General Assumptions

CHAPTER 5MODEL DEVELOPMENT

Chapter 4 has presented the rationale for a conceptual model of mastication where the rate processes of size reduction, work softening, absorption, dissolution and melting relate to the food properties that are able to be measured in the mouth which are temperature, volume, adhesiveness, particle size and deformability, and bolus deformability. The relationship between these rate processes and properties is paramount in tracking the progress of mastication where the objective to define the amount of mastication effort required to produce a swallowable bolus and the properties of that bolus. This chapter develops the conceptual model into a set of mathematical equations.

The model presented here is generalised; that is, it is not specific to any food type. The basic premise is that solid foods follow the same physical breakdown path where occlusion, i.e., size reduction and work softening, is of primary importance followed by the incorporation of saliva and the other rate processes.

5.1 General Assumptions

The model contains the following assumptions. Most have arisen in the discussion in Chapter 4.

1. The bolus is regarded as having two phases, a mobile interstitial free liquid-phase and a food particle-phase. The liquid-phase may contain, in addition to liquids (e.g., water, alcohols, vinegar, oil), the components of saliva, dissolved solids, molten fats and suspended solids. The particle-phase will contain solid, liquid, and air pores. The solid component may contain dissolvable solids, meltable fats and meltable gels.

2. The bolus occupies a single compartment and is well mixed meaning the interstitial liquid is evenly distributed into the interstitial spaces between the food particles. 3. The properties of the interstitial liquid are calculated using the simple mixture rule

based on composition. 4. Saliva flow rate is continuous.

5. The properties of specific heat capacity, and component solubility do not change with temperature.

6. The heat of dissolution is negligible.

5-2 8. Melting of fat is temperature dependent and is reliant on the known temperature

range and latent heat for melting of fats.

9. Heat transfer into the food is assumed to occur in two steps. First, heat enters the mouth from incoming saliva and the walls of the oral cavity, where heat transfer from the oral cavity is described by an overall heat transfer coefficient. This heat is blended into the well-mixed liquid phase of the bolus by convection (assumptions 1 and 5). Subsequently, heat transfers from the blended liquid phase to the particles.

10.Particles increase in temperature uniformly. The Biot number gives the ratio of the heat transfer resistances inside and at the surface of a body. When this is ≤ 0.1 the internal resistance is low and the body can be assumed to have a uniform temperature. For a spherical food particle in the mouth this occurs when it had a diameter ≤ 0.25 mm. Therefore, this assumption is a gross simplification for large food particles. However, given the short lifespan of solid particles before they are occluded, modelling a temperature profile would add significant complexity without significantly improving the model.

11.A discrete population balance model is used where particles are individually tracked. If particles are below a small size limit they are no longer individually tracked but are attributed to the liquid-phase as suspended solids.

12.Each particle has a chance of being selected for occlusion defined by a selection function.

13.Occlusion causes size reduction and/or work softening. When size reduction occurs, the breakage function is food type dependent. When work softening occurs, the degree of softening is dependent on the initial toughness and Young’s modulus of the food and a food specific Work Index.

14.Dissolution occurs from the particle surfaces into the liquid phase. However, generally comminution dominates size reduction and so the effect of dissolution on particle size is negligible and here is manifested only in the change in concentration of dissolvable solids within particles. It is assumed that the rate of dissolution can be approximated by a mass transfer coefficient. The rate of dissolution is constrained by the available free liquid and the concentration gradient. The mass transfer coefficient is food type dependent.

15.Melting occurs when the particle temperature reaches the melting temperature of the fat contained within the particle. This may occur over a range of temperatures for various fat fractions. The rate of melting is constrained by the heat flux. All

5-3 molten fat is assumed to transfer from the particle phase to the interstitial free liquid.

16. Occlusion of food can also compress the void volume within porous foods. This is food specific and is defined by a fractional compression per occlusion event. 17. Occlusion of food can express a mobile liquid phase. When size reduction occurs

the amount of mobile liquid phase released is proportional to the new surface area created which is both related to subject dentition and the food type. For the latter, some foods (like fresh carrot) fracture through cells, resulting in the liquid from the cells being released, whereas others (like cooked carrot) fracture along cellular boundaries and do not release liquid (Lillford, 2011). For foods that work-soften rather than reduce in size, occlusion can also express a mobile liquid phase where the amount expressed is food type and force dependent. It is assumed to be proportional to the food specific Work Index.

18. Wicking is simplified from the Washburn equation and assumed proportional to the surface area available and the potential for wicking defined by the difference between the liquid saturation and 100% saturation.

19. Swelling by hydration is not considered.

20. The food property thresholds are food dependent.