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groups:journal_club:2010fall:holes_in_fluids_merkt

Merkt, F. S. "Persistent holes in a fluid." Physical review letters 92.18 (2004):184501.

The Paper

The .pdf file can be found here (Note you need to be logged in to use this link)

An external link to the paper is here.

The DOI is 10.1103/PhysRevLett.92.184501

Discussion

Q: Could you give a brief review of the relevant fluid dynamics? For instance, what is shear rate and how does it relate to the holes?

A: The most basic concept here is viscosity, a measure of a fluid's flow-unfriendliness. If you apply shear stress (a force on the surface of the liquid parallel to that surface) to a highly viscous material, the moving upper layer will drag lower layers along with. A less viscous material will slide over itself more easily.

Viscosity is usually measured by putting a fluid between two parallel plates. The bottom plate is fixed, while the upper plate moves with some velocity v in the x-direction. This creates laminar flow in x, and the velocity u of the fluid drops off as you move away from the top plate in the y-direcion. Viscosity μ relates to this gradient as

τ = μ ∂u/∂y, Where τ is the shear stress (in units force per unit area.)

The shear rate is proportional to the velocity of this top plate. For the “simple shear” situation described above, it is just velocity, v, scaled with the plate separation, h. Shear rate γ = v/h.

For NEWTONIAN fluids, viscosity is independent of shear rate.

NON-NEWTONIAN fluids have viscosity that depends on shear rate (or cumulative stress over time, which I won't address here.) Deviations include: Shear-Thickening or “Dilatant” materials, which show viscosity to increase with shear rate. Shear-Thinning materials decrease viscosity with respect to shear rate.

The relationship between the viscosity/shear rate of the cornstarch solution in this paper is not made clear in this paper. The cornstarch solution demonstrates both a shear-thinning and shear-thickening response to a shear stress, as can be seen in Figure 6. The rapid increase of viscosity at the onset of the shear-thickening regime is labeled γc, and the paper suggests that this is the shear rate at the walls of the holes when they become stable.

Q: Can we please create a more inclusive Journal Club by retiring pseudonyms? –Ilana

If the questioner/answer chooses not to share their identity, so be it. None the less, inclusion is indeed the primary goal of the Journal Club. To this end, if someone wishes to name themselves, proper names only. –Joe

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