Albert Sanfeld

Mass transfer, marangoni effect, and instability of interfacial longitudinal waves: I. Diffusional exchanges

Abstract A general formalism is developed to study interfacial instability of two immiscible incompressible fluids. Mass diffusion fluxes across the interface are the determining step. The surface mass balance equation depends upon the surface diffusion and convection and on the net flux. Discussion is restricted to longitudinal perturbations. Using the concept of surface elasticity, necessary and sufficient instability conditions for oscillating and non oscillating regimes are given for long wavelengths. The obtained criteria are extensions of the Sternling and Scriven ones.

Mass transfer, marangoni effect, and instability of interfacial longitudinal waves. II. Diffusional exchanges and adsorption-desorption processes

Abstract A general formalism is developed to study interfacial convective instability of two immiscible incompressible fluids. As an extension of the previous development (see part I) mass transfer occurs through diffusional fluxes and through adsorption-desorption processes. A linear stability analysis is performed and restricted to pure longitudinal perturbations for long wavelengths. Only oscillatory regimes are considered. We derive the stability criteria which are related to the surface elasticity. Its explicit formulation is linked to the steady diffusional fluxes, to the adsorption-desorption barrier, to the diffusion coefficients, and to the kinematic viscosities.

A Viscoelastic Approach to the Hydrodynamic Stability of Membranes

Abstract A linear stability analysis for two rheological behaviors of biological or model membranes is performed. The membrane considered is symmetrical, incompressible, and uncharged. No account is taken of mechanical anisotropy. The two fluids adjacent to the membrane are Newtonian viscous fluids. Two viscoelastic behaviors of the membrane phase are studied (1) the Kelvin—Voigt viscoelastic “solid” model and (2) the Maxwell viscoelastic “liquid” model. The mechanical boundary conditions on both faces of the membrane are the transversal momentum balance (Laplace condition) and the longitudinal momentum balance (Marangoni—Levich condition) . The van der Waals attraction forces between the two faces of the membrane are taken into account. For the symmetrical systems considered, the two modes of wavy perturbations of the membrane are uncoupled: the in-phase motion of both surfaces (stretching mode) and the 180° out-of-phase motion (squeezing mode) . The dispersion relation of both modes is solved analytically for the two models, in the limit of long-wavelength perturbations. Comparison with examples of biological membranes instabilities is performed.

Transverse and longitudinal waves at the air-liquid interface in the presence of an adsorption barrier

Abstract Analytical and computer results are provided here for the onset of oscillatory convective motions induced at the free surface of a liquid open to air, when there is transfer of a surfactant from one to the other phase. Special attention is paid to the role of a potential barrier, the interfacial deformability of the surface, and the competition between sorption and solute diffusion processes.

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.

Hydrodynamic and chemical stability of fluid—fluid reacting interfaces: I. General theory for aperiodic regimes

Abstract Under nonequilibrium conditions, the coupling between surface chemical reactions and hydrodynamics can induce the onset of convection at an interface between two immiscible Newtonian fluids. A linear analysis of interfacial stability is performed for any number of fluctuating species. The uniform reference steady state is at rest. A nonequilibrium surface elasticity coefficient is defined in terms of the surface relaxation processes. The study is restricted to aperiodic regimes. It is qualitatively and quantitatively shown that unstable and marginal aperiodic regimes can occur only for negative values of the surface elasticity. The instability is due to the self-amplification of the fluctuations of the surface tension. The chemical kinetic conditions necessary for the occurrence of this phenomenon are discussed. Intrinsically (i.e., without convection) unstable—aperiodic regimes with respect to time—surface chemical reactions always induce nonoscillatory unstable mechanochemical regimes, for the same values of the chemical parameters, when these processes are coupled with hydrodynamics. The chemical positive feedback which is responsible for the intrinsic chemical instability is then the fundamental destabilizing factor for the interfacial instability. In the absence of feedback loops in the chemical scheme, unstable mechanochemical regimes are also possible owing to the competition between interfacial chemical and convective processes. The qualitative behavior of the solutions of the dispersion equation is discussed, as well as the roles of the viscosities in the bulk phases and in the surface. New and general stability conditions are obtained.

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.

Repulsive hydration forces between charged lipidic bilayers: A linear stability analysis

Abstract The stability of the aqueous film between two charged lipidic bilayers is investigated in order to express such phenomena as vesicle aggregation and fusion in model form. The three phases (the two external lipid phases and the internal electrolytic solution) are considered as viscous fluids and an intrinsic surface rheology is ascribed to the charged surface layers. The dynamic behaviour of the system, submitted to small fluctuations is analysed. A complete balance of forces is taken into account: at long approach distances the long-range repulsive electrical forces are due to the overlap of the double layers, while the attractive forces are the van der Waals forces, the range of which is larger than the film thickness. At short distances, strong repulsive hydration forces appear which decay exponentially with distance. The general dispersion equation displays two vibrational modes (bending and squeezing); the stability conditions of these are derived. A possible mechanism for the kinetics of vesicle aggregation and fusion is suggested.

Deformational instability of a plane interface with perpendicular linear and exponential concentration gradients

Abstract A linear, hydrodynamical stability analysis is carried out for the deformation of an originally plane interface between two immiscible liquid phases with perpendicular linear or exponential concentration gradients of a third component. The results are compared with observations on the ethylene glycol-ethyl acetate-acetic acid system studied by Orell and Westwater. The normal mode of maximum instability is well in accordance with the dimensions of the convection cells reported by these authors. Two critical wavelengths of perturbation are found in the case of an exponential profile, in contrast to the single critical wavelength found for a linear profile. This fact is qualitatively explained by means of an exergy release/excess dissipation principle pertinent to the appearance of hydrodynamical dissipative structures.