J . Chem. Soc., Furaduy Trans. 1, 1982, 78, 295-305 Kinetics and Equilibria of Tea Infusion Part 3.l-Rotating-disc Experiments Interpreted by a Steady-state Model BY MICHAEL SPIRO" AND DAVID S. JAGO Department of Chemistry, Imperial College of Science and Technology, London SW7 2 A Y Received 5th March, 1981 The kinetics of the extraction of a soluble constituent from tea leaf have been treated by a steady-state model. This leads to an overall rate constant made up of 3 main contributions which arise from the diffusion of the constituent through the leaf, its transfer across the leaf/water interface, and its diffusion away through the Nernst layer. That the last step was not the rate-determining one was shown by rotating-disc experiments. Koomsong tea dust was glued on to large discs and the rate of caffeine extraction at 80 O C measured at various rotation speeds.The rate was found to be independent of the speed. The viability of the experimental procedure was checked using discs coated with similarly-sized copper powder: here the rate of attack by dilute dichromate increased with increasing rotation speed in semi-quantitative agreement with the Levich equation. When one considers the popularity and commercial importance of tea, it is surprising how little attention has been paid to the kinetics of its infusion. Only during the last two years have quantitative measurements been published. Long2 determined the rate of extraction of all soluble material from a black tea blend, and Spiro and Siddiquel obtained rate constants for the infusion of theaflavins, thearubigins and caffeine from Koonsong Broken Pekoe. Both groups of workers derived simple kinetic equations of the type for the infusion of a single constituent such as caffeine; its concentration in the solution is c at time t and c, at equilibrium, and kobs is the overall rate constant. We shall begin by deriving this equation in such a way that the contributions to kobs of the various infusion steps are made manifest.THEORY In an infusion experiment, tea leaf of mass w is immersed in a volume I/ of water. Swelling of the leaf is taken to be essentially complete before significant solute extraction has occurred.lT3 The absorption of water by the leaf does not significantly diminish the solution volume when, as in our experiments, the water: leaf ratio is large.The swollen leaf may be conveniently regarded as a collection of lamina of width 2d and total surface area A . If the small area around the edges of the lamina is neglected, the leaf volume VIeaf equals 2d(A/2) = Ad. We shall now apply a steady-state treatment analogous to that used successfully for the kinetics at liquid/liquid interface^.^ The model is illustrated by the concentration profiles in fig. 1 . In these c' is the concentration of the particular constituent (in g dm+ or mol dmP3) in the centre of the leaf lamina, c; and c, its concentrations on the leaf side and on the solution side of the interface, respectively, and c its concentration in 295296 KINETICS OF TEA INFUSION ct s o h t ion Leaf s o l u t i o n 7 k- 1 distance distance l e a f solution distance FIG.1.-Schematic concentration profiles during tea infusion at (a) t = 0; (b) t = t ; (c) t = co. the bulk solution outside the Nernst diffusion layer of effective thickness 6. The first-order rate constants for transfer of the constituent across the interface are k , from leaf to solution and k-, in the opposite direction (both in m s-l). The partition coefficient K is therefore given by In the steady state, the flux J(in g s-l or mol s-l) of a soluble constituent like caffeine is given by the following kinetic equations: j = d(cV)/dt = ADIeaf (c’-c;)/~ = A(k, C; - k-, c,) = ADsoln (c,-c)/6 where eqn (4) and (6) are applications of Fick’s first law and the diffusion coefficients D are those of the constituent in question.Although Dleaf is likely to be dependent on either distance or concentration or both, the practice of replacing a non-Fickian diffusion system by a corresponding Fickian one is well e~tablished.