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Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.

Arrieta J, Cartwright JH, Gouillart E, Piro N, Piro O, Tuval I - PLoS ONE (2015)

Bottom Line: However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase.We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number.We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.

View Article: PubMed Central - PubMed

Affiliation: Mediterranean Institute for Advanced Studies (CSIC-UIB), E-07190 Esporles, Spain; Área de Mecánica de Fluidos, Universidad Carlos III de Madrid, E-28911, Leganés, Spain.

ABSTRACT
Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.

No MeSH data available.


Mixing quality depends on the accumulated geometric phase.(a) The time evolution of the degree of mixing quantified by the standard deviation of the concentration field in the domain. The black dotted line corresponds to the peristaltic wave; the red solid line to the standing wave and the green dotted line to the random wave. (b) and (c) show contours of concentration of χ after the same integration time, equivalent to 20 peristaltic cycles, shown in Fig 4(c) for the case of a stationary and random wave, respectively.
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pone.0130735.g005: Mixing quality depends on the accumulated geometric phase.(a) The time evolution of the degree of mixing quantified by the standard deviation of the concentration field in the domain. The black dotted line corresponds to the peristaltic wave; the red solid line to the standing wave and the green dotted line to the random wave. (b) and (c) show contours of concentration of χ after the same integration time, equivalent to 20 peristaltic cycles, shown in Fig 4(c) for the case of a stationary and random wave, respectively.

Mentions: Stomach contractions that correspond to a standing wave are akin to a zero-area reciprocal loop. As we anticipated for the journal-bearing case, reciprocal loops induce flow which does not generate any mixing. This is shown in Fig 5(b) where the concentration field after 20 cycles of the boundaries deforming as a standing wave is depicted. Since the induced geometric phase is , mixing is only controlled by (slow) diffusion.


Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach.

Arrieta J, Cartwright JH, Gouillart E, Piro N, Piro O, Tuval I - PLoS ONE (2015)

Mixing quality depends on the accumulated geometric phase.(a) The time evolution of the degree of mixing quantified by the standard deviation of the concentration field in the domain. The black dotted line corresponds to the peristaltic wave; the red solid line to the standing wave and the green dotted line to the random wave. (b) and (c) show contours of concentration of χ after the same integration time, equivalent to 20 peristaltic cycles, shown in Fig 4(c) for the case of a stationary and random wave, respectively.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4496066&req=5

pone.0130735.g005: Mixing quality depends on the accumulated geometric phase.(a) The time evolution of the degree of mixing quantified by the standard deviation of the concentration field in the domain. The black dotted line corresponds to the peristaltic wave; the red solid line to the standing wave and the green dotted line to the random wave. (b) and (c) show contours of concentration of χ after the same integration time, equivalent to 20 peristaltic cycles, shown in Fig 4(c) for the case of a stationary and random wave, respectively.
Mentions: Stomach contractions that correspond to a standing wave are akin to a zero-area reciprocal loop. As we anticipated for the journal-bearing case, reciprocal loops induce flow which does not generate any mixing. This is shown in Fig 5(b) where the concentration field after 20 cycles of the boundaries deforming as a standing wave is depicted. Since the induced geometric phase is , mixing is only controlled by (slow) diffusion.

Bottom Line: However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase.We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number.We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.

View Article: PubMed Central - PubMed

Affiliation: Mediterranean Institute for Advanced Studies (CSIC-UIB), E-07190 Esporles, Spain; Área de Mecánica de Fluidos, Universidad Carlos III de Madrid, E-28911, Leganés, Spain.

ABSTRACT
Mixing fluid in a container at low Reynolds number--in an inertialess environment--is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase," peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.

No MeSH data available.