involves relaxation of the elongated individual polymer chains. The work reported by Vadodaria and English [17] presents comprehensive information related to the extensional flow theory and determination of the dimensionless numbers, Deborah (De), elasto-capillary (Ec) and Ohnesorge (Oh). They set out to study the effects of inertia, elasticity and viscosity on this type of flow. These researchers determined extensional properties, relaxation times and extensional viscosity in dilute solutions of hydroxyethyl cellulose (HEC). These authors showed, for the first time, the presence of flow instabilities (beadon-a-string) in filament flow conditions before break-up. Such instabilities were attributed to the accumulation of viscoelastic efforts in the middle of the filament, causing an ‘elastic-recoil’ effect in the molecules that constitute the biopolymer. Instabilities causing a thinning in the filament formed between the plates of the rheometer and bridge that unites the secondary fluid filament. Solid foods
The study of extensional properties of solid and semisolids foods started in the 1980s [22]. Doughs are some of the most complex and interesting food materials because of the interactions involved during their preparation, and the in-depth understanding of the system can be related to the popularity of baking products. Studies on the relaxation and elastic recovery of doughs suggest that the elastic behavior of wheat dough is due to gluten produced during the processing [22,27,28,29]. Other studies showed that some extrinsic factors, such as extension rate and temperature, as well as intrinsic factors, such as water content and flour type, play an important role in the stress–strain behavior [27]. Extensional viscosity of doughs is related to sensory properties like loaf volume. Dobraszczyk and Morgenstern [27] reported on the most common rheological methods used in bread baking and their relationship to product functionality. Wheat flour doughs with water were analyzed by capillary and channel rheometers; the shear viscosity (hs), uniaxial extensional viscosity (hE,u) and extensional viscosity planar (hE,p) were determined. The doughs had a shear viscosity of 100 Pa s and exhibited shear thinning and extension thinning behavior. It was shown that hE,u and hE,p viscosities were five orders of magnitude higher than hs, and the uniaxial extensional viscosity was larger than the extensional planar viscosity. Current Opinion in Food Science 2016, 9:98–103
102 Food physics and material science
Several methods have been used to test the rheological properties of wheat dough in simple uniaxial and biaxial extensions (compression between lubricated surfaces or by bubble inflation). For wheat dough, extensional flows are important during mixing, sheeting, extrusion and pumping of pastry and dough. Most flow tests are achieved in shear under small deformations, but these conditions do not provide information about material behavior under large extension. Under extensional flow, entangled polymers (e.g., proteins and starch in wheat dough) show strain hardening, which is enhanced for polymers with a broad molecular and weight distribution, usually bimodal distribution and branching. Bread doughs show strain hardening in large deformations such as bubble expansion, and those extensional properties are an important issue in baking performance. Gluten is the main component responsible for the viscoelastic behavior of wheat dough. It is accepted that gluten proteins (gliadins and glutenins) are important for determining variations in baking quality; the insoluble fraction of high molecular weight (HMW) glutenins is related to differences in dough strength and baking quality amongst wheat varieties. Elongational rheology of HMW polymers is a sensitive indicator for changes in secondary structure, such as small increases in the size of the highest end of the molecular weight distribution or the presence of long chain branching. Structural studies of HMW subunits of gluten showed branching with a periodicity of 40– 50 nm. A branched structure contributed strongly to extension resistance and bubble wall stability under large deformation. The branching structure of gluten entangles with the surroundings polymers (e.g., proteins and starch), and stretching of the flexible backbone between entanglements produces strain hardening. This model shows that the number of branches and distance between entanglements have a significant effect on strain hardening. The entanglements are produced during development of the wheat dough and can be viewed as physical constraints between segments of the polymer chains as they are not free to move past each other. Relatively small variations in the highest end of the MWD or branching can produce a large increase in viscosity and strain hardening; both are likely to have a large effect on baking performance.
The determination of the rheological properties, particularly the extensional viscosity of food systems, is complex; therefore, it is recommended that the properties for each ingredient are characterized to elucidate the behavior and interactions that each will have on foods. Alternatively, theoretical development and mathematical models, as well as new equipment and techniques, for the determination of the extensional properties of solid, semi-solid and liquid foods provide important information regarding the interactions that occur between the macromolecules that constitute food systems. Applying that information can yield food with better texture and physical characteristics.
Conclusions
10. Haward SJ, Sharma V, Butts CP, McKinley GH, Rahatekar SS: Shear and extensional rheology of cellulose/ionic liquid solutions. Biomacromolecules 2012, 13:1688-1699.
Extensional properties of liquid, semi-solid and solid foods are important in equipment design and processing to predict sensory characteristics of the final product. The first attempt to determine extensional viscosity was achieved in synthetic polymers, giving mathematical bases to apply to biopolymers and more complex systems. The design of rheometers to test the extensional properties is important to obtain more reliable measurements in complex food systems where diverse macromolecules (proteins, starch, non-starch polysaccharides and lipids) are present and can interact during processing and storage. Current Opinion in Food Science 2016, 9:98–103
References and recommended reading Papers of particular interest, published within the period of review, have been highlighted as: of special interest of outstanding interest 1.