~ Elimination of the unknown concentrations c; and c, between eqn (4)-(6) now leads to Incorporation of eqn (2) in eqn (7) gives To eliminate c’ we must draw on the conservation equations. If T is the total amount of the soluble constituent in the system, then at times t = 0, t = GO and t = t, (9) respectively : = Ad&+ VC, (10) T = Adch c’ + c; = Ad (7) + A6 (T) + ( V - A6)c.M. SPIRO AND D. S. J A G 0 297 Combination of eqn (10) and (1 l), with the removal of c; and c1 by means of eqn (12) (4) and (6), gives A~(c’-c&) = V ( C , - c ) + - This makes it possible to eliminate (c’-c&) from eqn (8): On dividing through by kPl7 and making use of eqn ( 2 ) and (3), Kd 6 +- - - J (for short) Ak‘ =-I(&) Ak’ dt * Integration to eqn (1) follows directly.The overall first-order rate constant kobs can now be expressed in several ways: by applying eqn (2), ( 9 ) and (10). Since both A and Vieaf are proportional to the mass w of tea employed for a given type of leaf, it follows that kobs will vary linearly with w/ V . However, this variable term forms only a minor part of kobs in the experiments below. Combination of eqn (14) and (1 5) gives I A K 1 1 Kd 6 Kd2 -+- +-+- k,,(L’+>) = k. = k-, 2D,,,, Dsoln 2DSolnd‘ (16) The last term on the right-hand side of eqn (16) can usually be neglected as it will almost always be much smaller than the 6/Dsoln term. We now have 3 special cases according to the relative sizes of the other terms on the right-hand side: (i) If l/k-l is the largest term, k’ z k-, and the infusion is surface-controlled.It is worth noting that the relevant rate constant is that of the re-absorption of the constituent into the leaf. (ii) If the second term is the largest, k‘ z 2Dleaf/Kd and the rate-determining step is diffusion of the constituent through the swollen leaf. (iii) If 6/Dsoln is the largest term so that k’ Dsoln/6, the infusion is controlled by diffusion of the constituent across the Nernst layer. Whether step (iii) is the rate-determining one should be testable by allowing the infusion to take place on the surface of a horizontal rotating disc.For such a system, suitably designed, 6 is known to vary inversely with the square root of the angular velocity w (in rad s-l) according to the limiting Levich equation6 6 = 1.612 Dtoin vf u-4 (1 7) where v is the kinematic viscosity of the solution. Thus, if the rate of infusion from a tea-coated disc increases proportionately to z/u, the process is controlled by298 KINETICS OF TEA INFUSION diffusion of the constituent across the Nernst layer. On the other hand, step (i) or (ii) must be rate-determining if the infusion rate is independent of the rotation speed. The validity of the proposed method depends upon the applicability of the Levich equation to a tea-coated disc. Its surface irregularities (of the order of 1 mm) considerably exceed the thickness of the diffusion layer (S M 0.03-0.07 mm), contrary to the requirements of the theory.Certain experimental reports in the literature are, however, more encouraging. A set of small burrs on a disc surface did not affect the Levich equation7 and coarse sand glued to a large disc only slightly reduced the Reynolds number above which turbulence sets * Nevertheless, the only safe answer to the present problem can be obtained by performing an analogous experiment with a system of known properties. A suitable one is the dissolution of copper in acid dichromate soiutions : 3Cu + 14H+ + CT,O,~- -+ 3Cu2+ + 2Cr3+ + 7H,O. This reaction has been studied with a flat copper disc by Gregory and Riddifordg who found the rate to be proportional to dco and established that the slow step was diffusion of dichromate ions to the copper surface. At sufficiently high acidity the reaction was first order in dichromate with a rate constant given by k = DA/V6 (18) where D is the diffusion coefficient of the dichromate ion and A the area of the copper disc.When the Levich equation, eqn (17), for 6 is introduced, the dependence of k on the square root of the rotation speed follows naturally. Moreover, for a given rotation speed the value of 6 appropriate to this reaction at 25 OC is only 