## 1 Introduction

Tea is one of the most widely consumed beverages in the world. Different parts of the world follow different methods of preparation of tea. Tea bag infusion is a widely used method in the United States and Europe. In India loose tea leaves or tea particles are generally brewed in boiling water. The infusion time in all the methods varies from 1 min to 10 min, which results in different characteristics of tea infusion. Hence study of kinetics of tea infusion is important. Tea contains different constituents such as flavanols, catechins, gallic acid (GA) derivatives, etc. [1], which have different physical properties such as solubility, diffusivity. Also these constituents are located at different positions of tea leaf matrix [2, 3]. During the infusion process, hydration of tea occurs after which tea constituents dissolve in water (inside leaves/granules) and diffuse through tea leaf matrix to the bulk of infusion. Hydration step causes swelling of tea leaves/particles. All these simultaneous processes make tea infusion a complex phenomenon.

Infusion of tea has been studied by many researchers as summarized in Table 1. Long [4–6] studied the equilibrium and kinetics of tea infusion process. Long [6] modeled infusion kinetics using multicomponent diffusion law for first-order dissolution process. Spiro and Siddique [7] have defined the partition constant (*K*) as the ratio of concentration of tea constituent in infusion to that in the tea leaves/granules at equilibrium. Partition constants for tea constituents were estimated at different temperatures and found to be less than 1 g/ml. Spiro and Siddique [8] have developed a first-order kinetic expression for tea infusion process for tea leaves with laminar geometry. They found that values of activation energy were very low (4–12 kJ/mol), which suggested that infusion process is diffusion controlled. Spiro and Jago [9] derived the same kinetic expression by mass balance of tea constituents from leaf to water through Nernst diffusion layer. A better fit with experimental data was observed with inclusion of an intercept term. This equation is also applicable for spherical particles in case of coffee infusion [10]. Price and Spiro [11, 12] have examined the effect of size of the leaves on the partition constants and rate of infusion. Partition constants were independent of leaf size whereas rate constants had higher values for lower leaf sizes. Spiro et al. [13] and Jaganyi and Price [14] studied the temperature effects on extraction of caffeine from green and black tea. Values of hindrance factor (ratio of diffusivity through solution and particle/leaf) were found to be higher for both green and black tea. This indicates that infusion is a highly hindered process due to pore diffusion. Jaganyi and Mdletshe [15], Lian and Astill [16] have studied teabag infusion. They found that rate of infusion at dynamic condition was found to be much faster than at static condition of tea bag in water. Stapley [17] developed a model for tea infusion based on diffusion equations, which explains the fast infusion behavior observed during the initial stage of infusion. In some of the recent studies on tea infusion solid–liquid extraction model [18], model with two parallel diffusion process [19] and combined first- and second-order rate model [20] were used. Gujar et al. [18] also performed particle size study but at very low temperatures (28–56°C).

Literature review for tea infusion kinetics.

Reference | Tea material used | Type of experiment/study | Experimental conditions | Research highlights/parameters evaluated | |

[4] | Mixture of black orthodox tea | Equilibrium extraction (4 h) in sealed tube | Liquid:Leaf::10, 20, 30, 50, 100, 200:1 (wt. ratio) | Classification of tea components based on solubility (highly soluble, medium soluble and insoluble) | |

[5] | Mixture of black orthodox tea | Kinetic study in fixed bed reactor | Liquid:Leaf:: 4:1, 5:1 conditioning | Density of tea solute, specific water uptake | |

[6] | Mixture of black orthodox tea | Kinetic study in stirred reactor | Different stirring speedLiquid:Leaf:: 4:1, 5:1 | No effect of stirring Model based on first-order dissolution process | |

[7] | Koonsong Broken Pekoe | Equilibrium study in conical flask | Temperature: 79.5°C and 94°CWater:Leaf ratio=25 and 100 (w/v) | Partition constants Standard enthalpy change | |

[8] | Koonsong Broken Pekoe | Kinetic study in conical flask | Temperature: 79.5°C and 94°CWater:Leaf ratio=25 and 100 (w/v) | Rate constant Activation energy | |

[9] | Koonsong tea dust | Rotating disc experiment with tea dust | Different disc stirring speed | Rate constant Evaluation of external mass transfer limitations for infusion process | |

[11] | Black tea leaves and CTC tea | Equilibrium study in conical flask | Different tea leaf sizes | Partition constant: independent of particle size | |

[12] | Black tea leaves and CTC tea | Kinetic study in conical flask | Different tea leaf sizes | Higher rate constant for lower leaf sizeLess diffusivity of caffeine through tea leaves than that in aqueous solution | |

[13] | Green tea (Japan)Black tea (India) | Kinetic and equilibrium study in conical flask | Temperature, Tea weight to water ratio:: 1 g, 3 g, 4 g in 200 ml water | Rate constant Activation energy: Green tea > Black tea Diffusivity through tea leaves Hindrance factor | |

[14] | Black tea (LTP) | Kinetic and equilibrium study in conical flask | Temperature | Rate constant Activation energy: Green tea > Black tea | |

[15] | Black Assam orthodox tea | Kinetic study with loose tea and with tea bag | Temperature | Rate constant: Tea bag < Loose tea Activation energy of loose tea and tea-bag tea were practically the same | |

[16] | Round teabags with CTC tea | CFD simulations and experimental validation | Static and dynamic condition of tea bags during infusion | Relation between absorbance at 445 nm and soluble solid concentration in infusion Fast infusion with dynamic condition of tea bags than static condition | |

[17] | − | Modeling of tea and coffee infusion | − | Theoretical explanation for intercept in eq. (5) | |

