Role of Particle Size in Tea Infusion Process

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, H₂SO₄ (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.

Figure 1:

SEM images of S2. (A) 33×, (B) 500×.

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 (mm²) the diameter of the circle having same area as particles was determined using dA=4Aˉ/π. But the particles were not perfectly circular as seen from the values of shape factor. The average of circularity (cir) of all fractions is between 0.58 and 0.74. The average values of aspect ratio for fractions F2, F3 and F4 are between 1.3 and 1.6, as mentioned in Table 2. Thus instead of taking the d_A as a measure of diameter of particles, area–perimeter diameter dAP=dAcir was used as measure of dimension of particles. 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.

Table 2:

Shape parameters for fractions of tea granules.

	S1			S2
	d32	Circularity	Aspect ratio	d32	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:

(1)Number density=niNLB

where 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.

Figure 2:

PSD of ground tea: (A) S1, (B) S2. Dots represent value from image analysis and dashed lines are only for better representation.

Sauter mean diameter (d₃₂) for each fraction of particle size and original particles was determined using eq. (2). Values of d₃₂ are as shown in Table 2; d₃₂ represents the diameter of sphere having same volume to surface area ratio [23]:

(2)d32=∑ni(Bavg,i)3∑ni(Bavg,i)2

The d₃₂ is considered as a representative diameter for the respective fraction.

3.1 Evaluation of partition constants and initial content of tea constituents

Partition constant and initial content of tea particles are calculated for d₃₂ 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/m³ 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/m³, 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.

Figure 3:

Plot of 1/c_∞ vs 1/w for S1 at 60°C for different tea weight to water volume ratio. Dots represent experimental value and line represents the linear fit.

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.

Figure 4:

Infusion profiles of fractions and unground tea of (A) S1 at 60°C, (B) S2 at 60°C, (C) S1 at 80°C, (D) S2 at 80°C. Dots represent experimental value and vertical bar represents standard deviation.

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/m³) 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_∞–c)) vs “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.

Figure 5:

Plot of ln(c_∞/(c_∞–c)) vs time for S1 and its fractions at 60°C. Dots represent experimental value and vertical bar represents 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/d₃₂ value when the values of 1/d₃₂ are small (large granule size). When the value of 1/d₃₂ 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).

Figure 6:

Plot of initial rate vs inverse of d₃₂: (A) S1, (B) S2. Plot of initial rate versus inverse of d322: (C) S1, (D) S2. Dots represent experimental value and vertical bar represents standard deviation.

To know whether the rate of infusion is completely controlled by diffusion or not, the initial rate is plotted against inverse of square of d₃₂ 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/d₃₂² is linear for small values of 1/d₃₂² (larger granules). For small granule sizes below 0.63 mm (1/d₃₂² > 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 1.86² (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 (r″diss, kg/(m²s)) in the annular shell (Figure 7) can be represented by a reversible process as

where k₁ (kg of solid (granule)/(m²s)) 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/m³) 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).

Figure 7:

Representation of tea granule and annular shell.

Mass balance for the differential element is

where “J” is the diffusion flux across the differential element and cs∗ is the product of 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

During the initial stage of the process (initial rate), a very small amount of tea constituents has been transferred to the solution. Thus the concentration in the solid phase (c_s) is approximately constant throughout the tea granule. Thus cs∗ in the above equations can be considered as a constant. We introduce the following dimensionless variables:

where cb (kg/m³) is the concentration of tea constituents in the bulk infusion (the same concentration is present at the surface of tea granule); ψ is finite at λ=0 (at r=0) and ψ=1 at λ=1 (at r=R). The following differential equations can be written:

Equation (10) is rewritten using eqs (11) and (12) as follows:

Equation (13) can be rewritten by putting k−1AsρRˉ2D=α2 as

The numerator of the right-hand side of eq. (15) is the dissolution rate of tea constituents if all the internal surface area of tea granule is exposed to the bulk concentration of the liquid. The denominator of this equation is the diffusion rate through the tea granules. Thus, α2 represents the ratio of surface dissolution rate to the diffusion rate. This is a standard diffusion equation and the solution is given by [26]

The observed rate of infusion (rˉobs, kg/s) can be written as

Now, by differentiating eq. (16) with respect to λ and putting λ=1,

Therefore from eqs (17) and (18),

The maximum rate (rˉmax, kg/s) at which infusion can occur is the rate if all the internal surface area of granules is exposed to the external condition at the surface of granule. The rˉmax is expressed as

Now, fraction of the maximum infusion rate attained can be given as ratio of observed rate of infusion to the maximum (dissolution) rate of infusion from eqs (19) and (20) as follows:

Thus as per eqs (15) and (21), factor f′ can be defined as follows:

If the value of f′ is much less than 1, the rate of infusion process is not controlled by the diffusion of tea constituents through the granules. However if f′ is much greater than 1, rate of infusion is severely restricted by the diffusion.

