Two-film theory of flavour release from solids

International Journal of Food Science and Technology (1 995) 30,425-436

Two-film theory of flavour release from solids

B R Y A N P. H I L L S & M A R C U S H A R R I S O N * BBSRC Institute of Food Research, Nonvich Research Park, Colney Lane, Nonvich, NR4 7UA, UK

Summary

A new theory for flavour release from solid or semi-solid foods is proposed which uses two- layer, stagnant film theory to calculate the mass transfer coefficient for the flavour across the food-saliva interface. The theory is applied to the simple case of flavour release from a boiled sweet. By using the colours which dye the sweet as a substitute for flavour, the theoretical predictions are compared with experiment, both for simple solution of the dye into stirred water and for the more realistic case of mass loss on sucking in the mouth. The role of changing food-saliva interfacial area is explicitly incorporated into the theory and used as a basis for classifying flavour release from other types of food.

Keywords

Penetration theory, stagnant film theory.

Introduction

With the growing popularity of novel foods, including low fat foods and low alcohol bever- ages, it is becoming increasingly important for flavourists to understand the mechanisms of flavour release if they are to reproduce traditional foods successfully. Unfortunately very little research has been conducted into the release of volatiles from real solid or semi-solid foods in the mouth. This, no doubt, is due to the variety and complexity of even the simplest solid foods and the complexity of the mastication process. Instead most studies on flavour release have been limited to simple model systems composed of liquid mixtures and emulsions (Buttery et al., 1973; Maier, 1975; Kiekbusch & King, 1979; Lee, 1986; and Salvador et al., 1994). These liquid-based studies have established the following points.

Of all the possible food ingredients lipids usually have the strongest influence on partition coefficients and release rates in aqueous solutions. This is understandable as most volatiles are hydrophobic, and thus the volatile concentration will most often be greatest in the lipid phase. This greatly reduces the partitioning of volatiles into the aqueous and air phases (Buttery et al.. 1971, and Overbosch et al., 1991). The second point established by the liquid-based studies is that chemical binding of flavour compounds to proteins and polysaccharides lessens the amount of free flavour molecules available for perception (Nawar, 1966; Wientjes, 1968; and Godshall, 1988). A range of volatiles such as alcohols, aldehydes, ketones and phenols were found to bind to receptor sites on proteins by hydrophobic interactions (King & Solms, 1979) on dis- crete binding zones (Solms et al., 1986). The overall effect is to reduce the effective partition coefficient and give a reduced release rate (Overbosch et al., 1991). A third factor affecting

Authors’ address: BBSRC Institute of Food Research, Norwich Research Park, Colney Lane, Norwich, NR4 7UA, UK. * Correspondent. E-mail: [email protected]. Fax: +44 (0) 1603 507723.

0 1995 Blackwell Science Ltd 425

426 B. f? Hills & M. Harrison

flavour release rates from liquid emulsions is the mixing and dilution with saliva in the mouth (McNulty & Karel, 1973a-c; and McNulty, 1987). A fourth factor affecting flavour release from liquids and emulsions is mass transfer resistance across the liquid-gas interfaces. DeRoos & Wolswinkle (1 994) approximated this mass transfer process as a series of equilibrium mul- tiple extraction steps. However, it is highly questionable whether an intrinsically nonequilibrium mass transfer process can be approximated in this way since there is no explicit reference to an interfacial mass transfer coefficient. For this reason Darling et al. (1986) preferred to use penetration theory to study the interfacial mass transfer of isopentyl acetate from galactomannan and sucrose solutions into the head space. They concluded that interfacial surface regeneration is a significant physical factor controlling the availability of flavour for perception. Their work, however, only considered flavour release from aqueous solutions.

Very few mathematical models have been developed to described flavour release from solid and semi-solid foods in the mouth. All of the above factors such as binding to macromolecules and interfacial mass transport could be important with solid systems. In addition the release rate will be strongly influenced by the physical processes of mastication, mixing and dilution with saliva in the mouth, which are known to vary considerably between individuals (Brown, 1994).

To elucidate the role of these various factors and identify rate-limiting steps it is clearly necessary to develop a new theoretical approach for flavour release from solid foods in the mouth, and this paper is a first step. It first outlines the ideas behind our model of flavour release and the possible rate-limiting factors, then describes the model, develops it for the simple case of a perfectly spherical boiled sweet, and describes experimental results to test the validity of our flavour release model. We then consider the effects on the release of flavour for the same sweet which is chewed rather than sucked, followed by consideration of possible applications to other food systems.