[18] | Green tea | Kinetics and modeling | Different stirring speed, temperature (28°C to 56°C), particle size | Diffusivities of tea components | Solid–liquid extraction model |

[19] | Green tea | Kinetics and modeling | Temperature (50°C to 90°C) | Diffusivities of tea components | Model based on fast and slow diffusivities |

[20] | Yerba mate | Kinetics and modeling | Temperature (40°C to 70°C) | Diffusivities of tea components | Combined model based on second- and first-order rate |

Present work | Two types of CTC teas | Kinetics and evaluation of rate-controlling mechanism | Particle size Temperature 60°C and 80°C | Infusion kinetics using different size fractions Ratio of dissolution rate to diffusion rate and ratio of observed rate to diffusion rate were estimated Effective diffusivity was calculated |

The research done so far on tea infusion kinetics has shown that the infusion process is diffusion controlled. Apart from the diffusion there is possibility that the tea constituents situated at the outer surface of tea granules can simply dissolve in water in contact. This particular case is cited in some of the literature as an explanation of the fast infusion rate [9]. For this case diffusion may not play an important role as sufficient turbulence present in the system due to agitation minimizes external mass transfer resistance. Also transfer of constituent from the granule matrix by convection is not possible, as at such small size of pores viscous forces are dominant and do not allow the absorbed water to move freely. Thus convection need not be considered for the transfer of constituents from granule to bulk infusion. The only dominant mode of mass transfer is by way of diffusion through the pores of the granule. The effect of rate of dissolution of tea constituents from tea leaves/granules to water is not yet reported anywhere to the best of our knowledge. The reported values of diffusivity are based on the assumption of diffusion-controlled infusion kinetics. The objective of this work is to find the relative contribution of the diffusion and dissolution rate to the overall infusion rate. This was done by developing a new model for tea infusion based on quasi-steady-state assumption in the initial period of infusion. For this purpose, the effect of CTC (Crush, Tear and Curl) tea granule size on infusion kinetics is studied. Very few studies on infusion kinetics of CTC teas are found in the literature as can be seen in Table 1. In this study two different types of CTC teas and their ground fractions are explored to study the kinetics of tea infusion.

## 2 Materials and methods

### 2.1 Materials

Two different types of CTC tea samples S1 and S2 (Genus: *Camellia*; Species: *sinensis*; variety: assamica) were provided by Unilever Industries Limited, Bangalore. All infusion experiments were done using deionized (DI) water. Standard of GA, sodium lauryl sulfate, cetyltrimethyl ammonium bromide, oxalic acid dehydrate, 95% ethanol, H_{2}SO_{4} (98% w/w), potassium permanganate were procured from Sigma Aldrich Chemical Co. (Bangalore, India).

### 2.2 Methods

### 2.2.1 SEM images of tea particle

Tea used in the present study is CTC-type tea. CTC tea does not resemble tea leaf; rather it contains granular tea particles which are more or less spherical in shape. The scanning electron microscope (SEM) images of tea particles obtained using JSM-5200 (Jeol, Japan) operated at 15 KV are shown in Figure 1. It can be seen from the figure that the tea particle is agglomerate of crushed and processed tea leaf. Figure 1(A) shows the tea particle under 33× magnification. This particle is close to spherical in shape. The maximum dimension for this particle as seen from Figure 1(A) is approximately 3.2 mm. This dimension is much larger than the reported leaf thickness of ~0.18 mm [12]. Tea particle is also seen under greater magnification (500×) as shown in Figure 1(B). At this magnification some of the oval shape structures of size less than 30 µm are seen. These shapes resemble the stomata of leaf. The figure also shows porous structure of the particle. It is through these pores that the water diffuses inside the granule, dissolving the constituents of the leaf and these constituents diffuse out.

### 2.2.2 Preparation of different size fractions of tea particles and their size measurement

Tea particles (S1 and S2) were ground in mixer by pulse grinding with pulse of 5 sec with total grinding time of about 20 sec. Thus the possibility of heating is less. Ground tea particles were sieved through four sieves of different mesh sizes 850 μm, 710 μm, 500 μm and 212 μm. By sieving through these sieves, five fractions of different size ranges were obtained as retained on 850 μm (F1), between 850 μm and 710 μm (F2), between 710 μm and 500 μm (F3), between 500 μm and 212 μm (F4) and passing through 212 μm sieve (F5). Grinding done continuously for 10–20 sec produces large amounts of fine particles and fewer amounts of coarser particles. Intermittent grinding helped in getting uniform quantity of all fractions from the input. As the grinding is done for a short time period, the possibility of temperature increase and thereby changes in the characteristics of tea granule is less.

Images of the unground particles and their fractions were captured using digital camera (Sony DSC-HX-20V). The digital camera was mounted on tripod so that distance between camera lens and object (tea particles) is fixed for all images. Before capturing images of tea particles, image of an object of known dimension was taken for calibration. A conversion factor (ratio of pixel to mm) was obtained from the image of this object. Images of tea particles of different fractions were taken by maintaining the same height. Precaution was taken to spread the particles such that no two particles are in contact with each other. The captured images of tea particle fractions were processed using ImageJ™ (image analysis software). During processing an image is first converted to binary image. Then inbuilt function present in the software was used to determine area and shape factors (circularity, roundness, aspect ratio) of each particle. Using the conversion factor, area was converted from pixel unit to mm. For each fraction, 400–500 particles were analyzed.

From the obtained area (mm^{2}) the diameter of the circle having same area as particles was determined using *d*_{A} as a measure of diameter of particles, area–perimeter diameter *d*_{AP} is the diameter of a circle having same ratio of area and perimeter as particle. It is analogous to the surface volume diameter for the 3-D object [21]. Square root of circularity is taken, as from the definition; circularity is the square of the ratio of perimeter of a circle (having equal area as particle) to the perimeter of particle.

