Structure–composition relationships of the traditional balsamic vinegar of Modena close to jamming transition (part II): Threshold control parameters

Food Research International 45 (2012) 75–84

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Structure–composition relationships of the traditional balsamic vinegar of Modena close to jamming transition (part II): Threshold control parameters Pasquale Massimiliano Falcone ⁎, Massimo Mozzon, Natale Giuseppe Frega Department of Agricultural, Food, and Environmental Sciences, Polytechnic University of Marche, Brecce Bianche, 60131 Ancona, Italy

a r t i c l e

i n f o

Article history: Received 14 July 2011 Accepted 10 September 2011 Keywords: TBVM Vinegar Jamming Viscosity Microstructure Scaling behavior Modeling

a b s t r a c t The Traditional Balsamic Vinegar of Modena (TBVM) is a high-valuable Italian specialty that, for reasons not yet fully explained, may undergo non-equilibrium degrading phenomena involving phase separation and flow arrest caused by solidification with or without crystalline order. TBVM was probed for its microstructure and composition as well as for its flow ability under low- and high shear limits. Results indicated vinegar concentration, temperature and viscosity as three independent variables affecting the extent of solidification in TBVM. Polymer-mediated mechanisms and diffusion-limited kinetics were hypothesized for structure development. Three main experimental evidences offered a convincing proof unifying all solidification phenomena observed in TBVM under the concept of colloidal jamming transition: (i) simultaneous presence of fractallike aggregated colloids and polydispersed biopolymers; (ii) non-linear shear dependence above a critical level of vinegar concentration; (iii) a modified Krieger–Dougherty model satisfactorily described scaling behavior of relative viscosity accounting for the fractal dimension of jammed structure. Threshold for jamming in TBVM was defined in terms of critical concentration of the overall structure-active constituents (corresponding to 72°Bx and 40% w/w of the main sugars) and maximum resistance to the Newtonian flow (the onset for shear-thinning flow was achieved with a low-shear limiting viscosity of about 0.95 Pa·s). © 2011 Elsevier Ltd. All rights reserved.

1. Introduction TBVM is a high-value Italian specialty produced in the Modena province, which granted the PDO status (Protected Denomination of Origin) by the European Community (EC Council Regulation No. 813/2000). A Consortium has been legally recognized and charged to oversee vinegar farms for yielding according to the procedure coded in a specific disciplinary (GURI No. 124/2000). An independent Authority certifies the vinegar authenticity and fulfillment of disciplinary requirements according to accredited procedures (CERMET, 2009). Under a physical point of view, TBVM is an example of complex food dispersions undergoing profound chemical–physical changes throughout long-time aging. Such vinegar becomes more brown and viscous over decades. However, neither mechanism nor kinetics for texture development has been clarified until now. Time plays the central role in the overall production and the aging, the longest step, is fixed by law at a minimum of 12 years for receiving the appellation “Traditional Balsamic Vinegar of Modena” and at a minimum of

⁎ Corresponding author at: Dipartimento di Scienze Agrarie, degli Alimenti e del Territorio (Official English translation “Department of Agricultural, Food and Environmental Sciences” — Acronym “D3A”) Università Politecnica delle Marche, Brecce Bianche, 60131 Ancona, Italy. Tel.: + 39 071 220 4923; fax: + 39 071 220 4980. E-mail address: [email protected] (P.M. Falcone). 0963-9969/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.foodres.2011.09.003

25 years for granting the additional label “Extravecchio”. The latter is the most expensive vinegar on the world market. The basic technology of production can be divided into four main steps: (1) cooking of grape juice; (2) fermentation of the cooked must; (3) acetic oxidation of the fermented product; and (4) long-term aging. TBVM is the only vinegar around the world that is produced starting from cooked grape must (Solieri & Giudici, 2009) and the cooking process may take 18– 24 h or beyond. After cooking, the must undergoes alcoholic fermentation of sugars by yeasts, followed by acetic oxidation of the ethanol by acetic acid bacteria taking more or less one year to be fully completed. The aging starts inside the barrel set consisting of five or seven wooden casks having decreasing volumes. A coded procedure is followed for the annual refilling, consisting in withdrawing only a part of the vinegar from the smallest cask, which is then refilled with the vinegar coming from the next greater cask, and so on. The biggest cask receives new cooked and oxidized must; while, the smallest contains the most brown and viscous vinegar. The purpose of refilling is keeping in balance the three mass streams throughout the barrel set: the product loss by evaporation, the product withdrawn for the sale, and the leakages through the staves. Slow aging process should be allowed getting the authentic vinegar with the most appreciated rheological (Falcone, Verzelloni, Tagliazucchi, & Giudici, 2008) and sensorial properties (Giudici, Falcone, Scacco, & Lanza, 2009a; Giudici, Gullo, Solieri, & Falcone, 2009b). However, according to the law in force, titratable acidity (expressed as acetic acid equivalents) and density are the only two properties to be