The general flavour release model

Transportation of flavour volatiles from the food product to the gaseous phase is essentially a three phase problem involving the food, saliva and air phases (Fig. 1). It is highly unlikely that flavour is released into the head space directly from the solid food product and the transport of flavour from the saliva into the headspace can be treated by any of the above mentioned theories. In this paper we therefore focus on the transport from the solid food into the saliva phase. In Fig. 1, c, is the concentration of free flavour molecules in the food, which in the general case will differ from the total concentration of flavour in the food due to reversible chemical binding to macromolecules and metabolites comprising the food matrix (Dumont & Land, 1986). For simplicity this can be described by the chemical equilibrium

k t

k b PF P + F

C p l cp Cf

Chemical equilibrium has been assumed since it is unlikely that the chemical dissociation step, characterised by k,, is actually the rate-limiting step controlling flavour release. In the model we ignore the physiology of perception and simply assume that taste perception is proportional to c,, the concentration in the saliva, and flavour (or aroma) perception is proportional to cg. The physics of the problem therefore reduces to calculating the time dependence of cs and cg. It is also very unlikely that simple diffusion of flavour molecules in the bulk phases of the food or saliva determines the rate of flavour release in the mouth because mastication removes diffusion

0 1995 Blackwell Science Ltd. Inrernutional Journal of Food Science and Technology 30,425-436

Flavour relea.se.from solids 427

Interface of

Area A,, 4

Gas Phase

+ Liquid Phase

Food Product

Cf Vf

Interface of

Figure 1. Three phase schematic diagram illustrating the net transfer of flavour release from a d i d food. Volatile concentrations and phase volumes are denoted by c, and v, respectively. with the subscripts f. \ and g denoting the food, saliva and gas phases, respectively.

gradients and generates fresh interfaces. It is more probable that interfacial mass transfer (Coulson & Richardson, 1993) of flavour across the foodsaliva and/or salivdgas interfaces is rate limiting and this is the working hypothesis of the present paper. The first problem is therefore to identify which of several interfacial mass transfer theories, such as penetration theory or two-film theory (Fig. 2), best describes flavour release in the mouth. The second is the modelling of the time course of the interfacial surface areas during mastication. The third problem is the calculation of the time course of c\ and cg, which involves processes such as dilution with saliva and the individual patterns of mastication and swallowing. We begin by considering these aspects for the simplest possible case of flavour release from a boiled sweet using a two-layer stagnant film theory of the interfacial transport.

Flavour release model for a boiled sweet

In two-layer stagnant-film theory (Fig. 2), the resistance to mass transfer at the phase boundary in a liquid or gas lies wholly within a thin layer of thickness L’ adjacent to the surface. The fluid in immediate contact with this surface is at rest. It is further assumed that all regions further from this layer can be regarded as well stirred, and therefore of uniform composition. Transport across the film takes place by diffusion and the concentration gradient across the laminar layer is assumed to be linear. The driving force for flavour release across the interface is the nonequilibrium concentration difference for volatiles between the food product and saliva (or saliva and vapour) phase in the mouth. Equilibrium is obtained when the two phases obey the relation

0 1995 Blackwell Science Ltd. International Journal of’Food Science and Technology 30,425-436


Food Product

Interface

Aqueous Phase

Conceitration

Laminar Layer

c--4 X

Figure 2. Schematic diagram of flavour release across an interface (solid vertical line). Partitioning of the volatiles and efficient mixing in the aqueous phase produces the concentrations illustrated (solid horizontal line). In the stagnant layer model it is assumed that there exists a surface layer of thickness L,adjacent to the interface where the fluid remains stationary (bound by two vertical lines). The actual volatile concentrations can then be approximated by a linear concentration gradient across the stagnant layer (dotted line), through which the volatiles diffuse into the uniform bulk saliva concentration, c>.

where Ks, is the equilibrium partition coefficient between the two phases; and cf and cs are the concentrations of the volatile in the product and saliva phase, respectively. The rate of mass transfer across the boundary is given by

where M is the total mass of volatile that diffuses across the interface, D is the diffusion constant for a particular volatile, A(t) is the surface area of the interface, L, is the laminar thickness, and c;(t) and c,(t) are the concentrations of volatile at the interface and within the bulk, respectively.