Shape parameters for fractions of tea granules.

S1 | S2 | |||||

d_{32} | Circularity | Aspect ratio | d_{32} | Circularity | Aspect ratio | |

Unground | 1.17 mm | 0.743 | 1.328 | 1.99 mm | 0.700 | 1.331 |

F2 | 0.83 mm | 0.658 | 1.365 | 0.83 mm | 0.579 | 1.413 |

F3 | 0.63 mm | 0.644 | 1.411 | 0.63 mm | 0.592 | 1.453 |

F4 | 0.36 mm | 0.601 | 1.524 | 0.33 mm | 0.639 | 1.533 |

The whole range of particle size (*d*_{AP}) was divided into number of bins of size 0.05 mm. The number of particles lying in the respective bin size (frequency) was measured. Using the frequency (*n _{i}*), the number density for a particular bin was calculated as per the following formula:

*L*

_{B}is length/size of the bin and

*N*is the total number of analyzed particles of the fraction [22]. The number density was plotted against the average bin size to get particle size distribution (PSD) as shown in Figure 2. Dashed lines in the plot are for representation purpose only. Sieved fraction F2, F3 and F4 show narrow size distribution whereas unground S1 and S2 show wide PSD. Figure 2(A) depicts that fractions of S1 and original S1 are of different size ranges. For fractions F2, F3, F4 less than 10% of particles are below 0.65 mm, 0.5 mm and 0.2 mm and less than 10% of particles are above 0.95 mm, 0.75 mm and 0.45 mm, respectively. Thus 80% of the total number of particles for F2, F3, F4 lie in the range 0.65–0.95 mm, 0.5–0.75 mm and 0.2–0.45 mm, respectively. Similar plot for S2 and its sieved fractions is shown in Figure 2(B). Sieved fractions of S2 showed characteristics similar to fractions of S1. But size range for unground S2 is much wider as well as larger than unground S1. For S2, 80% of the total analyzed particles are in the size range of 1.6 mm–2.5 mm whereas those of S1 are between 0.9 and 1.35 mm.

Sauter mean diameter (*d*_{32}) for each fraction of particle size and original particles was determined using eq. (2). Values of *d*_{32} are as shown in Table 2; *d*_{32} represents the diameter of sphere having same volume to surface area ratio [23]:

*d*

_{32}is considered as a representative diameter for the respective fraction.

### 2.2.3 Cellulose, hemicellulose and lignin content

Cell wall constituents of tea such as cellulose, hemicellulose and lignin were determined in order to know the difference between the two tea types. The experimental procedure was followed as per the methods described by Ref. [24]. The cell constituents were evaluated by determining the NDF (neutral detergent fiber), ADF (acid detergent fiber) and ADL (acid detergent lignin) contents of the tea sample. The procedure can be summarized as follows: 1 g tea sample was treated with the neutral detergent solution (NDS) of sodium lauryl sulfate, pH-7. This dissolves the tea constituents as well as digestible cell contents such as starch and sugar. The residue obtained (NDF) contains cellulose, hemicellulose, lignin and ash. This residue is then treated with hot acid detergent solution (ADS) of cetyl trimethyl ammonium bromide in 1N H_{2}SO_{4}, which dissolves hemicellulose leaving behind cellulose, lignin and ash (ADF). By subtracting ADF from NDF quantity of hemicellulose is obtained. The residue obtained after ADS treatment was treated with buffered permanganate solution followed by demineralization solution (oxalic acid dehydrate in 95% ethanol) which oxidizes lignin leaving cellulose and ash as residue (ADL). By subtracting ADL from ADF quantity of lignin is obtained. The ADL was finally calcined at 550°C for 3 h. The weight loss obtained after calcination is the amount of cellulose present while the remaining is ash.

The values of the cell contents obtained for S1 and S2 are as shown in Table 3. It can be seen that the value of NDF for S2 is lower than that for S1. Thus the amount of digestible cell wall contents and tea constituents is more in S2 than in S1. Also the percent amount of cellulose and lignin present in S2 is less than that in S1. But more amount of hemicellulose is present in S2 as compared to S1. This suggests that S1 and S2 have different nature as far as leaf contents are concerned.

Cell contents of S1 and S2.

NDF % | Hemicellulose % | Cellulose % | Lignin % | Ash % | |

(±0.23) | (±4.5) | (±0.48) | (±2.1) | (±0.03) | |

S1 | 35.2 | 13.83 | 8.48 | 13.1 | 0.28 |

S2 | 32.88 | 16.78 | 6.69 | 9.11 | 0.3 |

Note: The value in brackets represents standard deviation.

### 2.2.4 Infusion experiment

Infusion experiments were carried out using 100 ml DI water and 2 g of tea (using different fractions of S1 and S2); 100 ml of DI water taken in desired vessel was heated to the required temperature using constant temperature water bath (±1°C). Tea particles were added to hot DI water (under stirring at constant rpm) instantly, using glass funnel. After addition of tea particles, samples were withdrawn at intervals of 0.5, 1, 2, 3, 4, 5, 10 and 15 min; 1 ml of sample was withdrawn each time using 15 cm long needle fitted on syringe. Withdrawn samples were filtered using cloth before transferring to sampling vial. Infusion time was kept as 15 min after which infusion was filtered immediately through Büchner funnel and volume of filtrate was measured.