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measured instrumentally and the commercial value of TBVM arises from the rank reached by sensory analysis that is usually performed by a panel of trained experts. The so-called “flowing syrupiness” is considered the most striking and clearly recognizable mouthfeel parameter. This sensory property is assessed through perception of the resistance to flow over the tongue surface or while sipping from a teaspoon as well as measuring of the time required to leave a testing bottle under poorly defined conditions. In the last years, there were evidences among vinegar producers that TBVM may undergo different solidification phenomena, all taking place under apparently “unexpectedly” conditions, either inside the casks used for aging and after its packaging inside hermetic bottles. Quasi-ordered columnar structures can be observed on side surface, a solid-like phase may parts from liquid bulk precipitating at the bottom of container or grow as a full-space spanning network. Despite the efforts of trained judges in quality assessment, vinegars granting high sensory scores and for which the solidification appeared later are quite frequent. Phrases such as gelation, coagulation, kinetic arrest, dynamic slowdown, and ergodic–nonergodic transition are usually used to loosely describe the solidification phenomena for a large number of colloidal systems and dispersed materials, under a wide variety conditions and for reasons that could appear quite unrelated to each other. Unfortunately, the major of the studies have been focused on model systems. A large number of hypotheses could be take into account based on different mechanisms and kinetics involving colloid formation and interaction both at microscopic and macroscopic scale (Cipelletti & Ramos, 2005; Ortix, Lorenzana, Beccaria, & di Castro, 2007; Zaccarelli, 2007). The main routes are spinodal decomposition, polymer-mediated depletion and absorption mechanisms but the true origin is a matter of continuous debate and ongoing researches (Archer & Wilding, 2007; Charbonneau & Reichman, 2007; Poon, 1998). Simultaneous or preferred mechanisms may concur to the solidification process, depending on the relative ratio between the amount and interaction energy among molecules and colloids. In spite of the huge works focused on model systems, few studies can be found in the literature concerning TBVM in some way related to the composition–structure relationships and phenomena of solidification. In a pioneering work, Newtonian flow behavior was observed in good quality vinegar samples appearing liquid at a visual inspection; shear-thinning behavior was observed in solidified vinegars, evidencing the shear-dependence of the bulk structure under stress-controlled conditions (Falcone et al., 2008). High-performance liquid size-exclusion chromatography, the method of choice for polymer characterization, was for the first time used to analyze TBVM composition allowing to recognize vinegar as a heterogeneous blend of co-polymers with molecular sizes spreading from 2 to beyond 2000 kDa (Falcone & Giudici, 2008). Such polydispersed compounds were supposed the end products of acidic-degradation reactions converting glucose and fructose. The two reducing sugars are present in a huge amount in TBVM, i.e. up to 40–60% in weigh, and they undergo conversion reactions activated by temperature during the cooking of the grape must (Falcone, Boselli, & Frega, 2011). The polymerization reactions take place throughout the entire period of aging with polydispersity, estimated as ratio between high-to-low average sizes, varying asymptotically toward either upper or lower limits (Falcone & Giudici, 2008). Recently, it was concluded that TBVM might undergo solidification phenomena through both equilibrium and out-ofequilibrium transitions including crystallization and jamming of amorphous flocs (Falcone, 2010). Data from High-Resolution Light Microscopy and X-ray Diffractometry proved that crystallization was caused by the ordered rearrangements of the α-D-glucose monohydrate molecules. Coupling Environmental Scanning Electronic Microscopy, Energy Dispersive X-Ray Spectroscopy and Size-Exclusion Chromatography, Falcone et al. (2011) tried to link for the first time the elemental composition to the jammed structure of TBVM. They

evidenced amorphous flocs of unidentified substances collapsing in a viscoelastic network close to jamming transition; values of C/O compatible with the presence of natural phenolics (such as grape condensed tannins) as well as of polymeric furfuryl compounds such as nitrogen-free melanoidins, and a polydispersity in the shear-thinning samples lower than in the Newtonian ones. Fe and Mg were also found higher and pH lower in the jammed fraction than in the liquid one: the pH was low enough to postulate self-assembling capacity of the vinegar melanoidins in the presence of Fe and Mg. Based on these experimental evidences, it was hypothesized that the solidification in TBVM is the result of the unbalance between two time-dependent phenomena, i.e. the increase of the bulk viscosity and the structure relaxation of such vinegar melanoidins. However, no hypotheses were made in order to identify thermodynamic and kinetic variables controlling the different solidification phenomena observed in TBVM. Moreover, predicting how colloidal and non-colloidal molecules may interact to produce desired physical states in TBVM is yet a big challenge for scientists. Forecasting is further complicated because phase changes might take place very slowly and beyond the experimental timeframe of the observations. Since TBV have a composition rich in electrolytes, including reducing sugars and metal ions as well as polymeric melanoidins, all the factors playing a role in solidification of colloidal models deserve an interest and should be taken into account to identify critical variables controlling solidification and why different structures can be observed in the jammed product. In the present work, we appointed a rapid and objective method for evaluating the extent of jamming in TBVM to be performed before sensory analysis. 2. Materials and methods 2.1. Samples Aliquots of seventy eight samples of TBVM, produced according to the specific disciplinary and for which vinegar producers claimed an aging period ranging from 12 to 25 years, were kindly provided as “good quality vinegars” by the Consortium for the protection of TBVM appellation. All samples were randomly chosen and withdrawn from different and independent vinegar farms aiming to have a broad distribution of product composition, viscosity and structure. The same Consortium provided further twenty samples that don't received the appellation after the official evaluation of the sensory quality because of their defective flowing syrupiness. Both the good quality and solidified vinegars were randomly coded using the alpha numeric labels “TBVM[n]” (with n varying from 1 to 98). An independent set of vinegar samples was also analyzed for changes in the structure during aging. The latter were withdrawn with from a six-casks barrel set, the management of which was intended for research purposes only. The vinegar age was expressed as residence time inside the barrel set and exactly calculated using the mathematical procedure appointed by Giudici and Rinaldi (2007). With this aim, the volume streams data available from beginning of vinegar production inside the barrel set were used for calculus. We were not able to calculate the true age of the other investigated vinegars, due to the lack of official data before recognizing the TBVM appellation. 2.2. Imaging and analysis of microstructure 2.2.1. High resolution light microscopy (HR-LM) All vinegar samples were imaged by HR-LM at 1000× magnification level using a Nikon Eclipse 80i fluorescence microscope. A DS5M CCD camera (Nikon Instruments Inc., Melville, NY, U.S.A.) allowed getting high-resolution details by an oil-immersion standard technique with or without standard filtering lens to enhance the image contrast of the dispersed phase. The nominal pixel sixe was 13.6 μm.