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Fischer P, Pollard M, Erni P, Marti I, Padar S: Rheological approaches to food systems. C R Phys 2009, 10:740-750.
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Bischoff White EE, Chellamuthu M, Rothstein JP: Extensional rheology of a shear-thickening cornstarch and water suspension. Rheol Acta 2010, 49:119-129.
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Bourbon AI, Pinheiro AC, Ribeiro C, Miranda C, Maia JM, Teixeira JA, Vicente AA: Characterization of galactomannans extracted from seeds of Gleditsia triacanthos and Sophora japonica through shear and extensional rheology: comparison with guar gum and locust bean gum. Food Hydrocoll 2010, 24:184-192.
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Demirkesen I, Mert B, Sumnu G, Sahin S: Rheological properties of gluten-free bread formulations. J Food Eng 2011, 96:295-303.
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Semenova M, Dickinson E: Effects of interactions between different biopolymers on the properties of food colloids. In Biopolymers in Food Colloids: Thermodynamics and Molecular Interactions. Edited by Burlakova E, Zaikov G. Leiden, The Netherlands: Koninklijke Brill NV; 2010:232-294.
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Weiss J, Kristbergsson K, Kjartansson GT: Engineering food ingredients with high-intensity ultrasound. In Ultrasound Technologies for Food and Bioprocessing. Edited by Feng H, Barbosa-Ca´novas GV. Weiss J. Springer; 2011:239-286.
11. Yang Y, Campanella OH, Hamaker BR, Zhang G, Gu Z: Rheological investigation of alginate chain interactions induced by concentrating calcium cations. Food Hydrocoll 2013, 30:26-32. 12. Choi H, Mitchell JR, Gaddipati SR, Hill SE, Wolf B: Shear rheology and filament stretching behaviour of xanthan gum and carboxymethyl cellulose solution in presence of saliva. Food Hydrocoll 2014, 40:71-75. 13. Rodrı´guez-Rivero C, Hilliou L, Martı´n del Valle EM, Gala´n MA: Rheological characterization of commercial highly viscous, alginate solutions in shear and extensional flows. Rheol Acta 2014, 53:559-570. www.sciencedirect.com
Extensional viscosity of foods Rodrı´guez-Gonza´lez and Bello-Perez 103
14. Torres MD, Hallmark B, Wilson DI: Effect of concentration on shear and extensional rheology of guar gum solutions. Food Hydrocoll 2014, 40:85-95. 15. Sharma V, Haward SJ, Serdy J, Keshavarz B, Soderlund A, Threlfall-Holmes P, McKinley GH: The rheology of aqueous solutions of ethyl hydroxy-ethyl cellulose (EHEC) and its hydrophobically modified analogue (hmEHEC): extensional flow response in capillary break-up, jetting (ROJER) and in a cross-slot extensional rheometer. Soft Matter 2015, 11:3251-3270. 16. Szopinski D, Handge UA, Kulicke WM, Abetz V, Luinstra GA: Extensional flow behavior of aqueous guar gum derivative solutions by capillary breakup elongational rheometry (CaBER). Carbohydr Polym 2016, 136:834-840. 17. Vadodaria SS, English RJ: Extensional rheometry of cellulose ether solutions: flow instability. Cellulose 2016, 23:339-355. 18. Chen J, Stokes JR: Rheology and tribology: two distinctive regimes of food texture sensation. Trends Food Sci Technol 2012, 25:4-12. 19. Ro´z˙an´ska S, Ro´z˙an´ski J, Ochowiak M, Mitkowski PT: Extensional viscosity measurements of concentrated emulsions with the use of the opposed nozzles device. Braz J Chem Eng 2014, 31:47-55. 20. Anna SL, McKinley GH: Elasto-capillary thinning and breakup of model elastic liquids. J Rheol 2001, 45:115-138. The authors contributed to the knowledge of the extensional properties of elastic fluids (Boger fluids). This article presents a comprehensive mathematical description of deformation of the fluid subjected to extensional flow also performed; they made a comparison of the behavior of elastic extensional properties of fluids with dumbbell models and a force balance on the filament that includes viscous, elastic and capillary forces. These authors’ results suggest initial conditions for conducting experiments of extensional flow when experiments are performed experiments filament breakup. 21. Chan PS-K, Chen J, Ettelaie R, Alevisopoulos S, Day E, Smith S: Filament stretchability of biopolymer fluids and controlling factors. Food Hydrocoll 2009, 23:1602-1609. 22. Andersson H, O¨hgren C, Johansson D, Kniola M, Stading M: Extensional flow, viscoelasticity and baking performance of gluten-free zein-starch doughs supplemented with hydrocolloids. Food Hydrocoll 2011, 25:1587-1595. 23. Sachsenheimer D, Hochstein B, Buggisch H, Willenbacher N: Determination of axial forces during the capillary breakup of liquid filaments – the tilted CaBER method. Rheol Acta 2012, 51:909-923. 24. De Dier R, Mathues W, Clasen C: Extensional flow and relaxation of semi-dilute solutions of schizophyllan. Macromol Mater Eng 2013, 298:944-953. 25. Desai PS, Larson RG: Constitutive model that shows extension thickening for entangled solutions and extension thinning for melts. J Rheol 2014, 58:255-279.
