Effects Of Surface Viscosity Research Articles

The effects of interfacial viscosity on the attenuation and phase speed of acoustic waves in bubbly liquids

The attenuation and phase speed of bubbly fluids have been shown to be highly dispersive due in part to the resonance response of individual bubbles. Surface-active materials, or surfactants, are known to dramatically alter the viscoelastic dynamics of an interface without affecting the bulk fluid properties. In this theoretical model the effects of surface viscosity on the propagation of linear pressure waves through a bubbly fluid are examined. The attenuation and phase speed are calculated for varying radii, void fraction, and interfacial viscosity for air bubbles in water. The results show an increase in attenuation for frequencies far removed from the bubble resonance for radii less than 100 microns. There is no significant increase in attenuation for larger bubbles (order 1 mm). Interestingly, near resonance, the interfacial viscous case has a lower attenuation than the clean interface, most likely due to the reduced radiation damping associated with smaller radial excursions. Likewise, resonance effects on the phase speed dispersion curve are also significantly diminished due to the interfacial viscosity. These results could be important for understanding propagation near the surface of the ocean, where surface-active materials can dramatically affect the dynamics of micron-sized bubbles and bubble distributions. [Work supported by ONR.]

Stokes flow in the presence of a planar interface covered with incompressible surfactant

The Lorentz solution for Stokes flow in the presence of a plane wall is generalized to a surfactant-covered interface, and the Stokeslet solution is derived. The result is used to describe the motion of a small particle in the presence of the interface. The surfactant is insoluble and nondiffusing. The effects of surface viscosity are included. Small variations in surfactant concentration are assumed; this assumption usually holds under small capillary number conditions.

Fluid motion of monomolecular films in a channel flow geometry

Surface pressure-driven flow of a monolayer in a channel flow geometry is studied and exact representations for the monolayer and subphase velocity fields are given in terms of solutions involving dual integral equations. The monolayer velocity profiles are examined as a function of the viscosity contrast between the monolayer and the subphase and the effects of a finite depth sublayer are investigated also. The calculated velocity profiles may prove useful for determining the effective surface viscosity of monolayer films from comparable experimental measurements.

Effects of surface viscosity on the finite deformation of a liquid drop and the rheology of dilute emulsions in simple shearing flow

The deformation of a liquid drop with constant isotropic surface tension and finite surface viscosity, evolving under the action of a simple shearing flow, is considered. The evolution of the drop from the spherical shape is computed using a novel implementation of the boundary integral method that incorporates the effects of interfacial rheology in an efficient manner. The numerical results confirm that surface viscosity acts to suppress the interfacial motion and reduce the magnitude of drop deformation. When the surface viscosity is sufficiently large, the drops maintain a compact shape at all capillary numbers. The effect of surface viscosity on the rheology of a dilute emulsion is considered, and it is found that, in all cases, a dilute emulsion behaves like a shear-thinning medium with some elastic properties.

Asymmetric Drainage in Foam Films N4.1

ABSTRACTDrainage of circular foam films is much more rapid when the drainage is asymmetric. The same basic mechanism is responsible for asymmetric drainage of thin circular films and marginal regeneration. A linear stability analysis showed that these phenomena are caused by a hydrodynamic instability that is produced by a surface-tension-driven flow and stabilized by surface viscosity, surface diffusivity and system length scale. A criterion for the onset of this instability was derived. Experiments performed on small circular films of aqueous solutions of SDS and SDS:l-dodecanol demonstrated the strong stabilizing effect of surface viscosity. Experimental results were found to be in good agreement with the predictions of the linear stability analysis. Finite difference simulations demonstrate the validity of the linear stability analysis for when the radius of curvature of the “barrier ring” is large compared to the transverse wave length of the instability. These simulations also show the circulation cells that relax the surface tension gradient and thus accelerate the drainage of the film.

酸化物融体の泡立ち性に及ぼす表面粘性の効果

酸化物融体の泡立ち性に及ぼす表面粘性の効果

Effects of surface viscosities on the stability of a draining plane parallel liquid film as a small bubble approaches a liquid‐gas interface

AbstractWhen a small bubble is driven through a liquid phase to a liquid‐gas interface, a thin liquid film forms between them and drains until an instability forms and coalescence occurs. Following Lin and Slattery (1982b), Chen et al. (1984) and Hahn et al. (1985) analyzed this process, neglecting the effects of electrostatic forces and of the surface viscosities. Here we extend their theory to include the effects of the surface viscosities. We employ a modification of the development by Barber and Hartland (1976; Flumerfelt et al., 1982) for a draining film bounded by parallel planes.For a large intermediate range of the surface viscosities, the coalescence time is a strong function of these parameters. Inclusion of the surface viscosities acts to moderate or even reverse trends previously established for the dependence of the coalescence time on the bubble radius, the viscosity of the film liquid, the interfacial tension, the strength of the London‐van der Waals forces, and the density difference between the two phases.

