Hydrodynamics of dielectric fluid films

Abstract

Abstract:We introduce a general hydrodynamic model to study the stability of lipid films against thermal fluctuations. As one novel aspect the model accounts before all for a complete intrinsic surface rheology of the film interfaces. Thus the rheological behaviour of the surface adsorbed lipids is modelled which screen the hydrophobic film interior against the aqueous exterior. For coloured films we demonstrate first the influence of electrical forces on the dynamics and film stability. For that we perform a linear stability analysis on a simplified mechanically symmetric film with i) symmetric surface charge distribution and ii) linear electric potential drop across the film. Based on the complete film model we then categorize the complete set of solutions of the linearized equations of motion and we study the growth rates of unstable film modes. Finally we discuss the stability properties of a black film after introducing a repulsive mechanism due to the steric hindrance of the interfacial lipids.

Stability of Streaming in an Electrified Maxwell Fluid Sheet Influenced by a Vertical Periodic Field in the Absence of Surface Charges

“…Due to the intricacy of the problem for the generalization to the Kelvin-Helmholtz flow of non-Newtonian dielectric fluids, we confine the analysis to weak viscoelastic effects. The introduction of the weak viscous effects is customary in the case of a Newtonian fluid (27,28) and should be understood in a manner similar to a viscoelastic problem, which makes the problem formulation much easier to handle, since periodic force and relative motions are included. If the viscous forces are very small in comparison with nonviscous forces, then viscoelasticty produces only a thin, weak vertical layer at the surface of separation, while the motion remains irrotational throughout the bulk of the fluids.…”

“…With these boundary conditions, the solution of the Laplace equation [20] yields the distribution of the potential field φ 1 in the three layers as given in the Appendix. Further, the solution of the Laplace equation [19] in view of the boundary conditions [26] and [27] gives the stream function ψ 1 and thus the distribution of the pressure P 1 in the three layers as presented in the Appendix.…”

“…Much work on instabilities in viscous films with space charges and varying dielectric constants (with practical connections to foam stability, flotation processes, detergent cleansing, and the stability of biomembranes) has been performed by researchers including Jain and Ruckenstein (21), Invanov et al (22), Maldarelli and Jain (23), Bisch (24), Sanfeld and Steinchen (25), Gallez et al (26) Wendel et al (27), and Mohamed et al (18). However, for horizontal constant velocities, it can be excluded that solutions exist.…”

Instability for Shearing of an Electrified Kelvin Fluid Sheet with or without Supporting Surface Charges

“…Due to relation [20], the normal component of the electric displacement at the surface of separation is continuous, while it is discontinuous according to the presence of surface charges and hence relation [22] is valid.…”

“…The electrical stress results from the dielectric forces. In deriving the characteristic equations when there are no surface charges on the unperturbed interfaces y = ±a, condition [20] will be taken into account. The electric conditions that have to be satisfied at y = ±a are conditions [34]- [37]; with these boundary conditions the solutions of Laplace equation [7] yield the distribution of the potential field φ in the three layers as given in the Appendix.…”