10% smaller than that for caffeine diffusion at 80 OC. Experiments were therefore carried out with both tea-coated and copper-coated discs as described below. EXPERIMENTAL PREPARATION OF TEA COATING To obtain a smoother surface we did not employ normal-sized tea leaf but a Northern Assam black tea dust (Koomsong) kindly supplied by Cadbury Typhoo Ltd.A subsequent size analysis with a mechanical sieve shaker showed that only 2% was retained on 25 mesh, 49% on 36 mesh, 40% on 52 mesh and 9% passed through 52 mesh. Several commercial glues were tested for their effectiveness in attaching tea to the underside of the disc. The glues, after drying, were evaluated by 3 criteria: the strength of bonding of the tea dust, the evenness of coverage by the tea, and the thickness or tightness of the tea layer. Double-sided Sellotape failed on all counts, Uhu No. 10 lacked bonding strength, Bostick No. 1 gave an insufficiently even cover and Superglue did not produce a tight enough layer. The best adhesion by all criteria was provided by thick layers of Copydex and Evostick.Both were employed. Copydex could be peeled off after a run while a scalpel was required to remove Evostick; the latter, however, showed better bonding characteristics when immersed in hot water and so became the preferred adhesive. To prepare the coating, the disc was turned face upwards and a thick layer of glue spread on its surface. A known weight of tea dust was poured on it to form a tea layer ca. 1 cm in depth. This was pressed down firmly and evenly. The glue was then left to dry for 2 h and the loose tea knocked off and weighed. Any glue that had seeped over the edge of the disc was cut off. This method of preparation gave a very satisfactory coating and the layer of loose tea left on the disc during drying protected the glued tea underneath from atmospheric moisture and loss of volatile constituents by evaporation.M .S P I R O AND D. S. J A G 0 299 THE DISC AND OTHER APPARATUS The kinetic runs with tea were carried out in a well-insulated and covered thermostat bath at 80 O C . This is one of the temperatures chosen by previous workers;l, it is high enough for typical infusion behaviour to be exhibited and for the avoidance of tea cream formation, and it is low enough to allow loss of water from the reaction vessel by evaporation to be corrected for (see Appendix). 80 78 0 1 3) 2 76 2 E !a 4 d 7 4 72 I I I I I I 1 2 3 I+ 5 t/min FIG. 2.-Temperat:ire against time curves obtained on immersing 7 cm discs rotating at 100 r.p.m. in 200 cm3 water in a thermostat bath at 80 "C : ( a ) brass disc, glass container; (b) Perspex disc, glass container; (c) Perspex disc, thin metal container.The disc was of the trumpet shape recommended for preventing interaction between the upper and lower fluid f l o w ~ . ~ The large diameter of the bottom face (7 cm) enabled sufficient tea to be attached. According to the accepted Reynolds number6 of 2 x lo5, streamline flow should be maintained at a 7 cm disc in water at 80 "C up to 570 r.p.m. In practice the rotation speed (held constant by a Servomex MC 43 motor controller) was never raised above 300 r.p.m. When a standard brass disc was immersed in the 200 cm3 of water at 80 OC in the glass reaction vessel, a sudden temperature drop of ca. 10°C was produced [fig. 2(a)]. Since pre-heating the disc was impractical, it was replaced by one made of Perspex.This possesses a much lower thermal conductivity and so absorbs heat from the reaction system more slowly. Fig. 2(6) shows that the temperature drop was smaller but still unacceptable. It is clear from the shape of the curve that more rapid heat transfer was required from the thermostat bath to the solution itself. The glass reaction vessel was therefore replaced by an appropriately sized container with thin metal walls: an empty lacquered 16 oz can (i.d. 10 cm) served admirably. Fig. 2(c) demonstrates the marked improvement in temperature stability. Such variation in solution temperature as remained was relatively unimportant in view of the low activation energies of the infusion