### 2.2.5 Equilibrium infusion experiment

Equilibrium infusion experiments for determination of partition constant were carried out at 60°C and 80°C using unground S1 and S5 and at 60°C using fraction F4 of S1. The method developed by Spiro and Siddique [7] was used to calculate the partition constant and the initial content of tea constituent per unit weight of tea granules (*c*_{s0}, kg/kg). A set of equilibrium infusion experiments were performed at different tea weight to water volume ratio. The volume of water was fixed at 50 ml and weight of tea granules was varied from 0.5 to 2 g for each experiment. Infusion was carried out for 15 min at constant temperature under stirring. After 15 min of infusion 1 ml of sample was withdrawn and infusion was filtered using Büchner funnel. The volume of infusion and wet weight of tea granule was measured. Sample was analyzed to get equilibrium concentration.

### 2.2.6 Sample analysis

Tea infusion samples were analyzed using UV-Vis spectrophotometer (Cary 50). Lian and Astill [16] have used UV-Vis method for the analysis of tea infusion samples. They have measured absorbance at 445 nm wavelength from which dissolved soluble solids (DSS) were estimated. Similar method was used for tea infusion sample analysis. Absorbance spectra of tea infusion samples were recorded which showed peaks at 205–210 nm and at 272 nm. Most of the tea constituents such as caffeine and GA derivative show absorbance maxima near 272 nm. Thus absorbance at 272 nm was monitored as a measure of extent of infusion. Tea infusions were diluted 100 times using DI water so that absorbance at 272 nm wavelength is below 1.

Most of the tea polyphenols are GA derivatives [1]. Also, GA is generally used as a standard for polyphenol measurement using Folin–Ciocalteu method. Thus GA was used here as standard for calibration of absorbance at 272 nm wavelength. Using the calibration equation absorbance of tea infusion samples was converted to GA equivalence (GAE). Thus GAE values presented in this paper as concentration of tea constituents are not the amount of GA that would be present in infusion but the equivalent amount of GA which would give same absorbance.

Due to sampling, certain amount of tea constituents is lost from the system. To account for this loss following equation was used to calculate GAE% (percent weight of GAE extracted per unit weight of tea granules):

*c*

_{b}is the measured concentration in bulk infusion and

*V*is the volume of infusion at time “

_{t}*t*”,

*V*

_{s}is the amount of infusion withdrawn at each sampling instant and

*w*is the weight of tea particles used for infusion.

*V*is obtained by addition of sample volume after time “

_{t}*t*” to the final volume of infusion. Thus GAE% calculated using eq. (3) includes the loss of solute occurred because of withdrawal of samples.

### 2.2.7 Evaluation of kinetic parameters and energy of activation

The kinetic expression developed by Spiro and Siddique [8] is as shown below:

*c*(kg/m

_{∞}^{3}) is the concentration of solutes in infusion at equilibrium;

*c*(kg/m

^{3}) is the concentration of solutes in infusion at time “

*t*”;

*k*

_{obs}(min

^{−1}) is the observed rate constant for infusion process;

*t*(min) is the time.

For better fit with experimental data eq. (4) is modified and generally written with inclusion of intercept, as shown in eq. (5):

*a*is the empirical parameter for better fit of kinetic data. Equation (5) is used for estimation of kinetics parameter (

*k*

_{obs}and

*a*) using kinetic data of infusion. The value of GAE (kg/m

^{3}) at 15 min is used as

*c*as equilibrium is attained before 15 min.

_{∞}*Regression*tool of

*Microsoft Excel*is used for the determination of these parameters within 90% confidence interval.

Activation energy for infusion of different particle size was calculated from the Arrhenius equation as shown below:

*k*

_{obs}is observed rate constants obtained using eq. (5),

*E*is the activation energy and

*R*is the universal gas constant. From the plot of ln(

*k*

_{obs}) vs 1/

*T*(K

^{−1}), value of

*E*was obtained for different size fractions.

### 2.2.8 Calculation of partition constant

Following equation was used for the determination of partition constant [7]:

*c*) were determined for different tea weight to water volume ratio as explained in Section 2.2.5.

_{∞}*c*vs 1/

_{∞}*w*for a set of equilibrium infusion experiment was drawn. From the values of slope and intercept

*c*

_{s0}and

*K*were calculated as per eq. (7).

## 3 Results and discussion

### 3.1 Evaluation of partition constants and initial content of tea constituents

Partition constant and initial content of tea particles are calculated for *d*_{32} equal to 1.17 mm and 0.36 mm (S1 tea type), respectively. The plot of 1/*c _{∞}* vs 1/

*w*is as shown in Figure 3 for 1.17 mm granules at 60°C. The plot is linear with small intercept. The value of partition constant and initial content is found to be 684.3 kg/m

^{3}and 0.0895 kg/kg, respectively. Similar plot drawn for 0.36 mm granules at 60°C is used to calculate

*c*

_{s0}and

*K*. For 0.36 mm,

*c*

_{s0}and

*K*are found to be 0.1017 kg/kg and 581.2 kg/m

^{3}, respectively. It can be seen from Figure 3 that the intercept is very small. Thus there are chances of error in the measurement of

*K*and

*c*

_{s0}. This error was explained to be up to 10% [11]. Thus within this error limit the values of

*c*

_{s0}and

*K*are equal for different granule sizes.

### 3.2 Infusion kinetics for different Sauter mean diameter tea fractions

Reproducibility in the measured values of GAE was checked by repeating the experiments for three times. Standard deviation and % error from average value of GAE for all sample instances of a particular experiment were calculated. The errors in measuring the values of GAE were found to be within ±5%.