There are two general weaknesses with this theory: first, LF cannot be measured independ- ently, and for this reason the quality ( D L J is replaced by the mass transfer coefficient, h,, which is measurable; and second, the concentrations at the surfaces will not be known, since only the bulk concentrations can be measured. However, the choice of a simple food system such as a boiled sweet greatly simplifies the problem by allowing a number of simple assump- tions to be made. These are that

the concentration of flavour (or dye), cf is constant and time independent throughout the sweet right up to the interface so that the equilibrium at the interface is given by

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Flavour release,from solids 429

where K, is the partition coefficient;

proportional to the coloured dye concentration throughout the sweet; and,

mass yields

the sweet is perfectly homogenous so that the volatile flavour concentration is directly

it is further assumed that the volume of the aqueous phase is constant so that conservation of

1 dM dc,- - dt vs dt '

where vI is the volume of saliva. Combining equations ( 2 4 ) we obtain

(4)

By further assuming that the sweet is perfectly spherical, and that it remains so as the sugar matrix dissolves, the surface area will decrease with time as

where A, is the initial area, and vf and vs are the volumes of the food and saliva phases, respectively. Substitution of equation (6) into (5) yields

which governs the concentration in the aqueous phase as a function of time. By rearranging equation (7) and making use of the substitutions

and

a = ( vf ) hDAOKsf

(9)

the following integral is obtained:

113

Y = [ s )

thus falling in the regime 0 < y ( t ) < 1. Here ~$00) is the concentration of dye in solution when the sweet has completely dissolved, and is given by


430 B. P. Hills C? M . Harrison

Equation 10 is evaluated numerically for given relative concentrations, y(t), using Simpson's rule yielding a value for the integral as a function of y(t). This result is then compared with experimental results using a as the fitting parameter. We now compare the predictions of this two-layer stagnant film theory by experiment.

Materials and methods

A. In vitro release A beaker containing 50 ml of distilled water was placed in a water bath thermostatted at

37°C. A single coloured boiled sweet was placed into the beaker so that the entire surface area was in direct contact with the distilled water. The water was stirred at a known and constant rate in order to maintain a uniform dye concentration within the bulk liquid, as required by theory. As the sweet is assumed to be perfectly homogenous in composition, the concentration of dye in solution is therefore a direct measure of the sugar matrix dissolved, and hence an indirect measure of the dye (flavour) released. The advantage of using coloured dye as op- posed to a flavour compound is twofold: first, this limits the experiment to two-phase problem, as the dye will remain in the aqueous phase; and second, the changing dye concentrations in the liquid phase are easier to measure experimentally.

The time course of the change in dye concentration in the liquid phase was determined using a spectrophotometer, on small aliquots of solution. Initially the spectrophotometer was used to scan a small aliquot of dye over a wide range of wavelengths (300-850 nm) in order to determine which wavelenght resulted in the maximum absorance of the incident beam. A small sample of solution was removed from the beaker at regular time intervals (60 s), and the absorbancy measured. Once measured the sample solution was returned to the beaker to maintain the initial volume of solution. The experiment continued until the sweet had completely dissolved. It was assumed that the normalized absorbance versus time curve is equivalent to the flavour concentration versus time curve so it was directly fitted with equation (10).

B. In vivo release A boiled sweet was sucked in the mouth and removed every 30 s with minimum of saliva

and weighed. This allowed the mass of the sweet to be recorded as a function of time. As already mentioned the sweets were assumed to be perfectly homogenous in composition, and hence the mass of sweet is directly proportional to the flavour released. The normalized mass versus time curve was assumed to be proportional to the flavour concentration-time curve and was therefore fitted with equation (10). The partition coefficient, Kcf, was determined by assuming that the solution at the interface was saturated with sugar, and therefore with dye. Absorption measurements were then used to determine the concentrations at the interface: Cl was obtained from a saturated solution, while C, was determined by dissolving a single sweet in a known volume of distilled water. In all calculations Ks, was taken to be 0.384.

