Interaction Potential between Droplets

In aqueous systems the most important repulsive potential arises from electrostatic repulsions. Droplets are usually charged to a greater or lesser extent, and their charged surfaces attract counter-ions from the solvent, forming a diffuse electrical double layer around each drop. The double layers around adjacent drops interact to 

Armed with the total interaction potential, the stability of simple emulsions may be understood. The droplets exhibit constant Brownian motion due to random thermal fluctuations. This leads to random encounters between droplets with the average magnitude of the force driving the encounter being of the order of the thermal energy of the system, kT, where k is the Boltzmann constant and T the absolute temperature. The outcome of the encounter then depends upon the form of the total interaction potential. 

With this analogy in mind, other scenarios may be investigated. Had the primary maximum been small compared to kT the marble would have traversed this obstacle and then accelerated down into the primary minimum. To continue the analogy the primary minimum must be considered as a very deep well from which droplets may not roll out. At this point the encounter event is over once more but this time with an unstable outcome. The particles are in intimate contact, held together by van der Waals forces that are so large that the process is essentially irreversible. This outcome corresponds to droplet coalescence. 

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Underlining that BCO and Diesel oil are not miscible a third component must be added to obtain a stable emulsion. This third component is called emulsifier (or surfactant). It changes the interfacial properties (namely interaction potential between droplets) of the system avoiding (or delaying) the emulsion s breaking. 

Figure 5.2 Colloidal interactions between emulsion droplets are characterized by the change in interaction potential with droplet separation.

FIG. 6 Schematic representation of interaction potentials between two emulsion droplets stabilized sterically. Ws, and Wj indicate, respectively, van der Waals, steric, and total interaction potentials. 

Some studies have been made of W/O emulsions the droplets are now aqueous and positively charged [40,41 ]. Albers and Overbeek [40] carried out calculations of the interaction potential not just between two particles or droplets but between one and all nearest neighbors, thus obtaining the variation with particle density or . In their third paper, these authors also estimated the magnitude of the van der Waals long-range attraction from the shear gradient sufficient to detach flocculated droplets (see also Ref. 42). 

The theory states that the forces between droplets can be considered as the sum of an attractive van der Waals part Va and a repulsive electrostatic part Er when identical electrical double layers overlap. As the origin of each force is independent of the other, each is evaluated separately, and the total potential of interaction Vt between the two droplets as a function of their surface-to-surface separation is obtained by summation... 

For W/O microemulsions, deviations from hard-sphere behavior are sometimes observed. The reason for this is that here there is a stronger tendency for attractive interactions and the formation of anisometric shapes. Here viscosity data can be used to determine the shape of the corresponding aggregates or to extract information regarding the interaction potential that exists between the droplets. From temperature-dependent experiments the binding enthalpy of the droplets can be determined. 

These ideas can help us to investigate the nature of interaction potential W, electrostatic repulsion and attraction W due to the exchange of oil molecules by segments of soap chains when the droplets approach each other (5) The balance between and will be either net repulsion or net attraction. 

Aggregation, flocculation, and coagulation are terms used to describe the destabilization process when attractive forces interact between droplets only separated by a thin film of the continuous phase. For small interaction potentials, flocculation or aggregation will be reversed by rehomogenization similar to creaming and sedimentation. 

For bridging flocculation to occur, several conditions must be met. The most obvious is that the droplet surfaces must be subject to polymer adsorption. In emulsions, the presence of surfactants at the interface, which are necessary for coalescence stability, means that only polymers with sufficient surface affinity to displace the surfactant from the siuface, or a specific affinity for the surfactant itself, may adsorb. A second condition places a lower limit on the size of the polymers in a given system. Clearly the partially coated droplets must encounter one another, coming close enough for a polymer molecule to span the gsq> between the droplets. This means that the polymer molecules must be able to extend past the primary maximum in the total interaction potential. The absolute limit on polymer size will be defined by the position of the primary maximum and the radius of gyration of the polymer molecules. However, in practice, when polymer molecules become adsorbed to drop surfaces the conformation of the polymer molecule frequently alters to allow multiple attachments to the drop surface, which may reduce the distance the polymer extends into solution. 

Hamaker. The contribution of the surface extension energy and/or bending elasticity to the pair interaction potential is also included. The extension of the drop surface upon the deformation corresponds to a soft interdroplet repulsion. All the remaining possible interactions (electrostatic, steric, depletion, etc.) can usually be treated in the framework of Deqaguin s approximation, which allows one to account for the two contributions of the total interaction energy (i) across the flat film and (ii) between the spherical surfaces surrounding the fllm. " Combined with relevant expressions for the hydrodynamic interactions, this approach could be used for studying the coalescence of Brownian emulsion and microemulsion droplets. ... 

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