Infusion profiles of S1 and S2 for different particle sizes are shown in Figure 4. The vertical bar over each data point represents the standard deviation from that value. For both the tea types at 60°C and 80°C infusions are faster with a decrease in particle size. It can be seen from Figure 4(A) that, for infusions of S1 at 60°C, values of GAE% at the end of 15 min increase slightly with a decrease in the particle size. Value of GAE% is 8.8 at the end of infusion for 1.17 mm particle size (unground S1). For F2 (0.83 mm), F3 (0.63 mm) and F4 (0.36 mm) GAE% at 15 min is 9.2, 9.7 and 10, respectively. For the smallest particle size, (fraction F4) the initial rate is much higher than other fractions. For F4, 60% of the total extraction occurs within 30 sec and 90% of extraction occurs in 3 min. After 3 min a large drop in rate of infusion is observed. In case of unground S1, F2 and F3 fractions nearly 80% of the infusion occurs in 5, 4 and 3 min, respectively. The amount of the GAE extracted in last 10 min for unground S1, F2, F3 and F4 is 23%, 17%, 11% and 6%, respectively.

Similar observations can be made from Figure 4(C) for infusions of S1 at 80°C. The value of final GAE% is practically the same and nearly 11.3% for all fractions as well as unground S1. Almost 75% of the total infusion for F4 is completed within 0.5 min. The infusion rate is practically zero after 5 min. Unground S1 and F2 show much slower infusions than that of F4. Half of the infusion is finished before 1 min for S1 and F2. At the end of 5 min 83% and 92% of tea constituents are leached out in case of S1 and F2, respectively. Almost 80% of the infusion of F3 occurs in 1 min and infusion is completed within 10 min. The figure suggests that equilibrium is attained faster in case of infusion at 80°C.

Kinetics of unground S2 and its fractions F2 (0.83 mm), F3 (0.63 mm), F4 (0.33 mm) are shown in Figure 4(B) and (D) at 60°C and 80°C, respectively. Different particle sizes of S2 are found to behave in similar way as that of S1. At 60°C almost 60% of the total extraction is finished within first 0.5 min for fraction F4. And within 10 min the complete infusion is completed. In case of unground S2, 25% of the total extraction occurred in 0.5 min. Also 36% of total extraction occurred in 1–5 min and 24% in the last 10 min. However for F4, the rate of infusion is much faster initially and drops substantially after 1 min of infusion. Also, fractions F2 and F3 exhibit initial fast rate of infusion with nearly 80% of infusion in 3 min and 2 min, respectively, at 60°C. Only 10% and 8% of the total infusion happens in the last 10 min for F2 and F3, respectively. Infusions of different particle sizes at 80°C are much faster than infusions at 60°C for S2. At 80°C, 90% of tea constituents are extracted in 4 min, 3 min and 2 min for F2, F3 and F4, respectively. For F4 infusion is completed within 5 min itself. In case of F2 and F3 only 6% and 2% of the total infusion happens in the last 10 min of infusion.

Figure 4 also shows that variation in profiles of unground tea and its fine fractions is more in case of S2 than S1. It can be because difference in sizes of unground particles and its fractions is more in case of S2 than S1. Infusion profile for unground S2 is similar to that of S1. But fractions of S2 show slightly faster infusion than respective fractions of S1 for a particular temperature. Thus it can be said that for a particular particle size, S2 shows faster infusion characteristics than S1. It is seen from infusion profiles that tea infusion process (in general) can be divided into three parts as (i) high initial rate, (ii) approximately constant or slowly decreasing rate and (iii) very slow rate. The time of occurrence of these steps depends upon the size of tea granules. For small tea granules (fraction F4) all these steps occurred within 5 min of infusion, whereas for unground tea very slow rate of infusion is observed after infusion time of 5 min.

### 3.3 Sensory score for S1 and S2 unground

The sensory analysis was done by the sensory panel using liquor made by brewing 2 g of tea in 200 ml of water for 2 min. Water was boiled and then the tea was added into it. The sensory scores for some of the attributes such as aroma (citrus, black tea and overall), redness, astringency, bitterness, flavor (overall and black tea) of S2 are higher than those for S1. The p value for these attributes is in the range of 0.045 to <0.0001. Thus as per sensory score, S2 has stronger sensory perceptions than S1. Also, the equilibrium values of GAE (at 15 min for 60°C and 80°C) are higher for S2 than those for S1. This suggests that GAE represents the overall sensory quality of tea infusion in case of S2 and S1.

### 3.4 Kinetic parameters for tea infusion

Rate parameters are determined using eq. (5) as per the plot shown in Figure 5, which shows the plot for unground S1 and its fraction for infusion carried out at 60°C. GAE (kg/m^{3}) value at 15 min is regarded as *c***_{∞}** and data up to 5 min was used. Use of the data after 5 min tends to give ambiguous results as explained earlier [12]. Figure depicts good linear fit for all particles. As the particle size is reduced, slight deviation from linearity is observed. This deviation is because of the faster initial rate at the start of infusion for finer fractions. Similar trend is observed for S1 at 80°C and for S2 at both 60°C and 80°C. The values of kinetic parameters evaluated from the plot of ln(

*c*/(

_{∞}*c*)) vs “

_{∞}–c*t*” are summarized in Tables 4 and 5. Values of

*k*

_{obs}and

*a*are shown with the 90% confidence interval. All the infusion data is well correlated by eq. (5) as p value is less than 0.05 for both

*k*

_{obs}and

*a*. Observed rate constants for both S1 and S2 are found to increase with a decrease in particle size at 60°C and 80°C. This shows that diffusion of tea constituents through the pores of tea particle matrix has an effect on the rate of the process. As the particle size is reduced the path through which constituents has to diffuse gets reduced. Similar trend is observed for intercept as well. Intercept shows an increase with decrease in particle size. This is because of higher specific surface area (surface area per unit mass) for smaller particles, leading to high initial rate due to dissolution of tea constituents on surface.

