Shelley L. Anna

Formation of dispersions using ‘‘flow focusing’’ in microchannels

A flow-focusing geometry is integrated into a microfluidic device and used to study drop formation in liquid–liquid systems. A phase diagram illustrating the drop size as a function of flow rates and flow rate ratios of the two liquids includes one regime where drop size is comparable to orifice width and a second regime where drop size is dictated by the diameter of a thin “focused” thread, so drops much smaller than the orifice are formed. Both monodisperse and polydisperse emulsions can be produced.

Microfluidic methods for generating continuous droplet streams

Microfluidic technologies have emerged recently as a promising new route for the fabrication of uniform emulsions. In this paper, we review microfluidic methods for synthesizing uniform streams of droplets and bubbles, focusing on those that utilize pressure-driven flows. Three categories of microfluidic geometries are discussed, including co-flowing streams, cross-flowing streams, and flow focusing devices. In each category we summarize observations that have been reported to date in experiments and numerical simulations. We describe these results in the context of physical mechanisms for droplet breakup, and simple theoretical models that have been proposed. Applications of droplets in microfluidic devices are briefly reviewed.

Elasto-capillary thinning and breakup of model elastic liquids

We study the elasto-capillary self-thinning and ultimate breakup of three polystyrene-based ideal elastic fluids by measuring the evolution in the filament diameter as slender viscoelastic threads neck and eventually break. We examine the dependence of the transient diameter profile and the time to breakup on the molecular weight, and compare the observations with simple theories for breakup of slender viscoelastic filaments. The evolution of the transient diameter profile predicted by a multimode FENE-P model quantitatively matches the data provided the initial stresses in the filament are taken into account. Finally, we show how the transient uniaxial extensional viscosity of a dilute polymer solution can be estimated from the evolution in the diameter of the necking filament. The resulting “apparent extensional viscosity” profiles are compared with similar results obtained from a filament stretching rheometer. Both transient profiles approach the same value for the steady state extensional viscosity, which increases with molecular weight in agreement with the Rouse–Zimm theory. The apparent discrepancy in the growth rate of the two transient curves can be quantitatively explained by examining the effective stretch rate in each configuration. Filament thinning studies and filament stretching experiments thus form complementary experiments that lead to consistent measures of the transient extensional viscosity of a given test fluid.

Microscale tipstreaming in a microfluidic flow focusing device

A microfluidic flow-focusing device is used to explore the use of surfactant-mediated tipstreaming to synthesize micrometer-scale and smaller droplets. By controlling the surfactant bulk concentration of a soluble nonionic surfactant in the neighborhood of the critical micelle concentration, along with the capillary number and the ratio of the internal and external flow rates, we observe several distinct modes of droplet breakup. For the most part, droplet breakup in microfluidic devices results in highly monodisperse droplets in the range of tens of micrometers in size. However, we observe a new mode of breakup called “thread formation” that resembles tipstreaming and yields tiny droplets in the range of a few micrometers in size or smaller. In this work, we characterize the growth of the thread and its maximum length as a function of flow variables and surfactant content, and we also characterize the period of droplet breakup as a function of these variables. Our results suggest possible methods for controlling the process. Using a simple flow visualization experiment as the basis, we report on preliminary efforts to model the thread formation process.

Role of geometry and fluid properties in droplet and thread formation processes in planar flow focusing

Droplet formation processes in microfluidic flow focusing devices have been examined previously and some of the key physical mechanisms for droplet formation revealed. However, the underlying physical behavior is still too poorly understood to utilize it for generating droplets of precise size. In this work, we formulate scaling arguments to define dimensionless variables which capture all the parameters that control the droplet breakup process, including the flow rates and the viscosities of the two immiscible fluids, the interfacial tension between the fluids and the numerous dimensions in the flow focusing device. To test these arguments, we perform flow focusing experiments and systematically vary the dimensional parameters. Through these experiments, we confirm the validity of the scaling arguments and find a power law relationship between the normalized droplet size and the capillary number. We demonstrate that droplet formation can be separated into an upstream process for primary droplet formation...

Coalescence and splitting of confined droplets at microfluidic junctions

The ability to merge two droplets is an important component of droplet-based lab-on-a-chip devices, yet flow-induced coalescence is difficult to achieve due to long film drainage times compared with relatively short residence times. We examine droplet collisions at a simple microfluidic T-junction and characterize the response for a wide range of droplet sizes and speeds. We find that three primary responses occur, where coalescence occurs easily at low collision speeds, smaller droplets traveling faster slip past one another without coalescing, and larger and faster droplets can break one another into multiple segments. The critical capillary number for coalescence agrees well with previously reported scaling for isolated droplet pairs when local curvature and speed are taken into account. The critical capillary number for splitting of droplets agrees well with a previously reported stability condition for individual droplets stretching in an extensional flow. Quantifying the necessary conditions for coalescence and non-coalescence behavior should enable the informed design of lab on chip devices based on discrete liquid segments.

