Capillary penetration for the development of a method for the assessment of shelf-life of foods

Temperature sensitive foods require monitoring of their time–temperature history in order to assure their safety and high quality. The same holds for other perishable products such as medical and pharmaceutical. The best means to have information on the time–temperature history of a product is by having measurement of these variables along the whole product shelf-life. As an answer to this need several time–temperature indicators have been developed and commercialized for monitoring the quality of food products. In this work a full history time–temperature indicator (TTI) has been designed and developed based on capillary penetration of safe and low surface tension liquids in micro porous polyethylene porous media. For the development of the indicator the appropriate porous media and penetration liquids were selected and capillary penetration of the selected liquids took place at two different temperatures. Based on the results of the capillary penetration experiments the TTI was developed and a prototype was evaluated in a food product in order to assess its capability to be used in food packaging. The results showed that the TTI is simple in use and could provide a quantitative and easy-to-read response. Moreover, the response of the TTI could be calibrated by changing several design parameters, in order to match the quality deterioration kinetics of the specific food product to be monitored.


Introduction
Time-Temperature Indicators (TTls) are small, inexpensive devices, providing easy to read, visual information of the thermal history of perishable products such as food, pharmaceutical and biomedical products and reflect cumulatively the time-temperature history of the product and their operation is based on an irreversible mechanical, chemical, enzymatic or microbiological change. They are typically designed in the form of a label, not requiring external sources of energy when in operation. In contrast to electronic devices (e.g. temperature recorders), TTls are suitable for application onto the packaging of single product items, due to their small size. They can be used to monitor the storage conditions, with reference to temperature, of perishable products both before purchase (from production to the point of sale) as well as during the period following purchase in which the end user has been in the possession of the product [1][2][3][4][5].
TTls may be classified into two main categories full-and partial-history type. Full-history TTIs change their state continuously whatever the temperature, thus giving an integrated time-temperature measure relative to the entire life of the product to be monitored. On the other hand, partialhistory TTIs have a temperature threshold above which the indicator manifests observable changes that vary according to the time-temperature integral. Based on the working principle TTIs could be classified into four categories biological, chemical, enzymatic and physical [2][3][4][5][6][7][8][9][10]. Regarding the physical TTIs there various categories such as diffusionbased, nanoparticle-based, nanofiber-based etc. [11][12][13][14]. The diffusion-based TTIs are based on a temperature-dependent diffusion of a colored chemical substance through a porous matrix. The measurable response is the distance of the proceeding diffusion front of colored chemical substance from the origin and the diffusion of chemical substance may depend on different factors, such as time and temperature, resulting in a clear and instantaneous color change. Most of the commercially available TTIs such as 3M Monitor-Mark™ and Timestrip® [15][16][17] are diffusion based informing the user on the exposure of the product at temperatures higher than recommended or on the product freshness and the remaining shelf-life [2,[4][5][6][7].
Moreover, for the successful application of a TTI prior determination and modeling of the t-T dependence of the shelf-life is required [5,[18][19][20]. Ficks law of diffusion and the Arrhenius equation are the main models describing diffusion based TTI's response [11,21,22]. To the authors knowledge there is no previous TTI described as capillary penetration based in porous media.
Diffusion and chemical reaction based TTIs present several disadvantages that do not allow their commercialization and application. Regarding technical issues, one of the major problems is the aging of the substrate and diffusing or reacting liquid affecting their accuracy [5]. Another important issue is their stability during storage since some of them require specific storage conditions [6,23]. In addition, some TTIs contain toxic compounds that can migrate into the food and contaminate it [5]. Furthermore, the TTIs response is often affected by other variables than the time-temperature profile (humidity, light, oxygen etc.) [5]. The use of cellulose as a diffusion medium in commercially available TTIs reduces their accuracy since ambient humidity can affect their response [5]. Regardless technical issues, the cost of currently available TTIs is a major factor that keeps them off the market for food applications since the cost is too high with respect to the generally low added value of food products.
Based on the above the preliminary requirements for a TTI can be summarized as follows: (i) reliability (ii) simple use, (iii) low cost (iv) unaffected by other conditions than temperature and time (v) small in size, (vi) easy to integrate into the package, (vii) ability to provide simple, continuous, and understandable indications (viii) use of safe and recyclable materials (ix) resistance to normal mechanical abuse [18,19,24].
Capillary penetration in porous media applies in a broad range of applications including textile, ceramic, printing, and pharmaceutical industries [25][26][27]. Recently there is an increasing development of diagnostic tests and rapid methods that utilize porous media and the principles of capillary penetration [28,29]. For spontaneous capillary penetration to occur in a porous medium the porous medium material/ liquid contact angle (θ) needs to be < 90 °C. The rate of capillary penetration depends mostly on the liquid (viscosity, surface tension and density) and porous medium properties (liquid/solid contact angle and pore sizes). Additionally, in the case that θ is < 90° and that, the effect of gravity on liquid penetration is absent or negligible, the flow in the capillary is laminar, the liquid meniscus is hemispherical, and an adsorbed film of the penetrating liquid pre-exists or forms previous to liquid penetration [30] the capillary penetration could be described by the Lucas-Washburn equation [31,32]: where h is the distance traveled by the liquid in time t, r eff the effective pore radius of porous medium, γ the surface tension of the liquid, η the viscosity of the liquid and θ the liquid-porous medium contact angle, The aim of this work is to apply the principle of capillary penetration in porous media in order to develop and evaluate a first prototype of a full-history TTI that it will provide a quantitative and irreversible indication of the time-temperature history of a product. The novelty of the TTI is not based only on its principle but also on the fact that the whole time-temperature history of the product is measured in contrast to most so-called diffusion based TTIs where temperature changes are recorded above a predefined temperature. Additionally, the TTI is designed so that it is simple in use, economic, safe for foods and medicine.