Rate parameters for different particle sizes of S1.

d_{32} (mm) | 60°C | 80°C | E (kJ/mol) | ||||

k_{obs} (min^{−1}) | a | R^{2} | k_{obs}(min^{−1}) | a | R^{2} | ||

1.17 | 0.242±0.016 | 0.226±0.049 | 0.996 | 0.295±0.033 | 0.374±0.101 | 0.989 | 9.73 |

0.83 | 0.291±0.043 | 0.310±0.129 | 0.982 | 0.412±0.039 | 0.378±0.118 | 0.992 | 17.34 |

0.63 | 0.362±0.043 | 0.388±0.131 | 0.988 | 0.474±0.314 | 0.782±0.593 | 0.898 | 8.35 |

0.36 | 0.397±0.079 | 0.872±0.239 | 0.967 | 0.632±0.121 | 1.300±0.368 | 0.968 | 22.98 |

Note: The results are expressed as mean±standard deviation.

Rate parameters for different particle sizes of S2.

d_{32} (mm) | 60°C | 80°C | E (kJ/mol) | ||||

k_{obs}(min^{−1}) | a | R^{2} | k_{obs}(min^{−1}) | a | R^{2} | ||

1.99 | 0.240±0.019 | 0.217±0.057 | 0.995 | 0.257±0.043 | 0.264±0.138 | 0.986 | 3.219 |

0.83 | 0.391±0.069 | 0.338±0.210 | 0.973 | 0.455±0.122 | 0.654±0.342 | 0.963 | 7.442 |

0.63 | 0.336±0.082 | 0.725±0.249 | 0.951 | 0.562±0.088 | 0.792±0.266 | 0.979 | 25.349 |

0.33 | 0.420±0.100 | 0.965±0.302 | 0.954 | 0.685±0.280 | 1.384±0.647 | 0.962 | 24.224 |

Note: The results are expressed as mean±standard deviation.

Values of activation energy are shown in Tables 4 and 5 for S1 and S2, respectively. It is seen that the values of activation energy exhibit an increase with a decrease in particle size. Also values of activation energy are much lower than those observed generally for kinetically controlled chemical reaction (>50 kJ/mol). This suggests that there are significant diffusion limitations for the tea infusion process.

### 3.5 Relation of initial rate with granule size

From the concentration profiles shown in Figure 4, the initial rate of infusion can be calculated. To check whether the process of infusion is dependent upon the external surface area of the particle, initial rate (kg/(kg s)) is plotted against inverse of particle size as shown in Figure 6. Figure 6(A) shows the plot for S1 and its fraction at 60°C and 80°C. It can be seen that initial rate increases rapidly with an increase in 1/*d*_{32} value when the values of 1/*d*_{32} are small (large granule size). When the value of 1/*d*_{32} becomes greater than 1.6 mm^{−1} (small granule sizes below 0.63 mm), the increase in the initial rate is very small. Similar observations can be made for infusion of S2 and its fraction at 60°C and 80°C from Figure 6(B).

To know whether the rate of infusion is completely controlled by diffusion or not, the initial rate is plotted against inverse of square of *d*_{32} as shown in Figure 6(C) and (D). If rate of infusion is completely diffusion controlled, the plot of initial rate versus inverse of the square of the size of granule should be linear. It can be seen in Figures 6(C) and (D) that the initial rate versus 1/*d*_{32}^{2} is linear for small values of 1/*d*_{32}^{2} (larger granules). For small granule sizes below 0.63 mm (1/*d*_{32}^{2} > 2), the initial rate deviates substantially from linearity. For example, if we consider two different granule sizes of S1, 0.63 mm and 1.17 mm, the ratio of their granule size is 1.86. If the infusion process was completely controlled by diffusion, the ratio of the initial rates would be 1.86^{2} (factor of 3.4). However, at 60°C, the observed ratio of the initial rate of these two granules is only 1.5. Thus rate of infusion is not completely controlled by diffusion alone. Thus effect of rate of dissolution on overall infusion rate needs to be studied.

### 3.6 Effect of diffusion and dissolution rate on overall rate of infusion

The process of infusion can be considered to be a combination of the two processes: (i) dissolution of components from tea matrix: first-order rate process and (ii) diffusion of the dissolved components through the pores of the granules. The dissolution process is physical in nature and, as a result, inherently a first-order process; therefore, first-order kinetics has been used. The concentration of the infused components in the infusion is low enough so that chemical effects are negligible. The process is thus of purely physical dissolution and hence it is fundamentally a first-order process. In the past, the transfer of tea constituents from tea granules to liquid has been successfully modeled using first-order kinetics [5, 8]. Apart from the tea infusion first-order kinetics has been used to model extraction processes accurately [10, 25]. Thus it was thought to consider the dissolution as a first-order process.

The kinetic process of dissolution of tea constituents per unit internal surface area of tea granule (^{2}s)) in the annular shell (Figure 7) can be represented by a reversible process as

*k*(kg of solid (granule)/(m

_{1}^{2}s)) is the first-order rate constant for the transfer of tea constituents from solid to water and

*k*

_{−1}(m/s) is the first-order rate constant for the transfer of tea constituents from water to solid;

*c*

_{s}(kg of tea constituents/kg of solid or in abbreviation kg/kg

_{s}) and

*c*(kg/m

^{3}) are the concentration in solid and water, respectively. The kinetic dissolution process can now be coupled with the diffusion process through the granule. For this, consider a differential element in the spherical tea granule (as shown in Figure 7).

