DURING MASTICATION
5.2 System Composition
The bolus system containing the two phases, an interstitial free liquid-phase and a particle- phase, each have components that need to be tracked during mastication. The following subsections describe composition by mass and volume and how they are related by density. 5.2.1 Mass
The bolus contains food particles and interstitial fluid. Every chew cycle, the mass balance is
bolus =liq+p Eq. 5-1
The components are
M
liq=Mliq, saliva+Mliq, expressed+Mliq, diss. sol. solids+Mliq, molten fat, oil Eq. 5-2
5-4 The term, Mp,solidsis the solid-phase contained in the food particles. It is regarded as including the insoluble solids, the undissolved soluble solids and the solid fat, given by
p, solids=p,insol. solids+p,undiss. sol. solids+p,solid fat Eq. 5-4 The term, Mp,liqis the liquid-phase contained in the food particles, which may be either bound or mobile and residing in pores and may be either water, dissolved, or solids oil given by
p,liq= ,, + Mp, liq, diss. solids + ,, Eq. 5-5
The definitions are:
• MBolus is the mass of the bolus [kg]; • Mliq is mass of the free liquid phase [kg]; • Mp is mass of the food (particles) [kg];
• Mliq, saliva is the mass of saliva in the free liquid phase [kg];
• Mliq, expressedis the mass of expressed liquid in the free liquid phase [kg];
• Mliq, diss. sol. solids is the mass of dissolved soluble solids in the free liquid phase [kg]; • Mliq. molten fat, oil is the mass of molten fat and oil in the free liquid phase [kg]. • Mp, solidsis the mass of solids in the food particles [kg];
• Mp,liq is the mass of the liquid-phase contained in the food particles which may be either bound or mobile and residing in pores [kg];
• Mp, insol. solidsis the component of Mp solids that is insoluble solids [kg];
• Mp, undiss. sol. solids is the component of Mp solids that is the mass of undissolved soluble solids [kg];
• Mp, solid fat is the component of Mp solids that is the mass of solid fat [kg]; • Mp, liq, water is the component of Mp,liq that is water [kg];
• Mp, liq, diss. solids is the component of Mp,liq that is dissolved solids [kg]; and • Mp, liq, oil is the component of Mp,liq that is oil [kg];
The volume of the bolus consists of particles and an interstitial space between the particles. The particles may contain solid, liquid and air in pores, and the interstitial space may contain liquid and air.
bolus =interstitial+p Eq. 5-6 The components are
5-5
Vp=p,solid+p,liq+p,air Eq. 5-8
The term Vinterstitial,liq is the volume of the fluid occupying the interstitial space within the bolus, which has the components
interstitial,liq=interstitial,saliva+interstitial,expressed+interstitial, diss. solids
+interstitial, moltenfat, oil
Eq. 5-9
The term Vp,solid is the solid component of the particle-phase and has the sub-components
p,solid=p,insol. solids+p,undiss. sol. solids+p,solidfat Eq. 5-10 The term Vp,liq is the liquid component of the particle-phase and has the sub-components
p,liq=p,liq,water+p,liq,diss. solids+p,liq,oil
Eq. 5-11
The definitions for the volume composition equations are: • Vbolus is the volume of the bolus [cm3];
• Vinterstitialis the volume of the interstitial space between the particles but within the volume of the bolus [cm3];
• Vp is the volume of the food particles [cm3];
• Vinterstitial,liq is the volume of the liquid-phase occupying the interstitial spaces [cm3]; • Vinterstitial, air is the volume of air occupying the interstitial spaces [cm3];
• Vinterstitial, saliva the component of Vinterstitial, liq that is saliva [cm3];
• Vinterstitial, expressed the component of Vinterstitial, liq that is expressed from the food [cm3]; • Vinterstitial, diss. solids the component of Vinterstitial, liq that is dissolved solids [cm3];
• Vinterstitial, molten fat,oil the component of Vinterstitial, liq that is the molten fat and oil [cm3]; • Vp,solid is the volume of the solid-phase within the food particles [cm3];
• Vp,liq is the volume of the liquid within the food particles [cm3]; • Vp,air is the volume of the air within the food particles [cm3]; • Vp, insol. solids is the component of Vp,solid that is insoluble solids [cm3];
• Vp, undiss. sol. solids is the component of Vp,solid that is undissolved soluble solids [cm3]; • Vp, solid fat is the component of Vp,solid that is solid fat [cm3];
• Vp, liq, water is the component of Vp,liq that is water [cm3];
• Vp, liq, diss. solids is the component of Vp,liq that is dissolved solids [cm3]; and • Vp, liq, oil is the component of Vp,liq that is oil [cm3].
5-6 The degree of saturation is a well-known parameter which defines the progress of powder granulation using a liquid binder (Hapgood, 2000). It is defined by the ratio Vinterstitial, liq/( Vinterstitial, liq + Vinterstitial, air) using the terms in Eq. 5-7. As the degree of saturation increases from a dry basis, it reaches a value where the cohesion of the powder (or here the bolus) is greatest. Further increases result in it becoming a paste (called wet massing in granulation) then a slurry. However, in mastication, the interstitial pore volume is impossible to measure because the food is continually being circulated. An alternate approach is needed. Because the objective is to define a threshold for the adhesiveness criterion (§4.3.3), it is proposed here that such an objective is reached when a critical excess liquid content is reached. The ratio of interest then becomes Vinterstitial,liq/Vp. This then means that the unknown Vinterstitial,air is not required in Eq. 5-7.
5.2.2 Density
Density links mass and volume. The aim here is to practically link them, two simple tests are possible. The first is the drying test which evaporates the water and can be done at a temperature (including freeze drying) which avoid melting fats. The second is the immersion test which can determine the open pore volume. Given that the drying test removes water and assuming no other volatiles are removed, the water-free food density is
=
−
−,−, Eq. 5-12
where the undefined terms are:
• Mparticle is the mass of the particle prior to the drying test [kg]; and • Mdried is the mass after the drying test [kg].
The denominator contains Vp,waterwhereas Eq. 5-8 above contains Vp,liq. Because the simple evaporation test only separates the water component, which means that equation Eq. 5-12 is an approximation of the solid-phase density of the food, i.e., ρfood≈ρp,solids . This is reasonable because Vp,liq will generally only be slightly larger than Vp,water where the difference is associated with liquid-phase dissolved solids and oils.
5-7 The food solid-phase density also equates to the sum of the ratios of mass fraction and component densities, which is important when accounting for mass flow between phases. Constant values of fat and soluble solid densities are used.
,= 1 ,. ,.+ ,. ,.+ , , = , , Eq. 5-13 where
• Xp,insol.solids = Mp,insol.solids/Mp,solid and ρp,insol.solids are the mass fraction and density of the insoluble solids [-, kg m-3
];
• Xp,sol.solids = Mp,sol.solids/Mp,solid and ρp,sol.solids are the mass fraction and density of the
soluble solids [-, kg m-3]; and
• Xp,solid fat = Mp,solid fat/Mp,solid and ρp,solid fat are the mass fraction and density of the solid fats [-, kg m-3].