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

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 $h/d = 5.2 \pm 0.9$ 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

Temporal and spatial heterogeneity in aging colloids: a mesoscopic model

A coarse-grained model of dense hard sphere colloids building on simple notions of particle mobility and spatial coherence is presented and shown to reproduce results of experiments and simulations for key quantities such as the intermediate scattering function, the particle mean-square displacement and the $\chi_{4}$ mobility correlation function. All results are explained by two emerging and interrelated dynamical properties: i) a rate of intermittent events, quakes, which decreases as the inverse of the system age t; ii) a length scale characterizing correlated domains, which increases linearly in log t. This leads to simple and accurate scaling forms expressed in terms of a single scaling variable Finally, we propose a method to experimentally extract the growing length scale of an aging colloid and suggest that a suitable scaling of the probability density function of particle displacement can experimentally reveal the rate of quakes.Comment: 5 pages 6 figure

Plot of interfacial viscosity from single particle diffusion measurements as a function of <i>h/d</i>.

<p>Filled circles denote particles of diameter 0.1 <i>μ</i>m, open circles denote particles of diameter 0.18 <i>μ</i>m and diamonds denote particles of diameter 0.5 <i>μ</i>m. The horizontal light shaded region represents <i>η</i>_<i>int</i> = 1.42±0.74 nPa⋅s⋅m based on the mean and standard deviation of the data for <i>h</i>/<i>d</i> < 5. The vertical dark shaded region represents the crossover from physical behavior at small <i>h</i>/<i>d</i> to unphysical behavior at <i>h</i>/<i>d</i> > 5.2±0.9. The horizontal error bars are due to uncertainties of <i>h</i>, and vertical error bars are due to uncertainties of <i>h</i> and <i>η</i>_2<i>D</i> (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0121981#pone.0121981.e004" target="_blank">Eq 4</a>).</p

Two particle correlations in a single soap film measurement as a function of particle separation <i>R</i>.

<p>Particles of diameter <i>d</i> = 0.18 <i>μm</i> were used, and soap film thickness was <i>h</i> = 0.46±0.04 <i>μm</i>. The solid lines are fits from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0121981#pone.0121981.e006" target="_blank">Eq 6</a> with <i>A</i> = 1.09 <i>μ</i>m²/<i>s</i>, <i>B</i> = 0.12 <i>μ</i>m²/<i>s</i> and <i>L</i> = 81 <i>μ</i>m. The data are computed from all particle pairs and averaging over a wide range of lag times <i>τ</i>.</p

Cartoon depicting soap film of thickness <i>h</i>, with a single representative particle of diameter <i>d</i> < <i>h</i>.

<p>On both air-film interfaces, representative soap molecules are shown. As discussed in the text, we believe it is likely that particles with <i>d</i> < <i>h</i> sit in the interior of the film, but we cannot rule out the possibility that some particles are trapped at the air-film interface.</p