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2.2.2. Confocal laser-scanning microscopy (CLSM) Without any sample preparation, the inner structure of vinegars was also analyzed using an inverted Leica DMIRBE confocal scanning microscope equipped with a Leica TCS 4D (Leica Laser Technik) argon-krypton laser. A power of 8 mW in each line (488, 568, 647 nm) and a primary magnification of ×100 (Leica planapochromatic × 100/NA1.4 objective) were used to get images. CLSM experiments were carried out in visible-light absorption mode, with an exposure time of 1 s per scan, and 16 scans at time were averaged to produce 512 × 512-pixel 2D images digitalized into 32-bit TIF format. A sampling step of 0.46 μm in the plane of section and 0.48 μm in the axial direction were applied.

evaporation of volatile compounds, a hermetic cover sealed the top of the cone-plate geometry during tests. All vinegar samples were analyzed under static shearing and flow curves were registered over a wide range of shear rates, i.e. 10 − 2 s − 1–10 3 s − 1. All the jammed vinegars, for which the solidification status was detected trained judges for sensory evaluation, were also analyzed under strain oscillating conditions before shearing experiments. Dynamic analysis was performed in a non-destructive way to evaluate both the elastic and viscous properties: preliminary tests were aimed at finding the limits for reversible rheological response, and finally a strain sweep frequency ranging between 1 rad/s and 200 rad/s was selected to get definitive viscoelastic data.

2.2.3. Image processing The ImageJ software v1.29 (Natl. Inst. of Health, Bethseda, Md., U.S.A.; available from http://rsb.info.nih.gov/ij or ftp://rsbweb.nih. gov/pub/image-j) was used to process off-line both the HR-LM and CLSM images aiming at analyze quantitatively the vinegar structure. To include sufficient morphological detail for analysis, a minimum region of interest (ROI) was designed as a square of length based on the average size of dispersed phase imaged by HR-LM: in this way, we were able to included sufficient morphological detail for the quantitative analysis of the vinegar bulk structure. Two-dimensional images (2D-CLSM) were reduced to 8-bit format and assembled into stacks to visualize the entire volume. Then histogram equalization was performed to reduce the inhomogeneity of the luminescent background and Otsu's method (1979) was chosen among various histogrambased algorithms for image segmentation. Before processing, the stacks of 2D-CLSM images were cleaned from digital noise with a standard 2pixels-gaussian filter: ten connected voxels (a volume of 1015 μm 3) was imposed as a threshold for isolated colloids to be analyzed. Volume reconstruction of the dispersed phase was carried using the “VolumeJ” plugin through raytrace-rendering algorithm to convert 2D-CLSM stacks into three-dimensional images (3D-CLSM) with cine frame increment of 1° and 128 as classifier threshold. Two parameters were estimated by processing the CLSM images and used to describe quantitatively the dispersed phase, i.e. overall volume fraction (ϕ) and fractal dimension (Df). The former was treated as a volumetric measure of the extent of jamming in TBVM. The latter was treated as a measure of morphological complexity of the jammed structure. The algorithm used to process digital images provides the count of all voxels and thresholded voxels inside ROI for each 2D-CLSM slice, and the volume fraction of colloids as 100 * (thresholded voxels) / (count of all voxels within ROI substack). Fractal dimension was calculated with the box-counting method (Biswas, Ghose, Guha, & Biswas; 1998) as the slope of the Richardson plot (plot of the log of perimeter of the dispersed phase against the log of square boxes length used to estimate the perimeter).

