Mathematical Model of Flavor Release from Liquids Containing Aroma-Binding Macromolecules Marcus Harrison* and Brian P. Hills Institute of Food Research, Norwich Research Park, Colney Lane, Norwich NR4 7UA, United Kingdom A mathematical model has been developed to describe flavor release from aqueous solutions containing flavor-binding polymers. First-order chemical kinetics is used to describe the reversible binding of the aroma and polymer, and the penetration theory of interfacial mass transfer is used to model flavor release across the gas-liquid interface. The model is used to predict the equilibrium partitioning properties and the rates of release of two volatiles, one hydrophilic (diacetyl) and the other hydrophobic (heptan-2-one), as a function of the binding constants and first-order rate constants. In general, the rates of release are shown to be more sensitive to changes in the binding constant than the rate constants. Increasing the flavor-binder interaction leads to decreased release rates and a lower final headspace aroma concentration. Nevertheless, the results suggest that in most situations the rate-limiting step for flavor release is not the chemical binding step but the transport of aroma across the liquid-gas interface. Keywords: Interfacial mass transfer; penetration theory; mass diffusion; partitioning; headspace INTRODUCTION The flavor perception of a particular food product is a major factor determining consumer acceptance. The quantity of flavor released into the oral cavity depends on the retention of flavor compounds in the food matrix and, therefore, on the nature of the ingredient-flavor interactions. Knowledge of the binding behavior of flavor compounds to different food components and their rates of release from the food matrix is therefore of great practical importance in the formulation of new food products. Interest in flavor binding has also been stimulated by attempts to use biopolymers as fat substitutes, but, so far, this has been of only limited success in terms of consumer acceptance (Plug and Haring, 1993). One possible reason may be that a decrease in fat content results in an increased rate of volatization (Harrison et al., 1997; Harrison and Hills, 1997), thus reducing the perceived flavor quality. Knowledge of the effects of macromolecule flavor binding on release rates could therefore assist in designing low-fat substitutes that give the same flavor release profiles as the original high- fat food. Experimental studies of flavor binding have been limited to simple aqueous mixtures containing polysac- charides and proteins. Selective binding of a particular volatile to a macromolecule present in a food lessens the effective free concentration available for release and hence can significantly alter the overall flavor available for perception (Overbosch et al., 1991). Various types of flavor-macromolecule binding interaction have been identified, including encapsulation, entrapment, and inclusion complexes (Solms, 1986; Godshall and Solms, 1992) and bond formation (Buttery et al., 1971; Le Thanh et al., 1992). The relative importance of these mechanisms obviously depends on the nature of the flavor and biopolymer, of which polysaccharides and proteins are the major categories. Polysaccharides can bind to volatiles in a number of ways. Some carbohydrates can bind to volatiles via hydrogen bonding between appropriate functional groups (Maier, 1975). Others, such as starch, consist of three- dimensional structures with hydrophobic regions ca- pable of forming inclusion complexes with various hydrophobic volatiles (Solms, 1986; Godshall and Solms, 1992). Cyclodextrins are capable of entrapping volatiles (Maier, 1975) and have been used to selectively bind certain undesirable off-flavors (Szente and Szejtli, 1988). In addition, cyclodextrins are especially effective in retaining flavor during drying storage and releasing the flavor upon hydration, e.g. in the mouth (Reineccius and Bangs, 1985). Proteins have also been shown to decrease the head- space concentration of volatiles in both aqueous and dry systems (Solms et al., 1973). Nawar (1973) showed that gelatin decreased the apparent volatility of methyl ketones. Gremli (1974) showed that an aqueous disper- sion of soy protein reduced the volatility of aldehydes and, moreover, that the percent decrease in volatility increased with the molecular size of the aldehydes. This result indicated that the magnitude of the interaction was a function of chain length. Franzen and Kinsella (1974) attempted to relate binding between various proteins and aldehydes or ketones to differences in intrinsic binding affinities, protein structure, and avail- able surface area. Very few mathematical models have been developed to describe time-dependent flavor release from liquid systems, and none have explicitly treated flavor-binding interactions. Darling et al. (1986) successfully modeled isopentyl acetate release from galactomannan and sucrose solutions into the headspace. They based their model on the penetration theory of interfacial mass transfer across the liquid-gas interface. They con- cluded that interfacial surface regeneration is a signifi- cant physical factor controlling the release of flavor into the headspace. Harrison et al. (1997) developed a mathematical model to describe flavor release from emulsions based on the assumption that the rate- limiting step is the transfer of flavor across the emul- sion-gas interface. They assumed that partitioning of * Author to whom correspondence should be ad- dressed [fax +44 (0) 1603 507723; e-mail harrisonm@ bbsrc.ac.uk]. 1883 J. Agric. Food Chem. 1997, 45, 1883-1890 S0021-8561(96)00787-X CCC: $14.00 © 1997 American Chemical Society