Microscopic flows are almost universally linear, laminar and stationary because Reynolds number, Re, is usually very small. That impedes mixing in micro-fluidic devices, which sometimes limits their performance. Here we show that truly chaotic flow can be generated in a smooth micro-channel of a uniform width at arbitrarily low Re, if a small amount of flexible polymers is added to the working liquid. The chaotic flow regime is characterized by randomly fluctuating three-dimensional velocity field and significant growth of the flow resistance. Although the size of the polymer molecules extended in the flow may become comparable with the micro-channel width, the flow behavior is fully compatible with that in a table-top channel in the regime of elastic turbulence. The chaotic flow leads to quite efficient mixing, which is almost diffusion independent. For macromolecules, mixing time in this microscopic flow can be three to four orders of magnitude shorter than due to molecular diffusion.
We visualize the flow induced by an isolated non-Brownian spherical particle settling in a shear thinning yield stress fluid using particle image velocimetry. With ReϽ 1, we show a breaking of the fore-aft symmetry and relate this to the rheological properties of the fluid. We find that the shape of the yield surface approximates that of an ovoid spheroid with its major axis approximately five times greater than the radius of the particle. The disagreement of our experimental findings with previous numerical simulations is discussed.
We discuss the role of elastic stress in the statistical properties of
elastic turbulence, realized by the flow of a polymer solution between two
disks. The dynamics of the elastic stress are analogous to those of a small
scale fast dynamo in magnetohydrodynamics, and to those of the turbulent
advection of a passive scalar in the Batchelor regime. Both systems are
theoretically studied in literature, and this analogy is exploited to explain
the statistical properties, the flow structure, and the scaling observed
experimentally. Several features of elastic turbulence are confirmed
experimentally and presented in this paper: (i) saturation of the rms of the
vorticity and of velocity gradients in the bulk, leading to the saturation of
the elastic stress; (ii) large rms of the velocity gradients in the boundary
layer, linearly growth with Wi; (iii) skewed PDFs of the injected power, with
exponential tails, which indicate intermittency; PDF of the acceleration
exhibit well-pronounced exponential tails too; (iv) a new length scale, i.e the
thickness of the boundary layer, as measured from the profile of the rms of the
velocity gradient, is found to be relevant and much smaller than the vessel
size; (v) the scaling of the structure functions of the vorticity, velocity
gradients, and injected power is found to be the same as that of a passive
scalar advected by an elastic turbulent velocity field.Comment: submitted to Physics of Fluids; 31 pages, 29 figures (resolution
reduced to screen quality
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