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26. Clark R: Evaluating syrups using extensional viscosity. Food Technol 1997, 51:49-52. The reference introduce at the use of extensional viscosity in liquid foods. The author give background of the equipment used to measurement extensional viscosity in liquid foods and proposes as tool for food scientist that formulate products. 27. Dobraszczyk BJ, Morgenstern MP: Rheology and the breadmaking process. J Cereal Sci 2003, 38:229-245. The review describes the rheological test methods used to breadmaking and their relationships to product functionality. 28. Turbin-Orger A, Shehzad A, Chaunier L, Chiron H, Della Valle G: Elongational properties and proofing behaviour of wheat flour dough. J Food Eng 2016, 168:129-136. 29. Le Bleis F, Chaunier L, Chiron H, Della Valle G, Saulnier L: Rheological properties of wheat flour dough and French bread enriched with wheat bran. J Cereal Sci 2015, 65:167-174. This study shows the effect of bran addition on rheological features of French bread. The results are important to design bread with high dietary fiber content. 30. Clasen C: Capillary breakup extensional rheometry of semi-dilute polymer solutions. Korea-Australia Rheol J 2010, 22:331-338. The work done by this author sets out in detail the extensional flow behavior of semi-dilute solutions; clearly explains the different regimes that show when these solutions are studied with Capillary break-up rheometer (CaBER), extensional deformation curves (D(t)/D0 versus t). In addition, built from the standpoint of theoretical and experimental changes and transitions experienced by the fluid (filament diameter) studied as function of time under effect rapid extensional deformation. It also establishes the use of dimensionless numbers for the description and analysis of extensional flow behavior in semi-dilute polymer solutions (hE,app(e )). This work is recommended by the clarity with which addresses the experimental and theoretical part (dimensionless numbers) studies of extensional flow of semi-dilute solutions. 31. Paradkar A, Kelly A, Coates P, York P: Shear and extensional rheology of hydroxypropyl cellulose melt using capillary rheometry. J Pharm Biomed Anal 2009, 49:304-310. 32. Moberg T, Rigdahl M, Stading M, Bragd EL: Extensional viscosity of microfibrillated cellulose suspensions. Carbohydr Polym 2014, 102:409-412. 33. Miller E, Clasen C, Rothstein JP: The effect of step stretch parameters on capillary breakup extensional rheology (CaBER) measurements. Rheol Acta 2009, 48:625-639. 34. Zell A, Gier S, Rafai S, Wagner C: Is there a relation between the relaxation time measured in CaBER experiments and the first normal stress coefficient? J Non-Newtonian Fluid Mech 2010, 165:1265-1274. 35. Campo-Deano L, Clasen C: The slow retraction method (SRM) for the determination of ultra-short relaxation times in capillary breakup experiments. J Non-Newtonian Fluid Mech 2010, 165:1688-1699.
Current Opinion in Food Science 2016, 9:98–103
ScienceDirect Extensional properties of macromolecules Francisco Rodrı´guez-Gonza´lez and Luis A Bello-Perez There is increasing interest in the food industry in the development of new or improved commercially available food products. New methods to test the characteristics of raw materials and products are necessary. The viscosity (consistency or texture) of foods is an important rheological variable during processing because it influences the equipment design necessary for food production. Additionally, viscosity determines functionality and consumer acceptance of foods. This review focuses on extensional viscosity characterization as a tool to aim the development of novel and improved food products and processes. Extensional deformation is involved in processes as extrusion, film blowing, and fiber spinning, but it is also important in determining and understanding interactions among food components (e.g., proteins, polysaccharides, and lipids) in food products (e.g., bread, pasta, syrups, snacks, and salad dressings). Address Instituto Polite´cnico Nacional, Centro de Desarrollo de Productos Bio´ticos, Km 8.5, Carretera Yautepec Jojutla, Colonia San Isidro, C.P. 62731, Yautepec, Morelos, Mexico Corresponding author: Bello-Perez, Luis A ([email protected])
Current Opinion in Food Science 2016, 9:98–103 This review comes from a themed issue on Food physics and material science Edited by Osvaldo Campanella For a complete overview see the Issue and the Editorial Available online 9th November 2016 http://dx.doi.org/10.1016/j.cofs.2016.11.003 2214-7993/# 2016 Elsevier Ltd. All rights reserved.
Introduction In recent decades, studies on the physical properties of many food systems have increased because the components and ingredients of food systems are directly related to the quality, nutrition and energy source that they can provide consumers [1–3], particularly lipid-based foods, proteins and carbohydrates. Food quality is defined by texture, color and sensory properties, which promote acceptance and preference by consumers. Food science has devoted several years of research to the study of individual ingredients in food systems, particularly stabilizing agents. Diverse research projects have attempted to elucidate the effects and changes that stabilizing agents in foods produce Current Opinion in Food Science 2016, 9:98–103
through the formation of physical and chemical interactions between macromolecules in the food matrix. Additionally, researchers have focused on the influence of the chemical characteristics of stabilizers on changes in viscous and elastic properties [1,4–17]. Studies on food systems and their ingredients have used several techniques, including differential scanning calorimetry, rheology shear and extensional flow, to determine physical parameters [1,7–17]. This work is a review of research related to rheological studies focused on the extensional flow applied to solid and liquids foods containing polymeric and nonpolymeric food components.
