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We use emulsion droplets as models for granular media.  In particular, we confine oil droplets (in water) between parallel two glass plates, deforming the droplets into quasi-two-dimensional pancake shapes.  At high droplet concentration, the quasi-2D droplets contact and deform each other, and from their deformations we infer the forces they exert on each other.  One major advantage of this system is that there is no static friction; thus, we are able to study how the properties of this frictionless system match up with frictionless simulations and how the results differ from prior work with frictional granular systems.  In this past year we have carefully developed this as a model system and obtained preliminary results.

The experiment has many possible parameters:  spacing between the glass plates, size of the oil droplets, polydispersity of the droplets, choice of oil, choice of surfactant, and others.  Our goal this first year has been to find the first set of parameters that “works” and collect data on how the system changes as a function of the area fraction of the droplets.  Thus, we have done a rapid preliminary exploration of many of these parameters, and have successfully obtained publication-quality data on one particular system.

Progress on picking experimental parameters:

We studied the overall experiment size.  Thin sample chambers (~10 microns thick) had several difficulties, such as ensuring that the glass plates were sufficiently parallel.  It turned out that if we scaled up these dimensions by 10, the experiment was much easier.

We have also found a good method to produce droplets.  Alberto Fernandez-Nieves at Georgia Tech is an expert on using microfluidic devices to produce monodisperse droplets, and he has taught us those methods.  We use these methods to produce monodisperse batches of droplets with controlled sizes, and we have made a binary mixture of droplets.  Our current experimental parameters are a sample chamber thickness of 100 microns, and droplet 2D diameters of 150 microns and 255 microns.  We visualize these droplets using regular optical microscopy and a low magnification objective.

We have also spent some time this past year investigating other parameters.  For example, we’re studying how changing the surfactant or changing the oil influences the results; and we’re trying to figure out what range of sample chamber thicknesses will be useful.  We plan to continue this parameter space exploration in the upcoming year, while at the same time using the current system to get more data.

Progress on analysis:

To determine the contact forces between a pair of droplets, we need to determine the contact area of the droplets.  From a typical 2D image, we can see contact lines between droplets.  Using differential interference contrast microscopy, we were able to measure the contact lines at each height and determine the contact area.  It is also straightforward to determine the overall outline of every droplet from 2D images.  From the droplet sizes and contact area, we can determine the forces between every pair of touching droplets.  At this point we believe our uncertainty in these forces is no greater than 10% for any given force.

Preliminary results:

We have investigated our binary sample as a function of area fractions.  For a variety of parameters, we see a transition to a jammed state at an area fraction of phi₀ ~ 0.85.  The simplest is to quantify the average deformation of droplets.  Droplets are circular below phi0, and become deformed once they start contacting each other above phi0.

Having identified droplets that are touching (with contact lines), we can count the number of neighbors each droplet has - the “coordination number” Z.  As a function of area fraction, we see critical scaling with this, (Z - 4) ~ (phi - phi0)^1/2.  This agrees with simulations of frictionless 2D particles (for example, O’Hern et al, Phys. Rev. E 68, 011306 [2003]).

The inter-droplet forces within a given sample are not distributed uniformly in space; some droplets feel large forces, and some feel much smaller forces.  We are studying the distribution of forces, P(F), as a function of area fraction.  This distribution is widest right around phi0, and gets narrower at higher area fractions.  This makes sense; in the limit that the droplets are extremely compressed (phi close to 1), the inter-droplet forces are more like a uniform hydrostatic pressure.

Ongoing work:

We are currently analyzing the spatial distribution of the large forces.  Given that the sample is static, the forces balance, and so we observe that the large forces form chains throughout the sample.  These are the so-called “force chains” that have been well studied in granular media.  We are trying to see how the force chains in our sample differ from prior experiments which had static friction.  For example, in the absence of static friction, do force chains bend less often?  Do they split more often?  We are writing a short paper demonstrating our system and detailing our observations of the inter-droplet forces near phi0, and plan to address these questions about force chains.  This work has been primarily conducted by graduate student Ken Desmond.

As mentioned above, we are also continuing to investigate experimental parameters.  We plan to write a longer paper giving a comprehensive description of our parameter space and pointing the way for optimal parameters for future experiments.  Understanding the parameter space is important to the long-term success of this project, past the period of the current funding.  This work is being done by graduate student Laura Golick.

We are also studying the flow of these quasi-2D emulsions.  The goal is to see how the sample flows and deforms under shear.  Here, viscous friction plays an important role, but our preliminary observations suggest that the inter-droplet forces still dominate the flow properties.  We plan to write a paper about plastic deformation in these samples as they flow.  This work is being done by graduate student Dandan Chen, which will nicely complement prior work she did at Emory studying similar questions in the flow of colloidal pastes.