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Injection of a viscoplastic material inside a tube or between two parallel disks: Conditions for wall detachment of the advancing front
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10.1122/1.3191779
/content/sor/journal/jor2/53/5/10.1122/1.3191779
http://aip.metastore.ingenta.com/content/sor/journal/jor2/53/5/10.1122/1.3191779

Figures

Image of FIG. 1.
FIG. 1.

Initial arrangement of a finite amount of viscoplastic fluid (a) in a semi-infinite pipe and (b) between parallel and coaxial disks.

Image of FIG. 2.
FIG. 2.

Schematic representation of the remapping scheme of the interfacial nodes (a) before and (b) after the procedure.

Image of FIG. 3.
FIG. 3.

Typical mesh with two levels of local refinement behind the advancing front for the flow between two disks with , , and at time

Image of FIG. 4.
FIG. 4.

Contours of the radial, upper half, and the axial, lower half, velocity component of a Newtonian fluid in a straight pipe at (a) , (b) , and (c) for . The interval between the max and min in each snapshot was divided by 16, 15, and 14 contour lines, respectively. The number of contour lines for in each of the three snapshots is 16, 14, and 14, respectively. The M2 mesh was used.

Image of FIG. 5.
FIG. 5.

Contours of the pressure field, upper half, and , lower half of a Newtonian fluid at time for . There are 31 contour lines for and 36 contour lines for the pressure.

Image of FIG. 6.
FIG. 6.

Variation in the axial distance between the flow front tip and the triple contact point , with the axial position of the front tip for a Newtonian fluid in a straight pipe with . Comparison with experimental data provided by Behrens et al. (1987). The same symbols have been used for all the experimental data, although the indicated variation is caused because the experiments took place with different fluids, pipe diameters, and flow rates.

Image of FIG. 7.
FIG. 7.

Contours of the second invariant of the stresses, upper half, and the axial component of the velocity, lower half, of a viscoplastic fluid in a straight pipe at (a) , (b) , and (c) . The dimensionless parameters are . The range between the maximum and minimum value of in each of the three snapshots was divided by 13, 11, and 10 contour lines, respectively. The number of isolines for the second invariant of the stresses in each snapshot is 28. The M2 mesh was used.

Image of FIG. 8.
FIG. 8.

Comparison of the analytical prediction for the axial velocity profile with numerical simulation along with at for .

Image of FIG. 9.
FIG. 9.

Contours of the second invariant of the stresses, upper half, and the pressure field, lower half of a viscoplastic fluid at (a) , (b) , and (c) for . In each of the three snapshots, we have plotted 40 isolines for and 30 isolines for the pressure. The M3 mesh was used.

Image of FIG. 10.
FIG. 10.

Time evolution of the shape of the fluid/air interface for a viscoplastic material with (a) and (b) . The rest dimensionless parameters are (a) and (b) .

Image of FIG. 11.
FIG. 11.

Time evolution of the axial component of the velocity at the interface tip for various Bn. The rest of the dimensionless parameters are .

Image of FIG. 12.
FIG. 12.

Variation in the axial distance between the flow front tip and the triple contact point , with the axial position of the front tip for various Bn numbers in a straight pipe.

Image of FIG. 13.
FIG. 13.

Dependence of the location of the triple contact point at detachment on its initial axial position for two sets of Bn numbers, each corresponding to a single , for pipe flow. The slope of the line with is 0.915, whereas the slope for is 0.918.

Image of FIG. 14.
FIG. 14.

Contours of the pressure field, upper half, and the radial velocity component, lower half, of a Newtonian fluid between two parallel disks at (a) , (b) , and (c) for . The number of contours for the pressure in each of the three snapshots is 24. The interval between these two extremes in is divided by 20, 26, and 24 contour lines in each of the three snapshots, respectively. The M1 mesh was used.

Image of FIG. 15.
FIG. 15.

Contours of the pressure field, upper half, and the radial velocity component, lower half, of a viscoplastic material between two parallel disks at (a) and (b) for . The number of contour lines for both variables in each of the two snapshots is 24. The M1 mesh was used.

Image of FIG. 16.
FIG. 16.

Contours of the axial, upper half, and the radial, lower half, velocity component of a viscoplastic material between two parallel disks at (a) , (b) , and (c) for . There are 25 contour lines for and 18 for in each one of the three snapshots.

Image of FIG. 17.
FIG. 17.

Time evolution of the shape of the fluid/air interface for a viscoplastic material with (a) , (b) , (c) , and (d) .

Image of FIG. 18.
FIG. 18.

Contours of the pressure field of a viscoplastic material with between two parallel disks at . The rest of the dimensionless parameters are . The number of contour lines shown is 24. The M1 mesh was used.

Image of FIG. 19.
FIG. 19.

Vectors of the velocity for a viscoplastic material with , relative to the tip velocity. (a) The entire domain where the area of minimum velocity is shown and (b) a close-up in the region of the triple contact point.

Image of FIG. 20.
FIG. 20.

Stresses of a viscoplastic material with between parallel disks. (a) Circumferential upper half and radial lower half. (b) Axial upper half and the shear stress lower half. The rest of the dimensionless parameters are . The number of contour lines is 12 for and 30 for each one of the other components of the stress tensor.

Image of FIG. 21.
FIG. 21.

Time evolution of the radial component of the velocity at the interface tip for various Bn. The rest of the dimensionless parameters are .

Image of FIG. 22.
FIG. 22.

Variation in the radial distance between the flow front tip and the triple contact point , with the radial position of the front tip for various Bn numbers between two parallel disks.

Image of FIG. 23.
FIG. 23.

Dependence of the location of the triple contact point at detachment on its initial radial position for three sets of Bn numbers, each corresponding to a single , for fluid injection between parallel disks. The slope of the line with is 0.871, the slope for is 0.959, and that for is 0.999.

Image of FIG. 24.
FIG. 24.

Contours of the second invariant of the stress tensor of a viscoplastic material with . The rest of the dimensionless parameters are .

Tables

Generic image for table
TABLE I.

Properties of the finite element meshes used in this paper.

Generic image for table
TABLE II.

Extent of unyielded region of a viscoplastic in a pipe material with , , and .

Generic image for table
TABLE III.

Comparison of the radius of unyielded domain in a pipe at various time instants between the analytically predicted value and the calculated one using the present code for a material with , , and .

Generic image for table
TABLE IV.

Comparison of the radius of unyielded domain in a pipe at various time instants between the analytically predicted value and the calculated one using the present code for a material with , , and .

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/content/sor/journal/jor2/53/5/10.1122/1.3191779
2009-09-01
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Injection of a viscoplastic material inside a tube or between two parallel disks: Conditions for wall detachment of the advancing front
http://aip.metastore.ingenta.com/content/sor/journal/jor2/53/5/10.1122/1.3191779
10.1122/1.3191779
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