**2. Differential scanning calorimetry for studying mass transfer within emulsions**

The test consists in submitting an emulsion sample, the volume of which being a few mm3, to a regular cooling and heating performed in a Differential Scanning Calorimeter, the volume of the cell being a few mm3. The emulsion samples are taken time to time from the mother emulsion wherein mass transfers are expected to occur at ambient temperature.

During the cooling of a pure material, the droplets dispersed in the emulsions are expected to freeze. Due to the need to the formation of a solid germ that requires a certain amount of energy, the freezing temperatures are lower than the melting ones and the theory shows they are scattered around a mean temperature T\* referred as the most probable freezing temperature of the droplets. The energy released during the droplets freezing is evidenced on the obtained freezing curve as a peak showing a bell shape if the polydispersity is low. Should the emulsion contains a rather large range of droplet sizes, the freezing curve will show more than one signal and the shape could be asymmetrical. The apex temperature of the signal that gives T\* can be correlated to the mean droplet size. On the contrary, as there is no delay in the melting phenomenon, all the droplets (whatever their size) will melt at the same temperature, which is the one observed for a bulk material. More theoretical developments of these phenomena can be found in literature (Clausse et al., 2005). Typical experimental results are given thereafter.

Figures 1 shows typical cooling curves obtained by DSC of pure water (Figure 1a) dispersed in W/O emulsions. For comparison, DSC of bulk water is given on Figure 1b. These curves represent the basic data needed to interpret the results obtained by DSC on emulsions. For a bulk material, its solidification will give a signal at a temperature higher than the one obtained for dispersed material (-18ºC for bulk water and -39 ºC for dispersed water). Between the melting temperature Tm and the freezing temperature Tc, the material still

chemically with the water of the dispersed droplets. Following this process, an example of

In mixed emulsions the transfer is due to the difference of composition between the two populations of droplets. The phase wherein they are dispersed plays the role of a liquid membrane and should this membrane be permeable to one of the material present in the

In multiple emulsions, the situation is very similar of the one observed in mixed emulsions, except that the phases involved in the mass transfer are the dispersed droplets in the globules (primary emulsion) and the continuous phase wherein the globules are dispersed. A difference in the composition between these two kinds of phases lead to a mass transfer,

Different techniques have been used to detect this kind of mass transfer in emulsions. They are based on the phenomena linked with the mass transfer, mainly: solidification and changes of the composition and the sizes of the phases involved in the mass transfer. Therefore classical techniques as spectroturbidimetry, light scattering, conductivimetry and rheology have been used. In this chapter the results obtained by using a technique that has been developed for charactering emulsions and their evolution due to mass transfer will be thoroughly described. The referred technique called DSC for Differential Scanning Calorimetry is described in the next section. Afterwards the results dealing with simple,

droplets a mass transfer occurs as it can be observed in a direct osmosis device.

the material of the globules playing in that case the role of a liquid membrane.

**2. Differential scanning calorimetry for studying mass transfer within** 

The test consists in submitting an emulsion sample, the volume of which being a few mm3, to a regular cooling and heating performed in a Differential Scanning Calorimeter, the volume of the cell being a few mm3. The emulsion samples are taken time to time from the mother emulsion wherein mass transfers are expected to occur at ambient temperature. During the cooling of a pure material, the droplets dispersed in the emulsions are expected to freeze. Due to the need to the formation of a solid germ that requires a certain amount of energy, the freezing temperatures are lower than the melting ones and the theory shows they are scattered around a mean temperature T\* referred as the most probable freezing temperature of the droplets. The energy released during the droplets freezing is evidenced on the obtained freezing curve as a peak showing a bell shape if the polydispersity is low. Should the emulsion contains a rather large range of droplet sizes, the freezing curve will show more than one signal and the shape could be asymmetrical. The apex temperature of the signal that gives T\* can be correlated to the mean droplet size. On the contrary, as there is no delay in the melting phenomenon, all the droplets (whatever their size) will melt at the same temperature, which is the one observed for a bulk material. More theoretical developments of these phenomena can be found in literature (Clausse et al., 2005). Typical

Figures 1 shows typical cooling curves obtained by DSC of pure water (Figure 1a) dispersed in W/O emulsions. For comparison, DSC of bulk water is given on Figure 1b. These curves represent the basic data needed to interpret the results obtained by DSC on emulsions. For a bulk material, its solidification will give a signal at a temperature higher than the one obtained for dispersed material (-18ºC for bulk water and -39 ºC for dispersed water). Between the melting temperature Tm and the freezing temperature Tc, the material still

hydrate formation will be described.

mixed and multiple emulsions will be described.

experimental results are given thereafter.

**emulsions** 

liquid is said to be under cooled. The degree of undercooling is defined by ΔT = Tm –Tc. For water, this degree is around 20°C for bulk water of a few mm3 and around 40°C for a population of microsized droplets. Another point to stress is that the shape of the signals is also different. This can be attributed to the way the material solidifies, very rapidly in a bulk sample or progressively in a dispersed phase as it has been indicated previously.