Extensional properties of foods Since the middle of the last century, rheology had many applications in different fields related to the production, handling and quality control of foods [1–3,13,17,18]; rheological studies include determining the deformation and shear rate of food systems produced by external forces [1,3,18]. Determination of the rheological properties of different ingredients and foods is useful because it can elucidate the composition, texture, and structural changes observed during agitation, processing, packaging, storage and consumption [1,3,13,18]. During those processes, foods are subjected to a combination of shear and extensional flow; therefore, it is important to know the structural changes on the food components that are produced by both flows [1,18]. Extensional flow is a deformation that involves elongation of the fluid molecules along the streamlines; according to the resulting deformation, the extensional flow may be classified as uniaxial or biaxial [2,15,17,19]. Uniaxial extensional flow is the most studied and developed from a theoretical and experimental standpoint [20,21–23]. Several studies on extensional flow in dilute, semi-dilute and concentrated polymer solutions have been performed using theoretical, experimental and numerical simulations [2,4,5,10–16,20,21–25]. Trouton proposed a relationship between extensional and shear viscosity for Newtonian fluids that states that: hE = 3h0, where hE is the extensional viscosity in the steady-state and h0 is the shear viscosity in zero-shear; at a low shear rate, Tr = hE/ h0 = 3 [4,15]. Despite the need to know the extensional flow properties of fluids, it was not until the 1970s and 1980s that the work in this field was conducted because of advances in theory development and new equipment technology. That work focused on determining the hE of high viscosity shear fluids (h > 1000 Pa s) as polymer melts [2,4]. Moreover, with the advent of technology and the development of www.sciencedirect.com
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electronic components, the first measurements of the extensional properties of low viscosity shear fluids (h 0.01–10 Pa s) were performed in the 1990s [2]. Recent research has discussed that the determination of the extensional properties of low viscosity fluids is influenced by effects of inertia, surface tension, and gravity because the magnitude of these effects are of the same order than viscoelastic responses [4,10,12,13,15]. The development of products (new or improved) with specific functionalities is a daily activity of the food industry. The specific functionalities of foods are necessary because consumers require products with sensory characteristics. Foods are formulated with diverse ingredients, such as hydrocolloids (gums), proteins, sugars, lipids, etc., and they influence the functionality (e.g., texture) and acceptability by consumers. One of the most important functionalities of foods is the viscosity. The addition of hydrocolloids to food formulation produces a ‘stringy’ appearance, meaning the product does not cleanly break when the container is tilted upward. Extensional viscosity measurement was proposed as a method to determine this sensory characteristic property [26]. Methods used to test high viscosity liquids include fiber wind-up and entrance pressure drop, whereas the opposed jets method was used to test low viscosity liquids. Liquid foods were the first materials used to determine hE, an important variable that gives information on the structural features of a liquid; also, hE is used in process design calculations, control processes, food process modeling and for determining the overall and sensory quality of liquid foods. It is well recognized that hE is sensitive to the molecular makeup of macromolecules, such as the chain-length distribution (in branching polymers) and arrangement of macromolecules (mainly proteins and polysaccharides) in the food matrix [27,28,29]. The diverse type of flow occurring during food consumption and processing such as swallowing, atomization, flow through porous media, turbulent flow reduction, etc., involves extensional flow. Solid materials are found in wide variety foods; wheat doughs are some of the most complex solids systems because of their elastic behavior due to the protein fraction and imbibed starch
granules in their network. Food systems are categorized as liquid and solid foods (including semi-solids).
Methods to determine extensional properties of foods From an experimental point of view, some of the largest challenges for determining the extensional properties of fluids are equipment designed to generate a homogeneous extensional shear free flow under steady strain rate conditions [2,20,30]. Despite of the measurement challenges, recently novel instruments to characterize extensional properties of a wide range of polymeric materials has been developed. They include measurement of pressure drops through a contraction in the capillaries and channels [31], using capillary rheometers [2,32], and the use of special rheometers for extensional flow, such as filament-stretching extensional rheometer (FiSER) [4] and capillary break-up extensional rheometer (CaBER) [15,16,20,24]. Therefore, studies on the extensional flow of viscoelastic fluids and diluted low viscosity fluids in shear free conditions have been increasing [2,13,15,16,20,21]. However, few researchers have related the study and determination of the extensional properties of biopolymers in solution [1,4,5,8,10,12,13, 15,16,21,24]. Table 1 summarizes the characteristics of the different instruments that have been used to study the extensional properties of biopolymers in solution and their application ranges. The studies indicate several drawbacks to obtaining information on the analyzed systems that should be considered during experiments.
