59th Annual Report on Research 2014

We have constructed an apparatus that subjects small (3-5 ml) samples of complex fluids to vertical vibrations at a controlled frequency and acceleration, typically in the range 60-80Hz and 10-30g, respectively, where g is gravitational acceleration. The fluids we have been testing are 1) concentrated suspensions of non-Brownian, spherical glass beads in aqueous solution, and 2) aqueous solutions of neutralized Carbopol gel. The latter is a transparent solution of polymer macromolecules that are charged at pH values close to neutral; the repulsive interaction caused by the charges causes a liquid-to-gel transition when a base is added to Carbopol solutions. Since many fluids used in oil recovery contain particulates and exhibit a yield stress, and are exposed to vibration from drilling processes, this research is directly relevant to the petroleum industry.

Both fluids show complicated and interesting behavior when subjected to controlled vibration. Over the past year, we have been working primarily with Carbopol 940 solutions. Carbopol is a polymerized form of polyacrylic acid that forms “microsponges” with diameters of 5-6 microns, surrounded by a layer of hydrophilic polymer strands that can extend 10-20 microns. These entities swell or shrink depending on the pH of the solution, forming a jammed or gelled medium that does not flow at rest.

The behavior of these gels when subjected to vibration differs significantly from particulate suspensions we are studying, but the underlying physics may be linked. An example of our observations is shown in the Table of Contents (TOC). Under select conditions, vibration of gelled Carbopol solutions yields a sample with holes arranged in a regular order. We have seen as few as 2 holes, and in some cases more than 8. In the TOC, there are 7 holes at the vertices of a heptagon, outside of which a new layer of holes has partially formed. These structures form over a range of frequencies that we have determined, and have used to create a “phase diagram” showing the types of structures that develop at different frequencies. Surprisingly, the type of structure that forms depends on the mass of the sample and the frequency, but not on the acceleration. The acceleration only affects the rate of formation of the geometric pattern; it does not select which pattern forms.

Although they are not hard spheres as in particulate suspensions, the microsponges in Carbopol constitute a dense core of soft particles that are crosslinked enough so as to preclude overlap. Furthermore, it is known that the heterogeneity in a Carbopol gel extends over length scales that can be significantly larger than the microsponge diameters. Similarly, it has been shown experimentally and through simulations that boundary effects extend to distances of hundreds of gel-particle diameters in flows of soft-particle gels. This heterogeneous microstructure is a feature that these gels share with particulate suspensions. Typically our sample heights are 5 mm, and we estimate the distance of boundary effects to be approximately 1.5 mm.

To provide additional insight into the topological changes we observe, we are using classical lubrication theory for shallow liquid layers. Lubrication theory has been used successfully to describe the wave patterns (i.e., Faraday waves) that develop in vibrated, shallow layers of Newtonian liquids. There are also reports in the literature of adapting it for a stick-slip transition that can lead to the growth of protuberances and holes in vibrated non-Newtonian fluids. In our modification, we use this theory to examine the possible consequences when the acceleration varies sinusoidally, and the resistance to flow, characterized by the viscosity, also varies with the acceleration. The viscosity variation may be related to a hysteresis in the microstructure of the gel, which is known to exist close to the yield stress. Alternatively, the bottom plate could affect the gel microstructure such that resistance to outward flow (away from the sample center), into a region decreasing in height, is greater than inward flow, into a region of increasing height.

The linearized form of lubrication theory predicts surface shapes that agree qualitatively with our results. In particular, in a cylindrical sample of fluid, an integer number of periodically arranged indentations is predicted. A second set of indentations farther from the sample center is also predicted by the theory, depending on which eigenvalues are most unstable. Such a second layer may be seen, for example, in the graphic TOC. Hole formation is predicted to be inhibited at higher frequencies, if the acceleration is fixed, which is also what we observe in our experiments. These results were presented at an international conference titled “Viscoplastic Fluids: From Theory to Application” in November, 2013.