processes.' With the tea leaf used previously a drop of 1 "C would decrease the rate of caffeine extraction by less than 0.2%. A set of blank experiments showed that the metal reaction vessel did not interact with water at 80 "C and that neither the disc, the dried glue nor the vessel adsorbed caffeine.Polyphenokaffeine interaction in the solution was minimised by using a large water:leaf ratio (> 100).300 KINETICS OF TEA INFUSION PROCEDURE FOR KINETIC EXPERIMENTS WITH TEA Sufficient distilled water to give a volume of 200 cm3 at 80 "C (194.4 g) was weighed into the metal reaction vessel. The vessel was sealed with a Perspex cover and allowed to come to thermal equilibrium in the thermostat. The tea-coated disc was then mounted on the shaft of the Servomex motor, the speed controller switched on with the speed preset, the Perspex cover removed from the reaction vessel and the rotating disc lowered into the water.It was important to carry out this sequence of operations quickly to minimise steam rising up and onto the disc. With practice the disc could be mounted and lowered within 5 s. Any air trapped by the disc emerged as a bubble within 2 s of immersion. Six samples of the solution were taken with a 1 cm3 pipette at 4 min intervals, with a further sample after 30 min to obtain the equilibrium concentration. Inaccuracy owing to temperature variations was reduced by leaving every sample in the pipette for the same length of time (1 5 s) between removal and delivery. Each sample was added to 7 cm3 distilled water in a 10 cm3 volumetric flask for rapid dilution to avoid cream formation; the volume was then made up to the mark to form solution E.l0 The caffeine was separated from the other tea constituents by passing a known aliquot of solution E down a chromatographic column of swelled polyamide CC6, followed by solvent extraction with chloroform and spectrophotometric analysis at 273.5 nm.Details are given elsewhere.lO The addition of solution to the columns was greatly facilitated in the present work by glassblowing funnel attachments to their tops. When the last sample had been taken, the metal reaction vessel was removed and weighed to find the water lost by evaporation and sampling. This amounted to 30-40 cm3 over a period of 30 min and was measured for each run. The water loss was not significant during the first three minutes when the kinetic samples were taken but considerably affected the equilibrium value.The necessary correction is derived in the Appendix. A kinetic run was also done with 1 g loose Koomsong tea dust in 200 cm3 water at 80 OC, with agitation by a mechanical overhead stirrer rotating at 100 r.p.m. KINETIC EXPERIMENTS WITH A COPPER-COATED DISC A quantity of copper powder was sieved with a mechanical shaker and, from the portions retained by each sieve, a mixture was made up to contain the same percentages of mesh sizes as in the tea dust. This copper powder was then attached with Evostick glue to the Perspex disc, exactly as described earlier. The copper-coated surface possessed the same general appearance as a tea-coated disc.The experiment was carried out in a thermostat at 25 OC with a glass reaction vessel of similar size and shape to the metal vessel used for the tea runs. The procedure followed that given by Gregory and Riddif~rd.~ A solution (300 cm3) of potassium dichromate (0.02 equiv dm-3) in sulphuric acid (1 mol dm-3) was placed in the vessel and allowed to come to thermal equilibrium while a stream of nitrogen was passed through it to remove dissolved oxygen. The disc was then set to rotate at 50 r.p.m. and lowered into the solution. Samples of the solution were withdrawn every 3 min with a 10 cm3 pipette and were added to portions (20 cm3) of ferrous ammonium sulphate (0.02 mol dm-3) in 1 mol dm-3 sulphuric acid. The excess ferrous ions were backtitrated against standard K,Cr,O, solution using as indicator N-methyldiphenylamine- p-sulphonic acid in H3P0, solution.Just before every second sample was taken the speed of rotation was changed so that it alternated between 50 and 300 r.p.m., being