Hydrostatic pressure cycling extraction of soluble matter from mate leaves

Journal of Food Engineering 116 (2013) 656–665

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Hydrostatic pressure cycling extraction of soluble matter from mate leaves Valesca Kotovicz, Everton Fernando Zanoelo ⇑ Federal University of Paraná, Polytechnic Center (DTQ/ST/UFPR), Department of Chemical Engineering, Jardim das Américas, 81531-990 Curitiba, PR, Brazil

a r t i c l e

i n f o

Article history: Received 9 October 2012 Received in revised form 24 November 2012 Accepted 18 January 2013 Available online 29 January 2013 Keywords: Aqueous extraction Leaves of mate Pulsed hydrostatic pressure Diffusion Convection in microchannels Modeling

a b s t r a c t The main aim of this study was to investigate the kinetics of solid–liquid extraction of soluble matter from leaves of Ilex paraguariensis assisted by pulsed hydrostatic pressure. A large set of experiments was carried out involving a mixture of distilled water and comminute leaves of mate fed in a batch extractor kept at approximately 16.7 °C. The influence of pressure on equilibrium solute concentrations and rate of extraction was examined in the pressure range from 91.4 to 338.2 kPa by applying or not hydrostatic pressure cycles. Whatever the case a significant increase of such responses with direct positive impact on extraction yield and time of extraction was experimentally observed by changing the investigated factor (e.g.; the extraction yield was increased from 13% at 91.4 kPa to approximately 34% and the time to have 90% of the highest efficiency was reduced from 17,000 s at 91.4 kPa to 6000 s by applying hydrostatic pressure pulses at only 338.2 kPa). An hybrid diffusive–convective model was suggested to represent the transient extraction of soluble compounds from the discoid particles. The classical Fick’s law described the two-dimensional diffusion for the static long periods of mass transfer at constant pressure, while a model dependent on the gamma function computed the fraction of solute periodically extracted by convection from the internal solid microchannels during the rapid pulses of hydrostatic decompression. For all the investigated conditions the proposed analytical model well reproduced the kinetic experimental results of solute mass fraction in the solid and liquid phase. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction An amazing average annual growth of 7.7% was registered for the Brazilian per capita intake of non-alcoholic ready-to-drink beverages prepared by infusion of shoots of Camellia sinensis and leaves of Ilex paraguariensis between 2005 and 2010 (ABIR, 2011). In this segment of beverages the aqueous extracts of mate have represented approximately 18% of the overall consumption with 13.9 million liters in 2004 and around 17.0 million liters in 2008 (ABIR, 2008). Based on this scenario and on the importance of mate crop and manufacturing in Brazil (e.g.; Zanoelo and Benincá, 2009; Rodrigues et al., 2010; Jensen et al., 2011), which is the second world-leading of mate production (Rodrigues et al., 2010), improvements in the conventional industrial process of solid– liquid extraction involving leaves of mate are strongly expected. The main reasons for such process optimization are the high temperatures and long operation time required to have high extraction yields. Such conditions have not only drastic impacts on costs, but they present not negligible detrimental effects on thermolabile compounds and sensorial properties of the marketed beverage. For instance, the maximum yield by infusion at atmospheric pressure estimated by using a reliable equilibrium model ⇑ Corresponding author. Tel.: +55 41 33613202; fax: +55 41 33613674. E-mail address: [email protected] (E.F. Zanoelo). 0260-8774/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jfoodeng.2013.01.015

(Jensen and Zanoelo, in press) (0.37 kg solute per kg dry solid) demanded extraction time longer than 36,000 s at temperatures close to the boiling point of water. Because the extraction time exponentially reduces when the yield of extraction decreases, a maximum extraction yield close to 80% of the aforementioned value was experimentally reported by infusion of mate leaves for only 1800 s (Sambiassi et al., 2002), but a high temperature equal to 348 K was again necessary to have it. An additional analogous investigation available in the literature (Linares et al., 2010) also confirms that conventional infusion of mate leaves is a time-consuming operation (t > 3600 s for equilibrium) whose maximum extraction yield (0.35 kg solute per kg dry solid) requires at least moderate temperatures (in this case T was approximately 343 K). Among the large number of innovative solid–liquid extraction processes reported in the literature, such as microwave-assisted and pulse electric field-assisted extraction (e.g.; Naviglio and Ferrara, 2008; Zhang et al., 2011; Lebovka et al., 2012), only supercritical fluid extraction (SFE) (Esmelindro et al., 2005; Cardozo et al., 2007; Jacques et al., 2007; Cassel et al., 2008), pressurized liquid extraction (PLE) (Jacques et al., 2006, 2008; Grujic et al., 2012) and ultrasound-assisted extraction (Jacques et al., 2006) have been tested in a laboratory scale to obtain soluble compounds from leaves of mate. Anyway, almost all of them were rather focused on the chemical characterization of the mate extracts (typically rich in saponins, caffeine, theobromine and chlorogenic acids)

