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Ultrafast ultrasonic imaging coupled to rheometry: Principle and illustration
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10.1063/1.4801462
/content/aip/journal/rsi/84/4/10.1063/1.4801462
http://aip.metastore.ingenta.com/content/aip/journal/rsi/84/4/10.1063/1.4801462
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Sketch and picture of the experimental setup. (a) Three-dimensional general view. (b) Top view of the gap of the Couette cell together with the path of the acoustic beam and the various axes and angles defined in the text. (c) Picture showing the water tank with the ultrasonic transducer facing a smooth, transparent Taylor-Couette geometry with dimensions (R 1 = 23 mm and R 2 = 25 mm) smaller than that used in the text.

Image of FIG. 2.
FIG. 2.

(a) Raw speckle signal s i (t, z) recorded after a single plane wave emission as a function of time t and transducer position z along the array. (b) Corrected speckle signal after removal of the fixed echoes in s i (t, z) (see text). The dashed lines at t = 38.7 and 41.5 μs indicate the limits of the gap as inferred from the calibration procedure described in Sec. III A . The signals are coded using linear color levels. Experiment performed in a Newtonian suspension of hollow glass spheres at 1 wt.% in water and sheared at s−1 (see the supplementary material for movie 1). 32

Image of FIG. 3.
FIG. 3.

(a) Beam-formed image S i (y, z) computed from the corrected speckle signal of Fig. 2(b) and shown as a function of y, the distance to the transducer array, and z, the position along the array. S i is normalized by its maximum value and coded in linear color levels. (b) Two successive beam-formed speckle signals S i (y, z) (in black) and S i+1(y, z) (in red) for a given position z = 14.9 mm along the transducer array. S i and S i+1 correspond to two different plane wave emissions separated by δt = 2 ms. (c) Enlargement of S i (y, z) (in black) and S i+1(y, z) (in red) over a window of width Δy = 2λ close to the inner bob [indicated as a dashed box in (b)]. This evidences a noticeable displacement of the speckle to the right when going from S i to S i+1. The dashed lines at y = 28.7 and 30.7 mm indicate the limits of the gap as inferred from the calibration procedure described in Sec. III A . Same experiment as in Fig. 2 (see also the supplementary material for movie 2). 32

Image of FIG. 4.
FIG. 4.

(a) Displacement map δy i (y, z) computed from two successive beam-formed images S i and S i+1 separated by δt = 2 ms. (b) Displacement map ⟨δy i (y, z)⟩ i averaged over 199 correlations between 200 successive images. The dashed lines at y = 28.7 and 30.7 mm indicate the limits of the gap as inferred from the calibration procedure described in Sec. III A . Same experiment as in Fig. 2 .

Image of FIG. 5.
FIG. 5.

(a) Axial velocity profiles v y, i (y, z) computed from the two successive beam-formed images S i and S i+1 used in Fig. 4(a) and shown for z = 7.4 (⧫), 15.1 (•), and 22.4 mm (■). (b) Axial velocity profiles v y (y, z) = ⟨v i (y, z)⟩ i averaged over 199 correlations between 200 successive images. The grey line shows the best linear fit of the full data set averaged over z. The dashed lines at y = 28.7 and 30.7 mm indicate the limits of the gap as inferred from the calibration procedure described in Sec. III A . Same experiment as in Fig. 2 .

Image of FIG. 6.
FIG. 6.

Tangential velocity profiles v(r) deduced from the calibration procedure [Eqs. (5) and (6) ] with y 0 = 28.66 mm and ϕ = 5.2° for different applied shear rates: (•), 10 (□), 15 (•), and 20 s−1 (▼). Data are averaged over 199 successive correlations and over the vertical direction z. Error bars show the standard deviation over z. Grey lines are the theoretical predictions for a Newtonian fluid [Eq. (10) ]. Inset: relative deviation δv/v computed as the standard deviation of v(r, z) over z relative to its mean value v(r). Experiments performed in a Newtonian suspension of hollow glass spheres at 1 wt.% in water.

