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The trajectory of sperm in the presence of background flow is of utmost importance for the success of fertilization, as sperm encounter background flow of different magnitude and direction on their way to the egg. Here, we have studied the effect of an unbounded simple shear flow as well as a Poiseuille flow on the sperm trajectory. In the presence of a simple shear flow, the sperm moves on an elliptical trajectory in the reference frame advecting with the local background flow. The length of the major-axis of this elliptical trajectory decreases with the shear rate. The flexibility of the flagellum and consequently the length of the major axis of the elliptical trajectories increases with the sperm number. The sperm number is a dimensionless number representing the ratio of viscous force to elastic force. The sperm moves downstream or upstream depending on the strength of background Poiseuille flow. In contrast to the simple shear flow, the sperm also moves toward the centerline in a Poiseuille flow. Far away from the centerline, the cross-stream migration velocity of the sperm increases as the transverse distance of the sperm from the centerline decreases. Close to the centerline, on the other hand, the cross-stream migration velocity decreases as the sperm further approaches the center. The cross-stream migration velocity of the sperm also increases with the sperm number.
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Anomalous tumbling of colloidal ellipsoids in Poiseuille flows
Shear flows cause aspherical colloidal particles to tumble so that their orientations trace out complex trajectories known as Jeffery orbits. The Jeffery orbit of a prolate ellipsoid is predicted to align the particle's principal axis preferentially in the plane transverse to the axis of shear. Holographic microscopy measurements reveal instead that colloidal ellipsoids' trajectories in Poiseuille flows strongly favor an orientation inclined by roughly đťś‹/8 relative to this plane. This anomalous observation is consistent with at least two previous reports of colloidal rods and dimers of colloidal spheres in Poiseuille flow and therefore appears to be a generic, yet unexplained feature of colloidal transport at low Reynolds numbers.
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- Award ID(s):
- 2104837
- PAR ID:
- 10511600
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review E
- Volume:
- 108
- Issue:
- 3
- ISSN:
- 2470-0045
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1103/PhysRevE.108.034609