The ratio of α for two granule sizes (say Rˉ1 and Rˉ2) can be written as follows using eq. (15):

Now, for the initial rate of infusion (zero time) the concentration in the bulk is zero (c_b=0). Thus the ratio of f′ at t=0 as per eq. (22) for two granule sizes is as follows:

Equations (23) and (24) can be solved simultaneously for α1 and α2 by knowing the values of observed rate of infusion per unit weight of tea granules for two granule sizes. Values of f and f′ can be calculated from the value of α using eqs (21) and (22).

For the calculation of D_e, eq. (22) can be rearranged as follows:

where cs0∗ is the concentration at interface at time t=0 which is equal to the product of c_s0 and K. As per eq. (25), the plot of f′ vs r′obsRˉ2ρ/cs0∗ should be a straight line passing through origin with slope D_e.

The values of robs′, α, f, f′, rate of dissolution or maximum rate of infusion (rmax′) are as shown in Table 6. Initial rates of infusion are higher for 0.36 mm and 0.33 mm fractions. Initial rates at 60°C are found to increase by 81% from 1.17 mm to 0.36 mm granules and 98% from 1.99 mm to 0.33 mm granules in case of S1 and S2 type tea, respectively. However, at 80°C this increment is found to be approximately 50% for S1 and S2. A decrease in α is observed with a decrease in d₃₂ for both S1 and S2 at 60°C as well as 80°C. The values of α show that diffusion rate is lower than dissolution rate above d₃₂ 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 α is less than 1. This suggests that diffusion rate is higher for 0.33 mm fractions when compared with unground particles.

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 f′ indicates low diffusion rate. The values of f′ are found to be higher for d₃₂ of 1.17, 0.83 mm of S1 and 1.99 mm (S2). Value of f′ is 11.14 and 10.45 for d₃₂ 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 d₃₂ (at both 60°C and 80°C) f′ is less than 1; hence diffusion rate is more than the observed infusion rate. Thus it is confirmed that for this value of d₃₂ (0.33 mm) infusion is kinetically controlled.

Using robs′ and f the values of rmax′ (dissolution rate) are calculated as per eq. (21). These values are as shown in Table 6. It can be seen that the dissolution rate is almost constant with respect to particle size and changes only with the temperature. This is one of the important results as rate of dissolution should not be the function of particle size. Also, if the granule properties would have changed due to grinding, rate of dissolution would have been different for different granule sizes. As expected, the rate of diffusion shows an increase with a decrease in particle size. The behavior of observed rate (rise with a decrease in particle size but not as dominant as rise in diffusion rate) depicts that rate of infusion is dependent on both the rate of dissolution and the rate of diffusion.

3.7 Effective diffusivity

The value of cs0∗ (=Kcs0) for 1.17 mm and 0.36 mm d₃₂ is found to be 61.23 kg/m³ and 59.11 kg/m³ (calculated from the values of K and c_s0 mentioned earlier in this section). Thus cs0∗ for both the sizes is approximately equal. Thus average value of cs0∗ is used for calculation of D_e. The plot of f′ vs r′obsRˉ2ρ/cs0∗ is as shown in Figure 8 for S1 and its fractions at 60°C and 80°C. The plot is linear and passing through origin with R² 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 m²/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 m²/s whereas D_fast was of the order of 10⁻¹² m²/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 m²/s and 1.62×10⁻¹¹ m²/s at 80°C. These values are more close to the values obtained in the present paper.

Figure 8:

Plot for the calculation of D_e. Dots represent the calculated values, vertical bar and horizontal bar represent standard deviation and line represents linear fit.

Assumptions made for simplification of calculation of α,f,f′ and its effect on conclusion drawn need to be known. In order to include the effect of irregularity of the shapes of tea particles, circularity is used. Thus diameter of equivalent circle is obtained, considering the irregular shape. Further, the use of Sauter mean diameter ensures that mean size obtained has same surface to volume ratio as of the whole fraction. Since mass transfer rate depends upon the surface area of the particles, the correct relevant parameter to describe the mass transfer process is the surface area per unit volume. In order to capture the surface area per unit volume, area-based weighted average is calculated whenever mass transfer occurs from particles. This is called the Sauter mean diameter, denoted as d₃₂ [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 d₃₂ of a respective fraction.