Materials
Polydimethylsiloxanes (PDMS) (Fungilab, Spain) with nominal viscosities of 1000 (S1000), 5000 S(5000), 12,500 (S12500), 100,000 (S10000) mPa s were used as penetrating liquids. Siloxanes oils were selected since they have high viscosity which does not change during the typical storage time of food products and are non-toxic materials used as an antifoaming agent in cooking oils. Additionally, PDMS is unaffected by oxygen in the atmosphere or humidity. Moreover, Sudan III (Sigma Aldrich) was used as a dye to colored siloxane oils for better visualization of penetration into the porous medium and as another option any food grade oil soluble dye could be used in order to ensure the safety of food products.
A polyethylene (PE) porous medium with nominal pore sizes 40-100 μm (Porex, Germany) was selected for the capillary penetration experiments and the development of TTI. The selection of the PE was made as it was found [33] that the capillary penetration rate in PE is unaffected by the ambient humidity. PE is also unaffected by atmospheric oxygen.

Principle and design of the TTI
The development of the TTI is based on the spontaneous capillary penetration of a low surface tension, spreading liquid in a polymeric porous medium. A schematic representation of the TTI components is shown in Fig. 1 The selection of the porous medium, the penetration liquid properties and the pore sizes are especially selected to be θ < 90 0 and constant during capillary penetration, gravity effects on the rate of penetration are negligible and the rest of conditions hold so that the Lucas-Washburn equation which describes capillary penetration can apply. This minimizes the variables affecting capillary penetration. The same principle was used earlier for the determination for the development of a rapid method for the determination of frying oil quality [28,34,35]. Based on the above if the porous medium characteristics as well as the penetrating liquid characteristics are adequately selected then the rate of capillary penetration of the penetration liquid into the porous medium will depend only on the η and γ of the liquid which change as a function of temperature and from Eq. (1): and since γ = f(T) and η = f(T) is h = f(t, T). Furthermore, the relation of η and T follows the Arrhenius equation [36] and the relation of γ and T follows the Ferguson's equation [37]. Consequently Eq. (2) could be written as: where γ 0 is a constant for each liquid, n is an empirical factor, T C is the critical temperature, A is the pre-exponential factor related to the viscosity of the liquid at a given temperature, E α is the exponential constant that is known as activation energy and R is the gas constant. Different types of liquids can be used as penetrating liquids for developing such a method but low surface tension, spreading, non-volatile liquids are preferable. In some TTIs fatty acids are used as penetration liquids [11]. Fatty acids have all the above properties. The selection of the molecular weight of fatty acids is such that they are solid below a given temperature. Nevertheless, once their melting temperature is surpassed they flow rapidly in the porous substrate which is often faster than the product quality deterioration. This is why different strategies in the geometry of the substrate are being used to control their flow [11].
In the present work PDMS of different molecular weights were used as penetrating liquids for the TTI. PDMS are low surface tension, spreading liquids that form a precursor film during penetration [31]. In addition PDMS are available at different molecular weights and a broad range of viscosities (5-2.000.000 mPa s) and therefore different storage conditions could be covered. PDMS do not solidify under custom food storage conditions and temperature variations make them flow in a porous medium slower or faster (Eqs. [2][3]. This makes the combination of the porous medium PDMS system to be able to cover the whole storage time as it will be shown in the following paragraphs.
In order to easily visualize the flow of PDMS in porous media an oil soluble dye could be used such as sodium or potassium salts of copper complexes of chlorophyllin, annatto etc.
A schematic representation of the function of the TTI is shown in Fig. 2. According to Fig. 2 the beginning of the function of the TTI starts with pressure of the liquid reservoir so that the film separating the reservoir and the porous medium breaks and the allows the liquid to come into contact with the porous medium and penetrate (Fig. 2a). Then the liquid penetrates at different rates according to the time-temperature profile (Fig. 2b), until it reaches the mark witch shows the end of product life-time.

Capillary penetration experiments
The capillary penetration experiments at 25 ± 1 °C took place using the set-up as previously [34]. The penetration liquid was put in an optical glass cell (704.001-OG, 32.5 × 35 × 35 mm, Helma Analytics) and then the porous substrate (20 × 50 mm) was put into contact with penetration liquids. The penetration front details were acquired with the aid of a CCD videocamera (XC-73CE, Sony). The position of the wicking front in the acquired images was determined by an especially developed algorithm, program and software [38].
For the experiments at 4 °C the optical glass with the penetration liquid as well the porous substrate were put in Fig. 1 Schematic representation of TTI a refrigerator set at 4 ± 4 °C. Once both the liquid and the porous medium had obtained the desired temperature they were put into contact as shown in Fig. 3. The penetration front details were acquired by a camera (SX230-Canon) and the position of the wicking front of images was determined as above.
All capillary penetration experiments in both temperatures were performed in duplicate.

Viscosity and surface tension of penetrating liquids
The surface tension measurements of all PDMS were performed with the pendant drop method (CAM 200, KSV, Biolin Scientific, Stockholm, Sweden) and axisymmetric drop shape analysis (Attension Theta Software, V. 4.1.9.8, Biolin Scientific, Biolin Scientific, Stockholm, Sweden). The surface tension of PDMS were determined as in [35]. All measurements were performed in triplicate.
The viscosity of PDMS at 25 °C was measured by the provider. The viscosity of PDMS at 4 °C was measured by using a DMA rheometer (Bohlin C-VOR 150, Malvern Instruments, Ltd, Worcestershire, UK) equipped with a Peltier plate system (− 30 to + 180 °C) for temperature control. Temperature was regulated at 4 °C and all measurements were performed in triplicate.
The viscosity and surface tension values of PDMS at 4 and 25 °C are presented in Table 1 Results and discussion

