optimum cork stopper diameter for a proper wine sealing performance when modifying bottleneck diameter: a first approach

Aim of the study : This study present a theoretical model that allow establishing the proper relationship between forces and di­ ameters that take part in sealing for ensuring an adequate closure during storage time, and obtained the optimum stopper diameter for a proper sealing performance when modifying bottleneck diameter. Area of study : The proposed model is of interested to the whole cork value chain from forest owners to natural cork stoppers manufacturers. Materials and methods : The optimum cork stopper diameter depends mainly on stopper quality and the compression rate applied in the bottling operation. In this study, we establish the stopper diameter when reducing bottleneck diameter, applying a compression rate of 33% when corking, and for natural cork stoppers which quality allows to recover its initial diameter to 96% after 24 h since compression. Main results : For a bottleneck diameter of 18 mm, the value of the stopper diameter should be at least of 22.3 mm, and for a bottleneck diameter of 17 mm, the value of the stopper diameter should be at least of 20.3 mm. Research highlights : These results try to solve one of the main worries of natural cork stopper manufacturers, which is the scar­ city of raw cork suitable for manufacturing them. However this study is also of interested to forest owners because the increment of cork suitable for natural cork stoppers manufacturing means an increment in cork value. compression rate; diameter recovery; relaxation force; relaxation ratio. abbreviations used: Ds (Cork Stopper Diameter); Dg (Caliper Diameter the Corking Machine); Db (Bottleneck Diameter); Dr (Recovered Diameter); Fc (Compression Force); Fr (Relaxation Force); CR (Compression Rate); RR (Relaxation Ratio); RD (Diameter Recovery).


introduction
Wine sealing is an important step of the wine making process. Its main priority is maintain wine quality during bottling, storage and shipping. Premium quality wines have traditionally been packed mainly in glass bottles sealed with natural cork stoppers. Glass, as an inert material, assures maximum impermeability towards oxygen, while cork stoppers foster a good evolution of wines by allowing slow migration of oxygen (Caillé et al., 2018). Natural cork stopper is the most valuable product that can be manufactured with high quality cork.
The main physical-mechanical variables dealing with a good sealing performance are: stopper density, the 2 compression force required to compress stopper diam eter to caliper closure diameter, the relaxation force exerted by the stopper against the glass surface after inserted into the bottle, the diameter recovery evolution after compression and the extraction force the final consumer must applied to extract the stopper Sánchez-González & Pérez-Terrazas, 2018). During the bottling operation, the stopper is inserted into the bottleneck by compress ing it with a caliper. Therefore, there is a close relation ship among stopper diameter, bottleneck diameter and caliper closure diameter. The stopper dimensions were settled dependent on the standardized inner dimensions of the bottleneck, in 24 x 44 mm as the optimal stopper dimensions for sealing most of still wines. Regarding caliper closure diameter, this is related with stopper diameter through the compression rate that is the ratio between the uncompressed stopper diameter and com pressed diameter. A good practice when bottling con sists in not applying compression rates above 33 % (Sánchez-González & Perez-Terrazas, 2018), because of the negative effect it has on the elasticity, the dia metric recovery and the relaxation force exerted by the fitted stopper in the bottleneck.
In order to produce natural cork stoppers of 24 mm, it is needed that harvested cork planks have a thickness of more than 27 mm. The reason is that the stopper axis is parallel to the cork oak stem axis. In a cork harvest, the percentage of cork suitable for natural cork stoppers manufacturing is very variable ranging from 35 % to 60 % (Rives et al., 2012;De mertzi et al., 2016). In addition, cork production is decreasing due to lack of regeneration and ageing of cork oak stands (Pasalodos-Tato et al., 2018). How ever, the demand for natural cork stoppers has in creased which is reflected in the evolution of natural cork stoppers exports in world leader countries in in the cork sector, Portugal and Spain (APCOR, 2018).
Given this situation, it is worthy to consider the pos sibility of reduce stopper diameter in order to increase the quantity of cork suitable for natural cork stopper manufacturing, but maintaining or improving the re quirements for a good sealing performance. For this purpose is needed to modify stopper diameter and bot tleneck diameter. The main aim of this study is to es tablish the proper relationship between forces and di ameters that take part in sealing for ensuring an adequate closure during storage time. We assumed that a proper closure is achieved when the relaxation ratio , remains constant irrespective of the values of the aforementioned diam eters. Based on that assumption, we intend to obtain the optimum stopper diameter for a proper sealing when reducing bottleneck diameter.