Surface viscosity of water

The recent suggestion1 that surface viscosity effects can arise from the molecularly diffuse nature of a fluid surface or interface has prompted this re-examination of data concerning capillary waves on the surface of water. Previous work2 has shown that the propagation of such waves is not compatible with the predictions of accepted theory for a surface having no abnormal rheological properties. These apparent discrepancies can be resolved in terms of one of the surface shear viscosities predicted by Goodrich. The existence of such surface viscosities for pure water suggests that caution must be exercised in interpreting surface viscosities observed for surface films in terms of molecular structure of, or interactions within the films.

Spherical drop of cytoplasm with an effective surface tension influenced by oscillating enzymatic reactions. A simplified model for the biological clock, cell division, and chemotaxis

A model suggested as a possible mechanism of a biological clock of the escapement type is constructed. A biological cell is treated as a spherical drop of cytoplasm with embedded contractile elements (microfilaments and microtubules). The contractile elements are thought to be positioned mainly in the thin layer of ectoplasm adjacent to the cell membrane. This layer is described as a mathematical surface with an “effective surface tension” and an “effective surface viscosity.” For simplicity, the synthesis of contractile elements is thought to be effectuated by one or more of the enzymes in a triangular enzyme cycle (Christiansen cycle). The enzyme concentrations in this model may perform damped oscillations around their stationary values, just as enzymes in real enzyme cycles. A fluid drop with surface tension is also able to perform damped oscillations. When the two systems are combined, calculations show that unstable, oscillatory solutions may be obtained. Those may generate limit cycles to be used in a mechanochemical clock. In a cell tissue we have the possibility of mechanical interaction between the cells and of nonlinear synchronization of the individual clocks. If there should not be a complete decoupling between the hydrodynamic and the chemical dispersion relations between complex growth constant and normal mode number, it is very important that the three surface diffusion coefficients of the enzymes are not all equal. Apart from that, calculations reveal several remarkable features of the model: (a) Stationary instabilities have loci which are independent of the absolute values of surface tension. The oscillatory modes have loci of marginal stability which depend on surface tension, except for the l = 1 surface harmonics. (b) For l = 1 (translation mode), stationary instability appears before oscillatory instability. This mode may therefore be used to model chemotaxis of unicellular organisms in the gradient of an external attractant. (c) The mode l = 2 (cell division mode) exhibits oscillatory instability before the appearance of stationary instability when the coupling parameter between enzyme kinetics and hydrodynamics is increased. The model may therefore be used to simulate the mitotic clock as well as the cell division process and various disturbances of the threshold values leading to cancer growth. (d) With the present model it is easy to obtain a perfect compensation of the temperature dependence of the chemical rate constants.

The effects of surface viscosity on the axisymmetric drainage of planar liquid films

AbstractThe Reynolds equation is extended to allow for the effects of shear and dilational surface viscosities on the axisymmetric drainage of planar films. It is shown that the number of immobile surfaces, n, may be expected to decrease with increasing film radius and bulk viscosity and with decreasing film thickness and surface viscosity, as observed experimentally. The predicted rate of film thinning agrees well with available experimental results.

Thermal instability induced by buoyancy and surface tension with radiative transfer

The onset of steady, cellular convection in a horizontal fluid layer heated from below is considered taking into account the possibility of radiative heat transfer in addition to conduction and convection. The radiation is found to have a stabilizing effect even in the presence of surface tension. The effect of surface viscosity and surface deflexion are also discussed. The coupling between the surface tension and buoyancy becomes weaker as the radiative heat transfer rate is increased.

Foam drainage, surface viscosity, and bubble size bias

The frequently neglected correction for statistical bias in the measurement of bubble size distribution at a surface is found to be significant for the size distributions involved in the foaming experiments, insofar as calculation of effective surface viscosity from the drainage theory that was developed earlier by the authors' group is concerned. However, with the establishment of an appropriate surface viscosity, the scatter in predicting the steady rate of foam overflow or drainage by the said theory is barely affected.

Gravitational Thinning of Films. Effect of Surface Viscosity and Surface Elasticity

Gravitational Thinning of Films. Effect of Surface Viscosity and Surface Elasticity

Stable numerical approximation of two-phase flow with a Boussinesq–Scriven surface fluid

We consider two-phase Navier--Stokes flow with a Boussinesq--Scriven surface fluid. In such a fluid the rheological behaviour at the interface includes surface viscosity effects, in addition to the classical surface tension effects. We introduce and analyze parametric finite element approximations, and show, in particular, stability results for semi-discrete versions of the methods, by demonstrating that a free energy inequality also holds on the discrete level. We perform several numerical simulations for various scenarios in two and three dimensions, which illustrate the effects of the surface viscosity.