V. Kotovicz, E.F. Zanoelo / Journal of Food Engineering 116 (2013) 656–665

657

Nomenclature

an b D d E

e c Jo J1 k K mso ml msol Mo

x P

positive roots of Jo (ran) proportionality constant in Eq. (19) (kg kg1) diffusion coefficient (m2 s1) thickness of the discoid particles of mate (m) efficiency of extraction (%) mass of solution entering the solid phase at a kth pressure pulse (kg) parameter of the equilibrium-dependent model (s1) Bessel function of order zero Bessel function of first order kth pressure pulse total number of applied pressure pulses dry mass of solid fed in the extraction chamber (kg) mass of solvent fed in the extraction chamber (kg) mass of solution leaving the solid phase at a kth pressure pulse (kg) moisture content of mate leaves (d.b.) pulse rate (s1) pressure of extraction (kPa)

(e.g.; Cardozo et al., 2007). A reliable evidence that extraction towards process optimization was not considered is the high pressure range (10,000–25,000 kPa) always adopted in these investigations (at least for SFE and PLE) (Esmelindro et al., 2005; Cardozo et al., 2007; Jacques et al., 2006, 2007, 2008; Cassel et al., 2008; Grujic et al., 2012) whose influence on the capital cost is important in a real industrial extraction unit. Moreover, water was never applied as solvent in these investigations involving SFE, PLE and ultrasound-assisted extraction of soluble matter from mate leaves, which is a mandatory elementary aspect for producing ready-to-drink tea-like beverages. In this framework, the current study mainly aims to enhance the rate of removal of soluble matter from leaves of mate by applying hydrostatic pressure cycling extraction (HPCE). The increase of the equilibrium solute concentration in the liquid phase is an additional important objective with direct positive consequences on the maximum yield of extraction. With these purposes the kinetics of solute extraction was experimentally investigated in the pressure range from 91.4 to 338.2 kPa at 1:600 pulses per second, or without pressure pulses, for 25,200 s. All the experiments were carried out in a cylindrical pressurized vessel where comminute leaves of mate and distilled water were placed at ambient temperature (17 °C). An hybrid diffusive–convective model whose solution was analytically obtained was suggested to reproduce the kinetics of solid–liquid extraction at all the investigated operating conditions. 2. Materials and methods 2.1. Experiments Leaves of mate dried on commercial scale and cut into smaller pieces by industrial equipments were used in the experiments of extraction. In order to have a relatively homogeneous mass of particles in terms of size and shape, which are factors that have significant effect on mass transfer during extraction (e.g.; Bucic´-Kojic´ et al., 2007), the material fed in the extractor was preliminarily taken to a size analysis. It was made with a set of only two screens of the Tyler standard series (12 and 20 mesh) (Perry and Chilton, 1973) arranged serially in a stack shaken manually. Only the material retained on the 20 mesh screen was removed and applied for the investigation of the kinetics of extraction. The particles were

r R

C T t Xl Xs Xs Xso Xse Xl Xle Y Y1 z

radial direction of diffusion (m) radius of the discoid particle of mate (m) gamma function temperature of extraction (°C) time of extraction (s) average solute mass fraction in the liquid phase (kg kg1) average solute mass fraction in the solid phase (kg kg1) solute mass fraction in the solid (kg kg1) initial solute mass fraction in the solid (kg kg1) equilibrium solute mass fraction in the solid phase (kg kg1) solute mass fraction in the liquid phase (kg kg1) equilibrium solute mass fraction in the liquid phase (kg kg1) extraction yield (%) yield when all the solute is extracted from the leaves (%) axial direction of diffusion (m)

shaped like discs 1.13  103 m in average diameter and 0.23  103 m thick. The diameter represents the arithmetic mean between the opening of the screen through which the fraction passed and the other on which it was retained, while the thickness is the mean of several measurements early made with a digital micrometer (Jensen and Zanoelo, in press). It is well-know that insufficient water removal during the stage of drying of solids negatively affects solid–liquid extraction from grains or vegetable matrices (e.g.; Hofmann et al., 2012). However, in the absence of a Brazilian legislation regarding the commercial limits for the moisture content of packed mate leaves (ANVISA, 2005) mate manufacturers usually produce a final product with high values for this parameter (Zanoelo et al., 2008). For instance, it typically well exceed the upper limit stated for commercial tea shoots (3.6% d.b.) (Temple and van Boxtel, 2000). Based on these aspects, the moisture content of the comminute leaves of mate used in all the extraction experiments (Mo = 8.0 ± 0.1% d.b.) was determined in triplicate by oven drying at 105 °C for 24 h (AOAC, 1990). Aqueous exhaustive extraction of soluble matter was performed to experimentally determine the total content of soluble constituents in the examined solid particles. The experiment was performed with a sachet made of filter paper (0.08 kg m2) containing 7  103 kg of solid sample. In order to have the sachet fully immersed in the solvent it was put within a heavy stationary stainless steel screen basket. The entire structure was placed in an extractor open to the atmosphere and filled with 0.4 kg of distilled water kept at the boiling temperature at 91.4 kPa by using a hot plate with a manual control of temperature (752A, Fisatom Equipamentos Científicos Ltda, São Paulo, Brazil). The extraction vessel was periodically refuelled with hot fresh water to replace the quantity evaporated during extraction for 18,000 s. The difference between the initial and final mass of leaves again determined by oven drying at 105 °C for 24 h (AOAC, 1990) represents the total content of solute initially found in the solid phase. Under the same identical conditions the procedure was repeated three times. It is valuable to be aware that besides the importance for commercial purposes of having revealed the large content of solute typically found in the leaves of mate, the current experiment makes possible to calculate the equilibrium solute concentration in the solid phase based on the monitored experimental results of solute mass fraction in the solvent. The initial and the equilibrium solute concentrations in