Capillary penetration experiments at 25 °C and 4 °C
In order to validate the working principle of the proposed TTI, capillary penetration experiments took place at 25 °C using the different viscosity penetration liquids. Figure 4 presents h 2 as a function of time (h 2 vs t) during capillary penetration of different viscosity PDMS in the PE porous medium. According to Fig. 4 the dependence of h 2 vs t is linear and this is a first indication of the applicability of Eq. (1) for the development of TTI. Since polydimethylsiloxanes are considered completely wetting liquids for which cosθ = 1 [34] the data presented in Fig. 4 could be used for the calculation r eff of PΕ porous medium using the Eq. (1) and the values of viscosity and surface tension of Table 1. For the determination of r eff the wicking rate was plotted as in [33,34] and presented in Fig. 5 The fitting of the points to the straight line passing through the origin is excellent as also verified using linear regression analysis and the r eff of PE was found equal to 2.59 μm.  The data of PDMS penetration at 25 °C show the performance of the system and TTI under development at this temperature. As can be seen at 25 ± 1 °C the dependence of h 2 vs t is rather linear and that repetitions of the experiment at a temperature varying ± 1 °C provide virtually the same results in terms of capillary penetration rate (R) (Fig. 4). Consequently at ± 1 °C the output of the TTI is virtually the same.
In continuation, in order to evaluate the applicability of Eq. (1) in lower temperatures capillary penetration experiments using the various siloxane oils took place at 4 °C (common temperature of storage of refrigerated foods and other perishable products) and the results presented in Fig. 6. Experiments at 4 °C took place in a commercial refrigerator and the variations of penetration rate as a function of time reflect the temperature variations in the refrigerator such variations present first indications of the sensitivity of the TTI to changes in temperature. Furthermore, for the higher viscosities (S12500, S100000) the experiments took place exceeding typical working hours and therefore there are some time gaps in the measurements. According to Fig. 6 the dependence of h 2 vs t is mostly linear. Some variations which are observed in the lines of S12500 and S100000 in Fig. 6 could be attributed in the variations of the refrigerator's temperature. Finally, in order to investigate under what temperature variation the TTI provides a different output experiments took also place at 22 and 24 °C. For these experiments S1000 was used as the penetrating liquid. The results (Table S1) show that the differences on capillary penetration rates at two temperatures were marginal but statistically significant. This is indicative that the threshold of the TTI is between 1 and 2 °C.
Comparison of Figs. 4 and 6 indicate a significant decrease in capillary penetration rate due to the decrease of temperature from 4 to 25 °C. Such a results is a first good indication that taking a food or medicine out of the refrigeration temperature could have a sensitive response of the indication. This can be also observed in the supplementary material presenting a different representation of the same data (Fig. S1).