Fig. 1. Cooling curves for water dispersed in an emulsion (a) and for bulk water (b)

From the electrical power dq/dt registers by the calorimeter it is possible to deduce the enthalpy power dh/dt involved by the freezing or melting of the sample. On using rather low scanning rate temperature less than 2K/min, dh/dt can be approximated by dq/dt. Therefore by a previous calibration done with pure materials, the area of the signal correctly delimited permits to determine ΔH, the total heat involved in the liquid-solid transition. This quantity divided by the energy involved per mass unit Δh permits to know the mass m involved in the transition. Δh for the freezing is different for the melting one due to the net influence of the temperature specially for water due to a rather high difference between the values of the heat capacities of ice and liquid water. Nevertheless this quantity can be estimated from data on heat capacities values and as far comparison of areas of signals are done, this point is not a problem by itself. Furthermore when it is possible the amount of material involved in the transition can be determined by the area of the melting signal at a known temperature at which Δh is found in the literature. Should a mass transfer induces a change of the initial mass m(t=0) of a material, the following of the area A(t) of either the

Mass Transfers Within Emulsions Studied by

Differential Scanning Calorimetry (DSC) - Application to Composition Ripening and Solid Ripening 747

material balance, the amount of material transferred can be determined. When it is possible another way to follow the transfer is to determine the areas of the freezing or better the melting signals for the droplets for which the composition does not vary, the transfer being from these droplets to the other droplets of different composition. The way these determinations are done will be more thoroughly described in the sections dealing with.

Fig. 2. Cooling and heating curves for a solution A+B dispersed within an emulsion

composition of the droplets made of A+B due to the transfer.

To summarize two ways for quantifying the mass transfer will be used. One from the determination of y (equation 2) and the other one from the calibration curve T\* versus the

**3. Mass transfer within simple emulsions. Solid ripening in W/O emulsions**  An example is given by the mass transfer between yet solid droplets and still liquid ones due to under cooling phenomena. This transfer not very well known but that has to be taken into account when during the storage of the emulsion, the temperature reaches values below the melting ones, is referred as solid ripening as far the equilibrium state in these conditions is all the dispersed material solid (Clausse et al. 1999b). The other type is encountered when a material is added in the continuous phase of an emulsion. It is expected to diffuse and to react chemically with the material of the dispersed droplets. At the end a stable solid material is also obtained. Formation of solid hydrates in petroleum industry is a typical

example of such a situation. It is this kind of transfer that is described thereafter.

An example of such solid ripening giving rise to the formation of a hydrate is illustrated by the study of trichlorofluoromethane (CCl3F) hydrate formation in W/O emulsions. CCl3F is a volatile liquid poorly soluble in water and forms a hydrate under mild conditions at 8.5°C and 1 bar. Therefore, CCl3F appeared to be a good candidate in order to mimic the conditions of gas hydrate formation in W/O emulsions as a model system (Jakobsen et al. 1996; Fouconnier et al. 1999, 2006). The solid hydrate phase is formed inside the dispersed droplets as the result of a chemical reaction between CCl3F molecules and water molecules present in the droplets. Actually, CCl3F molecules are initially dissolved in the oily

freezing signal or the melting signal allows to evaluate the transferred material z or the ratio of non-transferred material y. They will be given by the following equations:

$$z = m(t=0) - m(t) = \frac{\left[\Delta H(t=0) - \Delta H(t)\right]}{\Delta h} = A(t=0) - A(t) \tag{1}$$

$$y = \frac{m(t)}{m(t=0)} = \frac{\Delta H(t)}{\Delta H(t=0)} = \frac{A(t)}{A(t=0)}\tag{2}$$

Should the material contain additives, the cooling curves obtained will be different and dependent on the amount of solute present (Figure 2). For two compounds A+B forming solutions in all proportions and showing an eutectic point, the freezing curves show either one or two signals as it is shown on figure 2 for 6 compositions shown by dotted lines in the phases diagram T versus composition x given as molar fraction of component B in the solutions. Line starting from 0 *<sup>e</sup> A* represents the A solidification points versus composition and line starting from 0 *<sup>e</sup> B* , the B solidification points versus composition, E being the eutectic point of the binary. When a solution is dispersed within an emulsion the solidification of the droplets shows different results depending on the composition. A composition different from the eutectic point E, separates the sequence of the events. This point indicated as ε on the graph is found at the intersection of two lines that give the most probable solidification temperatures of A for x<xε and the most probable solidification temperatures of B for x>xε. The circles mimic the contents of the droplets regards to the solid materials present. They are drawn in front of the respective signals shown by DSC. For example for droplets the composition of which being given by dotted line 2, the cooling curve shows two signals, one showing the partial solidification of A and at a lower temperature the total solidification of the droplet, namely the solidification of B and the solidification of the remaining A still liquid. As it can be seen on the diagram, the signals shift with the composition. The temperature of the apex of the first signal observed gives the most probable solidification temperature as it was yet described for dispersed pure material. The heating curve represented on the figure 2 by the line 1\* for the composition represented by the dotted line 1, shows the eutectic melting followed by the progressive melting of component A until its complete dissolution when the equilibrium line is reached. This diagram is a schematic one for the case considered, solutions that can be mixed in all proportions and that show an eutectic point. In this chapter mixtures of hexadecane and tetradecane that enter in this case will be considered. Generally, especially for water + salt, the diagram is limited as far very concentrated solution in B being impossible to reach. That is the case for water + NaCl, solutions or water +urea solutions also treated in this chapter. For the purpose of studying mass transfer that induces changes in the composition of the