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V. Kotovicz, E.F. Zanoelo / Journal of Food Engineering 116 (2013) 656–665

(a)

(b)

Fig. 1. (a) Block diagram of the main operations involved in the current investigation. (b) Schematic set up of the extraction system under constant pressure and assisted by pulsed hydrostatic pressure.

the solid are the initial and boundary conditions necessary to have the kinetics of mate extraction computed from Fick’s law. A polycarbonate cylindrical vessel with an internal volume equal to 6  105 m3 was used to study the kinetics of aqueous extraction at constant pressure or assisted by pulsed hydrostatic pressure. The extraction chamber was fed with 3  102 kg of distilled water at ambient temperature and 1.5  103 kg of comminute leaves of mate wrapped in a filter paper (0.08 kg m2). The vessel was sealed at the upper end with an internal piston mechanically moved up to a fixed position (defined by Boyle’s law) to have a pressure equal to 135.3 kPa. In order to determine the solute concentration in the solvent phase two liquid samples of 5  103 kg were always removed from the extraction chamber at the end of the process. However, in the particular case of HPCE two additional liquid samples of 1.5  103 kg were collected 1200 s and 2400 s before stopping infusion. The solute concentration in the liquid phase was again determined by a gravimetric analysis, that is, the difference between the initial and final mass of liquid sample determined by oven drying at 105 °C for 24 h (AOAC, 1990) divided by initial mass of solution represents the solute found in the liquid phase. Extraction time equal to 3600 s, 7200 s, 10,800 s, 14,400 s, 18,000 s, 21,600 s and 25,200 s were adopted for both HPCE and under constant pressurization. The entire experimental procedure was repeated at 91.4 kPa (atmospheric pressure), 202.9 kPa, 270.5 kPa and 338.2 kPa, respectively. All the liquid samples were weighed in a digital balance (Ohaus Adventurer, Toledo do Brasil Indústria de Balanças Ltda, São Bernardo do Campo, Brazil) with a precision of ±107 kg and placed in an oven (Q.317 B242, Quimis Aparelhos Científicos, Diadema, Brazil) at 105 °C for 24 h to determine the mass of soluble matter in the liquid phase. A rate of pressure pulses close to 1:600 pulses per second was assumed for all the experiments involving hydrostatic pressure cycling extraction. It means that a 300 s extraction cycle at 135.3 kPa, 202.9 kPa, 270.5 kPa or 338.2 kPa and a 300 s cycle at 91.4 kPa were consecutively applied up to the final extraction time (3600 s, 7200 s, 10,800 s, 14,400 s, 18,000 s, 21,600 s or 25,200 s). An additional HPCE experiment was performed at 270.5 kPa under 1:1200 pulses per second (i.e.; 600 s pressurization/depressurization cycles) in order to verify the influence of pulse rate on the examined responses (rate of extraction and equilibrium solute concentration in the solvent phase).

A calibrated mercury-filled thermometer was applied for obtaining 182 measurements of initial and final temperature of the stirred solvent during extraction at all the investigated conditions. From such readings was emerged an average temperature equal to 16.7 ± 1.4 °C. The reliability of the Boyle’s law at the current conditions was checked by a comparison between actual static pressures (sensed by a bourdon gage in the relative pressure range from 0 to 196.1 kPa) and those calculated according to the ratio of uncompressed to compressed volume of gas in the cylindrical extraction chamber. Fig. 1a summarizes the main physical operations involved in the current investigation whose detail description was already presented, while Fig. 1b shows an schematic extraction system that contributes to better comprehend the procedure of extraction under pressurized conditions. 2.2. Modeling The analytical solutions of the Fick’s second law for a flat plate (Eq. (1)) and a long cylinder (Eq. (2)) (e.g.; Arpaci, 1966; Welty et al., 1984) were combined to represent the transient two-dimensional problem of diffusion in the discoid particles of mate in the absence of hydrostatic pressure pulses.

 1  npz np2  X s ðzÞ  X se 4 X 1 ; sin exp Dt ¼ d X so  X se p n¼1 n d

n ¼ 1; 3; 5 . . . ð1Þ

1  h i X s ðrÞ  X se 2 X J o ðran Þ ¼ exp Dtðan Þ2 ; R n¼1 an J 1 ðRan Þ X so  X se

n ¼ 1; 2; 3 . . . ð2Þ

an are the positive roots of Jo(ran), while Jo and J1 are the Bessel functions of order zero and first order, respectively (Zill and Cullen, 1989). As noticed in Eq. (3), the unsteady diffusion taking place from the circular flat faces of the disc (z direction) and from the planes perpendicular to its axis (r direction) may be expressed as the product of the two unsteady one-dimensional solutions given by Eqs. (1) and (2) (e.g.; Sissom and Pitts, 1972).

V. Kotovicz, E.F. Zanoelo / Journal of Food Engineering 116 (2013) 656–665

   X s ðr; zÞ  X se X s ðzÞ  X se X s ðrÞ  X se ¼ X so  X se X so  X se X so  X se

ð3Þ

The aforementioned one-dimensional solutions were obtained by assuming a solid with an initial uniform mass fraction (Xso) and constant mass diffusivity (D). Since no resistance to mass transfer was considered at the interfacial surface, Xse are the equilibrium concentrations in the solid phase computed with Eq. (4) at equilibrium. Eq. (4) is a mass balance for the solute that may be easily rearranged to have an expression explicit in the variable Xse in terms of Xle.