at each speed for 6 min. With practice it became possible to alter the speed during the 5 s prior to removal of the sample. The sampling itself took up to 3 s. It seems unlikely that errors introduced by these short operational periods significantly affected the results. A blank run showed that the acid dichromate solution attacked neither the disc nor the glue.M. SPIRO AND D. S. J A G 0 RESULTS AND DISCUSSION The copper dissolution results were treated in the manner of Bradley," who has shown that, for a first-order surface reaction in which aliquots of solution are removed, 30 1 i=j-1 F(c) = Viln(ci/ci+J = rcti (19) i-0 where Vi is the volume and ci the concentration after i aliquots have been removed and ti is the time of removal of thejth aliquot. It follows from eqn (17) and (18) that IC = kV = 0.620 Df v-4 CO: A .(20) 50 9 r.p.m. 300 I ' I 0 6 12 ' t/min 300 A I 24 FIG. 3.-Plot of the function F(c), as defined by eqn (19), against time for a kinetic experiment with a copper-coated disc at 25 O C . The rotation speeds per minute for the various sections of the experiment are specified at the top of the diagram. Fig. 3 shows a plot of the function F(c) against time. The slopes of the various sections are listed in table 1. It is evident that the rate of copper dissolution even from this coated disc markedly increased with increasing rotation speed.At any given speed the rate decreased as the reaction proceeded, probably due to a gradual reduction in the surface area A as the copper was etched away. A similar decrease of rate constant with time was observed in runs done at a constant speed throughout. The ratio of the rate at 300 r.p.m. to that at 50 r.p.m. can therefore be most fairly evaluated by302 KINETICS OF TEA INFUSION TABLE GRADIENTS OF THE SECTIONS OF THE RUN WITH A COPPER-COATED DISC SHOWN IN FIG. 3 rotation speed/ time period/ rev min-' min ~ / c r n ~ s-l 50 300 50 300 0-6 0.33 6-12 1.04 12-18 0.26 18-24 0.73 taking a section in the middle of the run and comparing it with the mean of its neighbouring sections: this leads to an average ratio of 3.5.Simply taking the average values of all the sections in table 1 gives a less reliable ratio of 3.0. The ratio expected from eqn (20) is (300/50)4 = 2.45. The Levich prediction is thus followed only semi-quantitatively. A second test can be made by calculating the effective surface area A of the copper-coated disc. From eqn (20), using the literature diffusion coefficient and kinematic viscosityg and the initial observed rate, we obtain A = 249 cm2. This is 6.5 times greater than the geometrical surface area of the disc employed. The extent of the diffusion layer is thus considerably increased by the irregularities of the surface. The increase appears to be greater the thinner the diffusion layer, since the rate rises more rapidly with rotation speed than the 2/u) factor.These results seem physically reasonable and extend our knowledge of the behaviour of discs with very rough surfaces. However, for the purposes of the present study it has been sufficient to demonstrate that the rate of a transport-controlled reaction at this rough surface rises at least as fast with increasing rotation speed as predicted by the Levich equation. Even with such an irregular coating, therefore, rotating-disc experiments should enable us to distinguish clearly between transport- and surface-controlled processes. We can now examine with some confidence the results of the tea experiments. It is helpful to look first at the infusion run with loose tea dust. Here, as found in the earlier experiments with loose tea leaf,' the plot of ln[c,/(c, - c)] against t was a straight line passing through the origin.Its slope kobs was 2.0, min-l, several times larger than the rate constants previously published for caffeine extracti0n.l The main reason is undoubtedly the much greater surface area A of the tea dust compared with that of the tea leaf used before. Exact comparison is not possible because the tea came from a different crop and the leaf: water ratio was not the same. All the runs with tea-coated