Here, and k are parameters which depend on the nature of the emulsion. This equation predicts that the creaming velocity decreases as the droplet concentration increases, until creaming is completely inhibited once a critical dispersed-phase volume fraction (0c) has been exceeded (Figure 7.5). In general, the value of depends on the packing of the droplets within an emulsion, which is governed by their polydispersity and colloidal interactions. Polydisperse droplets are able to fill the available space more effectively than monodisperse droplets because the small droplets can fit into the gaps between the larger ones (Das and Ghosh 1990), and so is increased. When the droplets are strongly attracted to each other, they can form a particle gel at relatively low droplet concentrations, which prevents any droplet movement (Figure 7.6). When the droplets are strongly repelled from each other, their effective size increases, which also causes complete restriction of their movement at lower values of 0c.
Polydispersity. Food emulsions contain a range of different droplet sizes, and the larger droplets cream more rapidly than the smaller droplets, so that there is a distribution of creaming rates within an emulsion (Figure 7.4). As the larger droplets move upward more
rapidly, they collide with smaller droplets (Melik and Fogler 1988, Dukhin and Sjoblom 1996). If the droplets aggregate after a collision, they will cream at a faster rate than either of the isolated droplets. Detailed information about the evolution of the droplet concentration throughout an emulsion can be obtained by using computer simulations which take into account polydispersity (Davis 1996, Tory 1996). For many purposes, it is only necessary to have an average creaming velocity, which can be estimated by using a mean droplet radius (r54) in the Stokes equation (Dickinson 1992, Walstra 1996b).
Droplet Flocculation. In many food emulsions, the droplets aggregate to form flocs (Section 7.4). The size and structure of the flocs within an emulsion have a large influence on the rate at which the droplets cream (Bremer 1992, Bremer et al. 1993, Walstra 1996a, Pinfield et al. 1997). At low or intermediate droplet concentrations, where flocs do not substantially interact with one another, flocculation tends to increase the creaming velocity because the flocs have a larger effective size than the individual droplets (which more than compensates for the fact that the density difference between the flocs and the surrounding liquid is reduced). In concentrated emulsions, flocculation retards creaming because a three-dimensional network of aggregated flocs is formed, which prevents the individual droplets from moving (Figure 7.6). The droplet concentration at which creaming is prevented depends on the structure of the flocs formed. A network can form at lower dispersed-phase volume fractions when the droplets in a floc are more loosely packed, and therefore creaming is prevented at lower droplet concentrations (Figure 7.6). These loosely packed flocs tend to form when there is a strong attraction between the droplets (Section 7.4.3).
Non-Newtonian Rheology of Continuous Phase. The continuous phase of many food emulsions is non-Newtonian (i.e., the viscosity depends on shear rate or has some elastic characteristics) (Chapter 8). As a consequence, it is important to consider which is the most appropriate viscosity to use in Stokes' equation (van Vliet and Walstra 1989, Walstra 1996a). Biopolymers, such as modified starches or gums, are often added to oil-in-water emulsions to increase the viscosity of the aqueous phase (Section 4.6). Many of these biopolymer solutions exhibit shear-thinning behavior; that is, they have a high viscosity at low shear rates which decreases dramatically as the shear rate is increased (Chapter 8). This property is important because it means that the droplets are prevented from creaming, but that the food emulsion still flows easily when poured from a container (Dickinson 1992). Creaming usually occurs when an emulsion is at rest, and therefore it is important to know the apparent viscosity that a droplet experiences as it moves through the continuous phase under these conditions. Typically, the shear rate that a droplet experiences as it creams is between about 10-4 to 10-7 s-1 (Dickinson 1992). Solutions of thickening agents have extremely high apparent shear viscosities at these low shear rates, which means that the droplets cream extremely slowly (Walstra 1996a).
Some aqueous biopolymer solutions have a yield stress (Tg), below which the solution acts like an elastic solid and above which it acts like a viscous fluid (van Vliet and Walstra 1989). In these systems, droplet creaming is effectively eliminated when the yield stress of the solution is larger than the stress exerted by a droplet as it moves through the continuous phase, i.e., tb> 2r(pj - p2)g(Dickinson 1992). Typically, a value of about 10 mPa is required to prevent emulsion droplets of a few micrometers from creaming. Similar behavior is observed in water-in-oil emulsions that contain a network of aggregated fat crystals which has a sufficiently high yield stress to prevent the water droplets from sedimenting.
The above discussion highlights the importance of carefully defining the rheological properties of the continuous phase. For this reason, it is good practice to measure the viscosity of the continuous phase over the range of shear rates that an emulsion droplet is likely to experience during processing, storage, and handling, which may be as wide as 10-7 to 103 s-1 (Dickinson 1992).
