Ronald J. Phillips, PhD, University of California (Davis)
Over the past year we have made significant progress in our program to study the effects of vibration on Bingham fluids. A graduate student, Jacob Wolf, elected to work on the project, and has constructed an experimental apparatus consisting of a shaker, an amplifier, and an accelerometer. We also have a camera set up to record events as they occur, and a computer to control the frequency and amplitude of the vibration. This bench-scale apparatus appears to be sufficient to meet our needs.
To date we have worked primarily with two types of fluid. First, we are using aqueous solutions of the polymer Carbopol which, when neutralized to varying extents with triethanol amine (TEA), forms a Bingham fluid (or gel) with a measureable yield stress. We have measured the rheology of the Carbopol solutions with a TA Instruments, AR1000 cone-and-plate rheometer, and we find that they are modeled very well by the Herschel-Bulkley constitutive model. In addition, we have been experimenting with highly filled suspensions of glass beads in either water or density-matched aqueous solutions. These two materials form our starting point for exploring the significance of density variations, and resultant inertia-induced stresses, in complex fluids undergoing vibration.
Our results at this point are preliminary, but nonetheless intriguing. The impetus for our effort was a report that, upon vibration, suspensions of cornstarch in water form holes in some cases, and finger-like protrusions in others. We have reproduced that behavior in our own experiments. We have also found that it is highly dependent on the extent to which the fluid is density-matched. The same is true for other materials as well. In suspensions of glass beads in water, for example, in less than one minute, vibration induces the formation of a “crown” consisting of finger-like protrusions at the outside of a drop; holes also form in the center in some conditions. However, if the suspending fluid is density-matched, or if the particles are less dense than the suspending fluid, no such structure forms. In the case of the Carbopol, even with no particles added, vibration of a gel-like sample can generate pinholes at regular positions at the periphery.
In terms of hydrodynamic theory, the phenomena we are observing constitute “free-surface” flows of complex fluids, which either contain suspended particles and/or exhibit a yield stress. To help us understand what we observe in the laboratory, we are performing simulations of these fluids with the open source software OpenFOAM. OpenFOAM is currently made available through Silicon Graphics Corporation, and provides a set of tools for simulating fluid flow by using the finite-volume method. We have already shown that, with OpenFOAM, we can compute Faraday waves, which are the waves that form at the top of vibrated, Newtonian fluids. The onset of formation of these waves, and the wavelengths, are in agreement with established stability analyses in the literature. We are therefore confident of our ability to compute free-surface flows. We have also performed preliminary simulations with Herschel-Bulkley fluids, and will continue those in the coming year.
Our goal is to study the effects of inertia and density variations on phenomena induced by vibration of these fluids. With our ability to vary the density differences in the suspension of glass beads, and vary the rheology of the Carbopol/TEA solutions, we believe we have a starting point for elucidating the physical causes of the formation of holes and protrusions in vibrated, complex fluids. In the long term, that understanding will improve our ability to control complex fluids such as cement and the drilling muds, which play an important role in oil production.