Annie Steinchen

Coupling between a transconformation surface reaction and hydrodynamic motion

Abstract Conditions are given for chemical and hydrodynamic instability of a cooperative transconformation reaction at the interface between two immiscible liquids.

Chemical and hydrodynamical analysis of stability of a spherical interface

Abstract The hydrodynamical and chemical stability of deformation of the interface of a spherical drop suspended in an infinite amount of another immiscible liquid is investigated by the methods of linear, hydrodynamical stability theory. The two bulk fluids are homogeneous and continuous throughout. A general determinantal dispersion relation is evaluated between the complex frequency of the perturbation and the number characterising the surface harmonic normal mode of perturbation in the case of an arbitrary number of fluctuating and reacting species on the interface. The coupling between chemical reactions, surface diffusion, and hydrodynamics is effected by the interfacial through the equation of state of the interface and by convection motions on the interface. Surface shear and dilatational viscosity are taken into account assuming the surface fluid to be Newtonian. The stability of a stationary state of the interfacial chemical reaction with the bulk fluids in hydrodynamical rest with regard to small perturbations in the surface concentrations and in the velocity of the fluid is then studied. The fluxes from the bulk fluids to the interface remain constant, or otherwise they are perturbed proportional to the fluctuations in the surface concentrations. The case of one fluctuating species and small drop radii is treated in detail. The necessary condition for the system to be unstable is that the surface chemical reaction is unstable itself. In addition, the coefficient of autocatalysis of the surface reactions has to exceed a threshold value composed by the quenching effects of surface diffusion and of the bulk and surface viscosities. In cases with more than one fluctuating species there exist possibilities for the total system to be unstable even for stable surface reactions. The present theory is an extension of the theory of oscillations of a viscous drop due to capillary forces. It is thought to be an introduction to the study of “kicking drops” and motile events connected with the deformation of the biological cell membrane.

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 Taylors 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.

Self-organised Marangoni motion at evaporating drops or in capillary menisci - thermohydrodynamical model

Abstract Thermocapillary convection has been observed both in capillaries and at the surface of evaporating sessile droplets. The present paper aims to give a model of the onset of these convective patterns. The model accounts for the self-induced surface gradient of temperature linked to the stronger mass transfer observed near the triple line region. The role of the apparent contact angle is also evidenced. Dimensionless quantities such as the Marangoni number and the partition coefficient are the key factors of the present analysis. The calculations show that for the same environmental conditions the convection can be influenced by the geometrical considerations. Indeed, the calculated Marangoni numbers are found to be greater in the capillary than in the drop for a wetting contact angle of less than π/4 ; for an angle greater than π/4 , the results are inverted.

A Local Thermodynamical Approach of Spherical and Plane Electrochemical Diffuse Layer

Abstract A local thermodynamic method was employed to calculate the potential, the field, and the surface charge in the diffuse layer around a colloidal particle. It was found that the effect of the molar volume of the counterions and the effect of the polarization were to lower the local concentration of the counterions and thus to reduce the surface charge for a given surface potential. The ratio of the surface charge calculated by this theory to that calculated by the Gouy-Chapman theory does not change significantly with the curvature of the colloidal particle. A limitation in the application of this theory is due to the lack of knowledge of the activity coefficients at zero field in the diffuse layer. Two nomograms (graphs) of the potential versus charge relation are presented.

Surface Stress on Isotropic Solids under Dissipative Processes

Abstract An attempt has been made in this paper to gather together theoretical results of important investigations of physical, chemical and mechanical properties of solid surfaces. In particular, we focus our attention on fundamental thermodynamical and mechanical quantities such as surface energy and stress which play a determining role in stability of micro- and nano-objects. Then, taking into account the non-autonomy of the surface, we define an extended pressure which includes irreversible effects due to mechanical and chemical processes in the surface and its underlying layer. This permits, more consistently, the proposition of a revisited Laplace formulation leading to a new interpretation of surface stress. Within the frame of homogeneous deformations, our theory now accounts for the aspect ratio and composition of the interfacial region as weighting factors of the variation of surface free energy with deformation of the surface.

Motion induced by surface-chemical and electrochemical kinetics

It is well known that motion at a liquid–liquid interface may be generated by the transfer of matter. The constraint is the difference in concentration profiles between both bulk phases. In the same way, surface-chemical, sorption or electrochemical reactions may also induce convection. The constraint in this case is related to the non-equilibrium kinetic steps. A general theory based on a linear analysis of stability shows the role of mechanical (density, viscosity, interfacial tension, surface elasticity), chemical (kinetic constants, composition) or electrochemical (electrical field, dielectric constant) parameters in the onset of interfacial deformations and movements. The stresses acting on the system are mainly due to Laplace–Kelvin and Marangoni effects. Experimental evidence observed for solvent-extraction reagents are analysed within the framework of our theory.

Thermodynamic stability of the solidification front during unidirectional growth from the melt

The thermodynamic analysis of the morphological stability of a planar solidification front during the unidirectional growth from the melt of a dilute binary alloy is developed on the basis of the Glansdorff-Prigogine theory extended for surfaces. The surface excess entropy balance is derived. The obtained explicit criterion gives the physical meaning of the stabilizing and destabilizing contributions. The link with the kinetic approach is discussed for the phase interface and the multilayer models.

Surface stress on isotropic solids under dissipative processes: Appendices

The existence of a stress on the surface of a crystal in the absence of any imposed constraint is due to the presence of a thin non-uniform layer. If in this region adjacent to the surface, atoms can be exchanged with the bulk of the solid, either by diffusion or auto-diffusion, it could be relatively easy to see how the surface may develop a state of tension. Suppose first that the surface is not deformed, and that it consists of the last layer of a uniform crystal lattice, without any variation in the intermolecular distances. To remove a particle from the surface, it is necessary to break fewer intermolecular bonds than if the particle is removed from the bulk phase. Therefore, in a non-deformed surface layer, the chemical potential of a particle should be greater than in the bulk of the solid. However, diffusion equilibrium between the surface and the bulk solid requires the equality of the chemical potentials in these two regions. Since in a uniform surface layer, the chemical potential is greater than in the solid, surface atoms should diffuse towards the interior, leaving vacancies in the surface. As a result, the parallel distance to the surface between the atoms will be in tension. In addition, changes along the normal distance to the surface occur between the last few layers of atoms, or in the polarization of the atoms. It is clear that the situation is much more complicated when the surface is deformed by an external constraint such

Chemical reactions in microdroplets and microbubbles. Thermodynamic approach

Abstract In small dispersed systems, the standard chemical potential of the components present in the curved phases is different from the one in phases with a flat interface. Thermodynamic properties of reactions in such systems, at mechanical equilibrium, may be different from those for the same reactions at the same temperature, in a phase with zero curvature. Among these properties, we study here the dependence of the equilibrium constant on the curvature, on the surface tension and on the stoichiometry of the process. Reactions in an electric field are also discussed.