Analysis of capillary penetration experiments and TTI response
Given the linearity of h 2 /t response the applicability of Lucas-Washburn equation for the case of our experiments (Figs. 4, 5, 6) the parameters of Eq. (2) could be varied in order to calibrate the response of TTI according to the required shelf-life of the perishable product.
The results of Table 1 show that the surface tension of PDMS is practically unaffected by the temperature for the temperature range examined herein (i.e. the change of γ is ~ 1% between the measured values in 4 and 25 °C and it is expected to be ~ 1% for the temperature range down to − 26 °C which are custom storage temperatures in commercial freezers). In addition, the PDMS molecular weight Fig. 4 Capillary penetration rate of PDMS (S1000, S5000, S12500, S100000) in the PE porous medium at 25 °C  Capillary penetration rate of siloxanes oils (S1000, S5000, S12500, S100000) in the PE porous medium at 4 °C does not affect the surface tension very much. Consequently, with little error Eq. (3) can be deduced into: Therefore for the adaptation of the TTI according to the shelf-life parameters of the perishable products three parameters can be varied (a) the viscosity of the penetration liquid, (b) the r eff of porous medium and (c) the length (size) of the TTI.
Some simple calculations were performed in order to evaluate the range of possible values of the functioning time of the TTI. Time is typically set equal to the shelf-life of the food product to be monitored, when stored at the recommended temperature. The length of the TTI was fixed to 3, 5, 7 and 9 cm and the relation between the penetration liquid and the operation time of TTI was calculated for temperatures equal to 4 °C and 25 °C that covers the storage at refrigeration and ambient conditions. According to the results reported in Fig. 7a and b, the TTI can be configured in order to operate for different shelf-life ranges by changing the PDMS molecular weight (and therefore its viscosity) and the porous medium height. As a consequence, a broad range of operating conditions such as refrigeration, freezing, ambient can be covered. In fact, the operation time could be increased up to 3 years, changing the length of the TTI, the r eff (use of a PΕ porous medium with lower pore sizes for the construction of TTI) and the viscosity of the penetration liquid (use of PDMS with higher viscosity values). Laboratory prototypes of the TTI were developed and used for experimental validation. The prototype (Fig. S2) consists of the PE porous medium (20 × 80 mm), the reservoir with the colored penetration liquid, the separation film and a mark that denotes the end of shelf-life of the product. Pressing the liquid reservoir the penetration liquid comes into contact with the TTI body and the operation of the TTI starts.
In order to validate the TTI functionality, a prototype was integrated on a food product and stored under constant temperature conditions and the progress of liquid penetration was recorded as a function of time. The food product selected for TTI evaluation was milk in a tetra-pack package which had recommended storage temperature of 4 °C and a shelf-life equal to 7 days. Taken into account the results of Fig. 7a, S5000 was selected as penetrating liquid and the distance between the edge of the TTI that was in contact with the penetration liquid and the mark which indicates the end of product self-life was equal to 5 cm. The package of milk was stored at the refrigerator at 4 °C and the progress of the penetration of S5000 in TTI (distance) was recorded every 24 h (Fig. 8).
