Flow fields in soap films: Relating viscosity and film thickness (original) (raw)

Flow fields in soap films: relating surface viscosity and film thickness

Phys Rev E, 2009

We follow the diffusive motion of colloidal particles in soap films with varying h/d, where h is the thickness of the film and d the diameter of the particles. The hydrodynamics of these films are determined by looking at the correlated motion of pairs of particles as a function of separation R. The Trapeznikov approximation [A. A. Trapeznikov, PICSA (1957)] is used to model soap films as an effective interface in contact with bulk air phases, that behaves as a 2D fluid. The flow fields determined from correlated particle motions show excellent agreement with what is expected for the theory of 2D fluids for all our films where 0.6 ≤ h/d ≤ 14.3, with the surface viscosity matching that predicted by Trapeznikov. However, for thicker films with h/d > 7 ± 3, single particle motion is faster than expected. Additionally, while the flow fields still match those expected for 2D fluids, the parameters of these flow fields change markedly for thick films. Our results indicate a transition from 2D to 3D fluid-like behavior occurs at this value of h/d.

Soap films as two-dimensional fluids: Diffusion and flow fields

2014

We observe tracer particles diffusing in soap films to measure the two-dimensional (2D) viscous properties of the films. We make soap films with a variety of water-glycerol mixtures and of differing thicknesses. The single-particle diffusivity relates closely to parameters of the film (such as thickness h) for thin films, but the relation breaks down for thicker films. Notably, the diffusivity is faster than expected for thicker films, with the transition at h/d = 5.2 ± 0.9 using the tracer particle diameter d. This indicates a transition from purely 2D diffusion to diffusion that is more three-dimensional. Additionally, we measure larger length scale flow fields from correlated particle motions and find good agreement with what is expected from theory of 2D fluids for all our films, thin and thick. We measure the effective 2D viscosity of a soap film using single-particle diffusivity measurements in thin films, and using the two-particle correlation measurements in all films.

2D to 3D transition in soap films demonstrated by microrheology

Eprint Arxiv 0807 4751, 2008

We follow the diffusive motion of colloidal particles of diameter ddd in soap films of varying thickness hhh with fluorescence microscopy. Diffusion constants are obtained both from one- and two-particle microrheological measurements of particle motion in these films. These diffusion constants are related to the surface viscosity of the interfaces comprising the soap films, by means of the Trapeznikov approximation [A. A. Trapeznikov, \emph{PICSA} (1957)] and Saffman's equation for diffusion in a 2D fluid. Unphysical values of the surface viscosity are found for thick soap films ($h/d > 7$), indicating a transition from 2D to 3D behavior.

The dynamics of a viscous soap film with soluble surfactant

Journal of Fluid Mechanics, 2001

Nearly two decades ago, Couder (1981) and Gharib & Derango (1989) used soap films to perform classical hydrodynamics experiments on two-dimensional flows. Recently soap films have received renewed interest and experimental investigations published in the past few years call for a proper analysis of soap film dynamics. In the present paper, we derive the leading-order approximation for the dynamics of a flat soap film under the sole assumption that the typical length scale of the flow parallel to the film surface is large compared to the film thickness. The evolution equations governing the leading-order film thickness, two-dimensional velocities (locally averaged across the film thickness), average surfactant concentration in the interstitial liquid, and surface surfactant concentration are given and compared to similar results from the literature. Then we show that a sufficient condition for the film velocity distribution to comply with the Navier–Stokes equations is that the typic...

Two-Dimensional to Three-Dimensional Transition in Soap Films Demonstrated by Microrheology

2009

We follow the diffusive motion of colloidal particles of diameter d in soap films of varying thickness h with fluorescence microscopy. Diffusion constants are obtained both from one-and two-particle microrheological measurements of particle motion in these films. These diffusion constants are related to the surface viscosity of the interfaces comprising the soap films, by means of the Trapeznikov approximation and Saffman's equation for diffusion in a 2D fluid. Unphysical values of the surface viscosity are found for thick soap films (h=d > 7 AE 3), indicating a transition from 2D to 3D behavior.

Measuring and overcoming limits of the saffman-delbrück model for soap film viscosities

PloS one, 2015

We observe tracer particles diffusing in soap films to measure the two-dimensional (2D) viscous properties of the films. Saffman-Delbrück type models relate the single-particle diffusivity to parameters of the film (such as thickness h) for thin films, but the relation breaks down for thicker films. Notably, the diffusivity is faster than expected for thicker films, with the crossover at h/d = 5.2 ± 0.9 using the tracer particle diameter d. This indicates a crossover from purely 2D diffusion to diffusion that is more three-dimensional. We demonstrate that measuring the correlations of particle pairs as a function of their separation overcomes the limitations of the Saffman-Delbrück model and allows one to measure the viscosity of a soap film for any thickness.

Thinning of soap films: the effect of surface viscosity

The gravitational thinning of soap films, or any thin liquid film stabilized by surfaceactive agents, has been analyzed mathematically. The flow was treated as quasi-onedimensional and quasi-steady, and the surface was assumed to be a two-dimensional, Newtonian fluid. The analysis is naturally a highly idealized version of the complex thinning processes that occur in nature; nevertheless, the results put certain limitations on the real process and should be of some help in interpreting experimental observations.

On the thickness of soap films: an alternative to Frankel's law

Journal of Fluid Mechanics, 2008

The formation of soap films by vertical withdrawal from a bath is typically described by Frankel's law, which assumes rigid film 'walls' and shear-like dynamics. Since most soap films have interfaces that are not rigid, and as the flow in the withdrawal of thin free films is typically extensional, we reconsider the theory of soap film formation. By assuming extensional flow dominated by surface viscous stresses we find that the film thickness scales as the two-thirds power of the withdrawal speed U. This speed dependence is also predicted by Frankel's law; the difference lies in the origin of the viscous resistance which sets the pre-factor. When bulk viscous stresses are important the speed dependence can vary between U 2/3 and U 2 .

Thickness Fluctuations in Turbulent Soap Films

Physical Review Letters, 2002

Rapidly flowing soap films provide a simple and attractive system to study two-dimensional hydrodynamics and turbulence. By measuring the rapid fluctuations of the thickness of the film in the turbulent regime, we find that the statistics of these fluctuations closely resemble those of a passive scalar field in a turbulent flow. The scalar spectra are well described by Kolmogorov-like scaling while the high-order moments show clear deviations from regular scaling just like dye or temperature fluctuations in 3D turbulent flows.

Instability of the Kolmogorov flow in a soap film

Physical Review E, 1999

We examine the instability of a soap film flow driven by a time-independent force that is spatially periodic in the direction perpendicular to the forcing ͑Kolmogorov flow͒. Linear stability analysis of an idealized model of this flow predicts a critical Reynolds number R c Ϸͱ2. In our soap film experiment, we find a critical value R c Ϸ70. This discrepancy can be ascribed to frictional effects from viscous coupling of gas to the film, which is neglected in the idealized model. The kinematic viscosity of the surrounding gas and the thickness of gas layers on each side of the soap film are varied in the experiments to better understand these frictional effects.