2.4. Composition properties

2.3. Flow analysis under stress-controlled conditions 2.3.1. Static and dynamic experiments Vinegar samples were analyzed for their shear viscosity using an ARES-G2 rheometer (TA-Instrument, New Castle, USA) with an angular resolution of 0.014 mrad. A cone-plate tool with a cone angle of 4° and a diameter of 40 mm was chosen to apply shear stress. It was assumed that the chosen geometry allowed a perfectly homogeneous stress within the gap between cone and plate to avoid shear-banding effects. Temperature was fixed at 25 °C with an accuracy of ±0.1 °C ensured by a thermostatted bath. Samples were loaded onto the plate geometry allowing them to come out gently from a vial. The waiting time required establishing a baseline shear history was fixed of 5 h. During this time, samples were able to release the gain of molecular configurational energy eventually caused by heat transfer imposed by the programmed temperature as well as by the mechanical stress due to the sample loading. In order to prevent the

2.4.1. Sec-exclusion high-performance chromatography (SEC-HPLC) Chromatographic separation was carried out using two polymerbased columns, i.e. TSK-gel GMPWXL and TSK-gel G3000PWXL connected in series to a TSK-gel PWH guard column in a HPLC system (Jasco Corp., Tokyo, Japan). A differential refractive detector (DRI) model RI-2031Plus was used as mass-sensitive detector. A standard mixture of narrow-sized polyethylenglycole/polyethylenoxide (PEG/ PEO) polymers was used to calibrate the size of the molecules of the vinegar in the range 2·10 − 2–10 3 kDa. The chromatographic software Clarity version 2.5.6.99 (DataApex Ltd. 2007, Prague, Czech Republic) was used to process SEC-DRI data: the elution times were converted into relative molecular sizes and the Mark–Houwink parameters K (12.5) and α (0.78) provided by (Cai, Bo, Cheng, Jiang, & Yang, 2004) for aqueous solution of PEG/PEO were used for the goal. Results were reported as distribution profiles of frequency against molecular size expressed in Dalton (Da). 2.4.2. Soluble solids concentration The concentration of the overall vinegar constituents was cumulatively estimated by determining the refractive index at 25 °C with a refractometer (mod. 2WA, Alessandrini, Italy) and expressed in the Brix scale. Specific enzymatic kits provided by Roche Co. (Darmstadt, Germany) coupled with a spectrophotometer UV–vis (Jasco mod. V-550, Tokyo, Japan) were used to determine the D-glucose, D-fructose, and acetic acid, and the concentration was expressed as percent by weight. 2.5. Statistical analysis All instrumental measurements were conducted by analyzing three aliquots of the same vinegar sample. The mean and standard deviation were calculated using Statistica, ver. 7.1 (Statsoft, Tulsa, OK, USA) and Duncan's multiple-range tests, with the option of homogeneous groups (p b 0.05) were performed to determine significant differences among data. ProFit, ver. 6.2.2 (Quantum Soft, Uetikon am See, Switzerland) was used for testing validity of rheological models to fit the experimental data through the Levenberg–Marquardt's algorithm. The goodness-of-fit was evaluated by means of the mean relative error according to Boquet, Chirifie, and Iglesias (1978), using the following expression: obs calc ηi −η 100 N E¼ ⋅∑i¼1 N ηcalc where, η obs and η calc are the relative viscosity observed experimentally and that calculated by Eq. (1) or (2). N are the number of the investigated vinegars. For comparative purposes, upper and lower confidence limits of the fitting parameters were also estimated according to the following numerical procedure. Gaussian distribution of variance was assumed

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and 100 fitting routines were carried out fitting the equations to the data within two-standard deviation range. In this way, 100 independent values for each fitting parameter were obtained: finally, they were treated as an independent set of data for statistical analysis. 3. Results and discussion 3.1. Bulk microstructure Fig. 1 shows the HR-LM details of TBVM withdrawn at different levels of aging. Time-dependent aggregation process was evident, with the formation of clusterized brown flocks at increased size and structure complexity. An average size area of the suspended particles was estimated. With this aim, number, perimeter and area of the suspended particles were estimated from the two-dimensional HR-LM images using a set of ImageJ's morphological operators appointed by Gabriel Landini (plugins files are freely available on the web site http://www.dentistry.bham.ac.uk/landinig/software/ software.html updated on 15/Apr/2011). These plugins analyze the 8-neighbors pixel connectivity returning exactly the number of pixels in the particles (8-connected pixels are neighbors to every pixel that touches one of their edges or corners and they are connected horizontally, vertically, and diagonally). Disregarding the “holes”, the algorithm estimates the particle area from the center of boundary polygon of the connected pixels (using this logic, the area of 1 pixel particles is 0, for a 2 × 2 square it is 1, etc.). HR-LM stacks containing ten two-dimensional images at least for each level of aging were simultaneously analyzed; while, the center of the statistical distribution of the area data was defined the average size for the particle size. Data indicated a distribution of particle size with a maximum of frequency around 10 mm and a size tailoring towards about 100 mm for the oldest vinegar: the most frequent