Electrical Charge. Charged emulsion droplets tend to move more slowly than uncharged droplets for two reasons (Dickinson and Stainsby 1982, Walstra 1986a). First, repulsive electrostatic interactions between similarly charged droplets mean that they cannot get as close together as uncharged droplets. Thus, as a droplet moves upward, there is a greater chance that its neighbors will be caught in the downward flow of the continuous phase. Second, the cloud of counterions surrounding a droplet moves less slowly than the droplet itself, which causes an imbalance in the electrical charge which opposes the movement of the droplet.
Fat Crystallization. Many food emulsions contain a lipid phase that is either partly or wholly crystalline (Mulder and Walstra 1974, Boode 1992, Dickinson and McClements 1995). In oil-in-water emulsions, the crystallization of the lipid phase affects the overall creaming rate because solid fat (p ~ 1200 kg m-3) has a higher density than liquid oil (p ~ 910 kg m-3). The density of a droplet containing partially crystallized oil is given by pdr0plet = ^sfc psolid + (1 - ^sfc) Puqmd, where ^SFC is the solid fat content At a solid fat content of about 30%, an oil droplet has a similar density as water and will therefore neither cream nor sediment. At lower solid fat contents, the droplets cream, and at higher solid fat contents they sediment. This accounts for the more rapid creaming of milk fat globules at 40°C, where they are completely liquid, compared to at 20°C, where they are partially solid (Mayhill and Newstead 1992).
As mentioned above, crystallization of the fat in a water-in-oil emulsion may lead to the formation of a three-dimensional network of aggregated fat crystals, which prevents the water droplets from sedimenting (e.g., in butter and margarine) (Dickinson and Stainsby 1982). In these systems, there is a critical solid fat content necessary for the formation of a network, which depends on the morphology of the fat crystals (Walstra 1987). The importance of network formation is illustrated by the effect of heating on the stability of margarine. When margarine is heated above a temperature where most of the fat crystals melt, the network breaks down and the water droplets sediment, leading to the separation of the oil and aqueous phases.
Adsorbed Layer. The presence of a layer of adsorbed emulsifier molecules at the surface of an emulsion droplet affects the creaming rate in a number of ways. First, it increases the effective size of the emulsion droplet, and therefore the creaming rate is increased by a factor of (1 + 5/r)2, where 8 is the thickness of the adsorbed layer. Typically, the thickness of an adsorbed layer is between about 2 and 10 nm, and therefore this effect is only significant for very small emulsion droplets (<0.1 |im). Second, the adsorbed layer may alter the effective density of the dispersed phase, p2 (Tan 1990). The effective density of the dispersed phase when the droplets are surrounded by an adsorbed layer can be calculated using the following relationship, assuming that the thickness of the adsorbed layer is much smaller than the radius of the droplets (5 << r):
The density of the emulsifier layer is usually greater than that of either the continuous or dispersed phase, and therefore the adsorption of emulsifier increases the effective density of the dispersed phase (Tan 1990). The density of large droplets (r >> 5) is approximately the same as that of the bulk dispersed phase, but that of smaller droplets may be altered significantly. It is therefore possible to retard creaming by using a surface-active biopolymer which forms a high-density interfacial layer.
Brownian Motion. Another major limitation of Stokes' equation is that it ignores the effects of Brownian motion on the creaming velocity of emulsion droplets (Pinfield et al. 1994, Walstra 1996a). Gravity favors the accumulation of droplets at either the top (creaming) or bottom (sedimentation) of an emulsion. On the other hand, Brownian motion favors the random distribution of droplets throughout the whole of the emulsion because this maximizes the configurational entropy of the system. The equilibrium distribution of droplets in an emulsion which is susceptible to both creaming and Brownian motion is given by the following equation (ignoring the finite size of the droplets) (Walstra 1996a):
where $(/) is the concentration of the droplets at a distance h below the top of the emulsion, and is the concentration of the droplets at the top of the emulsion. If $(h) = then the droplets are evenly dispersed between the two locations (i.e., Brownian motion dominates), but if $(h) << $0, the droplets tend to accumulate at the top of the emulsion (i.e., creaming dominates). It has been proposed that if $(h)/$0 is less than about 0.02, then the influence of Brownian motion on the creaming behavior of emulsions is negligible (Walstra 1996a). This condition is met for droplets with radii greater than about 25 nm, which is nearly always the case in food emulsions.
Complexity of Creaming. The above discussion has highlighted the many factors which need to be considered when predicting the rate at which droplets cream in emulsions. In practice, it is difficult to simultaneously account for all of these factors in a single analytical equation. The most comprehensive method of predicting gravitational separation in emulsions it is to use computer simulations (Pinfield et al. 1994, Tory 1996).
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