Physics of extensional properties During a study on the extensional flow of polymer solutions, it is common to establish a dimensionless number for dynamic measurements and material functions, for example the Trouton ratio (Tr = hE/h0). This expression is a function of the Hencky strain (eH = e0t) and Deborah number (De = le0), where l is the longest relaxation of the molecules constituting the polymer solution, which can be obtained from small strain oscillatory flow dynamic tests. Furthermore, methodologies established
Table 1 Summary of extensional rheometer designs and application to biopolymers in solution. Instrument type Entrance flow Opposed jet Geometries with a hyperbolic contraction Filament stretching, constant volume, medium viscosity Capillary breakup rheometry
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Flow
Shear viscosity range (s 1)
Limitations
Uniaxial extension Uniaxial extension Uniaxial extension
>1 0.01–1 0.01–500
Variable strain rate, mixed with shear Variable strain rates and strain histories Variable strain rate, mixed with shear
[31] [19] [2,32]
Uniaxial extension, constant strain rate Uniaxial extension
1–1000
Sample gripping limited to medium and high viscosity Inertial and surface tension dominate at low viscosity, variable strain rates
[4]
0.01–10
References
[4,5,8,10,12, 13,15–17]
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for determination of the extensional properties of fluids involve specimen’s surfaces exposed to such forces as gravity (g) and surface tension of the fluid (g), among others. On the other hand, some of the dimensionless numbers involving forces previously mentioned include: the capillary number, Ca = h0e0R/g, where R is a characteristic length in the experiment (i.e., the radius of the filament in cases where a CaBER instrument is used), and the elasto-capillary number, EC = lg/h0R. Finally, for experiments where the force of gravity shows a strong influence in determining the extensional properties of the fluid, the Bond number is used, B0 = rgR2/g, which establishes a relationship between the force of gravity and forces from the fluid surface tension, and where r is the density of the fluid. In some investigations related to the extensional properties of dilute and semi-dilute fluids, dimensionless numbers have been used for the analysis and interpretation of results [13,17,18]. The following section gives more details about the use of dimensionless numbers for the analysis of results obtained with a CaBER. According to the theory developed for extensional flow of viscoelastic fluids [20,30], the changes in the diameter of the filament as a function of the time (D(t)/D0 versus t) are assessed in the CaBER, and they can be used to determine the relaxation time of the fluids [10,13,14,16,17,20,30]. However, only studies of quantitative predictions for dilute solution and empirical relationships for very dilute solutions in extensional flow have been reported [20,31,33– 35]. Furthermore, in extensional flow experiments with a CaBER, the deformation behavior as a function of time is complex, and a steady state for the study of polymers in solution is not reached. Therefore, an extensional viscosity apparent (hE,app = g/Re) is considered, assuming that the extensional stress in the fluid is equal to the surface pressure (g/R) [17,20,30]. Some studies reported [17,30] that for a better interpretation of extensional flow studies on semi-dilute polymer solutions, the curves obtained with a CaBER can be divided into four different regimes. Regime I shows strong contributions from gravity and is characterized by a thinning behavior. For analysis of the flow regime, the Bond number can be used, and you can define the lower limit of the regime. For values below B0 0.2, the effect of gravity may be neglected. Regime II is below the critical Bond number and is controlled by a balance of capillary pressure (g/R) and viscous stress (hEe) on the filament. In this regime, the radius of the filament is still large, which leads to a low extensional rate, with a Newtonian behavior and Tr = 3. In the Regime II, Clasen [30] noted that the extension rate increased as a function of time, while the hE,app remained constant. In the Regime III, a visco-capillary balance is show; however, the surface pressure and hence the extension rate is high Current Opinion in Food Science 2016, 9:98–103
enough so the solution is showing an extensional thinning, originating disentanglement and orientation of the polymers molecules in the solution. In this regime, the apparent extensional viscosity decreases as the extensional rate increases. The Regime IV shows the onset of an elasto-capillary balance, where the surface pressure is in equilibrium with the elastic force of the disentangled polymer chains. Within this regime, the diameter of the filament has an exponential decay with time and then it is close to breakup (see Figures 2 and 3 of Ref. [10]). Conversely, studies in Regime IV on semi-dilute polymer solutions, which are controlled by thinning elastic behavior, have only been developed from a qualitative point of view [36]. In the case of concentrated solutions, analyses have been conducted from a comparative standpoint on the behavior of the dynamic thinning suffering strand in Regime III and IV as a function of time in order to predict when one concentrated polymeric solution would show a transition from the extensional flow regime to Regime III to Regime IV. In this sense, Anna and McKinley [20] proposed the dimensionless number, EC, which relates the elastic part of the viscous material portion to the thinning and break-up of the filament.