discs displayed the form exemplified in fig. 4, with positive intercepts followed by the expected straight-line plots. The results are summarised in table 2. The most likely explanation for the intercepts is that some caffeine had been extracted from the tea dust by the glue solvent.As the glue dried the solvent evaporated and the caffeine left on the surface then dissolved rapidly when the disc was immersed in hot water. It is consistent with this view that the intercepts were dependent on the glue used: the values with Evostick were fairly reproducible from run to run and were significantly smaller than those with Copydex. Various alternative explanations for the intercepts were ruled out by the appropriate blank experiments. The main discussion must centre on the linear sections of the plots in fig. 4. Their slopes, by eqn (l), give the rate constants which are listed in the last column of table 2. They are seen to be reasonably reproducible (s.d. kO.03 min-l) at a givenM . SPIRO AND D. S . J A G 0 303 0.7r 0 1 2 3 t/min FIG. 4.-Plot of a typical kinetic run with a tea-coated disc at 80 O C .The figures are those from the first run with Evostick at 50 r.p.m. in table 2. TABLE 2.-sUMMARY OF KINETIC RUNS USING DISCS COATED WITH KOOMSONG TEA DUST AT 80 OC rotation speed/ c,/ 10-4 glue rev min-' w/g mol dmP3 intercept k,,,/min-l Cop ydex 100 Copydex 100 Evostick 50 Evostick 50 Evostick 50 Evostick 100 Evostick 100 Evostick 100 Evostick 300 Evostick 300 1.4 1.3 1.3 1.3 1.4 1.3 1.3 2.4 1.3 1.3 10.8 11.2 16.5 16.6 13.1 14.9 7.4 15.7 9.9 10.0 0.40 0.30 0.15 0.18 0.20 0.3 1 0.16 0.23 0.18 0.20 0.25 0.30 0.16 0.18 0.19 0.15 0.2 I 0.15 0.15 0.17 rotation speed and with a particular adhesive. That the rate at 100 r.p.m. with Copydex was larger than with Evostick may well be due to the fact that in Copydex runs a number of leaves became detached from the disc during extraction.The rate of infusion of free particles is much faster as was shown by the experiment with loose tea. Subsequent runs were therefore carried out with Evostick only, at a series of rotation speeds. Inspection shows that the rate constants are quite independent of the speed, the average value of kobs being 0.18 min-l at 50 r.p.m., 0.17 min-l at 100 r.p.m. and 0.16 min-l at 300 r.p.m. Had the infusion of caffeine been transport-controlled, the rate constant at 300 r.p.m. would have been 2.45 times larger than at 50 r.p.m. on the basis of the Levich equation. The evidence from the copper-coated disc suggests that a 3.5-fold increase would have been more likely for the irregular tea-coated disc used.We can therefore conclude with confidence that the rate-determining step is not diffusion of caffeine across the Nernst layer. Theoretical support for this conclusion comes from a comparison of the relative sizes of the solution-diffusion term 6/DSo1, and the leaf-diffusion term Kd/2D,,,, in304 KINETICS OF TEA INFUSION eqn (16). The diffusion coefficient of caffeine in solution at 80 O C is estimated as 2.02 x m2 s-l from its measured value12 at 25 OC and application of the Stokes-Einstein equation on the assumption that the effective radius r is independent of temperature (k is the Boltzmann constant, q the viscosity of the medium). The diffusion coefficient in the leaf should be smaller. The partition constant K , given by eqn (23) in the Appendix as K& Keaf/w, is ca.0.9. From eqn (17) the value of 6 at 80 O C and 100 r.p.m. is 0.053 mm and d may be taken as 1 mm. Thus 6/DSo1, = 2.6 x lo4 s m-l D = kT/6nqr (21) and Kd/2Dleaf > 2.2 x lo5 s m-l. The contribution of the latter to the inverse rate constant is a factor of ten greater. Diffusion of caffeine through the Nernst layer should therefore be much faster than its diffusion through the leaf. These calculations do not, however, distinguish between intra-leaf diffusion and interfacial transfer as the rate-determining steps. Such a distinction could be made if it were possible to carry out extraction experiments with leaf of different thickness. In the previous work1 with Koonsong Broken Pekoe the values of kobs were