Christopher D. Jones
Former Postdoc
PhD, University of Colorado at Boulder, 2007
BA, The Colorado College, 1999


Current research interests: foams, liquid crystals
Research techniques: x-ray diffraction, polarized light microscopy, atomic force microscopy, dielectric spectroscopy, particle image velocimetry, image analysis


Rheology of foams:
Christopher D. Jones, Kerstin Nordstrom, DJ Durian

Rheology is the study of flow. Foams are materials that flow in an interesting way. We wish to characterize the stress/strain relationships found in many foams, and to pursue this interest we have constructed the following apparatus:

We have a tall column (approx. 120 cm by 10 cm by 2.5 cm), in which we have a pressure driven foam flow, as denoted with the black arrows, initiated with a gas bubbling into soapy water from below. The front and back faces of the channel are acrylic sheet, which is very slippery to the foam - there’s no distortion in flow or bubble shape due to these surfaces. The sides of the apparatus can either be “sticky” (sand paper) or “slippery” (bare acrylic). With the sticky sides, we see a “no slip” condition - almost no bubbles flow at the surface of the wall, but within just a few bubble diameters flow is not constrained.

The call out image in the figure above is one frame from a video of the flowing foam, where the average bubble diameter is 4mm, which has been consistent for us at relatively low flow rates. This image is cut off on the right at the center of the channel.

By measuring the depth the foam depresses the water (due to its weight), and the liquid fraction (obtained by measuring resistance of foam with brass electrodes) of the foam for the full length of the column, we can use a simple force balance equation to obtain a driving pressure, which we can then relate directly to the stress the foam feels between the driving pressure and the no-slip sides. This is shown below, where x is the distance from the middle of the channel, and L is the length of the channel of foam.


In the top-right plot above, we show the velocity profile at several flow rates. Velocity profiles are obtained via particle image velocimetry. The x-axis goes from the center of the cell, at x equals zero, to the sandpaper at x equals 5.08cm. With all this information - depression height h and average liquid fraction <ε>, as well as the velocity profile and channel dimensions, we have all the pieces we need to look into the stress/strain relationship for the foams we’re investigating, which are shown in the bottom-right plot.

Coarsening dynamics of 2d foams on a curved surface:
Christopher D. Jones, Jennifer Rieser, Adam Roth, DJ Durian

The evolution of 2d foams is a study has enjoyed broad interest both from experimental and theoretical sides. In 1951, von Neumann’s law for 2d coarsening on a planar surface was derived [1]. This law interestingly showed that a bubble with 6 neighbors will not change in size over time, while bubbles with more neighbors (larger bubbles) increase in size, and bubbles with fewer neighbors (smaller bubbles) decrease in size.


We have developed a planar-geometry apparatus, that maintains a constant pressure even as excess solution drains out, that allows us to experimentally probe dry 2d foams and confirm von Neumann’s law. Work along these lines has been done before, especially by Stavans [2], but we have attempted to develop a system that continuously drains early in the experiment, becomes a very stable 2d foam during the experiment, and allows us to follow bubble size versus number of neighbors over long periods of time. An example of a data set is shown above, with the inset indicating the number of neighbors the plotted bubble had before and after a topological change. This experiment is useful background for our next step, explained below.

Forty years after von Neumann, Avron and Levine were able to generalize this law to curved surfaces [3]. This result showed that when the surface curvature is positive (such as a bowl), then for a certain size bubble with less than 6 neighbors the bubble will not change size over time. A bubble with 6 or more neighbors on a positively curved surface will always increase in size. The case of negatively curved surfaces (such as a saddle) gives the result that at less than 6 neighbors a bubble will always shrink, and with more than 6 neighbors the bubble will maintain it’s size for only certain sizes, but will otherwise grow.

This result has not yet been tested experimentally. To pursue this, we have developed an apparatus of two nested domes (positive curvature), with differing sizes which accommodate a constant spacing between them at all points on the hemisphere. We fill the gap between the two domes with a foam, and watch the foam coarsen over time. We use a solution of soapy water with glycerine (the glycerine slows the drainage of the fluid in the films between bubbles), so that the primary coarsening mechanism is diffusion of gas between neighboring bubbles. The gas diffusion is driven by a pressure differential between two bubbles of different size and film curvature.


With this apparatus we will be able to determine coarsening statistics of an individual bubble’s size, its number of neighbors, and the number of bubbles in the system, all with respect to time. In doing so we will be able to establish an experimental response to the previous theoretical work.

[1] J. von Neumann, Metal Interfaces (American Society for Metals, Cleveland, 1952) p. 108.
[2] J. Stavans,
Physica A 194, 307 (1993).
[3] J.E. Avron and D. Levine, Physical Review Letters 69, 208 (1992).