Extensional properties of liquid and solid foods: overview Liquid foods
Haward et al. [10] achieved shear rheological characterization and extensional flow of dilute and semi-dilute solutions of cellulose dissolved in an ionic liquid at concentrations used to produce fibers by electrospinning (fiber spinning and spraying). Extensional flow measurements determine the extensional relaxation time that is related to the elongation of the cellulose molecules through the effect of extensional stress. Haward et al. showed that more concentrated solutions exceeded the limit of entanglements among molecules, causing a significant increase in the extensional relaxation times of these solutions. de Dier et al. [24] investigated the effect of the stiffness of Schizophyllan polysaccharide molecules in solution (water and DMSO) on their extensional properties. They studied the behavior of biopolymers with concentrations in the semi-dilute regime (0.77–5.2 g/L) on the extensional properties. Those authors used a CaBER for extensional flow experiments and observed a thinning fluid filament diameter as a function of time for all solutions analyzed, using DMSO as the solvent. The graphs of the reduction in diameter as a function of time were divided into three flow regimes. The first was related to a Newtonian flow regime, in which the properties of the solvent show a strong influence. The subsequent regime showed exponential decay, and the final regime was linear before www.sciencedirect.com
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the break-up of the filament. They observed that the extensional relaxation time (lE) showed power-law behavior as a function of the concentration of the biopolymer (lE C0.9). Furthermore, aqueous solutions of Schizophyllan showed a more pronounced Newtonian regime and relaxation times as a function of concentration, showing a higher power index (lE C1.52) compared to DMSO solutions; this result was attributed to a possible increase in chain stiffness based on the solvent used. The determination of extensional relaxation times for Schizophyllan solutions in both solvents establishes the response of the macromolecules, single random coil or triple helical structure, as a function of polysaccharide concentration. On the other hand, Rodrı´guez-Rivero et al. [13] studied the effect of the concentration of alginate solutions free of salts to establish that this biopolymer has a transition from a polyelectrolyte to a neutral polymer. These authors investigated this effect with rheological characterizations, which consisted of shear flow and extensional flow experiments. These results showed that relaxation times were dependent on the concentration of the alginate solutions. The authors found that at large Hencky strain, the concentrated solutions showed a decreased in the apparent extensional viscosity; this pattern is shown when the chains of polymer are fully extended and the diameter of filament decays linearly with the time. Torres et al. [14] studied the extensional flow behavior of guar gum in aqueous solutions over a wide range of concentrations (1–10 g/dL). The authors observed a transition dilute regime and viscous behavior at levels lower than 10 g/dL, but at higher concentrations, the data showed typical behavior for solutions with entanglements and a viscoelastic material (gel-like) structure. Through extensional flow analysis, they also found that solutions with concentrations less than 10 g/dL showed an increase in the apparent extensional viscosity (hE,app) as a function of the Hencky strain (eH), which reached a constant asymptotic value. Similar behavior for high strain values (Hencky > 3) was exhibited by guar gum solutions with concentrations greater than 10 g/dL. However, they showed a maximum value of hE at a value of eH 1.2, which increased with concentration. This maximum was attributed to the presence of entanglements in that concentration range. Moreover, Szopinski et al. [16] studied the rheological properties of shear and extensional flow in polysaccharide guar gum derivatives (carboxymethylhydroxypropyl and hydroxypropyl) in the concentration regimes of semi-dilute and concentrated by dissolving the derivatives in distilled water and adding 0.1 M NaNO3 + 200 ppm NaN3. Szopinski et al. conducted an analysis of the relaxation times obtained from different experiments to establish a characteristic relaxation behavior of fluids under these parameters. These authors found that the extensional relaxation time (lE) of the different solutions was shorter than the shear relaxation www.sciencedirect.com
time that was obtained from shear flow (ls) experiments. They showed that the ratio of the relaxation times shows a power-law dependence parameter with the concentration of polysaccharide solution, that is, lE/ls (C[h]) 2. This result was attributed to two different behavior processes of the polymer chains. The first is a slow process that is related to the shear preventing entanglements of molecules, and the second process, which is carried out in the last extensional flow step, involves relaxation of the elongated individual polymer chains. The work reported by Vadodaria and English [17] presents comprehensive information related to the extensional flow theory and determination of the dimensionless numbers, Deborah (De), elasto-capillary (Ec) and Ohnesorge (Oh). They set out to study the effects of inertia, elasticity and viscosity on this type of flow. These researchers determined extensional properties, relaxation times and extensional viscosity in dilute solutions of hydroxyethyl cellulose (HEC). These authors showed, for the first time, the presence of flow instabilities (beadon-a-string) in filament flow conditions before break-up. Such instabilities were attributed to the accumulation of viscoelastic efforts in the middle of the filament, causing an ‘elastic-recoil’ effect in the molecules that constitute the biopolymer. Instabilities causing a thinning in the filament formed between the plates of the rheometer and bridge that unites the secondary fluid filament. Solid foods
