**4.3 Model of kinetics of composition ripening**

The mechanism of composition ripening has to be considered when a composition gradient exists within the emulsion under study. To model the mass transfer, the mixed emulsions are pictured as: two oil phases of different nature compartmented and separated by a plane liquid aqueous membrane or two aqueous phases of different composition compartmented and separated by a plane liquid membrane made of oil (Figure 19).

Mass Transfers Within Emulsions Studied by

**5. Multiple emulsions** 

Differential Scanning Calorimetry (DSC) - Application to Composition Ripening and Solid Ripening 765

considered and it could be improved by taking account the changes of the characteristics of

Multiple or double emulsions are systems in which a liquid phase is dispersed into globules which in turn are dispersed into another immiscible liquid phase (Garti & Lutz, 2004; Benichou et al., 2007). The liquid phase dispersed as microdroplets in the globules is called the internal phase whereas the liquid phase in which are dispersed the globules is called the external phase. Therefore a multiple emulsion contains three liquids phases and are classified as either Water-in-Oil-in-Water (W/O/W) emulsions or Oil-in-Water-in-Oil emulsions (O/W/O) (Pal, 2011; Muschiolik, 2007). The inner dispersed droplets are separated from the external phase by a layer of the globules phase (Garti & Lutz, 2004). Multiple emulsions are liquid carriers for entrapped and release of active or reactive molecules in pharmaceutics, cosmetics, food and industrial applications. Nevertheless, W/O/W multiple emulsions are more studied because they have higher potential to become commercial products than O/W/O multiple emulsion (Benichou & Aserin 2007). For instance, in cosmetics the release of an encapsulated drug inside an aqueous globule of a W/O/W emulsion can be directly liberated by breaking of the globules via mechanical stress (Muguet et al., 2001; Tejado et al., 2001). In pharmaceutics, drugs can be protected by the membrane until it reaches its target and then released by controlled release (Garti & Lutz, 2004; Hai & Magdassi, 2004; Tejado et al., 2005). Controlled release can by operated via swelling of the globules (or Ostwald swelling) which consists in an increase in size of the inner dispersed droplets due to a difference of chemical potential on both sides of the membrane leading to a water mass transfer from the external phase to the internal phase (Geiger et al., 1998; Grossiord & Stambouli, 2007; Lutz et al., 2009). As a consequence, the volume of the oily globules increases and when the resistance of the membrane becomes

In water waste treatments which also involve W/O/W emulsions, the toxic compound present in the external phase has to diffuse through the membrane to be entrapped in the inner droplets. In such separation processes, selectivity of the membrane is an important parameter (Kentish & Stevens, 2001; Kumbasar, 2009). Indeed when a compound has to be extracted from a solution containing a variety it is important that only the compound to be extracted diffuses through the membrane. In order to promote selectivity of the membrane, a carrier can be added into the membrane phase (Venkatesan & Meera Sheriffa Begum, 2009; Ng et al., 2010). A carrier is a molecule which can form a complex with the toxic compound at the external interface and transport it to the internal phase where the toxic compound will be entrapped (Hasan et al., 2006; Frasca et al., 2009). High selectivity means that the carrier holds a good affinity with the toxic compound in order to exclusively transport it through

In separation applications, the instability of the multiple emulsions can reduce significantly the efficiency of the process. Indeed, if Ostwald swelling or coalescence of the globules occurs, such mechanisms can lead to the break of the globules. The extracted molecule is then directly released in the external phase which ruins the extraction process (Yan & Pal,

If O/W/O multiple emulsions have been less extensively studied, they can also finds potential applications in food, cosmetics and controlled delivery drugs (Benichou et al.,

the emulsion with time due to the transfer, and the emulsifier influence.

insufficient, the globule breaks liberating the active compound.

the membrane (Kaghazchi et al., 2006).

2001, 2004; Mortaheb et al., 2008).

Fig. 19. Picture of mixed emulsion in the model of mass transfer

It has been demonstrated in the presented work and in the literature that the transport of pure water in W/O mixed emulsion or the transfer of pure tetradecane in O/W mixed emulsion is increased when surfactant making micelles is present as the micelles can incorporated the transferred molecules and facilitate their transport through the continuous media. To quantify the transfer, the flux J is introduced and expressed in terms of chemical potential gradient *grad*μaccording to the following equation:

$$\vec{j} = -\mathbf{L} \times \overline{grad}\,\mu\tag{7}$$

With L being the factor related to the transferred material diffusion coefficient and the transferred material concentration in the membrane. By using this model, it has been possible to express the changes of the number of material moles in the compartment I containing pure material, 1( ) *<sup>I</sup> n t* versus time t. This number decreases versus time ,the material being transferred between two populations of droplets in direction of the decreasing chemical potential. For example, water being transferred from the pure water droplet to the water+solute droplets or tetradecane being transferred from the pure tetradecane droplets to the hexadecane droplets. A mathematical treatment and thermodynamic considerations developed (Clausse et al., 1995a) allow obtaining the following relation:

$$\sum V^{I} \left[ n\_1^{I} (t=0)^{1\dagger 3} - n\_1^{I} (t)^{1\dagger 3} \right] - \left[ n\_1^{I} (t=0)^{4\dagger 3} - n\_1^{I} (t)^{4\dagger 3} \right] = 2 n\_1^{II} v\_1^{2\dagger 3} (V\_0^{I})^{1\dagger 3} \frac{L\_D}{\dddot{d}} \tag{8}$$

In this equation, V and v are the total volume and the molar volume, respectively, and Lp and *d* are the permeability coefficient and the mean diameter of the droplets, respectively. Furthermore, n1 and n2 are the moles numbers of water and solute or the moles numbers of tetradecane and hexadecane, respectively. Lp is a parameter difficult to know as it is linked to unknown parameters such as the width of the equivalent membrane, the water diffusion coefficient or the tetradecane diffusion coefficient and the water concentration or the tetradecane concentration in the membrane. Nevertheless, it is possible from this model to predict the lapse of time necessary to reach equilibrium, when all the pure water molecules has migrated from the pure water droplets to the water+solute droplets, or when the tetradecane molecules has migrated from the pure tetradecane droplets to the diluted hexadecane droplets. This point is reached when 1() 0 *<sup>I</sup> n t* = . Similar treatments dealing with water transfer within multiple emulsions have been given in the literature (Clausse et al., 1995b; Potier et al., 1992).

In each studied case, the water transport in W/O mixed emulsion and the tetradecane transfer in O/W mixed emulsion, experimental results are fairly well fitted by the model proposed. Although this model is not perfect, it gives the main physical parameters to be considered and it could be improved by taking account the changes of the characteristics of the emulsion with time due to the transfer, and the emulsifier influence.
