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Strong squeeze flows of yield-stress fluids: The effect of normal deviatoric stresses
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10.1122/1.4794912
/content/sor/journal/jor2/57/3/10.1122/1.4794912
http://aip.metastore.ingenta.com/content/sor/journal/jor2/57/3/10.1122/1.4794912

Figures

Image of FIG. 1.
FIG. 1.

Schematic of the velocity profiles in squeeze flows of (a) Newtonian material, and (b) Bingham plastic. The current sample thickness is denoted by h.

Image of FIG. 2.
FIG. 2.

Sketch of a sample with the coordinate axes.

Image of FIG. 3.
FIG. 3.

The experimental setup: (a) schematic, (b) image of the squeezing apparatus.

Image of FIG. 4.
FIG. 4.

(a) Flow curves of Carbopol solution C1 at two different concentrations of NaOH. Parallel-plate viscometer: 2% NaOH (solid line) and 4% NaOH (dashed-dotted line). Vane viscometer: 2% NaOH (dashed line) and 4% NaOH (dotted line). All lines are practically indistinguishable in this graph. (b) Flow curves of Carbopol solution C3 at two different concentrations of NaOH. Parallel-plate viscometer: 2% NaOH (solid line) and 4% NaOH (dashed-dotted line). Vane viscometer: 2% NaOH (dashed line) and 4% NaOH (dotted line). In panel (b), the viscosity values measured in strong squeeze flow of C3 with 2% NaOH (symbols) are superimposed using the same strain rate axis for both shear rate in simple shear and the uniaxial elongation in the radial direction in squeezing. (c) Flow curves of bentonite dispersion B10. Parallel-plate viscometer: (solid line), vane viscometer (dashed line). In panel (c), the viscosity values measured in strong squeeze flow of B10 (symbols) are superimposed using the same strain rate axis for the shear rate in simple shear and the uniaxial elongation in the radial direction in squeezing.

Image of FIG. 5.
FIG. 5.

Typical deformation curves: (a) Area A versus time t, and (b) the corresponding A(t) dependences for S1. Curve 1 corresponds to 165 g, curve 2 to 305 g, and curve 3 to 465 g.

Image of FIG. 6.
FIG. 6.

Typical deformation curves: (a) Area A versus time t, and (b) the corresponding A(t) dependences for S2.5. Curve 1 corresponds to 165 g, curve 2 to 305 g, and curve 3 to 465 g.

Image of FIG. 7.
FIG. 7.

Viscosity obtained from the squeeze flows of S1 (squares) and S2.5 (circles). Horizontal dashed lines depict the viscosity values provided by the manufacturer of these oils.

Image of FIG. 8.
FIG. 8.

Upper row: Carbopol solution C3 being strongly squeezed under a mass load of 230 g. Lower row: Bentonite dispersion B10 being strongly squeezed under a mass load of 465 g. (a) t = 0, (b) 32.5 ms, (c) 39 ms, (d) 45.5 ms. 1—The aggregate of black dye that did not move during the squeezing process. 2—The aggregate of black dye that was smeared because it was deeply embedded into the sample. The dashed circles correspond to the initial circumference of the samples of C3 (in the upper row) and B10 (in the lower row). In the upper row for C3, the bigger dark ring is created by incoming light from the light source being partially refracted due to the sample geometry. Therefore, the inner circumference of the dark ring represents where the material ceases to make contact with the top and bottom disks and the outer circumference represents the leading edge of the sample. In the lower row for B10, the outer circumference of the dark area corresponds to the leading edge of the sample. There is no dark ring in this case because the material is opaque.

Image of FIG. 9.
FIG. 9.

Typical deformation curves for C3. (a) A(t), and (b) the corresponding A(t) dependences. Curves 1 correspond to 230 g, 2-to 305 g, and 3-to 465 g. The inset in panel (a) resolves the initial stage of sample spreading. Weak squeezing: The load was applied softly.

Image of FIG. 10.
FIG. 10.

Typical deformation curves for B10. (a) A(t), and (b) the corresponding A(t) dependences. Curves 1 correspond to 230 g, 2-to 305 g, and 3-to 465 g. The inset in panel (a) resolves the initial stage of sample spreading. Weak squeezing: The load was applied softly.

Image of FIG. 11.
FIG. 11.

Comparison of deformation curve for Newtonian (S1, S2.5) and Bingham (C3 and B10) materials under a squeezing load of 465 g. (a) Short time evolution. (b) Longer time behavior. Curve 1—S2.5, 2—S1, 3—C3, and 4—B10. Weak squeezing: The load was applied softly.

Image of FIG. 12.
FIG. 12.

Typical deformation curves for (a) C3 and (b) B10 in strong squeezing. Curve 1: 230 g, curve 2: 305 g, curve 3: 465 g, and curve 4: the tangent line corresponding to the instant when the maximum rate of spreading occurs for curve 3.

Image of FIG. 13.
FIG. 13.

Shear layer thickness relative to the sample semithickness during the entire squeezing process for (a) C3 solution and (b) B10 dispersion. The mass load corresponding to curve 1 was 230 g, and to curve 2 was 465 g. The relative shear layer thicknesses corresponding to the maximum slopes of the dependences A(t) are designated by open circles.

Image of FIG. 14.
FIG. 14.

The experimental deformation curves with the crossover asymptotics of Eqs. (20) and (22) . (a) C3 and (b) B10 under a mass load of 465 g. The solid line depicts the experimental data; the short-dashed line, Eq. (20) ; and the long-dashed line, Eq. (22) . The long-dashed lines are plotted according to Eq. (22) with τ = 0.00253 s for C3 and τ = 0.00545 s for B10.

Tables

Generic image for table
TABLE I.

H of several Carbopol solutions with NaOH added.

Generic image for table
TABLE II.

Viscosity of the silicone oils measured in the squeeze experiments vs standard values. The viscosity values listed are the averages of two trials.

Generic image for table
TABLE III.

Viscosity and the characteristic time τ for Carbopol solution C3 and bentonite dispersion B10 established in strong squeeze experiments. The characteristic time τ, which is affected not only by the viscous forces but also by the yield stress, is introduced in Eqs. (21) and (22) .

Generic image for table
TABLE IV.

Experimental data for the yield stress of C3.

Generic image for table
TABLE V.

Experimental data for the yield stress of B10.

Generic image for table
TABLE VI.

Elongational strain rate during strong squeezing, , elongational strain rate at saturation, calculated using Eq. (23) , and shear strain rate, established in squeezing experiments with C3 and B10.

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/content/sor/journal/jor2/57/3/10.1122/1.4794912
2013-03-13
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Strong squeeze flows of yield-stress fluids: The effect of normal deviatoric stresses
http://aip.metastore.ingenta.com/content/sor/journal/jor2/57/3/10.1122/1.4794912
10.1122/1.4794912
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