Xl ¼

sÞ mso ðX so  X  ml ð1  X s Þ

ð4Þ

The equilibrium solute mass fractions in the stirred solvent (Xle) were tuned on the kinetic experimental results of Xl at the different investigated pressures based on Eq. (5), which considers that the initial solvent contains no solute. It is the first-order equilibriumdependent model extensively presented in the literature to describe solid–liquid extraction processes in a simplified way (e.g.; Linares et al., 2010; Pin et al., 2011). Both the adjustable parameters in Eq. (5) (Xle and Y) were computed by applying the Levenberg–Marquardt method of optimization.

X l ¼ X le ½1  expðctÞ

X s ðzÞ  X se 1 ¼ d X so  X se

Z

d



0

 X s ðzÞ  X se dz X so  X se

ð6Þ

 1  np2  X s ðzÞ  X se 8 X 1 ; ¼ 2 exp Dt 2 X so  X se p n¼1 n d X s ðrÞ  X se 1 ¼ X so  X se pR2

Z

R 0

X s ðrÞ  X se ¼ 2 X so  X se R

n¼1

n ¼ 1; 3; 5 . . .

ðan Þ2

h

exp Dtðan Þ2

i

ð7Þ

ð8Þ

)

i ¼ 1; 2; 3 . . . ; j ¼ 1; 3; 5 . . .

;

n ¼ 1; 2; 3 . . .

 R d  X s  X se 1 X s ðr; zÞ  X se dzdhdr ¼ r X so  X se X so  X se pR2 d 0 0 0    Z R Z 2p   1 X s ðrÞ  X se ¼ dhdr r X so  X se p R2 0 0  Z d   1 X s ðzÞ  X se  dz d 0 X so  X se

¼ 1ðk ¼ 1Þ;

K=2 X msol ðkÞ

e

K=2 X msol ðkÞ

ð10Þ

( ) 1 h i X s  X se 4X 1 2 ¼ 2 exp Dtðan Þ X so  X se R i¼1 ðan Þ2  1  np2  8 X 1 ; exp Dt  2 2 p j¼1 n d i ¼ 1; 2; 3 . . . ; j ¼ 1; 3; 5 . . .

msol ðkÞ

ð11Þ

The diffusion coefficient in Eq. (11) was tuned on the set of experimental solute mass fractions in the liquid phase by involving

k¼1

e

1 1 3 3 ðk ¼ 2Þ; ðk ¼ 3Þ; ðk ¼ 4Þ; ðk ¼ 5Þ . . . 2 2 8 8 ð13Þ

2 X Cðk þ 1=2Þ ¼ 1 þ pffiffiffiffi p k¼1 Cðk þ 1Þ ðK=2Þ

ð9Þ

Z 2p Z

ð12Þ

The modeling approach currently applied to describe internal convection is presented in detail in the literature (Ivanov and Babenko, 2005; Babenko et al., 2009). Anyway, it begins by representing the mass ratio of solution leaving to that entering the solid phase at a kth pressure pulse (Eq. (13)). The sum of the terms of this sequence may be written as a convergent series in terms of the gamma function for the total number K of applied pulses (Eq. (14)). However, it is more convenient to define it as an integral of a time dependent function (Eq. (15)), whose solution is easily found (Eq. (16)).

k¼1

From Eq. (10) one can easily observe that the one-dimensional solutions represented by Eqs. (7) and (9) may be again combined to evaluate the average solute mass fraction for two-dimensional transfer in the discoid particle of mate leaves (see Eq. (11)).

Z

( ) 1 h i X s  X se 4X 1 2 ¼ 2 exp Dtðan Þ X so  X se R i¼1 ðan Þ2 rffiffiffiffiffiffiffiffiffi!  1  np2  eX 8 X 1 8wt le  exp Dt 1þ ;  2 p j¼1 n2 d mso p

e

 Z 2p   X s ðrÞ  X se r dhdr X so  X se 0

( 1 4X 1

the simplex method of optimization and an objective function that is the sum of the square differences between the experimental and calculated kinetic results at a particular investigated pressure. The relation between the mean solute mass fraction in the solid and in the liquid is expressed by Eq. (4). A model that accounts for the effect of applying pressure pulses on the average mass of solute extracted from the leaves of mate is given by Eq. (12). It is the aforementioned expression to describe diffusion for the periods of extraction at constant pressure (Eq. (11)) with a term to compute solute transfer by internal convection for the instantaneous pulse of decompression. Such term (the last right-side one in Eq. (12)) represents the mass of solute flowing from the capillaries to the bulk liquid phase divided by the total mass of dehydrated leaves in the extraction chamber. It is basically derived from a model that describes the mass of solution (solute + solvent) removed from the solid at any t extraction time under the influence of pressure pulses (Ivanov and Babenko, 2005).

ð5Þ

The average mass fraction in the solid for the infinite slab up to any time was obtained by evaluating the integral defined by Eq. (6) whose solution is shown in Eq. (7). An analogous procedure, but involving the integral presented in Eq. (8), was applied to compute the transient responses of average solute mass fraction for the long cylinder (Eq. (9)).

