The Rayleigh Taylor instability of a concentrated suspension

Motivation

Diluted suspensions (packing fraction Φ<2%) can for many purposes be treated as Newtonian fluids with a relative viscosity μ_susp=μ_fluid(1+2.5Φ+O(Φ²))
(A. Einstein, Ann. d. Phys. 19, 289 (1906) and 34, 591 (1911))

However, the multitude of equations for the relative viscosity in the high packing fraction regime poses the question if a concentrated suspension is still well characterized as a fluid. To test this, we studied the linear instability of the interface between a concentrated suspension and clear water and compared it to the well studied Rayleigh Taylor instability which takes place, when a more dense fluid is stratified on top of a less dense fluid.

Experimental Setup

The experiments are performed in a closed Hele Shaw cell of 16 x 8 x 0.4 cm. By turning the cell around a horizontal axis an initially sedimented layer of glass beads forms a layer of concentrated suspension on top of pure water.

Figure 1
Experimental setup.

As shown in Figure 1 the preparation of the initial state with a rotating motion leads to a 2 layer flow inside the cell. Nevertheless, in the co-moving frame the lower edge of the suspension-water interface shows a classical instability, which is demonstrated in Figure 2.

Figure 2
Temporal evolution of the sand-water interface. The width of the images is 6.8 cm.

Results

After tracking down the suspension-water interface we do a Fourier decomposition. Then the temporal evolution of each Fourier mode is tried to fit with an exponential growth law as shown in Figure 3.
The average growth rate of these fits as a function of the wavenumber of the corresponding Fourier mode is plotted in Figure 4. This dispersion relation can then be compared to the theoretical predictions of a 2 fluid model.

Figure 3
Temporal evolution of the Fourier mode with k=7 cm^-1. The solid line is an exponential fit. The values belong to the experiment presented in Figure 2.

Figure 4
Exponential growth rates of the Fourier modes.

Conclusion

The interface of a concentrated suspension stratified over the pure fluid shows a density driven instability. A comparison of the measured dispersion relation with the theoretical results for a 2 fluids model indicates that concentrated suspensions show still fluidlike behaviour. More work is needed as neither the viscosity nor the density of the suspension were measured in the experiment so that these variables were fit parameters in the comparison with the theory.

Publications

In collaboration with

Andreas Engel
Universität Oldenburg

Adrian Lange
MPI, Dresden

Ingo Rehberg
Universität Bayreuth

Michael Scherer

Camilla Völtz

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