Results

Fig. 3 shows the release of dye from a single boiled sweet as a function of time for a stirring rate of 1 1.7 rps. At short times the release rate of dye is linear, as expected from equation (7). At long times the release rate progressively decreases with time as the surface available for mass transfer decreases. A theoretical plot using equation (10) is shown as a comparison, and corresponds to a fitting parameter, a, of 550. From this fit an approximate value for the mass transfer coefficient, h,, of 2.37 x was obtained. The above procedure was performed for a number of different stimng rates (J) in the range of 6.7-1 1.7 rps, from which the corresponding


Flavour release from solids 43 1

' 0 200 400 600 800 1000

Time (s) Figure 3. Relative concentration of dye released from a single boiled sweet into solution as a function of time. The aqueous phase was constantly mixed by a magnetic stirrer at a rate of 1 1.7 r.p.s. The experimental points are denoted by solid diamonds, while the theoretical fit is represented by a solid line.

mass transfer coefficients were calculated. Fig. 4 shows a linear relationship between the stirring rate (J in rps) and the log of the mass transfer coefficient. A plot of the log of h, as a function of the log of J yields an approximate mathematical relationship between these parameters:

h, = J o 9 ' x ~ S X I O - ~ , (13)

where the units of h, and J are meters per second and per second, respectively. It should be noted that as these experiments were performed on ellipsoidal, not spherical, sweets, the surface area available for mass transport was slightly than that described by equation (6), especially at longer times where the sweet becomes elongated. This probably accounts for the faster experimental release rate at longer times in Fig. 5 than predicted by theory. The theoretical curves were fitted to the data points obtained during the initial stages of the experiment where the sweets were more spherical. Fig. 5 also illustrates the results for a single in-vivo experiment and shows the proportion of mass of the sweet dissolved in the mouth as a function of time. Again using equation (10) a theoretical curve was fitted and an effective mass transfer coefficient of 3.43 x 1 0-5 was obtained. Using equation (1 3) this corresponds to an effective stirring rate of approximately 17.7 rps which is considerably faster than any of the stirring rates used in the in vitro studies. This suggests that the action of the tongue cannot be realistically modelled as a stirring phenomenon but rather as a mechanical rubbing process.

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432 B. P. Hills & M. Harrison

-10.6

Y

rrl

rrl 0

rw rw a2

6 -10.8 bl 0

rw m d 2 e v1 v1 5 -11.0

s rw 0

M

-11.2

6 .O 10.0 12.0

Stirring Rate (rps) Figure 4. Relationship between stirring rate (J r.p.s.) of the aqueous phase and the natural log of the mass transfer coefficient (hJ.

Equation (13) implies that the mass transfer coefficient increases with stirring rate as Jo9'. This is an interesting observation because penetration theory predicts a Jo.5 dependence if the mean contact time of a fluid element at the interface is assumed to be proportional to the reciprocal of the stirring rate (Darling et al., 1986). In two-layer stagnant film theory increasing the stirring rate is expected to reduce the thickness of the stagnant layer and hence increase the mass transfer rate but there is no simple relationship between stirring rate and film thickness. Our results suggest that penetration theory is not applicable to the boiled sweet experiment, at least over the range of stirring rates used in these experiments.

Fragmentation of a boiled sweet

The above model was chosen for its simplicity: only a small number of reasonable assump- tions need be made to obtain an expression for the surface area as a function of time. However, in reality it is unlikely that a boiled sweet will be sucked until completely dissolved. Usually


Flavour release from solids 433

0.5

%

n

c

1 0.4 0 m m - w

3 Oe3

g o.2 ccr 0

.r(

t: 0

8 0.1 a"

0

I / + /

/

/

0 100 200 300 400 500 Time (s)

Figure 5. Proportion of mass dissolved of the boiled sweet as a function of' time (in s) for both the in rGtro and in v i v o experiments. For the in v i m experiment the aqueous phase was constantly mixed by a magnetic stirrer at a rate of 10.0 r.p.s. The experimental points are denoted by solid squares, while the theoretical fit is represented by a solid line. For the in vivo experiment the experimental points are denoted by solid diamonds, while the theoretical t i t is represented by a dashed line.

1 chew

L

~ fi Zchewl ~ 64 x

L L/2 L/4

A(0)=6L2 A( 1 )= 1 2L2 A(2)=24L2 Figure 6. Diagram to illustrate a simple multi-fragmentation theory of a cube. After one chew the cube fragments into eight cubes of equal size. After a second chew each of these smaller cubes are again fragmented again into eight smaller cubes, i.e. 64 in total, thus increasing the surface area at an exponential rate.