As it can be seen from Fig. 8, which reports the progress of the S5000 as a function of time and the penetration front progress, the distance covered by the liquid was 5 cm in 7 days. This is in accordance with the calculations were performed based on the results of Fig. 7a and the shelf-life of the milk. The obtained results validate the effectiveness of TTI in typical food storage conditions. As also shown in Fig. 7 for longer storage times the higher viscosity liquids can be used.
In order to estimate the performance of the TTI under variable time-temperature conditions Eq. (4) was used. The case of pasteurized milk with storage time of 7 days (168 h) was examined and two different conditions were applied (a) storage temperature is kept constant at the suggested by the manufacturer refrigeration temperature (i.e. 168 h at 4 °C) ( Fig. 9) and (b) the cold chain is broken at several instances during 7 days storage (for 48 h at 4 °C, then for 1 h at 25 °C, then for 95 h at 4 °C, then for 0.5 h at 25 °C and finally for 23.5 h at 4 °C). For this case the S5000 was selected as a penetrating liquid and the mark indicating the end of product self-life was set to 5 cm. As can be seen from Fig. 9 the variation of the temperature affects the progress of the penetration. In further detail, the increase of storage temperature induces an increase in penetration rate and consequently an increase in the distance covered by the penetrated liquid. The distance covered by the liquid in case of the TTI that stored at 4 °C for 168 h was equal to 5 cm after 168 h that corresponds to the end of the product self-life. On the contrary the TTI that stored at 4 °C with periods at 25 °C the liquid covered the distance of 5 cm after 80 h and after the storage at 25 °C for 1 h. These simulation results provide promising indication of the sensitivity of the TTI to changing storage conditions.

Conclusions
In this work the principle of capillary penetration were applied for the development of a full-history TTI. Extensive study of capillary penetration took place at two different temperatures and using various penetrating liquids in order to verify the applicability of Lucas-Washburn equation for the development of TTI. The TTI was designed, developed and tested and the results showed that the proposed TTI could be a promising solution for time-temperature monitoring since it is capable to provide a visual response that is quantitative and easy to read. Moreover, the response of the TTI could be calibrated selecting and changing various design parameters in order to match the degradation kinetics of the specific food product to be monitored. In more detail the operation time of TTI may be increased up to 3 years by selecting the viscosity of capillary penetration liquid and the r eff of the porous medium as well as changing the size (length) of the TTI. The testing of the TTI prototype showed that it provides a quantitative indication, and the indication is irreversible and never stops advancing. Although the propertied of the penetration liquids used and the equations indicate a potential use of the indicator at freeze temperatures (i.e. − 18 °C or lower), further research is required in order to assess the TTI response in subzero conditions.
Author contributions EPK conceptualization, design of experiments and methodology; DG, GD, EF, SP investigation; EPK and DG formal analysis and writing; All authors have read and agreed to the published version of the manuscript.
Funding Open access funding provided by HEAL-Link Greece. There is no funding to report.

Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Conflict of interest The authors declare no conflicts of interest.
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