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Oscillatory and steady streaming flow in the anterior chamber of the moving eye.

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Title: Oscillatory and steady streaming flow in the anterior chamber of the moving eye.
Authors: Dvoriashyna, M.1 mariia.dvoriashyna@edu.unige.it, Repetto, R.1, Tweedy, J. H.2
Source: Journal of Fluid Mechanics. 3/25/2019, Vol. 863, p904-926. 23p.
Subjects: Anterior chamber (Eye), Biological fluid dynamics
Abstract: We study the flow induced by eye rotations in the anterior chamber (AC) of the eye, the region between the cornea and the iris. We model the geometry of the AC as a thin domain sitting on the surface of a sphere, and study both the simpler case of a constant-height domain as well as a more realistic AC shape. We model eye rotations as harmonic in time with prescribed frequency $\unicode[STIX]{x1D714}_{f}$ and amplitude $\unicode[STIX]{x1D6FD}$ , and use lubrication theory to simplify the governing equations. We write the equations in a reference frame moving with the domain and show that fluid motion is governed by three dimensionless parameters: the aspect ratio $\unicode[STIX]{x1D716}$ of the AC, the angular amplitude $\unicode[STIX]{x1D6FD}$ and the Womersley number $\unicode[STIX]{x1D6FC}$. We simplify the equations under the physiologically realistic assumptions that $\unicode[STIX]{x1D716}$ is small and $\unicode[STIX]{x1D6FC}$ large, leading to a linear system that can be decomposed into three harmonics: a dominant frequency component, with frequency $\unicode[STIX]{x1D714}_{f}$ , and a steady streaming component and a third component with frequency $2\unicode[STIX]{x1D714}_{f}$. We solve the problem analytically for the constant-height domain and numerically as the solution of ordinary differential equations in the more realistic geometry. Both the primary flow and the steady streaming are shown to have a highly three-dimensional structure, which has not been highlighted in previous numerical works. We show that the steady streaming is particularly relevant from the clinical point of view, as it induces fluid mixing in the AC. Furthermore, the steady flow component is the dominant mixing mechanism during the night, when the thermal flow induced by temperature variations across the AC is suppressed. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
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  Data: Oscillatory and steady streaming flow in the anterior chamber of the moving eye.
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  Data: <searchLink fieldCode="AR" term="%22Dvoriashyna%2C+M%2E%22">Dvoriashyna, M.</searchLink><relatesTo>1</relatesTo><i> mariia.dvoriashyna@edu.unige.it</i><br /><searchLink fieldCode="AR" term="%22Repetto%2C+R%2E%22">Repetto, R.</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Tweedy%2C+J%2E+H%2E%22">Tweedy, J. H.</searchLink><relatesTo>2</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Fluid+Mechanics%22">Journal of Fluid Mechanics</searchLink>. 3/25/2019, Vol. 863, p904-926. 23p.
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  Data: <searchLink fieldCode="DE" term="%22Anterior+chamber+%28Eye%29%22">Anterior chamber (Eye)</searchLink><br /><searchLink fieldCode="DE" term="%22Biological+fluid+dynamics%22">Biological fluid dynamics</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We study the flow induced by eye rotations in the anterior chamber (AC) of the eye, the region between the cornea and the iris. We model the geometry of the AC as a thin domain sitting on the surface of a sphere, and study both the simpler case of a constant-height domain as well as a more realistic AC shape. We model eye rotations as harmonic in time with prescribed frequency $\unicode[STIX]{x1D714}_{f}$ and amplitude $\unicode[STIX]{x1D6FD}$ , and use lubrication theory to simplify the governing equations. We write the equations in a reference frame moving with the domain and show that fluid motion is governed by three dimensionless parameters: the aspect ratio $\unicode[STIX]{x1D716}$ of the AC, the angular amplitude $\unicode[STIX]{x1D6FD}$ and the Womersley number $\unicode[STIX]{x1D6FC}$. We simplify the equations under the physiologically realistic assumptions that $\unicode[STIX]{x1D716}$ is small and $\unicode[STIX]{x1D6FC}$ large, leading to a linear system that can be decomposed into three harmonics: a dominant frequency component, with frequency $\unicode[STIX]{x1D714}_{f}$ , and a steady streaming component and a third component with frequency $2\unicode[STIX]{x1D714}_{f}$. We solve the problem analytically for the constant-height domain and numerically as the solution of ordinary differential equations in the more realistic geometry. Both the primary flow and the steady streaming are shown to have a highly three-dimensional structure, which has not been highlighted in previous numerical works. We show that the steady streaming is particularly relevant from the clinical point of view, as it induces fluid mixing in the AC. Furthermore, the steady flow component is the dominant mixing mechanism during the night, when the thermal flow induced by temperature variations across the AC is suppressed. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1017/jfm.2018.889
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      – Code: eng
        Text: English
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        PageCount: 23
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      – SubjectFull: Biological fluid dynamics
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            – D: 25
              M: 03
              Text: 3/25/2019
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              Y: 2019
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