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Top picture: isosurfaces of Xanthan, colored by the velocity, at level α/α max = 30%. Initial value is displayed with transparency, while the value after 24 time steps is displayed with solid colors. Zooms exhibit locations with highest and lowest velocity regimes (respectively in red and blue). Bottom left picture: similar but colored by the shear rate. Bottom right picture: mean velocity of polymer at concentration higher than a level α p , quantifying the difference between water and diluted polymer.

Top picture: isosurfaces of Xanthan, colored by the velocity, at level α/α max = 30%. Initial value is displayed with transparency, while the value after 24 time steps is displayed with solid colors. Zooms exhibit locations with highest and lowest velocity regimes (respectively in red and blue). Bottom left picture: similar but colored by the shear rate. Bottom right picture: mean velocity of polymer at concentration higher than a level α p , quantifying the difference between water and diluted polymer.

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This study provides the analysis of the generalized 3D Stokes problem in a time dependent domain, modeling a solid in motion. The fluid viscosity is a non-linear function of the shear-rate and depends on a transported and diffused quantity. This is a natural model of flow at very low Reynolds numbers, typically at the microscale, involving a miscib...

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... right picture: mean velocity of polymer at concentration higher than a level α p , quantifying the difference between water and diluted polymer. Figure 6 displays the motion of the polymer (initial concentration α is displayed in transparency, and its value after 24 iterations is displayed in solid). On this figure, coloring shows the shear rate on the one hand and the velocity on the other hand. ...

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Citations

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Thesis
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