The study of extensional properties of solid and semisolids foods started in the 1980s [22]. Doughs are some of the most complex and interesting food materials because of the interactions involved during their preparation, and the in-depth understanding of the system can be related to the popularity of baking products. Studies on the relaxation and elastic recovery of doughs suggest that the elastic behavior of wheat dough is due to gluten produced during the processing [22,27,28,29]. Other studies showed that some extrinsic factors, such as extension rate and temperature, as well as intrinsic factors, such as water content and flour type, play an important role in the stress–strain behavior [27]. Extensional viscosity of doughs is related to sensory properties like loaf volume. Dobraszczyk and Morgenstern [27] reported on the most common rheological methods used in bread baking and their relationship to product functionality. Wheat flour doughs with water were analyzed by capillary and channel rheometers; the shear viscosity (hs), uniaxial extensional viscosity (hE,u) and extensional viscosity planar (hE,p) were determined. The doughs had a shear viscosity of 100 Pa s and exhibited shear thinning and extension thinning behavior. It was shown that hE,u and hE,p viscosities were five orders of magnitude higher than hs, and the uniaxial extensional viscosity was larger than the extensional planar viscosity. Current Opinion in Food Science 2016, 9:98–103
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Several methods have been used to test the rheological properties of wheat dough in simple uniaxial and biaxial extensions (compression between lubricated surfaces or by bubble inflation). For wheat dough, extensional flows are important during mixing, sheeting, extrusion and pumping of pastry and dough. Most flow tests are achieved in shear under small deformations, but these conditions do not provide information about material behavior under large extension. Under extensional flow, entangled polymers (e.g., proteins and starch in wheat dough) show strain hardening, which is enhanced for polymers with a broad molecular and weight distribution, usually bimodal distribution and branching. Bread doughs show strain hardening in large deformations such as bubble expansion, and those extensional properties are an important issue in baking performance. Gluten is the main component responsible for the viscoelastic behavior of wheat dough. It is accepted that gluten proteins (gliadins and glutenins) are important for determining variations in baking quality; the insoluble fraction of high molecular weight (HMW) glutenins is related to differences in dough strength and baking quality amongst wheat varieties. Elongational rheology of HMW polymers is a sensitive indicator for changes in secondary structure, such as small increases in the size of the highest end of the molecular weight distribution or the presence of long chain branching. Structural studies of HMW subunits of gluten showed branching with a periodicity of 40– 50 nm. A branched structure contributed strongly to extension resistance and bubble wall stability under large deformation. The branching structure of gluten entangles with the surroundings polymers (e.g., proteins and starch), and stretching of the flexible backbone between entanglements produces strain hardening. This model shows that the number of branches and distance between entanglements have a significant effect on strain hardening. The entanglements are produced during development of the wheat dough and can be viewed as physical constraints between segments of the polymer chains as they are not free to move past each other. Relatively small variations in the highest end of the MWD or branching can produce a large increase in viscosity and strain hardening; both are likely to have a large effect on baking performance.
The determination of the rheological properties, particularly the extensional viscosity of food systems, is complex; therefore, it is recommended that the properties for each ingredient are characterized to elucidate the behavior and interactions that each will have on foods. Alternatively, theoretical development and mathematical models, as well as new equipment and techniques, for the determination of the extensional properties of solid, semi-solid and liquid foods provide important information regarding the interactions that occur between the macromolecules that constitute food systems. Applying that information can yield food with better texture and physical characteristics.
Conclusions
10. Haward SJ, Sharma V, Butts CP, McKinley GH, Rahatekar SS: Shear and extensional rheology of cellulose/ionic liquid solutions. Biomacromolecules 2012, 13:1688-1699.
Extensional properties of liquid, semi-solid and solid foods are important in equipment design and processing to predict sensory characteristics of the final product. The first attempt to determine extensional viscosity was achieved in synthetic polymers, giving mathematical bases to apply to biopolymers and more complex systems. The design of rheometers to test the extensional properties is important to obtain more reliable measurements in complex food systems where diverse macromolecules (proteins, starch, non-starch polysaccharides and lipids) are present and can interact during processing and storage. Current Opinion in Food Science 2016, 9:98–103
References and recommended reading Papers of particular interest, published within the period of review, have been highlighted as: of special interest of outstanding interest 1.
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11. Yang Y, Campanella OH, Hamaker BR, Zhang G, Gu Z: Rheological investigation of alginate chain interactions induced by concentrating calcium cations. Food Hydrocoll 2013, 30:26-32. 12. Choi H, Mitchell JR, Gaddipati SR, Hill SE, Wolf B: Shear rheology and filament stretching behaviour of xanthan gum and carboxymethyl cellulose solution in presence of saliva. Food Hydrocoll 2014, 40:71-75. 13. Rodrı´guez-Rivero C, Hilliou L, Martı´n del Valle EM, Gala´n MA: Rheological characterization of commercial highly viscous, alginate solutions in shear and extensional flows. Rheol Acta 2014, 53:559-570. www.sciencedirect.com