very similar for caffeine, theaflavins and thearubigins which points to intra-leaf diffusion although the associated activation energies were smaller than would be expected for a diffusion-controlled process on the basis of the Stokes-Einstein equation.Further work will be needed to clarify this point. APPENDIX COMPARISON OF THEORIES Both the two-phase model employed in the previous papers,l.lO (the ‘old’ model) and the steady-state theory developed in the present paper (the ‘new’ model) make use of a partition constant K and rate constants k, and k-l. It should be emphasized that these symbols do not represent identical quantities in the two theories. They do not even possess the same units. It is useful, however, to demonstrate certain relationships that exist between them. If xo is the fraction of a particular constituent in mass w of the leaf as received (in g per kg of leaf or mol per kg of leaf) then, according to eqn (6) and (8) in Part 1,l0 the total amount of the constituent in the system is given by T = x0w = c, V+ c,w/Kb,,j (22) where K,’,, is a fictional partition coefficient based on a situation in which the leaf remains unchanged during infusion. It also follows from eqn (10) and (2) of the present paper that T = C, V+ c’, F(;eaf = C, v+ I/;eafc,/Knew.In consequence Feaf - w 3.45w -_--____ - 2 . 7 0 ~ . Knew K:ld &ld The partition constants differ because the ‘old’ values refer to the mass of the original leaf (K;ld) or the swollen leaf (Kold) while Knew is based on the volume of the swollen leaf with no allowance for the diminution of the solution volume.M .SPIRO AND D. S. J A G 0 305 As regards the rate constant k1, kobs = (kL1)old from eqn (4)’ = (k&d Ax0/3.53c, from eqn (l),l (2)’ and (5)l = (k-’ K)old Ax0/3.53c, = (k-lK)old Aci Feaf/3.53wc, from eqn (9) and (22) from eqn (6)’ = A($) (S) (&) from eqn (2) Knew = (k-l)old A( 5) (0.98 - 0.76Kold (24) c, from eqn (23). The resemblance to eqn (15) of the new formulation is closest if the rate-determining step is transfer of the constituent across the interface so that k‘ = (k-l)new, in which case Thus (k-l)new/ = (k-l)old (0*98 - 0.76K0d * (26) The major difference between the two k-, values lies in the factor V . This originates in the way the velocity of infusion was expressed: as dc/dt in the old model and as J = d(cV)/dt in the new. The other difference between the equations is due to the neglect in the new model of the volume change when water is taken up by the leaf. The forward rate constants k , also differ by two factors, the solution volume V and the density of the swollen tea leaf, according to the equation CORRECTION FOR WATER LOSS B Y EVAPORATION The c, value we require for eqn (1) is that given by eqn (22): xow = C,(V+W/K;ld). In the laboratory experiment, however, A T (mol or g) of caffeine have been removed by sampling and a volume A V of water has been lost by evaporation and sampling. The measured equilibrium concentration of caffeine, C,, is therefore given by XoW - A T = c,( V - A V+ w/Kild). In practice, A T is small for six 1 cm3 samples. The value of KAld for caffeine extraction from Koonsong Broken Pekoe at 80 O C was found be tolo 0.25 g cmP3 so that W/K;ld 4 V. The correction is therefore not sensitive to uncertainties in either w or K&. Part 2, M. Spiro and S. Siddique, J. Sci. Food Agric., 1981, 32, 1135. V. D. Long, J . Food Technol., 1979, 14, 449. V. D. Long, J . Food Technol., 1978, 13, 195. W. J. Albery, A. M. Couper, J. Hadgraft and C. Ryan, J . Chem. SOC., Faraday Trans I , 1974, 70, 1124. J. H. Petropoulos and P. P. Roussis, J . Chem. Phys., 1967, 47, 1491 and 1496. A. C. Riddiford, Adv. Electrochem. Electrochem. Eng., 1966, 4, 47. ’ G. T. Rogers and K. J. Taylor, Nature (London), 1963, 200, 1062. * T. Theodorsen and A. Regier, Nut. Advis. Comm. Aeronaut., Rep., 1944, 793. lo Part 1, M. Spiro and S. Siddique, J . Sci. Food Agric., 1981, 32, 1027. l 1 R. S. Bradley, Trans. Furaduy SOC., 1938, 34, 278. D. P. Gregory and A. C. Riddiford, J . Electrochem. SOC., 1960, 107, 950. M. McCabe, Biochem. J., 1972, 127, 249. (PAPER 1 /373)