Edge
instability and its interplay with bulk shear flows
Suzanne Fielding
Durham University, UK
Abstract
This seminar will review recent progress
in understanding theoretically the edge fracture instability in sheared complex
fluids, and the interplay of edge fracture with bulk shear flows.
In the most common rheological experiment,
a sample of complex fluid is sandwiched between plates and sheared. Commonly
encountered beyond a critical (material and device dependent) shear rate is the
phenomenon of edge fracture: the free surface where the fluid sample meets the
outside air destabilises, rendering accurate rheological measurement impossible.
Edge fracture is often discussed as one of the most important limiting factors
in rotational rheometry. From a fluid mechanical
viewpoint, it is an important example of a hydrodynamic instability in a free
surface viscoelastic flow.
Following a brief introduction to the
basic phenomenon of edge fracture, I will present the results of recent linear
stability analyses and direct nonlinear simulations of the phenomenon. An exact
analytical expression will be presented for the onset of edge fracture,
expressed in terms of the shear-rate derivative of the second normal stress
difference, the shear-rate derivative of the shear stress, the jump in shear
stress across the interface between the fluid and the outside air, the surface
tension of that interface, and the rheometer gap size. Our findings also afford
a full mechanistic understanding of the instability, which we have carefully validated
against our simulations. They also suggest a possible route to mitigating edge
fracture, potentially allowing experimentalists to achieve and accurately
measure stronger flows than hitherto.
The final part of the talk will discuss
the interplay of edge disturbance/instability with the bulk shear flow, with a
particular focus on shear banding in the fluid bulk. (In the first part of the
talk above, the bulk flow was assumed homogeneous and unbanded.)
First, I will discuss how edge disturbances can induce a quasi-bulk apparent
shear banding that persists far into the bulk. (To paraphrase this scenario
“edge fracture causes bulk shear banding”.) Second, I will discuss opposite case,
in which bulk shear banding induces edge fracture. Numerical results will then
demonstrate a more general interplay between surface and bulk physics, in
between these two extreme causalities.
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