Session A21: Colloids I: Emulsions, Foams, and Suspensions

Bubble size distribution in a steady-state column of aqueous foam.

We report on measurements of the distribution of bubble sizes in a vertical column of aqueous foam. The sample is generated and maintained in steady-state by continuous bubbling of gas ($\mathtt{CO}_2$) in a surfactant solution ($\mathtt{H}_{2}\mathtt{O}$ + AOS + NaCl) at the bottom of a tall Lucite cylinder. The constant flow of gas produces nearly identical bubbles that accumulate at the liquid/foam interface and subsequently move up with constant velocity. The distribution of bubble sizes depends on height, being monodisperse near the bottom, turning bidisperse at some intermediate height, and then becoming polydisperse further up in the column. This behavior is exclusively due to coarsening and drainage, since film-rupture and convection are not observed. The development of a bidisperse distribution cannot be explained by mean-field theories of coarsening, in which bubbles of a given size grow or shrink at a rate that depends only on their size in comparison with a mean size.   

Rheology of Foams Bubble by Bubble

We present rheological measurements of single bubbles, and collections of bubbles to investigate cooperative effects between the bubbles that comprise a foam. For small numbers of monodisperse bubbles we measure the elastic behavior and yield stresses, and make comparisons with polydisperse foams composed of many bubbles. We also present a technique for measuring an ageless foam, where the bubble size and liquid volume fraction remain constant, outside of a microgravity environment.   

Pattern formation in flowing foams.

We report on a new fingering morphology which an expanding air bubble generates in a foam flowing due to an applied pressure across a Hele-Shaw cell. Previous studies have only looked at patterning when the background is stationary. Our simulations using the Glazier \& Grainer's Cellular Potts model show that the transition between the different morphologies depend on the rate of bubble flow into the foam. Since the rate of bubble in-flow is related to the shear strain rate, this agrees with previous experiments which have shown fingering morphologies in foams depend on the shear strain rate. The new mushroom morphology occurs for a high rate of bubble inflow corresponding to a very low shear strain rate. It is associated with a highly non-uniform velocity profile of the bubbles in the foam. These new morphologies should be easy to observe experimentally.   

Rigidity percolation in foamy sands

When subjected to a small shear stress, an aqueous foam behaves as a linear viscoelastic materials, whereas large applied shear stress triggers bubble rearrangement which causes the foam to flow as a viscous liquid. The elastic behavior arises from the surface tension of the gas-liquid interfaces. We study experimentally how the shear modulus and the yield stress of foam are modified if non colloidal solid particles of controlled size are dispersed in the sample. We show that even small amounts of non colloidal particles added to a foam can enhance the viscoelastic shear modulus by more than an order of magnitude. The yield stress is also increased, but to a smaller extent. The scaling of the elasticity enhancement with solid fraction qualitatively agrees with that predicted by an effective medium rigidity percolation model in the superelastic limit. To gain insight about the interactions between solid particles that are involved in the rigidity percolation, we study the dependence of the percolation threshold with particle to bubble size ratio.   

Diffusive liquid transport in poroelastic materials : the case of foams in microgravity

On Earth, the liquid inside an aqueous foam irreversibly flows due to coupled gravitational and capillary effects. In microgravity, one can study liquid transport with only capillarity as a driving force. Here, we report results of capillary imbibition experiments performed in parabolic flights in which we follow how and where some liquid locally injected into a foam spreads with time. Different setup geometries, imbibition modes and bubble surface mobilities are studied. New behaviors, not observed on ground, with high liquid fractions are found. Comparisons with theoretical models are presented, allowing us to find their limits of validity as the liquid fraction is increased. These experiments also give us some insights on the convective instability occurring on ground, and allow us to discuss the analogy with diffusive liquid transport and swelling in other poroelastic materials, like plants and tissues.   

Structure and dynamics of foam-like emulsions

We report the results of real-space, microscopic experiments on model concentrated emulsions ($\phi > 0.65$) in which the continuous and dispersed phases are both index- and density-matched. Like foams, these systems coarsen and age due to diffusion of fluid from small to large droplets, but unlike foams, they are transparent and do not drain during the course of an experiment. Thus we are able to probe their internal structure and dynamics at volume fractions ranging from 0.65 to 0.90. Measurements of the mean-squared displacement of small tracer particles embedded in the emulsion reveal that the system exhibits non-thermal stress fluctuations with Lorentzian power spectral density. We relate these fluctuations to intermittent droplet rearrangements, presumably driven by coarsening, that we observe directly through confocal microscopy.   