Mass balance for the differential element is

*J*” is the diffusion flux across the differential element and

*c*

_{s}and

*K*, which is concentration in liquid phase at the solid–liquid interface. During the initial period of the process, when infusion is very dilute, and a very small amount of the components is transferred out of the tea matrix, quasi-steady state can be assumed (

*dc/dt*=0). Also, the diffusive flux (

*J*) can be written in terms of effective diffusivity

*D*

_{e}. The above equation becomes

*c*

_{s}) is approximately constant throughout the tea granule. Thus

^{3}) is the concentration of tea constituents in the bulk infusion (the same concentration is present at the surface of tea granule);

*r*=0) and

*r*=

*R*). The following differential equations can be written:

The ratio of

*c*

_{b}=0). Thus the ratio of

*t*=0 as per eq. (22) for two granule sizes is as follows:

*f*and

For the calculation of *D*_{e}, eq. (22) can be rearranged as follows:

*t*=0 which is equal to the product of

*c*

_{s0}and

*K*. As per eq. (25), the plot of

*D*

_{e}.

The values of *f*, *d*_{32} for both S1 and S2 at 60°C as well as 80°C. The values of *d*_{32} of 0.63 mm. For fraction size of 0.33 mm (of S2) at both 60°C and 80°C the diffusion rate is more than the dissolution rate as

Different rates of *f* and

d_{32} (mm) | f | |||||

S1 (60°C) | 1.17 | 3.82±0.10 | 4.71±0.44 | 0.50±0.04 | 11.14±1.33 | 7.62 |

0.83 | 4.71±0.28 | 2.90±0.58 | 0.68±0.08 | 5.75±1.24 | 6.89 | |

0.63 | 5.67±0.11 | 2.72±0.26 | 0.71±0.03 | 5.22±0.73 | 8.01 | |

0.36 | 6.93±0.01 | 1.54±0.08 | 0.87±0.01 | 2.06±0.19 | 7.96 | |

S1 (80°C) | 1.17 | 5.84±0.12 | 3.49±0.04 | 0.61±0.01 | 7.50±0.13 | 9.51 |

0.83 | 6.93±0.14 | 2.27±0.00 | 0.77±0.00 | 3.95±0.01 | 9.02 | |

0.63 | 7.90±0.19 | 1.94±0.02 | 0.81±0.00 | 3.07±0.06 | 9.70 | |

0.36 | 9.07±0.29 | 1.13±0.60 | 0.92±0.05 | 1.18±0.90 | 9.82 | |

S2 (60°C) | 1.99 | 3.68±0.08 | 4.48±1.03 | 0.52±0.10 | 10.45±3.06 | 7.07 |

0.83 | 5.46±0.14 | 1.59±0.58 | 0.86±0.07 | 2.18±1.22 | 6.32 | |

0.63 | 6.40±0.38 | 1.48±0.37 | 0.88±0.05 | 1.92±0.78 | 7.28 | |

0.33 | 7.30±0.51 | 0.82±0.09 | 0.96±0.01 | 0.62±0.13 | 7.63 | |

S2 (80°C) | 1.99 | 6.40±0.41 | 2.91±0.15 | 0.68±0.02 | 5.78±0.44 | 9.37 |

0.83 | 7.93±0.51 | 0.97±0.01 | 0.94±0.01 | 0.89±0.01 | 8.42 | |

0.63 | 9.40±0.74 | 1.05±0.04 | 0.93±0.01 | 1.21±0.07 | 10.06 | |

0.33 | 9.53±1.11 | 0.51±0.42 | 0.98±0.02 | 0.26±0.05 | 9.70 |

Note: The results are expressed as mean±standard deviation.

For particle sizes of 0.83 mm and above, the values of *f* are much less than 1 (except for F2 of S2 at 80°C). This suggests that the observed initial rate of infusion is much lower than maximum possible infusion rate (dissolution rate). Values of *f* approach 1 for 0.36 mm and 0.33 mm fractions; 0.36 mm granule size shows the value of *f* equal to 0.87 and 0.92 at 60°C and 80°C, respectively. For 0.33 mm size fractions, *f* is 0.96 and 0.98 at 60°C and 80°C, respectively. Hence these fractions offer negligible diffusion resistance. For 1.17 mm granules (S1), observed rates are much less than maximum possible rate as can be seen from the values of *f* at 60°C and 80°C. Same is the case with 1.99 mm granules (S2). It can be seen that values *f* are more for similar sized fractions of S2 than that of S1. Thus, it can be said that S2 offers less diffusion resistance than S1 of similar size.

The value of *f* close to 1 shows that maximum possible rate of infusion is achieved. In the case of S1, even for lowest size (0.36 mm) *f* is 0.92 at 80°C. This suggests that it is possible to get higher rate of infusion by raising the infusion temperature above 80°C or by decreasing the particle size below 0.36 mm. In case of fraction F4 (0.33 mm) of S2 at 80°C, *f* is 0.98. Thus almost maximum rate is achieved. Hence 0.33 mm and 80°C would be the better size and temperature with which infusion can be made for S2 tea type.

High value of *d*_{32} of 1.17, 0.83 mm of S1 and 1.99 mm (S2). Value of *d*_{32} equal to 1.17 mm and 1.99 mm, respectively, at 60°C, which explains the lower diffusion rate. In case of 0.33 mm of d_{32} (at both 60°C and 80°C) *d*_{32} (0.33 mm) infusion is kinetically controlled.