average-size value was used as length scale threshold for ROI design and successive CLSM image processing. Under a physical standpoint, the product concentration on aging is the major force driving structure development in vinegar. The substitution of the water loss for evaporation with a more concentrated vinegar as required by the refilling procedure favors increasing of collision among preexisting colloids as well as between them and vinegar solutes, especially in the less viscous bulk of young vinegars. Upon aggregation, these particles collide due to their Brownian motion and stick together to form clusters. The clusters themselves continue to diffuse, collide and form yet larger clusters or droplets due to short-scale attractive interactions. This process is a non-equilibrium, kinetic growth process resulting in a polydispersed mass distribution throughout aging. Representative HR-LM images of the set of vinegars for which the exact age was not available were reported in Fig. 2. TBVM[14] and TBVM[68], resembling the aging vinegars, contain a little amount of suspended matter that appeared amorphous and of small size, i.e. lesser than 50 μm. The microstructure of TBVM[23] and TBVM[77] samples showed more irregular and connected flocs the most of which with size beyond 10 3 μm. Both TBVM[1] and TBVM[3] showed the simultaneous presence of amorphous brown flocs and ordered structures (prismatic-oblate with size ranging between 10 2 μm and 10 4 μm). Similar crystalline forms of α-D-Glucose monohydrate were identified by X-Ray analysis in a previous work (Falcone, 2010). The structure development in other colloids and soft-matter systems undergoing solidification is usually to produce on macroscopic scale a similar complex texture, with and without the formation of a crystalline order (Liu & Nagel, 2001). The imaging method used in the present work do not allowed getting sufficiently stable CLSM images for all the vinegars claimed as “good quality” samples. Difficulties were attributed to the relatively

1-year old TBVM

3,5-years old TBVM

6-years old TBVM

9-years old TBVM

11,5-years old TBVM

14-years old TBVM

Fig. 1. Typical evolution of the bulk structure of the TBVM throughout 14 years of aging inside a six-casks barrel set. High-Resolution Light Microscopy taken the images with a 13.6 pixel resolution and image size of 640 × 480 pixels.

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TBVM[14]

TBVM[68]

TBVM[23]

TBVM[77]

TBVM[3]

TBVM[1]

Fig. 2. Typical appearance of bulk structure of the TBVM that undergo spontaneous solidification. The images were taken by high-resolution light microscopy with a 13.6 pixel resolution and image size of 640 × 480 pixels.

a) 2D-slce across TBVM[23]

b) 3D-rendering of TBVM[23]

c) 2D-slce across TBVM[3]

d) 3D-rendering

of TBVM[3]

Fig. 3. Representative 2D- and 3D details of TBVM with shear-thinning and transient shear-thickening microstructure as imaged by CLSM in TBVM[23] and TBVM[3], respectively. The 2D-images have 0.45 × 0.45 × 0.46 μm voxel resolution. Rendered data (b) and (d) refer to 967 μm3 and 1308 μm3 volumes of vinegar.

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higher dynamics of the dispersed phase in those vinegars with low shear viscosity. Consequently we were able to determine both the volume fraction and fractal dimension only for the set of twenty solidified vinegars. Representative two-dimensional slices and rendered volumes of jammed vinegars were reported in Fig. 3: 2D- and 3DCLSM images are relative (a, b) to the TBVM[23] (with size of 229 μm × 103 μm × 41 μm, 967 μm 3) and (c, d) to the TBVM[3] (with size of 228 μm × 140 μm × 41 μm, 1308 μm 3). Numerical segmentation and reconstruction procedures were robust and effective to render significant details of both isolated and aggregated colloids in all jammed vinegars. The structure complexity is qualitatively visualized by the light gradient irregularity and light absorption distribution across the volume (the black background indicates the liquid bulk). A rough perimeter is well recognizable in the 2D images; a hierarchical architecture is well evident from the 3D-images. For the sake of the example, Fig. 4 shows the Richardson-plot for the TBVM[1], TBVM[3], TBVM[23], and TBVM[77] samples. Quantitative analysis was performed directly on 3D-CLSM images and results indicated that all jammed structures are fractal-like their architecture showing self-similarity from colloidal to macroscopic scale. Moreover, the fractal architecture did not changed as a function of the volumetric extent of the jamming. In fact, Df values all ranged between 1.9121 and 1.9588, while ϕ (referring to the overall volume of the dispersed phase) varied from about 4.83 up to 48.26%. The values calculated for Df allowed us to hypothesize that solidification in TBVM may be the result of diffusion-limited aggregation process, in which the rate of structure development can be limited solely by the time between the collisions of the clusters due to their diffusion. As proved for the most of colloidal and dispersed systems (Lin et al., 1989), the liquidto-solid-like transition produces fractal structures with fractal dimension of about 1.8 for diffusion-limited and 2.1 for reaction-limited cluster aggregation process, respectively. 3.2. Modeling the shear-dependence of the flow The dispersed phase is responsible in all the investigated solidified vinegars of tenuous solid-like aggregates or micro gels of flocs, that are or not able to affect significantly the flow behavior under controlled conditions. Rheological data, in fact, showed that the experienced shear rate was related to the shear stress often in a complicated, nonlinear way. Different rheological behavior was observed ranging from Newtonian response with different shear viscosities independent from the shear rate, to the shear-thinning behavior with Newtonian response detectable both at low- and high-shear rates. Representative flow

Fig. 5. Rheological data representing (a) Newtonian flow and (b) shear-thinning dependence of the TBVM flow. Continuous curve represent the best-fit of Herschel–Bulkley function used as model for rheological response in the range of shear rate 10 s− 1–103 s− 1.

curves corresponding to the samples TBVM[14] and TBVM[33] are reported in Fig. 5a and b. Three-parameters Herschel–Bulkley's function (1926) was used as a rheological model of the applied shear stress (σ) over the range of shear rate (γ) between 10 s − 1 and 103 s − 1: 0 n