Mean Field Theory of Foam Aging

We describe our work on the geometrical properties of a random foam as a function of the number of faces, based on Isotropic Plateau Polyhedra [1,2].~ Analytic values of specific area, the stretching moment, and curvature can be obtained for these geometrical constructs.~ The expression for curvature is a ratio of the volume to the area of the foam cell.~ Focusing on this quantity will allow a better description of the coarsening of a foam.~ Conclusions from this mean field study will be discussed. [1] Glicksman M., \textit{Phil. Mag.,} \textbf{85 }(2005) 3. [2] Hilgenfeldt S., Kraynik A., Reinelt D., and Sullivan J. \textit{Europhys. Lett}. \textbf{67} (2004) 484.   

Emulsions Droplet Capture Mechanism in Porous Media

This study was undertaken to investigate the physics of emulsion flow in porous media. The objective of experiments were to study the applicability of oil-in-water emulsion as a plugging agent in the vicinity of the well bore for thousands of Canadian gas wells that are continuously leaking gas to surface. The motion of oil droplets and the capture mechanisms were investigated through visualized experiments. Well-characterized emulsions were injected into a micro model resembling a two parallel plate model packed with glass beads. Effects of emulsion properties and wettability of the medium were studied on a plugging mechanism. The results demonstrate the reduction in permeability mainly due to droplets size exclusion compared to the pore constrictions. Also, smaller droplets may lodge and coalesce in pores crevices thereby accelerating the blockage process. Moreover, more viscous emulsions are more effective compared with the less viscous ones due to combined effects of capillary and viscous forces. The deposition of droplets was adjusted through utilizing different preflush solutions. Criteria were set for enhancing emulsion penetration depth thereby defining the extent of the blocked region. In conclusion, this work characterizes the physics of emulsion flow in porous media and demonstrates its application as a novel sealant in near well bore region. The novelty, which constitutes a step-change in technology, is a method that emplaces an emulsion at a desired location in underground media.   

Wigner Crystals from Charge Stabilized Water in Oil Emulsions

A drop of water shaken or sonicated in a CHB-Decalin oil mixture produces a stable emulsion of 1-100 micron scale water droplets. The interdroplet correlations indicate strong electrostatic repulsion. When the preparation is by sonication the particle size is smaller and more uniform and the water droplets arrange in a BCC structure characteristic of a Wigner Crystal. The lattice constants are up to 20 microns. We suggest that the water droplets deionize the organic solvent due to water's high dielectric constant and hydration energy. This decreases the electrostatic screening. A slight preference of the water hydration energy for different ionic species will lead to slightly larger droplet uptake of one charge over the other and will result in the droplets being charged. The amount of charging can be controlled by changing pH. Experiments with oil-water and colloids will also be discussed.   

Microrheological Study of the Time Dependent Gelation of Single Wall Carbon Nanotube Suspensions

Single wall carbon nanotubes (SWNTs) dispersed in water using an anionic surfactant, sodium dodecylbenzene sulfonate (NaDDBS) form reversible gels because of the bonding between the individual nanotubes (L.A. Hough, M.F. Islam, P.A. Janmey and A. G. Yodh Phys. Rev. Lett. \textbf{93}, 168102 (2004)). We study the time dependence of this reversible gelation using particle tracking microrheology. We empirically collapse the mean square displacement onto a single master curve that extends over several decades in time using a time-cure superposition. The frequency scaling exhibited by the viscoelastic moduli obtained from the master curve is remarkably similar to that of semiflexible polymer networks. By comparing the results from a range of initial SWNT concentrations below and above the rigidity percolation threshold, we gain insight into the evolution of structure during gelation. This work has been partially supported by the NSF through Grants DMR 05-20020 (MRSEC) and DMR-0505048, and by NASA grant NAG8-2172.   

Yielding and flow of soft particle dispersions: the role of elasto-hydrodynamic interactions.

