Magnetophoresis of paramagnetic metal ions in porous media.

We report a numerical investigation of the magnetophoresis of solutions containing paramagnetic metal ions. Using a simulated magnetic field of a superconducting magnet and the convection-diffusion model, we study the transport of transition metal salts through a porous medium domain. In particular, through a detailed comparison of the numerical results of magnetophoretic velocity and ion concentration profiles with prior published experiments, we validate the model. Subsequent to model validation, we perform a systematic analysis of the model parameters on the magnetophoresis of metal ions. Magnetophoresis is quantified with a magnetic Péclet number Pem. Under a non-uniform magnetic field, Pem initially rises, exhibiting a local maximum, and subsequently declines towards a quasi-steady value. Our results show that both the initial and maximum Pem values increase with increasing magnetic susceptibility, initial concentration of metal solutes, and ion cluster size. Conversely, Pem decreases as the porosity of the medium increases. Finally, the adsorption of metal salts onto the porous media surface is modeled through a dimensionless Damkohler number Daad. Our results suggest that the adsorption significantly slows the magnetophoresis and self-diffusion of the paramagnetic metal salts, with a net magnetophoresis velocity dependent on the kinetics and equilibrium adsorption properties of the metal salts. The latter result underscores the crucial role of adsorption in future magnetophoresis research.

Cavitation Rheology of Model Yield Stress Fluids Based on Carbopol.

Measuring the surface tension of yield stress fluids has remained a critical challenge due to limitations of the traditional tensiometry techniques. Here, we overcome those limits and successfully measure the surface tension and mechanical properties of a model yield stress fluid based on Carbopol gels via a needle-induced cavitation (NIC) technique. Our results indicate that the surface tension is approximately 70 ± 3 mN/m, and is independent of the rheology of yield stress fluid over a wide range of yield stress values σy = 0.5-120 Pa. In addition, we demonstrate that a Young modulus smaller than E < 1 kPa can be successfully measured for Carbopol gels with NIC method. Finally, we present a time-resolved flow structure around the cavity in a host of yield stress fluids, and assess the impact of fluid rheology on the detailed form of flow around the cavity. Interestingly, prior to the critical point associated with cavitation, the yield stress fluid is weakly deformed suggesting that the measured surface tension data reflect the near equilibrium values. Beyond the critical point, the yield stress fluid experiences a strong flow that is controlled by both the critical pressure and the non-Newtonian rheology of the yield stress fluid.

Probing self-assembled micellar topologies via micro-scale diffusive dynamics of surfactants.

HYPOTHESIS: Surfactants spontaneously self-assemble in aqueous solutions and are critical in energy, biotechnology, and the environment. The self-assembled micelles may experience distinct topological transitions beyond a critical counter-ion concentration, yet the associated mechanical signatures are identical. By monitoring self-diffusion dynamics of individual surfactants in micelles via a non-invasive 1H NMR diffusometry, we may distinguish various topological transitions overcoming challenges associated with traditional microstructural probing techniques. EXPERIMENTS: Three micellar systems based on CTAB/5mS, OTAB/NaOA and CPCl/NaClO3 are considered at various counter-ion concentrations, and their rheological properties are assessed. A systematic 1H NMR diffusometry is conducted and the resulting signal attenuation is measured. FINDINGS: With no counter-ion, surfactants self-diffuse freely with a mean squared displacement Z2∼Tdiff in the micelles. As counter-ion concentration increases, self-diffusion becomes restricted with Z2∼Tdiffα, and α→0.5. Beyond the viscosity peak, for the OTAB/NaOA system that shows a linear-shorter linear micelle transition, Z2∼Tdiff0.5. Conversely, for the CTAB/5mS system that experiences a linear wormlike-vesicle transition above the viscosity peak, a free self-diffusion is recovered. The diffusion dynamics in CPCl/NaClO3 are similar to those of OTAB/NaOA. Hence, a similar topological transition is surmised. These results highlight the unique sensitivity of the 1H NMR diffusometry to micelles topological transitions.