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434 B. I? Hills & M . Harrison

fragmentation occurs due to chewing, resulting in a dramatic increase in surface area and a pulse of flavour release from the newly created surfaces. On the other hand, an individual (with strong teeth!) may prefer to chew the boiled sweet from the instant of ingestion. Mastica- tion will therefore produce fragmentation and consequently provide successively increasing surface areas for interfacial mass transfer. In this section we will compare the initial volatile release rates at short times for the two methods of eating a boiled sweet.

First, we shall consider the case of sucking a boiled sweet. At short times there will be no appreciable decrease in the surface area available for mass transfer, hence Aft) -+ A, in equation (7). Then integration of equation (7) yields

c,(t) = Ksfcf 1 - exp -- 1 [ h::otll. However, as we are concerned only with short times the exponential in equation (14) can be expanded to first order so that

A similar approach can be applied to the case of chewing a boiled sweet. Here A(t) is independent of the concentration of dye in the aqueous phase, and hence equation (7) can be integrated to yield

Again we are concerned only with short times, therefore expanding the exponential in equation (1 6) yields

The ratio of dye concentrations released into the aqueous phase is then given by

Equation (1 8) can be used as an experimental test to compare various theoretical models of fragmentation. As an example, we present a simple theory based on multifragmentation of a cube (Fig. 7). Consider a cube of side L which after one bite is fragmented into eight identical cubes of side W2. The surface area from this bite will increase from 6L2 to 1 2L2. After n chews the surface area is given by

A(n) = 6L22". (19)

By changing variables to time with the substitution n=t/te where te is the mean time between chews, and a little manipulation, equation (19) becomes

A(t) = 6L2 exp[ [ log 21.

Substitution of equation (20) into (18) produces


Flavour release from solids 43s

fort >> tc. Equation (21) increases exponentially at long times (t >> te), and therefore demon- strates the dominant role of chewing and fragmentation in increasing surface area in extracting flavour. Other fragmentation models based, for example, on fractal fragmentation can, of course also be considered.

Applying mass transfer theory to other types of food

Although in these initial investigations we have limited ourselves to the simplest case of flavour release from a boiled sweet very similar principles are expected to hold with other types of food. Interfacial mass transfer equations of the form of equation ( 5 ) can be developed for most foods but the different food types will vary according to the time dependence of the interfacial surface area, A(t). For this purpose it may be useful to classify foods into a number of categories. First are foods such as dry biscuits that rapidly disintegrate on chewing and form a paste in the mouth. This necessarily involves a large initial increase in surface area. In contrast many food materials such as bread or chewing gum mix with saliva in the mouth to form a bolus whose overall surface area is essentially constant. Continual exchange of fresh saliva with that inside the bolus results in flavour release into the aqueous phase, therefore allowing perception. Cellular tissue such as apple represents a third and particularly simple category of solid food where interfacial mass transfer theory need not be considered. Instead each bite crushes the tissue and releases a certain volume of juice which mixed with saliva. The calculation of c,as a function of chewing pattern is therefore particularly straightforward. These other categories of food are outside the scope of the present paper but will be analysed in greater detail in subsequent publications.

Conclusions

In this paper we have presented a general framework for flavour release form solid foods in the mouth based on the assumption that the rate-limiting step is mash transfer across the food-saliva interface. Our experimental in v i m results for the case of flavour release from a boiled sweet suggest that the interfacial transport is reasonably well described by two-layer stagnant film theory rather than penetration theory. On the other hand our in vivo sucking experiments gave an effective stirring rate which suggests that the mechanical action of the tongue is best described as a rubbing with an abrasive surface rather than as simple stirring of the saliva.

An important aspect of the theoretical model is the role of surface area in determining flavour release rates. The simple exponential fragmentation model for the effect of chewing a boiled sweet emphasizes the importance of surface area effects and we have proposed a simple classification of solid food materials based on the rate of change of the interfacial surface area. Future work will be directed at extending the model to these other food categories.

Acknowledgments

We would like to thank our colleagues at the Institute of Food Research in Reading for many useful conversations.

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Two-film theory of flavour release from solids

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