σ ¼ σ 0 þ K ⋅ðγYÞ

where, consistency index (K), flow index (n), and yield shear stress (σ0) were treated as simple fitting parameters. The flow index measures the degree to which flow departs from Newtonian type. Finally, the yield stress was used to quantify the amount of stress vinegars eventually experienced before it yields and begins to flow. The goodness-of-fit indicated the equation of state satisfactorily described the flow behavior. The E was always less than 5%. For the most of “good quality” TBVM samples the rheological response was linear as indicated by n approaching to 1 and a negligible σ0. According to this rheological model, shearthinning is due to the increase of the hydrodynamic forces induced by shearing up to effectively compete with the colloid-to-colloid interaction: Newtonian response can be recovered with shear rate approaching infinity. 3.3. Rheological behavior experienced at very-low shear rates Fig. 4. Richardson plot used to estimate the scaling properties of jammed samples of TBVM through the box-counting method of 3D-CLSM images. Df is the fractal dimension of jammed microstructure.

More complex rheological behavior was observed for a number of solidified vinegars at very-low shear rates, i.e. ranging between 10 − 2 s − 1 and 10 s − 1. Under these conditions, some vinegars

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undergo reversible (transient) shear-thickening before shear-thinning behavior. Conversely, the remaining solidified vinegars exhibited shear-thinning behavior alone. Fig. 6a shows the reversible thickening response for the samples TBVM[1], TBVM[3], TBVM[23], TBVM[72] and TBVM[77] respectively. For these vinegars, the kinetics of the shear-thickening response was quasi-instantaneous and completely reversible. Thickening was interpreted as a result of a structuring process induced by hydrodynamic forces leading to the formation of transient clusters bound together. The same vinegars showing reversible shear-thickening also showed viscoelastic behavior over a large range of strain sweep frequency, i.e. 10–200 rad/s. Fig. 6b shows the dynamic mechanical spectrum registered for the sample TBVM[33] for which the elastic component followed a well-shaped trend with dynamic oscillations experienced between 10 and 30 rad/s (1.6 Hz–4.7 Hz). This finding corroborated the transient shear-thickening observed under static shearing conditions. The elastic modulus (G′) was greater than viscous modulus (G″) over the entire frequency range of strain oscillation. This behavior is typically observed in a gel-like structure under dynamic shearing. The viscous response (G″) increased with shear frequency but it was yet about 2.5 times lower than the elastic one at 200 rad/s (31 Hz): at this strain frequency, vinegar structure bears a stress of about 1500 Pa, i.e. about the stress required to completely recover the Newtonian flow at high shear rates (Fig. 5b). The elasticity in jammed vinegars was attributed to both the structural features (packing of the flocs) and weak forces

Fig. 6. Rheological data representing (a) transient shear-thickening dependence of the TBVM; and (b) viscoelastic flow behavior under dynamic shearing conditions of the TBVM also showing transient shear-thickening dependence.

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attracting colloids each other. A convincing proof was the effect a mild heating treatment in which vinegar was kept for 10 min at 60 °C in which the heat affected the vinegar structure to such an extent that its flow changed from non-Newtonian to Newtonian-like flow regime. Similar effects by temperature fall under the jamming concept depicted by Liu and Nagel (1998) for a large number of colloidal systems. Fig. 7 shows the regime transition observed for the sample TBVM[33]. A very smooth shear-thickening dependence was yet recognizable as highlighted by the red curve that passes from 0.175 Pa·s to 18.7 Pa·s from low to high shear rate providing evidence of the memory capacity of the overall structure-active constituents.

3.4. Modeling the flow behavior in low- and high-shear limits We tried to analyze the shear-thinning behavior of TBVM in lowand high-shear limits and assuming simultaneously the validity of two theories, both widely accepted for the other colloidal and dispersed systems. The first is the Liu and Nagel's (1998) model according to which temperature, density and viscosity are three independent variables controlling jamming. The second is the concentration dependence of the relative viscosity according to Krieger and DoSugherty (1959), for which mutual interaction of colloids was also taken into account according to Potanin, de Rooij, van den Ende, and Mellema (1995), and Quemada and Berli (2002). With this aim we treated TBVM as a concentrated dispersion of structure-active constituents including colloids, all dispersed in a vinegar medium consisting of aqueous solution consisting of glucose, fructose and acetic acid alone. Thus, the original Krieger–Daugherty model was modified to account simultaneously for the vinegar concentration as well as for the extent of its jammed structure: fractal dimension was assumed as an indirect measure of mutual interaction among colloids, while the Brix values were used as a quantitative estimation of the overall structure-active constituents including colloids. The refractometric measurements were carried out before the vinegar samples undergo shearing experiments: in such a way, refractometric measurements were affected by the presence of dispersed structures in their native form. We calculated only an apparent relative viscosity for the shear-thinning samples, due to the difficulty to determine by image analysis the volume fraction of the dispersed phase for the high-quality vinegars. This choice was supported by results from previous works in which the apparent viscosity of shear-thinning TBVM was about two orders of magnitude greater than Newtonian viscosity of aqueous solutions of the three major constituents alone

Fig. 7. Rheological data representative of thermal-induced transition from shearthickening to Newtonian-like flow regime.