659

1þ

rffiffiffiffiffiffiffi Z 2w

PK=2

k¼1 msol ðkÞ

e



1þ

p

ð14Þ

t

tð1=2Þ dt

ð15Þ

0

rffiffiffiffiffiffiffiffiffi! 8wt

p

ð16Þ

Multiplying the numerator on the right-hand side of Eq. (16) by the equilibrium solute concentration in the liquid phase gives the mass of solute in the solution removed by decompression at the solid–liquid interface. At this point is just necessary to remember that Eq. (12) depends on the constant mass of solution (e) forced into the particle at every pressure pulse, so it was tuned on the kinetic experimental results obtained by applying HPCE at the four different considered pressures. The same method of optimization and objective function early applied to determine the diffusion coefficient were again adopted to calculate the adjustable model parameter e. 3. Results and discussion Fig. 2 shows the extraction curves at 135.3 kPa, 202.9 kPa, 270.5 kPa and 338.2 kPa without applying hydrostatic pressure

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0.02

0.6

0.016

(b)

0.6

0.5

0.016

0.5

0.012

0.4

0.012

0.4

0.008

0.3

0.008

0.3

0.004

0.2

0.004

0.2

0.1 25200

0

0 0

6300

12600

18900

Xs

Xl

0.02

Xs

Xl

(a)

0

6300

18900

0.1 25200

t (s)

t (s)

(d)

0.6

0.5

0.016

0.5

0.012

0.4

0.012

0.4

0.008

0.3

0.008

0.3

0.004

0.2

0.004

0.2

0.1 25200

0

0.016

Xs 0 0

6300

12600

18900

t (s)

Xs

0.6

Xl

0.02

0.02

Xl

(c)

12600

0

6300

12600

18900

0.1 25200

t (s)

Fig. 2. Experimental (symbols) and calculated (lines) average solute mass fractions in the liquid and solid phase during the extraction of soluble matter from leaves of mate under constant hydrostatic pressure (a: 338.2 kPa; b: 270.5 kPa; c: 202.9 kPa; and d: 135.3 kPa) at 16.7 °C. Solid lines: Eq. (11) (two-dimensional diffusion); dashed line: Eq. (7) (one-dimensional diffusion in a flat plate).

pulses. For all the cases the shape of the curves is the same, that is, as time passes the average solute mass fraction exponentially decreases in the solid and increases in the liquid phase. In other words, the contact between the solid and solvent causes solute to move from the particles to the liquid phase in such a way that the rate of extraction falls with time. Such a behavior is not only well described by Fick’s law of diffusion as shown in Fig. 2, but also by the simplified equilibrium-dependent model (R2  0.96) applied to determine the equilibrium solute concentration in the liquid phase. Remember that this is the boundary condition imposed to have the solutions of the transient one-dimensional and twodimensional diffusive problems. The results presented in Fig. 2 also confirm that Eqs. (7) and (11) satisfy the initial condition in the solid phase. However, more important than that is the high percentage of soluble matter (42% ± 3%) initially found in the dry leaves of mate (see Fig. 2 at t = 0), which emerges from three readings of the same variable, i.e., 42.6%, 38.6%, and 44.9%. As already commented in the literature (Jensen and Zanoelo, in press), it supports the commercial importance of mate to produce non-alcoholic tea-like beverages. An almost identical content of solute in dry basis was early obtained by the same authors (Jensen and Zanoelo, in press) and at least by other three independent researchers (Escalada et al., 1998; Valduga et al., 2001; Linares et al., 2010). It supports the reliability of the current experimental procedure of exhaustive extraction and corroborates the results currently calculated with the Fick’s law whose solution depends on the initial solute concentration in the solid.

A comparison between the unsteady average solute mass fraction in the liquid phase for the discoid particle and for onedimensional diffusion in a flat plate is also shown in Fig. 2. The effect of neglecting mass transfer from the lateral surface of the discs (i.e.; the effect of finite cylindrical length) lowers in average the solute mass fractions by 8% ± 7%. The high standard deviation for the considered set of computed data suggests the considerable variation of the relative difference with pressure, but mainly with time. In fact, for some particular conditions the solute mass fraction calculated with Eq. (11) was up to 35% greater than the value determined from Eq. (7). Such results confirm the importance of the edges on the short thin discs that represent the comminute leaves of mate. Fig. 2 also reveals a positive effect of pressure on both extraction rate and solute equilibrium concentration in the stirred solvent. It is clear that both the responses increase when the force continuously exerted by the piston and transmitted to the solid– liquid system was increased. However, an important aspect that is not promptly observed in Fig. 2 is that such parameters, whose trends with pressure are definitely best seen by examining Fig. 3a and b, are strong functions of pressure in certain different regions of pressure. The equilibrium solute concentration is not significantly affected by the pressure at very high pressures, that is, when P approaches infinity, but in the vicinity of the atmospheric pressure it is almost linearly increased with P. On the other hand, the extraction rate essentially depends on the effective diffusion coefficient, which rises marginally near the atmospheric pressure, but it increases without limit as P becomes infinite. Eqs. (17)

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V. Kotovicz, E.F. Zanoelo / Journal of Food Engineering 116 (2013) 656–665

(a)

(b) D-Datm (x1013) (m2/s)

0.028

Xle

0.021

0.014

0.007

12

8

4

0 0 0

200

0

400

200

P (kPa)

P (kPa)

50

0.02

0.6

0.016

0.5

40

0.012

0.4

30

0.008

0.3

0.004

0.2

10

0.1 25200

0

0 0

6300

12600

18900

Y (%)