Concentrated dispersions of soft particles such as emulsions, colloidal pastes and granular suspensions exhibit many fascinating phenomena such as yielding, shear thinning, aging and memory, slip and fracture. Elucidating the physical parameters controlling these properties and the mechanisms at work is a formidable challenge. Recently we have found that various soft particle pastes share in common universal flow properties that can be characterized with very simple constitutive equations involving the solvent viscosity, the bulk elasticity and geometrical factors. We shall describe a generic flow model based on internal slip and non-contact elasto-hydrodynamic forces between squeezed particles$^{1}$ that quantitatively accounts for the measured properties. This approach offers new routes to predict the bulk non-linear rheology of pastes. $^{1}$S.P. Meeker, R.T. Bonnecaze, M. Cloitre, \textit{Phys. Rev. Lett.} \underline {\textbf{92}}, n\r{ } 198302 (2004).   

Mixture Stress in a Non-Uniform Suspension

In nature, most suspensions are non-uniform and the particles are subjected to external forces, such as gravity. The external force induces relative motions between the particles and the fluid, which introduce a new degree of freedom. We investigate the ensemble averaged stress system in a non-uniform suspension of equal spheres with external forces. It is found that, as a consequence of the spatial non-uniformity of the particle distribution and the relative motion between the two phases, new terms arise in the symmetric part of the bulk stress. In addition, an anti-symmetric contribution is found even in the absence of external torques. All the new terms in the stress tensor depend on the particle volume fraction and the gradient of the relative velocity but, for a given volume fraction, are independent of the particle size. To determine the new transport coefficients for small volume fractions, the renormalization method is extended to the non-uniform situation. For finite volume fractions, numerical simulations of several prototypical physical problems are carried out, from which the new transport coefficients are calculated. The numerical results agree well with the dilute limit calculations.   

Brownian Motion of an ellipsoid

We report direct digital-video-microscopy measurements of the Brownian motion of isolated anisotropic (ellipsoidal) particles in water under quasi-2D confinement. The probability density function (PDF) of displacements in the lab-frame is found to be nonGaussian. This effect originates from the anisotropy of the hydrodynamic drag coefficient. The transition from anisotropic to isotropic diffusion and the correlations between translational and rotational motions are also measured. The observations are confirmed numerically and understood theoretically via a Langevin formalism. We also observed the ratio of diffusion coefficients, $D_a/D_b$, along long and short axes, respectively, could be larger than 2, the theoretical upper limit in three dimension.   

Sound propagation in nanofluids

The thermal properties of nanofluids, i.e. liquids containing nanoparticles of sizes in the 3 to 100 nm range, have recently been shown to exhibit an unexpectedly large enhancement in thermal conductivity. While this enhancement has been observed for metallic nanoparticles and carbon nanotubes, the physical origin of the enhancement remains to be understood. The propagation of acoustic waves through a nanoparticle-laden colloidal fluid system offers many advantages towards understanding its thermal properties. We report on results of Brillouin scattering which probes the frequency range of $\sim $1 -- 100 GHz to study sound propagation in such complex fluids which possess structures on length scales larger than the molecules that comprise the host fluid. Thus compared to simple liquids, nanofluids possess additional relaxation mechanisms that can be observed in the frequency dispersion of the sound propagation. We present light scattering results from nanofluids comprised of a suspension of relatively long (1 - 2 $\mu $m) 20 nm diameter single-walled carbon nanotube bundles dispersed in N,N dimethylformamide.   

Electrokinetic Phenomena of Colloidal Suspensions

We investigate the colloidal particle motion of colloid suspension in which giant electrorheological effect has been found. The colloids consist of urea coated Ba$_{0.8}$Rb$_{0.4}$TiO(C$_{2}$O$_{4})_{2}$ particles suspended in silicon oil. In the experiment, a cell with cross-aligned top and bottom stripe-electrodes is used. The electric potential, the field and the field gradient, therefore, possess different space distribution. Significant difference of colloids motions and equilibrium particle distributions are observed under ac, dc and ac+dc fields. The result suggests dipole may not be the only factor for colloid aggregation (meso-structure), and hence, its electrorheological effect. *also at Hong Kong University of Science and Technology and Lawrence Berkeley National Laboratory