Extensional viscosity of foods Rodrı´guez-Gonza´lez and Bello-Perez 103
14. Torres MD, Hallmark B, Wilson DI: Effect of concentration on shear and extensional rheology of guar gum solutions. Food Hydrocoll 2014, 40:85-95. 15. Sharma V, Haward SJ, Serdy J, Keshavarz B, Soderlund A, Threlfall-Holmes P, McKinley GH: The rheology of aqueous solutions of ethyl hydroxy-ethyl cellulose (EHEC) and its hydrophobically modified analogue (hmEHEC): extensional flow response in capillary break-up, jetting (ROJER) and in a cross-slot extensional rheometer. Soft Matter 2015, 11:3251-3270. 16. Szopinski D, Handge UA, Kulicke WM, Abetz V, Luinstra GA: Extensional flow behavior of aqueous guar gum derivative solutions by capillary breakup elongational rheometry (CaBER). Carbohydr Polym 2016, 136:834-840. 17. Vadodaria SS, English RJ: Extensional rheometry of cellulose ether solutions: flow instability. Cellulose 2016, 23:339-355. 18. Chen J, Stokes JR: Rheology and tribology: two distinctive regimes of food texture sensation. Trends Food Sci Technol 2012, 25:4-12. 19. Ro´z˙an´ska S, Ro´z˙an´ski J, Ochowiak M, Mitkowski PT: Extensional viscosity measurements of concentrated emulsions with the use of the opposed nozzles device. Braz J Chem Eng 2014, 31:47-55. 20. Anna SL, McKinley GH: Elasto-capillary thinning and breakup of model elastic liquids. J Rheol 2001, 45:115-138. The authors contributed to the knowledge of the extensional properties of elastic fluids (Boger fluids). This article presents a comprehensive mathematical description of deformation of the fluid subjected to extensional flow also performed; they made a comparison of the behavior of elastic extensional properties of fluids with dumbbell models and a force balance on the filament that includes viscous, elastic and capillary forces. These authors’ results suggest initial conditions for conducting experiments of extensional flow when experiments are performed experiments filament breakup. 21. Chan PS-K, Chen J, Ettelaie R, Alevisopoulos S, Day E, Smith S: Filament stretchability of biopolymer fluids and controlling factors. Food Hydrocoll 2009, 23:1602-1609. 22. Andersson H, O¨hgren C, Johansson D, Kniola M, Stading M: Extensional flow, viscoelasticity and baking performance of gluten-free zein-starch doughs supplemented with hydrocolloids. Food Hydrocoll 2011, 25:1587-1595. 23. Sachsenheimer D, Hochstein B, Buggisch H, Willenbacher N: Determination of axial forces during the capillary breakup of liquid filaments – the tilted CaBER method. Rheol Acta 2012, 51:909-923. 24. De Dier R, Mathues W, Clasen C: Extensional flow and relaxation of semi-dilute solutions of schizophyllan. Macromol Mater Eng 2013, 298:944-953. 25. Desai PS, Larson RG: Constitutive model that shows extension thickening for entangled solutions and extension thinning for melts. J Rheol 2014, 58:255-279.
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26. Clark R: Evaluating syrups using extensional viscosity. Food Technol 1997, 51:49-52. The reference introduce at the use of extensional viscosity in liquid foods. The author give background of the equipment used to measurement extensional viscosity in liquid foods and proposes as tool for food scientist that formulate products. 27. Dobraszczyk BJ, Morgenstern MP: Rheology and the breadmaking process. J Cereal Sci 2003, 38:229-245. The review describes the rheological test methods used to breadmaking and their relationships to product functionality. 28. Turbin-Orger A, Shehzad A, Chaunier L, Chiron H, Della Valle G: Elongational properties and proofing behaviour of wheat flour dough. J Food Eng 2016, 168:129-136. 29. Le Bleis F, Chaunier L, Chiron H, Della Valle G, Saulnier L: Rheological properties of wheat flour dough and French bread enriched with wheat bran. J Cereal Sci 2015, 65:167-174. This study shows the effect of bran addition on rheological features of French bread. The results are important to design bread with high dietary fiber content. 30. Clasen C: Capillary breakup extensional rheometry of semi-dilute polymer solutions. Korea-Australia Rheol J 2010, 22:331-338. The work done by this author sets out in detail the extensional flow behavior of semi-dilute solutions; clearly explains the different regimes that show when these solutions are studied with Capillary break-up rheometer (CaBER), extensional deformation curves (D(t)/D0 versus t). In addition, built from the standpoint of theoretical and experimental changes and transitions experienced by the fluid (filament diameter) studied as function of time under effect rapid extensional deformation. It also establishes the use of dimensionless numbers for the description and analysis of extensional flow behavior in semi-dilute polymer solutions (hE,app(e )). This work is recommended by the clarity with which addresses the experimental and theoretical part (dimensionless numbers) studies of extensional flow of semi-dilute solutions. 31. Paradkar A, Kelly A, Coates P, York P: Shear and extensional rheology of hydroxypropyl cellulose melt using capillary rheometry. J Pharm Biomed Anal 2009, 49:304-310. 32. Moberg T, Rigdahl M, Stading M, Bragd EL: Extensional viscosity of microfibrillated cellulose suspensions. Carbohydr Polym 2014, 102:409-412. 33. Miller E, Clasen C, Rothstein JP: The effect of step stretch parameters on capillary breakup extensional rheology (CaBER) measurements. Rheol Acta 2009, 48:625-639. 34. Zell A, Gier S, Rafai S, Wagner C: Is there a relation between the relaxation time measured in CaBER experiments and the first normal stress coefficient? J Non-Newtonian Fluid Mech 2010, 165:1265-1274. 35. Campo-Deano L, Clasen C: The slow retraction method (SRM) for the determination of ultra-short relaxation times in capillary breakup experiments. J Non-Newtonian Fluid Mech 2010, 165:1688-1699.
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