(d)

Xs

Xl

(c)

400

Y∞(Xs→0)≈42 %

P→∞

≈338 kPa ≈270 ≈203

20

≈135 ≈91 kPa

0

6300

12600

18900

25200

t (s)

t (s)

Fig. 3. (a) Equilibrium solute mass fractions in the liquid phase (symbols: tuned on experimental results with Eq. (5); line: calculated with Eq. (17)). (b) Diffusivity (symbols: tuned on experimental results with Eq. (11); line: calculated with Eq. (18)). (c) Experimental (symbols) and calculated (lines) average solute mass fractions in the liquid and solid phase at ambient temperature and atmospheric pressure. Solid lines: Eq. (11) (two-dimensional diffusion); dashed line: Eq. (5) with parameters determined by Jensen and Zanoelo (in press). (d) Calculated extraction yield (Eq. (19)) at different pressures without applying hydrostatic pressure pulses.

and (18) summarize the dependence of both these parameters upon pressure at the investigated operating conditions.

X le ¼ 2:204  102 ½1:0  exp ð  3:434  103 PÞ

ð17Þ

D ¼ 4:542  1013 þ 5:261  1016 exp ð2:169  102 PÞ

ð18Þ

According to our point-of-view any possible explanation for the observed effects of pressure depends on an elementary understanding of the internal structure of the investigated solid. As occurs for leaves in general (e.g.; Roberts et al., 2000), fractions of interior gas (CO2, O2, water vapor), usually referred to as intercellular air spaces (e.g.; Woolley, 1983) are found between the irregularly shaped cells of the spongy mesophyll parenchyma in fresh leaves of mate. Although dehydrated leaves no more consume or produce any gas involved in the photosynthesis, and leaves usually shrink during drying (e.g.; Temple and van Boxtel, 1999) (a mandatory preliminary operation for solid–liquid extraction), the comminute leaves of mate can be still considered a highly porous solid containing internal gas. Such gas when compressed is believed to cause internal implosions with rupture of plant tissues that makes the interior of the cells rich in soluble matter exposed to solvent. Whatever the mechanism by which cell disruption takes place (e.g.; cavitation) during extraction (microwave-assisted, pulse electric field-assisted, ultrasound-assisted, high-pressureassisted), it not only shifts the equilibrium towards high extraction yields (i.e.; increases Xle), but always reduces the time of extraction

(i.e.; increases D) (Zhang et al., 2011; Lebovka et al., 2012). The increase of the effective diffusion coefficient may be also attributed to changes in the porosity and tortuosity (Greenkorn and Kessler, 1972), as well as to the gradient of pressure formed between the inner and outer cell membranes (Lebovka et al., 2012). The kinetics of solute extraction from the leaves of mate at atmospheric pressure and ambient temperature is presented in Fig. 3c. Typical curves of extraction quite close to results based on evidences already reported in the literature were obtained (Jensen and Zanoelo, in press). The transient two-dimensional diffusion model was again able to describe correctly the experimental solute concentration, so the estimated diffusivity (the first rightside term in Eq. (18)) may be compared with the few analogous results available in the literature (Linares et al., 2010; Jensen and Zanoelo, in press). From this analysis emerges a diffusion coefficient that is in the magnitude of the same transport property obtained by Jensen and Zanoelo (in press), but two orders of magnitude lower than that determined by Linares et al. (2010). Such discrepancy may be mainly attributed to the extraction conditions, which were almost identical in the case of the current experiments and those performed by Jensen and Zanoelo (in press) (i.e.; T = 16.7–18 °C, P  91.4 kPa, discoid particles of mate with R = 0.65  103 m and d = 0.23  103 m, b = ratio between water and the dry solid 22–25), but moderately different when both of them are compared to that adopted by Linares et al. (2010) (i.e.; T = 40–70 °C, P = atmospheric pressure, particles of mate with d = 0.22–0.27  103 m, b  8). Moreover, it is necessary to

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(b)

0.4

r/R=0

r/R=0.84

Xs 0.25

0.3

0.92

0.3

0.35

r/R=

r/R= 0.88

0.35

0.4

Xs

(a)

0.25

r/R=0.96

0.2

0.2

r/R=0.99 0.15

0.15 0

0.2

0.4

0.6

0.8

0

1

0.2

0.4

(c)

0.6

0.8

1

0.6

0.8

1

z/ δ

z/ δ

(d)

0.3

0.25

0.3

Xs

Xs

0.25

0.2

0.2

0.15

0.15 0

0.2

0.4

0.6

0.8

1

z/ δ

0

0.2

0.4

z/ δ

Fig. 4. Calculated (Eq. (3)) solute mass fraction of the discoid particle of mate leaves for extraction time equal to 3600 s (a), 7200 s (b), 10,800 s (c) and 14,400 s (d) at 270.5 kPa.

consider that different modeling approaches were adopted for the examined cases, which could be at least in part responsible for the observed differences among these diffusivities. From a practical point-of-view the enhance of extraction yield most clearly reveals the positive influence of pressure on extraction. Such response has a visible impact on the cost of raw materials (water and mate leaves), which is the main economical concern whether the extraction is performed at ambient temperature (energy costs minimally contributes for increasing the overall manufacturing cost at such circumstances). For that reason Fig. 3d shows the unsteady yields computed with Eq. (19) in the pressure range from 91.4 to 338.2 kPa. The estimated variable is linearly proportional to the average mass fraction in the liquid phase, which contributes to better comprehend the influence of pressure on solute concentration presented in Fig. 2. The proportionality constant b in Eq. (19) is the ratio between the mass of water and dry solid.