Helical Locomotion in Yield Stress Fluids.

We report three stages for locomotion of a helical swimmer in yield stress fluids. In the first stage, the swimmer must overcome the material's yield strain to generate rotational motion. However, exceeding the first threshold is not sufficient for locomotion. Only when the viscous forces are sufficiently strong to plastically deform the material to a finite distance away from the swimmer will net locomotion occur. Once locomotion is underway in the third stage, the yield stress retards swimming at small pitch angles. Conversely, at large pitch angles, yield stress dominates the flow by enhancing swimming speed. Flow visualizations reveal a highly localized flow near the swimmer in yield stress fluids.

Kinetics of shear banding flow formation in linear and branched wormlike micelles.

We investigate the flow evolution of a linear and a branched wormlike micellar solution with matched rheology in a Taylor-Couette (TC) cell using a combination of particle-tracking velocimetry, birefringence, and turbidity measurements. Both solutions exhibit a stress plateau within a range of shear rates. Under startup of a steady shear rate flow within the stress plateau, both linear and branched samples exhibit strong transient shear thinning flow profiles. However, while the flow of the linear solution evolves to a banded structure at longer times, the flow of the branched solution transitions to a curved velocity profile with no evidence of shear banding. Flow-induced birefringence measurements indicate transient birefringence banding with strong micellar alignment in the high shear band for the linear solution. The transient flow-induced birefringence is stronger for the branched system at an otherwise identical Wi. At longer times, the birefringence bands are replaced by a chaotic flow reminiscent of elastic instabilities. Visualization of the flow-induced turbidity in the velocity gradient-vorticity plane reveals quasi-steady banding with a turbidity contrast between high and low shear bands in the linear solution. However, the turbidity evolves uniformly within the gap of the TC cell for the branched solution, corroborating the non-banded quasi-steady velocimetry results. Finally, we show that while elastic instabilities in the linear solution emerge in the high shear band, the flow of branched solution at high Wi becomes unstable due to end effects, with growing end regions that ultimately span the entire axial length of the TC cell.

Linear versus branched: flow of a wormlike micellar fluid past a falling sphere.

We report experiments on flow of wormlike micellar solutions past a falling sphere. By increasing the salt-to-surfactant concentration ratio, and beyond a viscosity peak, wormlike micelles experience a transition from linear to branched microstructure. Two viscoelastic wormlike micelles with salt to surfactant concentrations on each side of the viscosity peak are considered. Our results indicate three significant differences in flows of branched and linear micelles. First, while the sphere drag correction factor rapidly decreases upon increasing Weissenberg number in linear micelles, it shows an apparent local maximum at Wi ≈ 3 in branched micelles. Second, despite its high viscoelasticity, the time-averaged flow of branched micelles around the falling sphere exhibits a fore-and-aft symmetry, while a strong negative wake is observed in linear micelles at relatively weaker flows. Third, branched micelles exhibit a stronger flow-induced birefringence than linear micelles in an otherwise identical condition. Our hypothesis is that subject to strong flows around the falling sphere, branched micelles can relax much more efficiently than linear wormlike micelles through sliding of the branched junctions. This additional stress relaxation mechanism may facilitate micellar orientation, produce a marginal sphere drag reduction and a Newtonian-like flow profile around the falling sphere. Finally, unsteady flow is observed in both linear and branched micellar solutions beyond some critical thresholds of the extensional Weissenber number. Our results corroborate a recently proposed criterion for onset of instability in flow of wormlike micelles past a falling sphere, thereby, suggesting that micellar branching does not affect the mechanism of flow instability.

Nuclear Magnetic Resonance Diffusometry of Linear and Branched Wormlike Micelles.