droplets, only the lines that give the most probable solidification temperature of either A or B will be considered. This curve will be referred as the calibration curve that gives the most probable freezing temperature T\* versus the composition of the droplets. The undercooling given by the interval of temperatures between the equilibrium lines, and the lines that give the most probable solidification temperatures is not a constant as the figure lets assuming, but in fact it is changing with the composition and the drawing of the calibration curve needs to study samples of various compositions as it will be described later on. Determining the temperature from the freezing signal allows determining the composition of the droplets and therefore from the knowledge of the formulation of the emulsions and by doing a

freezing signal or the melting signal allows to evaluate the transferred material z or the ratio

[ ( 0) ( )] ( 0) ( ) ( 0) ( ) *Ht Ht z mt mt At At h*

> () () () ( 0) ( 0) ( 0) *mt Ht At <sup>y</sup> mt Ht At*

Should the material contain additives, the cooling curves obtained will be different and dependent on the amount of solute present (Figure 2). For two compounds A+B forming solutions in all proportions and showing an eutectic point, the freezing curves show either one or two signals as it is shown on figure 2 for 6 compositions shown by dotted lines in the phases diagram T versus composition x given as molar fraction of component B in the

eutectic point of the binary. When a solution is dispersed within an emulsion the solidification of the droplets shows different results depending on the composition. A composition different from the eutectic point E, separates the sequence of the events. This point indicated as ε on the graph is found at the intersection of two lines that give the most probable solidification temperatures of A for x<xε and the most probable solidification temperatures of B for x>xε. The circles mimic the contents of the droplets regards to the solid materials present. They are drawn in front of the respective signals shown by DSC. For example for droplets the composition of which being given by dotted line 2, the cooling curve shows two signals, one showing the partial solidification of A and at a lower temperature the total solidification of the droplet, namely the solidification of B and the solidification of the remaining A still liquid. As it can be seen on the diagram, the signals shift with the composition. The temperature of the apex of the first signal observed gives the most probable solidification temperature as it was yet described for dispersed pure material. The heating curve represented on the figure 2 by the line 1\* for the composition represented by the dotted line 1, shows the eutectic melting followed by the progressive melting of component A until its complete dissolution when the equilibrium line is reached. This diagram is a schematic one for the case considered, solutions that can be mixed in all proportions and that show an eutectic point. In this chapter mixtures of hexadecane and tetradecane that enter in this case will be considered. Generally, especially for water + salt, the diagram is limited as far very concentrated solution in B being impossible to reach. That is the case for water + NaCl, solutions or water +urea solutions also treated in this chapter. For the purpose of studying mass transfer that induces changes in the composition of the droplets, only the lines that give the most probable solidification temperature of either A or B will be considered. This curve will be referred as the calibration curve that gives the most probable freezing temperature T\* versus the composition of the droplets. The undercooling given by the interval of temperatures between the equilibrium lines, and the lines that give the most probable solidification temperatures is not a constant as the figure lets assuming, but in fact it is changing with the composition and the drawing of the calibration curve needs to study samples of various compositions as it will be described later on. Determining the temperature from the freezing signal allows determining the composition of the droplets and therefore from the knowledge of the formulation of the emulsions and by doing a

Δ = −Δ = =− = = = − <sup>Δ</sup> (1)

<sup>Δ</sup> = = = <sup>=</sup> Δ= = (2)

*<sup>e</sup> A* represents the A solidification points versus composition

*<sup>e</sup> B* , the B solidification points versus composition, E being the

of non-transferred material y. They will be given by the following equations:

solutions. Line starting from 0

and line starting from 0

material balance, the amount of material transferred can be determined. When it is possible another way to follow the transfer is to determine the areas of the freezing or better the melting signals for the droplets for which the composition does not vary, the transfer being from these droplets to the other droplets of different composition. The way these determinations are done will be more thoroughly described in the sections dealing with.

Fig. 2. Cooling and heating curves for a solution A+B dispersed within an emulsion

To summarize two ways for quantifying the mass transfer will be used. One from the determination of y (equation 2) and the other one from the calibration curve T\* versus the composition of the droplets made of A+B due to the transfer.