Y ¼ 100bðX l Þ

ð19Þ

In agreement with the results of equilibrium solute concentration shown in Fig. 3a at low pressures, an almost linear variation of the extraction yield with respect to the pressure is observed in Fig. 3d at long extraction time. Again, the extraction yield does not increase indefinitely with pressure, but approaches a maximum value that is obtained when the average Xl is 1.946  102. Such mass fraction, calculated with Eq. (4) at an average Xs equal to zero, is close to the maximum Xle from Eq. (17), i.e., Xle shown in Fig. 3a when P approaches infinity. The plots of Y versus time also give curves whose slopes before the equilibrium follow exactly

the same dependence on pressure already evidenced for the diffusion coefficient in Eq. (18) and Fig. 3b. Therefore, if the pressure raises much beyond 338.2 kPa a straight line with slope that approaches +1 is expected in Fig. 3d at the initial extraction time. Fig. 4 illustrates the mass fraction distribution in the discoid particles of mate leaves in terms of two dimensionless relative positions at four different extraction time (3600 s, 7200 s, 10,800 s, 14,400 s) and under constant pressure (270.5 kPa). For all the cases, the solute concentration is symmetrically distributed with respect to both the axial and radial axes, i.e., @Xs/@r = 0 at r = 0 and @Xs/@z = 0 at z = d/2. It occurs because the lower and upper flat face, as well as the entire perimeter of the disc are in contact with a liquid phase at identical solute concentration. As expected, a comparison among Fig. 4a–d shows that the concentration at the same fixed position decreases as extraction time increases. Fig. 4 also reveals that the plots of Xs against z/d more significantly vary with r/R close to the external radial layers (approximately from r/R > 0.8). As already supposed the mass transport in the radial direction has a minor impact on the axial concentration profiles away from the lateral surface of the disc. The results of hydrostatic pressure cycling extraction at 135.3 kPa, 202.9 kPa, 270.5 kPa and 338.2 kPa are presented in Fig. 5. The most important aspect that emerges from these plots is that the computed average solute mass fractions in the liquid phase for HPCE (Eq. (12)) are always higher than those calculated (Eq. (11)) without applying hydrostatic pressure pulses. As one may promptly infer from Fig. 5, these estimated results may only be compared because the hybrid diffusive–convective model represented by Eq. (12) well describes the HPCE curves for the entire period of extraction. The cause of the positive influence of hydrostatic

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0.02

0.6

0.016

(b)

0.6

0.5

0.016

0.5

0.012

0.4

0.012

0.4

0.008

0.3

0.008

0.3

0.004

0.2

0.004

0.2

0

6300

12600

18900

Xs

Xs 0

Xl

0.02

Xl

(a)

0.1 25200

0 0

6300

t (s)

18900

0.1 25200

t (s)

(d)

0.6

0.5

0.016

0.5

0.012

0.4

0.012

0.4

0.008

0.3

0.008

0.3

0.004

0.2

0.004

0.2

0.016

Xs 0 0

6300

12600

18900

Xs

0.6

Xl

0.02

0.02

Xl

(c)

12600

0

0.1 25200

0

6300

12600

18900

0.1 25200

t (s)

t (s)

Fig. 5. Experimental (symbols) and calculated (lines) average solute mass fractions in the liquid and solid phase for HPCE at 338.2 kPa (a), 270.5 kPa (b), 202.9 kPa (c) and 135.3 kPa (d) (T = 16.7 °C) with 1:600 pulses per second. Solid lines: Eq. (12) (hybrid diffusive–convective model); dashed line: Eq. (11) (two-dimensional diffusion).

pressure pulses on extraction is the movement of solution (water + solute) through the microchannels found in the comminute leaves of mate. It means that solute transfer from the solid to the liquid bulk phase occurs for a very short period at any time the extraction chamber is depressurized. Such periodical removal of solute by convection explains the enhance of the extraction evidenced in Fig. 5 for HPCE. A large number of theoretical investigations available in the literature supports the importance of convection on the extraction under the influence of pressure pulses (e.g.; Abiev and Ostrovskii, 2001; Ivanov and Babenko, 2005; Babenko et al., 2009). Experimental studies available in the literature reported analogous advantageous of applying extraction assisted by pulsed hydrostatic pressure at similar conditions and involving a similar mechanism of mass transfer (Naviglio, 2003; Naviglio et al., 2007, 2008, 2009). Pressure cycling technology has also been applied with different purposes, but at much higher pulse rates and pressure (e.g.; Bradley et al., 2000; Okubara et al., 2007; PBI, 2007; Szabo et al., 2010). At such more drastic conditions the pulses of pressure are believed to contribute to cavitation, which typically occurs when involving some innovative techniques of extraction (Zhang et al., 2011; Lebovka et al., 2012), with consequent disruption of cellular structures (PBI, 2007). The last term on the right-hand side of the Eq. (12) is in essence responsible for increasing the rate of extraction at all the investigated pressures, but in a fashion that the observed increase of average Xl reduces with pressure. From a mathematical perspective, the sharp reduction of the single adjustable parameter of the hybrid model with pressure is sufficient to explain such behavior (see Fig. 6a and Eq. (20)). The non-linear influence of pressure on HPCE

curves computed with the hybrid diffusive–convective model is better shown in Fig. 6b. Eq. (20) is an empirical expression that represents the influence of pressure during hydrostatic pressure cycling extraction on the tuned model parameter (e) of the hybrid diffusive–convective model. The coefficients of such a correlation were calculated by applying the Levenberg–Marquardt method of optimization in order to minimize the sum of the square differences between the experimental and calculated results shown in Fig. 6a.