Using *f* the values of

### 3.7 Effective diffusivity

The value of *d*_{32} is found to be 61.23 kg/m^{3} and 59.11 kg/m^{3} (calculated from the values of *K* and *c*_{s0} mentioned earlier in this section). Thus *D*_{e}. The plot of *R*^{2} value of 0.97 and 0.99 for 60°C and 80°C, respectively. The values of *D*_{e} are 2.23×10^{−10} and 4.34×10^{−10} m^{2}/s at 60°C and 80°C, respectively. The linear nature of the plot shown in Figure 8 suggests that internal structure of tea granule matrix is intact even after grinding as all the fractions show same diffusivity value. These values of diffusivity can be compared to available data in literature. But it should be noted that the values of *D*_{e} presented in this paper are representative for all tea constituents in terms of GAE. The values of *D*_{e} for different tea components were estimated for fast and slow stages of infusion by Ziaedini et al. [19]. *D*_{slow} was of the order of 10^{−14} m^{2}/s whereas *D*_{fast} was of the order of 10^{−12} m^{2}/s at 60°C. These values are 2–4 orders of magnitude less than the values obtained here. This may be because of the green tea leaves used by Ziaedini et al. [19], whereas in the present study CTC tea is used. CTC tea undergoes different processing which ruptures the cell walls which might be helping in faster diffusion. Spiro et al. [13] showed that *D*_{e} for caffeine through green and black tea leaves is 2.2×10^{−11} m^{2}/s and 1.62×10^{−11} m^{2}/s at 80°C. These values are more close to the values obtained in the present paper.

Assumptions made for simplification of calculation of *d*_{32} [23]. Another important assumption is quasi-steady state for the initial period of tea infusion. During the initial period of process, infusion concentration is very less. And concentration inside tea is very large as compared to infusion concentration. Thus for a short period of time the change in concentration of tea can be assumed to be very less, which implies the quasi-steady state. Also, as the quasi-steady state is assumed at the initial period of infusion, the particle size required for the calculation is taken as *d*_{32} of a respective fraction.

## 4 Conclusion

Tea infusion kinetic study is performed with tea granules of different sizes, obtained by grinding and sieving. Fine fraction shows faster infusion kinetics than unground tea granules. At 80°C for S2 tea, for a decrease in Sauter mean diameter from 1.99 mm to 0.33 mm the rate constant showed an increase from 0.257 min^{−1} to 0.685 min^{−1}. A quasi-steady-state model is developed to find the relation between rates of infusion, diffusion and dissolution. This model gives better understanding of the process. For the granule size of 0.83 mm and above, the dissolution rate is much higher than the diffusion rate. Thus infusion process using these particle sizes is highly hindered by diffusion limitations. As granule size is reduced, the observed rate of infusion shows an increase and approaches dissolution rate. For 0.33 mm granule size, observed infusion rate is almost equal to the dissolution rate. This shows that for 0.33 mm granule size, mass transfer limitations are completely eliminated and rate of infusion is controlled by the dissolution rate.

The values of effective diffusivity obtained for S1-type tea are 2.23×10^{−10} m^{2}/s and 4.34×10^{−10} m^{2}/s at 60°C and 80°C, respectively. This value is independent of the granule size at both temperatures. The infusion rates have been qualitatively linked to the sensory perception.

The authors would like to thank Unilever Industries Limited for funding the research project. One of the authors Raosaheb A. Farakte would like to thank the University Grants Commission (UGC) for providing financial support.

## Nomenclature

a | empirical parameter in kinetic rate expression |

A | frequency factor in Arrhenius equation (min |

A_{s} | Surface area of tea granule matrix per unit weight (m |

Surface area of a granule measured using image analysis (mm | |

B_{avg,i} | Average bin size of the |

c | concentration of tea constituents in water inside the pore of tea matrix (kg/m |

c_{b} | concentration in bulk infusion at time |

cir | circularity |

c_{s} | concentration in tea solid (kg/kg) |

c_{s0} | concentration in solid phase at time |

concentration at solid–liquid interface (kg/m | |

c_{∞} | concentration in infusion at equilibrium (kg/m |

d_{32} | Sauter mean diameter (mm) |

d_{A} | diameter of circle of same area as granule (mm) |

d_{AP} | area–perimeter diameter (mm) |

D_{e} | effective diffusivity (m |

E | activation energy (kJ/mol) |

f | ratio of observed rate to maximum rate |

ratio of observed rate to diffusion rate | |

J | diffusion flux across the differential element (kg/(m |

K | partition constant (kg/m |

k_{1} | first-order rate constant for the transfer of tea constituents from solid to water (kg of solid (granule)/(m |

k_{−1} | first-order rate constant for the transfer of tea constituents from water to solid (m/s) |

k_{obs} | rate constant (min |

L_{B} | length/size of the bin (mm) |

n_{i} | frequency of the bin “ |

N | total number of particles analyzed for a fraction |

R | universal gas constant (J/(mol K)) |

radius of tea granule (m) | |

rate of dissolution of tea constituents per unit surface area of tea matrix (kg/(m | |

r | inner radius of annular shell (m) |

Δr | thickness of differential element (m) |

observed rate of infusion (kg/s) | |

maximum rate (dissolution rate) (kg/s) | |

observed rate of infusion (kg/(kg s)) | |

maximum rate of infusion (dissolution rate) (kg/(kg s)) | |

diffusion rate (kg/(kg s)) | |

T | temperature (K) |

V | initial volume of infusion (m |

V_{t} | volume of infusion at time “ |

V_{s} | volume of sample (m |

volume of infusion at equilibrium (m | |

w | weight of tea granules used for infusion (kg) |

weight of tea granules at equilibrium (kg) |

### Latin symbols

ρ | density of tea granules (kg/m |

dimensionless concentration | |

λ | dimensionless length |

ratio of dissolution rate to diffusion rate |

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