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(Falcone et al.; 2008). Shear viscosity of such ternary solution was linked to concentration of the solutes through a second-order function (Falcone, Chillo, Giudici, & Del Nobile, 2007). As a consequence, the apparent relative viscosity was calculated dividing Newtonian viscosity to shear viscosity (ηm) of the ternary vinegar medium; while, ηm was calculated starting from the concentration data of glucose, fructose and acetic acid measured in the entire set of the investigated TBVM. The estimated values of ηm were plotted in Fig. 8 as a function of sugar concentration where the shape of each circle point indicates the experimental standard deviation in the sugar measurements (always b5%). Concerning the apparent relative viscosity, 10 s− 1 and 10 3 s− 1 shear rates where all shear-thinning vinegars approached Newtonian response were considered as the low- (LSLV) and high-limits (HSLV) for shear viscosity, respectively. Within these two shear-limits, we were able to analyze data avoiding yields stress and shear-thickening vinegars for which, notoriously, the Krieger–Daugherty function is not a suitable rheological model. The two equations proposed to describe the changes in the apparent relative viscosity under low- and high-shear limiting conditions are reported in the following:   ηlow C − Df ⋅ C max ¼ 1− C max ηm

ð1Þ

and   ηhigh C − Df ⋅ C max ¼ 1− C max ηm

ð2Þ

where, ηlow and ηhigh are the low- and high-shear limiting viscosity measured at 10 s − 1 and 10 3 s − 1, respectively. The apparent relative viscosity is 1 when the shear viscosity of the whole TBVM is equal to that of its bulk medium; while, an increase of apparent relative viscosity can be reasonably attributed to the increase of the concentration of the other structure-active constituents and to strength of their interaction. C is the concentration of the overall structure-forming constituents including colloids (expressed in °Bx). Cmax is the maximum packing fraction referring to the structure-forming constituents. Cmax was treated as the only fitting parameter. Df is the fractal dimension of jammed structure from analysis of 3D-CLSM images. In the case of TBVM, fractal dimension was used on behalf of

Fig. 8. Shear viscosity values referring to aqueous solutions simulating glucose, fructose and acetic acid composition of TBVM. Data estimated using the second-order equation provided by Falcone et al. (2007) and used for calculating the apparent relative viscosity of TBVM.

hydrodynamic shape factor (or intrinsic viscosity) present in the original Krieger–Daugherty's equation of state. Df used in the Eqs. (1) and (2) can be considered a structure-related parameters linking together the packing and strength of interaction among vinegar colloids. Df did not changed as a function of the extent of the jamming and we assumed it constant under low- and high-shear limiting for the flow. As can be inferred from data reported in Fig. 9, the apparent relative viscosity of TBVM increased with respect to a power-law function according to the proposed equation of state. To make easier the reading in the figure, η(10 s − 1) and η(10 3 s − 1) were indicated as (LSLV) and (HSLV), respectively. The horizontal and vertical bars represent two standard deviations for the experimental refractometric and viscosity measurements, respectively. Direct comparison between LSLV and HLSV allows objective discrimination among vinegars with Newtonian response from that showing shear-thinning behavior. In the first case, in fact, the arithmetic ratio equate 1; otherwise it is always lower than 1. The ratio between LSLV and HLSV can be used as a rheological measure of the extent of jamming. The goodness-of-fit (E% was less than 10%) successfully confirms the validity of both the hypotheses on which the rheological model was based and the physical meaning of Cmax is the maximum concentration of the structure-active substances including colloids at which the rheological response undergoes regime transition. The estimated values of Cmax were 77.2°Bx (±0.4) and 79.3°Bx (±0.6) for LSLV and HSLV, respectively. The two critical concentrations allow recognizing three distinct regions in Fig. 9. In the Region A, TBVM behaves as Newtonian fluid with no discernable shear dependence as HSLV is almost equal to LSLV; whereas, shear-thinning behavior may be observed in Region B as LSLV>HSLV. In the Region C, HSLV is much smaller than LSLV and liquid-like viscoelastic, transient shear-thickening and strong shear-thinning was observed. These three regions resemble that of polymeric-colloidal suspensions for which the so-called “overlap or entanglement concentration” is reached before observing non-linear flows. 3.5. The threshold of jamming and composition A three-independent parameters threshold for jamming was individuated for which the critical limits were recognized (i) 72°Bx; (ii) 40% w/w of sugars and (iii) low-shear limiting viscosity (measured at 10 s − 1) of 0.95 Pa·s. Solidification was associated to the loss of linearity in rheological response and in particular to the onset for shear-thinning behavior. This critical rheological point was

Fig. 9. Apparent relative viscosity of TBVM at the high- and low-shear limits. TBVM behaves as a concentrated dispersion of structure-active constituents for which can be recognized Newtonian flow regime in Region A, shear-thinning in Region B and viscoelastic and transient shear-thickening in Region C.