An interlaboratory comparison of measurements from filament-stretching rheometers using common test fluids

Following development of a filament-stretching extensional rheometer at Monash University, similar rheometers have been designed and built in other laboratories. To help validate the basic technique, a collaborative program was undertaken to compare results from several instruments. First, three test fluids prepared at the University of California at Berkeley were characterized in steady and transient shear flows there and at the Massachusetts Institute of Technology (M.I.T.), and then tested in extensional rheometers at M.I.T., Monash and the University of Toronto. Each fluid is a constant-viscosity solution of narrow-molecular-weight-distribution polystyrene dissolved in oligomeric polystyrene. The solute molecular weights are 2.0, 6.5, and 20 million g/mol, and the polymer concentration in each fluid is 0.05 wt. %. From linear viscoelastic measurements, the Zimm relaxation times of the fluids are found to be 3.7, 31, and 150 s, respectively. The scaling of relaxation times with molecular weight indicat...

Interfacial dynamics and rheology of polymer-grafted nanoparticles at air-water and xylene-water interfaces.

Particle-stabilized emulsions and foams offer a number of advantages over traditional surfactant-stabilized systems, most notably a greater stability against coalescence and coarsening. Nanoparticles are often less effective than micrometer-scale colloidal particles as stabilizers, but nanoparticles grafted with polymers can be particularly effective emulsifiers, stabilizing emulsions for long times at very low concentrations. In this work, we characterize the long-time and dynamic interfacial tension reduction by polymer-grafted nanoparticles adsorbing from suspension and the corresponding dilatational moduli for both xylene-water and air-water interfaces. The dilatational moduli at both types of interfaces are measured by a forced sinusoidal oscillation of the interface. Surface tension measurements at the air-water interface are interpreted with the aid of independent ellipsometry measurements of surface excess concentrations. The results suggest that the ability of polymer-grafted nanoparticles to produce significant surface and interfacial tension reductions and dilatational moduli at very low surface coverage is a key factor underlying their ability to stabilize Pickering emulsions at extremely low concentrations.

A non-gradient based algorithm for the determination of surface tension from a pendant drop: Application to low Bond number drop shapes

The pendant drop method is one of the most widely used techniques to measure the surface tension between gas-liquid and liquid-liquid interfaces. The method consists of fitting the Young-Laplace equation to the digitized shape of a drop suspended from the end of a capillary tube. The first use of digital computers to solve this problem utilized nonlinear least squares fitting and since then numerous subroutines and algorithms have been reported for improving efficiency and accuracy. However, current algorithms which rely on gradient based methods have difficulty converging for almost spherical drop shapes (i.e. low Bond numbers). We present a non-gradient based algorithm based on the Nelder-Mead simplex method to solve the least squares problem. The main advantage of using a non-gradient based fitting routine is that it is robust against poor initial guesses and works for almost spherical bubble shapes. We have tested the algorithm against theoretical and experimental drop shapes to demonstrate both the efficiency and the accuracy of the fitting routine for a wide range of Bond numbers. Our study shows that this algorithm allows for surface tension measurements corresponding to Bond numbers previously shown to be ill suited for pendant drop measurements.

Using bulk convection in a microtensiometer to approach kinetic-limited surfactant dynamics at fluid-fluid interfaces.

The impact of transport of surfactants to fluid-fluid interfaces is complex to assess and model, as many processes are in the regime where kinetics, diffusion and convection are comparable. Using the principle that the timescale for diffusion decreases with increasing curvature, we previously developed a microtensiometer to accurately measure fundamental transport coefficients via dynamic surface tension at spherical microscale liquid-fluid interfaces. In the present study, we use a low Reynolds number flow in the bulk solution to further increase the rate of diffusion. Dynamic surface tension is measured as a function of Peclet number and the results are compared with a simplified convection-diffusion model. Although a transition from diffusion to kinetic-limited transport is not observed experimentally for the surfactants considered, lower bounds on the adsorption and desorption rate constants are determined that are much larger than previously reported rate constants. The results show that the details of the flow field do not need to be controlled as long as the local Reynolds number is low. Aside from other pragmatic advantages, this experimental tool and analysis allows the governing mechanisms of surfactant transport at liquid-fluid interfaces to be quantified using flow near the interface to decrease the length scale for diffusion, separating the relevant timescales.