material and methods
A sample of natural cork stoppers were used to de termine the optimum stopper diameter for a proper sealing when reducing bottleneck diameter. To do so, in a first step it was obtained which values should have the coefficient k for a proper sealing when using cork stoppers of high quality using bottlenecks of different diameters, by the execution of two mechanical tests under standard bottling conditions, a compression test and a relaxation test. In a second step, and assuming as the optimal sealing conditions the standard ones, i.e. cork stoppers of 24 mm of diameter fitted in bottle necks of 19 mm of dimeter, the stopper diameter was calculated.

Sampling
A randomly selected batch of 500 one-piece natural cork stoppers of the first commercial quality and nominal dimensions of 24x44 mm were sent to the INIA-CIFOR cork laboratory from a Spanish cork stop per manufacturer. A sample of 35 cork stoppers se lected with the criteria of having similar values of density were used. This criteria was applied to try to play down the influence of stopper density in its me chanical properties (Anjos et al., 2008;Anjos et al., 2014;Rosa & Fortes, 1988). The sample of 35 natural cork stoppers were randomly subsampled in 7 groups with 5 stoppers per group, corking each group using different diameters of the tube that simulate bottleneck. Those diameters were 17, 18, 18.4, 19, 20, 21 and 22 mm. Cork stopper were acclimatized at 20 °C and 65 % of relative humidity. Stabilization was considered to have been achieved when the weight variation in two consecutive weighings was less than 0.024 g (which is equivalent to a humidity difference of 0.1 %). Once acclimatized, stoppers were weighed and measured using Mitutoyo ID-F150 digital vernier calipers. Room conditions during the measures were an ambient temperature of 20 ºC ± 4 ºC and relative humidity of 50% ± 10%. Stoppers density was cal culated as already reported in González-Hernández et al. (2014).

mechanical tests
The biaxial compression force (Fc) in the model ling sample set was measured using a semiauto matic corking machine equipped with a load cell (UTILCELL, Mdo: 650 SNo 460775(02) Emax: 3 Optimum cork stopper diameter when modifying bottleneck diameter 2Tn), as already reported in González-Hernández et al. (2014). Cork stoppers were inserted in each bottleneck tube by applying the same compression rate of 33 %.
The diameter recovery evolution of each cork stop per was assessed by measuring the stopper diameter 24 hours after the test with Mitutoyo ID-F150 digital vernier callipers.
The relaxation force (Fr)

Statistical analysis
For each measured variable, the mean, standard deviations, minimum and maximum were calculated. In a preliminary analysis, the assumptions of normal ity, independence and homogeneity of the variance were verified. The hypothesis of no differences among stopper included in each subsampled group was tested using ANOVA. The differences were examined using pairwise comparisons according to the Tuckey test. All tests were conducted at the α=0.05 level and all analy ses were carried out using the SAS software version 9.4 (SAS Institute Inc., 2016).

