Emulsions stability, from dilute to dense emulsions -- role of drops deformation.

The present paper starts with a review of fundamental descriptions based on physico-chemical laws derived for emulsions with a special interest for eventual evidences of drops deformation. A critical analysis of theories and experiments is given that leads the authors to propose new static and dynamic models for the approach to flocculation and coalescence of two deformable drops in dense and dilute environments of other neighboring drops. The model developed is based on an old paper by Albers and Overbeek for W/O dense emulsions with non-deformable particles, that has been improved recently first by Sengupta and Papadopoulos and then by Mishchuk et al. to account for all the interaction forces (electrostatic, van der Waals and steric). The basic idea here rests in the assumption that the flat surface area of the two coalescing drops, interacting in the field of other particles, increases when the distance between the particles decreases according to an exponential law with a characteristic length related to the disjoining force in the inter-particle film and to the capillary pressure that opposes flattening. The difficulty lies, indeed, in manifold interpretations on experimental observations so that no clear conclusion can be derived on mechanisms responsible for the deformation of droplets. This is why, from a pure theoretical and physical point of view, according to rather complicated models, we propose a much more simple approach that permits to define a capillary length as part of virtual operations. In a static approach, this length is based on analogy with electricity, namely repulsion leads to flatness while attraction to hump. Therefore this brings us to a definition of a length depending on the maximum value of the disjoining pressure in competition with the capillary pressure. Gravity also promotes flocculation, therefore we compare the maximum values of the surface forces acting between the surfaces of two floculating particles to gravity. Finally, considering that in most publications on emulsions foams and colloidal systems, much attention is paid on the role of the drainage in the stability process, we devote the last section to the drainage between flattened drops. We first describe briefly Taylor's approach and extend Reynolds revisited formulae taking into account the viscous friction, the disjoining pressure, the film elasticity and the wetting angle weighting the capillary pressure through the characteristic length. Our calculated values are compared to some experimental data. In conclusion to make this long paper as useful as possible for research purposes, we have the hope that our understanding of emulsion stability is not only based on knowledge of numerous theoretical and experimental works sometimes controversial given in a critical way but that it gives a new approach based on an interpretation of the drop deformation in terms of a characteristic length linked to a deformation number analogous to a Bond number.