Image of FIG. 7.
FIG. 7.

Start-up of shear in a Newtonian suspension of hollow glass spheres at 1 wt.% in water and sheared at s−1 in the laminar regime. (a) Velocity maps v(r, z, t) at different times t indicated on the top row. Each map corresponds to an average over 50 pulses sent every millisecond (see also the supplementary material for movie 3). 32 (b) Stress response σ(t) recorded simultaneously to the velocity maps. The symbols indicate the times corresponding to the images shown in (a). Inset: magnification of the stress response σ(t) (in black) together with the instantaneous shear rate (in red) imposed by the rheometer. (c) Velocity profiles ⟨v(r, z, t)⟩ z averaged over the whole height of the transducer array and shown at t = 0 (□), 0.075 (⋄), 0.15 (△), 0.225 (▽), 0.375 (○), 0.7 (◁), and 1.275 s (▷) consistently with (a) and (b). The grey line shows the velocity profile expected for a Newtonian fluid in the laminar regime [Eq. (10) ]. Inset: time evolution of ⟨v(r, z, t)⟩ z at r = 0.01, 0.46, 0.98, 1.43, and 1.95 mm from top to bottom.

Image of FIG. 8.
FIG. 8.

Start-up of shear in a Newtonian suspension of hollow glass spheres at 1 wt.% in water and sheared at s−1 in a vortex flow regime. (a) Velocity maps v(r, z, t) at different times t indicated on the top row. Each map corresponds to an average over 50 pulses sent every 0.5 ms (see also the supplementary material for movie 4). 32 (b) Stress response σ(t) (in black) recorded simultaneously to the velocity maps together with the instantaneous shear rate (in red) imposed by the rheometer. The symbols indicate the times corresponding to the images shown in (a). Inset: apparent viscosity . (c) Velocity profiles v(r, z, t) at t = 2.375 s and for z = 19.25 (white symbols, outflow boundary), 20.5 (gray symbols, in between outflow and inflow), and 21.5 mm (black symbols, inflow boundary). The gray line shows the velocity profile expected for a Newtonian fluid in the laminar regime [Eq. (10) ].

Image of FIG. 9.
FIG. 9.

Start-up of shear in a solution of wormlike micelles ([CTAB] = 0.3 M, [NaNO3] = 0.34 M) seeded with hollow glass spheres at 1 wt.% and sheared at s−1 in the shear-banding regime with Taylor-like vortices. (a) Velocity maps v(r, z, t) at different times t indicated on the top row. Each map corresponds to an average over 100 pulses sent every 1 ms (see also the supplementary material for movie 6). 32 Each of the N seq = 200 sequences of N = 100 pulses is separated from the next one by 0.5 s. (b) Stress response σ(t) (in black) imposed by the rheometer recorded simultaneously to the velocity maps together with the instantaneous shear rate (in red). The symbols indicate the times corresponding to the images shown in (a). Inset: apparent viscosity . (c) Velocity profiles ⟨v(r, z, t)⟩ z averaged over the whole height of the transducer array and shown at t = 1.8 (□), 2.3 (∗), 2.8 (+), and 9.8 s (△). The gray line shows the velocity profile expected for a Newtonian fluid in the laminar regime [Eq. (10) ]. Inset: velocity profiles v(r, z, t) at t = 39.8 s and for z = 10.5 (white symbols, outflow boundary), 9.5 (gray symbols, in between outflow and inflow), and 8.5 mm (black symbols, inflow boundary).

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/content/aip/journal/rsi/84/4/10.1063/1.4801462
2013-04-16
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Ultrafast ultrasonic imaging coupled to rheometry: Principle and illustration
http://aip.metastore.ingenta.com/content/aip/journal/rsi/84/4/10.1063/1.4801462
10.1063/1.4801462
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