e ¼ 7:514  101 expð1:165  102 PÞ

ð20Þ

Fig. 7a reports two sets of experimental kinetic results for HPCE obtained at identical operating conditions (i.e.; T = 16.7 °C, P = 270.5 kPa), except for the pulse rate. It promptly reveals that almost all the solute concentration at 1:1200 pulses per second tend to fall between the limits of the error bars that represent the same results at 1:600 pulses per second. In other words, it is quite evident there is no significant change in the considered responses produced by the modification in the level of the investigated factor. On a commonsense basis, it means the influence of pulse rate on extraction curves was negligible at the examined conditions. Fig. 7b presents a comparison between the curves of maximum and minimum efficiency of solute extraction. Efficiency is currently defined (see Eq. (21)) as the ratio between the yield at a particular extraction time and that obtained if all the solute is removed from the leaves of mate (Y1 = 42%).

E ¼ 100

Y Y1

ð21Þ

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(a)

(b)

30

3.70xPatm

0.016

20

0.012

Xl

ε (x104) (kg)

0.02

10

2.96xPatm 2.22xPatm

0.008

1.48xPatm

0

0.004

Patm -10

0 0

100

200

300

400

500

0

6300

P (kPa)

12600

18900

25200

t (s)

Fig. 6. (a) Adjustable model parameter of the hybrid diffusive–convective model for describing the kinetics of HPCE (symbols: tuned on experimental results reported in Fig. 5 by involving Eq. (12)). (b) Influence of pressure on calculate unsteady solute mass fractions in the liquid phase (Eq. (12)). Operating conditions: HPCE, T = 16.7 °C and x = 1/ 600 s1.

(a)

0.016

(b) 100 16.7 oC, 338.2 kPa

80

0.012

E (%)

Xl

60 0.008

0.004

101.5 oC, 91.4 kPa

40 20

16.7 oC, 91.4 kPa

0

0 6300

12600

18900

25200

0

t (s)

6300

12600

18900

25200

t (s)

Fig. 7. (a) Effect of pressure pulse rates on kinetic results of average solute mass fractions in the liquid phase at ambient temperature and at 270.5 kPa (bars: x = 1/600 s1; lozenges: x = 1/1200 s1). (b) Experimental (symbols) and calculated (lines) extraction efficiencies at different operating conditions.

A maximum efficiency of approximately 80% was obtained by applying hydrostatic pressure pulses at 338.2 kPa, while a poor extraction with efficiencies not higher than 30% was observed by infusion at atmospheric pressure. A further important aspect emerged from Fig. 7b for HPCE is the time required to have the highest efficiency, which is much shorter than that taken to obtain an analogous response by infusion at atmospheric pressure. An additional curve of extraction whose efficiency is also approximately 80% at equilibrium, but for infusion at atmospheric pressure, is presented in Fig. 7b. It was drawn with Eq. (5) by involving empirical relations dependent on temperature to compute the model parameters (Jensen and Zanoelo, in press). The purpose of such curve is to evidence that a high temperature (close to the boiling point of water at atmospheric pressure) with detrimental effects on energy consumption and on recovery of thermolabile species is necessary to have the same maximum efficiency early found for HPCE at ambient temperature.

4. Conclusions Experiments of solute extraction from leaves of mate were performed in a batch extractor with water as solvent and by applying or not hydrostatic pressure pulses. A large set of kinetic experimental results of solute concentration were obtained over the pressure range from 91.4 to 338.2 kPa at ambient temperature

for 25,200 s. The rates of solute removal and equilibrium solute concentration were increased when extraction was assisted by hydrostatic pressure pulses. Analogous changes on the same responses were always observed by modifying the pressure, but a negligible influence of pulse rate on the unsteady solute mass fractions was revealed at the investigated conditions. Both the diffusive and hybrid diffusive–convective model correctly described the kinetics of extraction without and with pressure pulses, respectively. On the whole, the findings suggest the performance of the typical operation of extraction of soluble matter from leaves of mate, i.e., infusion at atmospheric pressure, may be markedly increased (the efficiency was increased from 30% at 91.4 kPa to 80% and the time to have 90% of the highest efficiency was reduced from 17,000 s at 91.4 kPa to 6000 s) by applying hydrostatic pressure pulses at only 338.2 kPa. Such innovative technique also avoid the typical negative impacts of temperature that would be expected by infusion close to the boiling point of water at atmospheric pressure. References Abiev, R.Sh., Ostrovskii, G.M., 2001. Modeling of matter extraction from a capillary porous particle with a bidisperse capillary structure. Theoretical Foundations of Chemical Engineering 35, 254–259. ABIR-Associação Brasileira das Indústrias de Refrigerantes, 2008. Dados de mercado 2008. Evolução de bebidas não alcoólicas por categorias – 2004 a 2008. (Last access 20.09.12).

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