Diffusion studies using nuclear magnetic resonance (NMR) spectroscopy were conducted on two model surfactant solutions of cetyltrimethylammonium bromide/sodium salicylate (CTAB/NaSal) and cetylpyridinium chloride/sodium salicylate (CPCl/NaSal). By increasing the salt-to-surfactant concentration ratio, these systems display two peaks in the zero-shear viscosity and relaxation time, which are indicative of transitions from linear to branched micellar networks. The goal of this work is to assess the sensitivity of NMR diffusometry to different types of micellar microstructures and identify the mechanism(s) of surfactant self-diffusion in micellar solutions. At low salt-to-surfactant concentration ratios, for which wormlike micelles are linear, the surfactant self-diffusion is best described by a mean squared displacement, Z2, that varies as Z2 ∝ Tdiff0.5, where Tdiff is the diffusion time. As the salt concentration increases to establish branched micelles, Z2 ∝ Tdiff, indicating a Brownian-like self-diffusion of surfactant molecules in branched micelles. This result indicates that NMR diffusometry is capable of differentiating various types of micellar microstructures. In addition, the self-diffusion coefficient of the surfactant molecules in linear and branched micelles are determined, for the first time, by comparing the existing restricted diffusion models and are shown to be much slower than the diffusion of proton molecules in the bulk. Moreover, in linear and moderately branched wormlike micelles, the dominant mechanism of surfactant self-diffusion is through the curvilinear diffusion of the surfactant molecules along the contour length of the micelles, whereas in the branched micelles, before the second viscosity maxima, the surfactant self-diffusion could arise from a combination of micellar breakage, exchange between micelles and/or the bulk.

Transient evolution of flow profiles in a shear banding wormlike micellar solution: experimental results and a comparison with the VCM model.

In this paper we investigate the flow of a shear banding wormlike micellar fluid based on cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal). The flow is studied in a custom-built Taylor-Couette (TC) cell via a combination of particle tracking velocimetry and in situ rheology. The spatiotemporal evolution of the velocity profile across the rheometer gap is tracked after an imposed step in the shear rate. In a range of shear rates the mixture shows shear banding behavior, that is distinct and differing shear rate profiles across the gap. As the shear bands form temporally, an elastic recoil including negative velocity (that is in the opposite direction to that of the imposed motion) is observed in a subset of the gap. While elastic recoil has been reported in experiments on monodisperse polymers [S. Ravindranath, et al., Macromolecules, 2008, 41, 2663-2670], on a wormlike micellar solution in a cone-plate rheometer [P. E. Boukany and S. Q. Wang, Macromolecules, 2008, 41(4), 1455-1464], and in theoretical studies [L. Zhou, et al., J. Non-Newtonian Fluid Mech., 2014, 211, 70-83; J. M. Adams, et al., J. Rheol., 2011, 55, 1007-1032] of wormlike micellar flows, it has not been previously reported in experiments on shear banding wormlike micelles in Taylor-Couette flows. Additionally, the mixture shows significant wall slip at the outer (stationary) Couette cylinder at high shear rates. Experimental results are compared to simulations of models of wormlike micelles, particularly the VCM model [L. Zhou, et al., J. Non-Newtonian Fluid Mech., 2014, 211, 70-83]. There are differences between the experimental results for this fluid and those reported previously. The difference arises from the size of the elasticity number which for the fluid reported in the paper is four orders of magnitude larger than that of other preparations.

A flow visualization and superposition rheology study of shear-banding wormlike micelle solutions.