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defined by the lower but significant difference between the LSLV and HSLV. Fig. 10 shows the distribution of the jamming extent as measured by the ratio between LSLV and HSLV (in the figure indicated as HSLV/LSLV) as a function of °Bx. Statistical differences were detected starting from 72°Bx, therefore, this value was proposed as a threshold for jamming in TBVM. Rheological data allowed us to individuate also the corresponding concentration of the sugars at which jamming starts to extent. Fig. 11 shows the distribution of low-shearing limiting viscosity values with respect to both the °Bx and sugars data. The availability of three-independent properties individuating threshold for jamming makes it possible developing independent analytical procedures for monitoring the extent of solidification in TBVM. The choice of LSLV rather than HSLV allows saving time for the experimental determination of the vinegar viscosity. Moreover, TBVM producers could use routinely any low-cost viscosimeter able to experience shorter range of shear rate in quality control activities. Only for discriminative and classification purposes, principal component analysis was also performed treating concentration of sugars (Sugars) and acetic acid (AcH) as well as °Bx values and HSLV/LSLV as independent variables. The two first principal components (Factor1 and Factor2) were retained explaining more than 70% of the experimental variance and used to classify all the investigated TBVM samples, Fig. 12. As suggested by the signs and magnitude of the eigenvalues, all composition variables had an independent effect on the vinegar flow behavior. However, the extent of jamming, expressed by the decrease of the ratio HSLV/LSLV, was more correlated to the °Bx rather than the concentration of the major vinegar constituents providing compelling evidence of the minor contribute of glucose, fructose and acetic acid to the structure-capacity among all vinegar constituents. 3.6. A possible mechanism for vinegar jamming We tried to compare and discuss rheological and compositional data in order to infer a possible mechanism for colloid aggregation responsible to the extent of solidification in TBVM. SEC-profiles indicated that all vinegars contain different classes of polymeric constituents with the jammed vinegars containing less dispersed molecular size than Newtonian ones. Fig. 10 reports the molecular size distribution corresponding to the Newtonian samples such as TBVM[14], TBVM[68], TBVM[30], and TBVM[54]

Fig. 10. Extent of jamming in TBVM as a function of °Bx.

83

Fig. 11. Extent of jamming in TBVM as a function of °Bx and sugars concentration. A three-independent parameters can be used to individuate threshold for jamming in TBVM (critical limits at 72°Bx, 40% w/w of sugars and at η (10 s− 1) of 0.95 Pa·s).

against shear-thinning samples such as TBVM[77] and transient shear-thickening samples, i.e. TBVM[1] and TBVM[3]. A complex and opposite role of polymeric melanoidins could be hypothesized in vinegar jamming. While the self-assembling capacity of the vinegar melanoidins to form colloids and aggregates was recently hypothesized due the presence of Fe and Mg and to the low pH (Falcone et al., 2011), an indirect and opposite role of such biopolymers cannot be excluded. As proved for other colloidal and dispersed systems, short-ranged Van der Waals attraction could be responsible for the colloid formation according to the DLVO model (Russel, Saville, & Schowalter, 1989) but as the polymer concentration in the continuous phase increases, a critical concentration is reached above which the free polymers is excluded from interparticle space due to osmotic depletion resulting in attractive forces among particles and eventually in the flocculation (Tadros, 1982a, b). Furthermore, a fraction of the polymeric compounds include sugar-derived melanoidins that are electrically charged in nature and they could adsorb onto the surface of colloids already present in vinegar with a stabilizing effect on their dispersion. The presence

Fig. 12. Score and eigenvector distribution from principal component analysis classifying TBVM samples with respect to their rheological and composition properties.

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addressing some theoretical and practical aspects of TBVM production. References

Fig. 13. Molecular size distribution of the TBVM constituents. Data were from SEC-DRI profiles and correspond to Newtonian (TBVM[14], TBVM[68], TBVM[30], TBVM[54]), shear-thinning (TBVM[77]) and transient shear-thickening (TBVM[1], TBVM[3]) samples of TBVM.

of polymeric melanoidins into the vinegar bulk (Fig. 13) could be responsible of three counterbalanced effects that are (1) colloid formation, (2) colloid aggregation via osmotic depletion and (3) increase of the bulk viscosity that reduces the kinetics of colloid aggregation. 4. Conclusions Vinegar was investigated for its composition, molecular size distribution, and microstructure as well as for its flow behavior under stress-controlled conditions. Temperature, vinegar concentration and viscosity appeared three independent variables affecting the extent of jamming in TBVM according to the widely accepted hypothesis for jamming in other colloidal and dispersed systems. The simultaneous presence of fractal-like flocs and polydispersed melanoidins, non-linear shear dependence above a critical level of vinegar concentration, and scaling behavior of relative viscosity supported hypothesis for melanoidins-mediated mechanisms and diffusion-limited kinetics for colloid formation and aggregation responsible of the solidification in TBVM. The methodology coupling rheological and composition measurements could be an effective and affordable method for rapid and objective evaluation of the extent of jamming in TBVM before performing sensory analysis. It offers the possibility to individuate a threshold for jamming in the TBVM production, otherwise non detectable through the official procedure for quality assessment, through the determination of three independent properties, i.e. the refractive index (or Brix), the sum of glucose and fructose, and shear viscosity (measured at 10 s − 1). Acknowledgments Part of the work was supported by Università Politecnica delle Marche (Grant 2011–2012). The author is grateful to the CIGS Department of the University of Modena and Reggio Emilia (Italy) for the imaging facilities and technical support. A particular acknowledgment is due to the Prof. Paolo Giudici for its scientific support in

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