results and discussion theoretical model
The strain-stress curves described for cork by Fortes et al. (2004) and Mano (2002) are very similar to those that take place during corking. In the formers, the compression load is done in a unique axial direc tion, while during corking the cork stopper is sub jected to a concentric compression. Fig. 1 shows a schematic depiction of the evolution of the stress strain hysteresis loop during corking, sealing period and uncorking.
During corking, the cork stopper diameter is com pressed from its initial value (Ds) to the caliper diameter of the corking machine (Dg). The stress applied increases to a maximum value of compres sion (Fc, point C in Fig. 1) describing the loading curve 0C. At point C, when the cork stopper is fitted in the bottleneck of diameter (Db), the stress is re duce from the compression force (Fc, point C in Fig. 1) to the relaxation force (Fr, point H in Fig.  1) and simultaneously the diameter of the cork stop per is partly recovered from Dg to Db, describing the unloading curve CH. When the cork stopper is fitted in the bottleneck the diametric recovery goes on describing the whole unloading curve until reach ing the maximum value of the recovered diameter (Dr) that the stopper will reach as long as the wine is bottled.  The similarity of triangles ACF and ABE allows get ting to: For a given value of bottleneck diameter (Db), the values of Fc and F1 can be related through a coef- Replacing k in (2) we get to: If we take into account that the recovered diameter (Dr) can also be expressed as a function of the diameter recovery (RD) and the caliper closure diameter can also be expressed as a function of the compression rate (CR). Then equation (4) can be expressed as a function of those variables: Where Fr is the relaxation force; Fc is the compres sion force; k is the relaxation coefficient, Ds is the stopper diameter, Db is the bottleneck diameter, Dr is the recovered diameter, Dg is the caliper closure diam eter, RD is the diameter recovery and CR is the com pression rate. The relationship between Fr and Fc can be expressed by means of the relaxation ratio (RR) : Where k values depends on the quality of cork stoppers, the compression rate applied when corking, the bottleneck diameter and the stopper diameter. If we were able to determine which values should have the coefficient k for a proper sealing when using cork stoppers of a given qual ity, applying the same compression rate and using different bottlenecks diameter, we could establish the proper stopper diameter for each bottleneck diameter by applying the following equation obtained from equations (5) and (6): The stopper diameter depends mainly on the bot tleneck diameter (Db), the compression rate (CR) and the stopper quality, because the relaxation ratio (RR) and the diametric recovery (RD) depends on stopper quality and the compression rate applied in the bottling operation (Anjos et al., 2008;Fortes et al., 2004;González-Hernández et al., 2014).

optimum stopper diameter when reducing bottleneck diameter
The statistics values for each measured variable are shown in Table 1. ANOVA indicated no significant differences in biaxial compression force (Fc) values among subsample groups (F value = 1.92 p value = 0.1772). This result was expected because the same compression rate was used. The compression force takes mean values of 228.91 daN, between 193.80 and 261.00 daN ( Table 1). These values are very similar to those obtained by previous studies (Beorlegui, 2014;González-Hernández et al., 2014;Prades et al., 2014) for natural cork stopper of the same quality which is expected since measurement was taken in the same way using a clamp or caliper which means that are values of biaxial compression.
The maximum relaxation force (Fr) applied by each stopper against the bottleneck tube, and measured using the device developed in the INIA-CIFOR Cork Labora tory (González-Hernández et al., 2012), shows sig nificant differences among subsampled groups of stoppers (Table 1 and Fig. 2) except for 18.4 mm which mean values is not significantly different from the man value for 18 mm and 19 mm. As expected, the relaxation force decrease as the bottleneck diameter increase when using natural cork stoppers of 22 mm of diameter.
The diametric recovery (RD) after 24h from com pression do not show significant differences among subsampled groups of stoppers. Since the same com pression rate was applied in all of them, this result was also expected. The mean value for the whole modelling sampled set was 95.929 % ranging from 94.539 % to 97.433 %. Then, it can be considered that after 24h after compression to 33 % the tested natural cork stop pers recovered 96 % of its initial diameter. In Fig. 1, Dr refers to the value of the recovered diameter that cork stopper would reach 24 h after being fitted in the bottleneck, we are going to consider that this diameter is the 96 % of the stopper diameter. Following this assumption, we have calculated k values for the model ling sampled set ( Table 1).
The relationship between bottleneck diameter and k follows a parabolic pattern (Fig. 3)

conclusions
The theoretical model presented in this study allow to establish the proper relationship among stopper di ameter, bottleneck diameter and compression rate for ensuring an adequate closure during storage time, and obtained the optimum stopper diameter for a proper sealing performance when modifying bottleneck diam eter. In this study, we establish the stopper diameter when using bottleneck diameter of 17 and 18 mm, ap plying a compression rate of 33% when corking, and for natural cork stoppers which quality allow recover ing a 96 % of its initial diameter 24 h after compres sion. These results are a first approach to one of the main worries of natural cork stopper manufacturers, which is the scarcity of raw cork suitable for manufac turing them. The proposed model must be validated in oncoming studies, applying this reduction, and consid ering both, cork stoppers quality and wine sealing performance. However these results are also of inter ested to forest owners because the increment of cork suitable for natural cork stoppers manufacturing means an increment in cork value.