In this paper, we use rheometry and flow visualization to study the dynamics of the interface between shear bands in a wormlike micellar solution sheared between concentric cylinders, i.e., in a Taylor-Couette (TC) cell, and to evaluate the stress diffusion coefficient and the stress correlation length in the Johnson-Segalman model. Two wormlike micellar solutions are studied: an aqueous solution of CTAB-NaNO3 and a solution of CPCl-NaSal in brine. These systems are highly elastic, exhibit Maxwellian behavior in linear viscoelasticity experiments, and shear banding in nonlinear experiments [S. Lerouge, et al., Soft Matter, 2008, 4, 1808-1819, M. A. Fardin, et al., Soft Matter, 2012, 8(39), 10072-10089, P. Ballesta, et al., J. Rheol., 2007, 51, 1047]. A large, custom-built, computer controlled TC cell allows us to rotate both cylinders independently and to visualize the flow in the r-z plane using a CCD camera. At low shear rates, the flow is stable and the fluid appears homogeneous throughout the gap between the cylinders. Above a critical shear rate, a shear banding transition occurs. This manifests itself in the formation of two distinct bands in the r-z plane, with an interface between the two bands. For sufficiently high ramp speeds, multiple steps of interface evolution are identified, as noted by Radulescu, Lerouge, and others [O. Redulescu, et al., Europhys. Lett., 2003, 62, 230, S. Lerouge, et al., Soft Matter, 2008, 4, 1808-1819]. We quantify the interface travel using direct visualization and use this measure, as well as superposition rheometry [P. Ballesta, et al., J. Rheol., 2007, 51, 1047], to determine the stress diffusion coefficient D and the stress correlation length ζ in the Johnson-Segalman model. These parameters are evaluated at different temperatures, shear rates, and gap sizes. We find that the stress diffusion coefficient and the stress correlation length exhibit a strong dependence on the gap of the Taylor-Couette cell for both shear-banding systems. For the CTAB-NaNO3 system, we report a linear dependence of the stress diffusion coefficient on temperature for the parameter range considered. In addition, we find that for this system, the stress diffusion coefficient is independent of shear rate. For the CPCl-NaSal system, we observe the same color changes in the sample reported by others on extended light exposure; however, we find that different histories of light exposure do not affect the measured stress diffusion coefficient.

Size segregation in sheared two-dimensional polydisperse foam.

We report experiments on simple shear of a monolayer of bidisperse and polydisperse bubbles in a Couette device. The bubbles segregate according to their sizes, with larger ones in the middle of the gap and smaller ones closer to the walls, when the shear rate and the bubble size ratio are each above a threshold. The spatial distribution of the larger bubbles becomes flatter across the gap as its area fraction increases. To explain these observations, we adapt a model for monodisperse emulsions that predicts the spatial distribution of droplets as an outcome of the competition between migration away from the walls and shear-induced diffusion. The dense packing of bubbles in our foam intensifies bubble-bubble interaction, which manifests itself both in lateral migration due to wall repulsion and in collision-induced diffusion. After accounting for this difference via an effective capillary number based on the deformation of the bubbles, the model predicts the observed bubble distributions accurately.

Size-differentiated lateral migration of bubbles in Couette flow of two-dimensional foam.

We report experiments on lateral migration of bubbles in a two-dimensional foam sheared in a narrow-gap Couette device. A larger bubble in an otherwise monodisperse bubble raft migrates toward the center of the gap as long as the bubble size ratio and the shear rate are each above a threshold. The migration speed is roughly two orders of magnitude higher than that of a single bubble, and increases with the shear rate and the size ratio. The bubble also deforms much more than an isolated one at the same shear rate. Modifying the Chan-Leal solution for the migration of a single submerged bubble or drop, we derive a formula that successfully predicts all the migration trajectories recorded in the experiment. The threshold for migration corresponds to the wall repulsion force overcoming the capillary force in the two-dimensional foam. The size-differentiated bubble migration provides an explanation for previously observed size segregation in sheared three-dimensional polydisperse foams.

Anomalous coalescence in sheared two-dimensional foam.

We report an experimental study on shearing a monolayer of monodisperse bubbles floating on liquid in a narrow-gap Couette device. The bubbles in such a "bubble raft" coalesce only if the shear rate exceeds a threshold value. This is in contrast to the conventional wisdom that bubbles and drops coalesce for gentler collisions, at shear rates below a critical value. Furthermore, the threshold shear rate increases with the bubble size and the viscosity of the suspending liquid, contravening reasoning based on capillary number. Through visualization and scaling arguments, we investigate several plausible mechanisms for the anomalous coalescence. None explains all aspects of the observations. The most promising model is one based on inertial forces that compress the bubbles radially inward and accelerate film drainage.